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PROHITECH – EARTHQUAKE PROTECTION OF HISTORICAL BUILDINGS BY REVERSIBLE

MIXED TECHNOLOGIES

WORK PACKAGE 9 DEVELOPMENT OF CALCULATION MODELS

Draft

WP Leader: Dan Dubina, “Politehnica” University of Timisoara, Romania (ROPUT)

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Main Deliverables D III - Reversible mixed technologies for seismic protection: set-up of calculation methods

Deliverables: D10 Set-up of analytical models for special materials and special devices for the seismic structural control; D11 Development of simplified models for the global seismic analysis of historical constructions.

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List of content

LIST OF CONTENT......................................................................................................................................................................3 INTRODUCTION..........................................................................................................................................................................8 INTEGRATED SUMMARY OF CALCULATION MODELS..............................................................................................10 D10 – SET-UP OF ANALYTICAL MODELS FOR SPECIAL MATERIALS AND SPECIAL DEVICES FOR THE SEISMIC STRUCTURAL CONTROL.....................................................................................................................................18 1. MODELS AND PERFORMANCE CRITERIA FOR STRUCTURAL ELEMENTS OF DIFFERENT MATERIAL ..................................................................................................................................................................................18

1.1. MASONRY ELEMENTS – CLAY BRICK ..........................................................................................................................18 1.1.1. Introduction............................................................................................................................................................18 1.1.2. General problems of the material and element behavior......................................................................................18 1.1.3. Models for masonry component materials (Material model) ...............................................................................21 1.1.4. Models for masonry as a composite material (Element model – walls)...............................................................21 1.1.5. Analysis types and performance criteria...............................................................................................................36 1.1.6. Design assisted by testing:.....................................................................................................................................36 1.1.7. References: .............................................................................................................................................................36

1.2. MARBLE AND LIMESTONE............................................................................................................................................39 1.2.1. Introduction............................................................................................................................................................39 1.2.2. Material properties ................................................................................................................................................39 1.2.3. Linear analysis parameters - Young’s modulus and Poisson’s ratio ...................................................................40 1.2.4. Tensile strength ......................................................................................................................................................40 1.2.5. Fracture toughness ................................................................................................................................................42 1.2.6. Reference:...............................................................................................................................................................44

1.3. CONCRETE / REINFORCED CONCRETE..........................................................................................................................44 1.3.1. Materials ................................................................................................................................................................44 1.3.2. Modelling of elements ............................................................................................................................................45 1.3.3. Beam effective width ..............................................................................................................................................48 1.3.4. Beam-column joints................................................................................................................................................51 1.3.5. Shear resistance of members .................................................................................................................................56 1.3.6. Anchorage failure ..................................................................................................................................................58 1.3.7. Rotation capacity of elements ................................................................................................................................59 1.3.8. References ..............................................................................................................................................................59

1.4. IRON ELEMENTS ...........................................................................................................................................................60 1.4.1. Introduction............................................................................................................................................................60 1.4.2. Material model .......................................................................................................................................................61 1.4.3. Element model ........................................................................................................................................................61 1.4.4. Reference:...............................................................................................................................................................64

1.5. TIMBER ELEMENTS ......................................................................................................................................................65 1.5.1. Introduction............................................................................................................................................................65 1.5.2. Models for material................................................................................................................................................65 1.5.3. Models for Elements...............................................................................................................................................69 1.5.4. Connections............................................................................................................................................................69 1.5.5. System model ..........................................................................................................................................................70 1.5.6. Analysis type...........................................................................................................................................................70 1.5.7. Reference:...............................................................................................................................................................70

2. MODELS AND PERFORMANCE CRITERIA FOR STRUCTURAL ELEMENTS OF DIFFERENT MATERIAL ..................................................................................................................................................................................72

2.1. RIVETED CONNECTION.................................................................................................................................................72 2.1.1. Introduction............................................................................................................................................................72 2.1.2. Hand made calculation models .............................................................................................................................72 2.1.3. Numerical vs. Hand made calculation ..................................................................................................................77 2.1.4. Experimental vs. predicted shear strength ............................................................................................................77 2.1.5. References ..............................................................................................................................................................78

2.2. ARCHITRAVE CONNECTION..........................................................................................................................................78

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2.2.1. Introduction............................................................................................................................................................78 2.2.2. Basic concept .........................................................................................................................................................78 2.2.3. Architrave connection tests with main results.......................................................................................................80 2.2.4. Numerical simulation with applied fracture criteria ............................................................................................84 2.2.5. Large scale modelling of ancient temples with columns and architraves ............................................................93 2.2.6. References: .............................................................................................................................................................94

2.3. ANCHORS IN MARBLE ..................................................................................................................................................94 2.3.1. Introduction............................................................................................................................................................94 2.3.2. Basic concept .........................................................................................................................................................95 2.3.3. Summary experimental results...............................................................................................................................96 2.3.4. A design criterion based on the experimental results ...........................................................................................98 2.3.5. Practical implementation of the design criterion................................................................................................101 2.3.6. Conclusions ..........................................................................................................................................................102 2.3.7. References: ...........................................................................................................................................................102

2.4. POST-INSTALLED ANCHORS IN CONCRETE.................................................................................................................103 2.4.1. Introduction..........................................................................................................................................................103 2.4.2. Design of post-installed anchors .........................................................................................................................103 2.4.3. Types and methods of post-installed anchors......................................................................................................104 2.4.4. Material, shape and dimensions of post-installed anchors.................................................................................106 2.4.5. Design strength ....................................................................................................................................................108 2.4.6. Applying post-installed anchors in low-strength concrete .................................................................................111 2.4.7. Structural design in the case of shear RC wall ...................................................................................................113 2.4.8. References: ...........................................................................................................................................................117

2.5. PURE ALUMINIUM SHEAR PANELS..............................................................................................................................117 2.5.1. Introduction..........................................................................................................................................................117 2.5.2. Description of the device .....................................................................................................................................117 2.5.3. Material model .....................................................................................................................................................119 2.5.4. System model ........................................................................................................................................................120 2.5.5. Analysis procedure...............................................................................................................................................124 2.5.6. References ............................................................................................................................................................124

2.6. MAGNETORHEOLOGICAL DEVICES ............................................................................................................................125 2.6.1. Description of the device .....................................................................................................................................125 2.6.2. Device models ......................................................................................................................................................126 2.6.3. References: ...........................................................................................................................................................130

2.7. STEEL BUCKLING RESTRAINED BRACES.....................................................................................................................136 2.7.1. Introduction..........................................................................................................................................................136 2.7.2. Description of the device/technique ....................................................................................................................137 2.7.3. Material model .....................................................................................................................................................139 2.7.4. Element model ......................................................................................................................................................139 2.7.5. Connections..........................................................................................................................................................146 2.7.6. System model ........................................................................................................................................................147 2.7.7. Analysis types .......................................................................................................................................................148 2.7.8. Performance criteria............................................................................................................................................148 2.7.9. References ............................................................................................................................................................150

2.8. EBF – ECCENTRIC BRACED FRAMES..........................................................................................................................152 2.8.1. Description of EB technique ................................................................................................................................152 2.8.2. Analytical methods for the design of EB .............................................................................................................155 2.8.3. References: ...........................................................................................................................................................160

2.9. METAL SHEAR PANEL ................................................................................................................................................161 2.9.1. Introduction..........................................................................................................................................................161 2.9.2. Description of the device/technique ....................................................................................................................161 2.9.3. Interpreting models ..............................................................................................................................................162 2.9.4. References: ...........................................................................................................................................................164

2.10. FRP – FIBER REINFORCED POLIMERS ........................................................................................................................165 2.10.1. Introduction .....................................................................................................................................................165 2.10.2. Description of the FPR device/technique .......................................................................................................165 2.10.3. Analytical methods for the design of FRP......................................................................................................166 2.10.4. Masonry reinforcement ...................................................................................................................................172 2.10.5. Connections .....................................................................................................................................................172 2.10.6. Pefrormance criteria.......................................................................................................................................174

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2.10.7. References: ......................................................................................................................................................174 2.11. PIN INERD ...............................................................................................................................................................176

2.11.1. Introduction .....................................................................................................................................................176 2.11.2. Description of the device/technique................................................................................................................176 2.11.3. Behavior of INERD connections.....................................................................................................................177 2.11.4. Design reules for the INERD connection .......................................................................................................178 2.11.5. Capacity design criteria..................................................................................................................................180 2.11.6. System model ...................................................................................................................................................180 2.11.7. Analysis types ..................................................................................................................................................180 2.11.8. Performance criteria.......................................................................................................................................180 2.11.9. References: ......................................................................................................................................................181

3. MODELS AND PERFORMANCE CRITERIA FOR SUB-SYSTEMS ....................................................................182 3.1. MASONRY WALLS STRENGTHENING WITH METAL BASED TECHNIQUES ....................................................................182

3.1.1. Introduction..........................................................................................................................................................182 3.1.2. Basic concept .......................................................................................................................................................182 3.1.3. Design assisted by testing (see Chapter 1)..........................................................................................................183 3.1.4. Analytical calibration ..........................................................................................................................................184 3.1.5. Experimental calibration .....................................................................................................................................185 3.1.6. Numerical approaches .........................................................................................................................................187 3.1.7. Reference..............................................................................................................................................................188

3.2. CONFINED MASONRY .................................................................................................................................................189 3.2.1. Introduction..........................................................................................................................................................189 3.2.2. General.................................................................................................................................................................189 3.2.3. In-plane stiffness evaluation of masonry-infill walls ..........................................................................................191 3.2.4. In-plane strength evaluation of masonry-infill walls ..........................................................................................193 3.2.5. Infill with openings...............................................................................................................................................196 3.2.6. Application to the case study ...............................................................................................................................198 3.2.7. References ............................................................................................................................................................204

3.3. MASONRY WALLS STRENGTHENING WITH FRP COMPOSITES....................................................................................206 3.3.1. Introduction..........................................................................................................................................................206 3.3.2. Generalities ..........................................................................................................................................................206 3.3.3. In-plane shear capacity evaluation of unreinforced masonry walls strengthened with FRP composites .........207 3.3.4. In-plane strength evaluation of masonry-infill walls strengthened with FRP systems ......................................209 3.3.5. References ............................................................................................................................................................209

3.4. REINFORCED CONCRETE STRUCTURES RETROFFITED WITH STEEL JACKETING .........................................................210 3.4.1. Introduction..........................................................................................................................................................211 3.4.2. Example of reinforcement calculation to increase ductility of a column ...........................................................211 3.4.3. Example of reinforcement calculation to increase column resistance to axial force.........................................214 3.4.4. References ............................................................................................................................................................216

3.5. TIMBER COMPOSITE FLOOR........................................................................................................................................216 3.5.1. Introduction..........................................................................................................................................................216 3.5.2. Description of Device / Technique ......................................................................................................................216 3.5.3. Material Model.....................................................................................................................................................216 3.5.4. Element Model .....................................................................................................................................................218 3.5.5. Connections..........................................................................................................................................................221 3.5.6. System Model .......................................................................................................................................................221 Analytical Method Considering Slip ..................................................................................................................................222 Slip Moduli..........................................................................................................................................................................226 3.5.7. Analysis Types......................................................................................................................................................227 3.5.8. Performance Criteria...........................................................................................................................................227 Effective Bending Stiffness .................................................................................................................................................228 Normal Stresses ..................................................................................................................................................................228 3.5.9. References ............................................................................................................................................................229

3.6. DEVELOPMENT OF DESIGN RULES FOR THE IRON COLUMNS REINFORCED BY FRP ...................................................229 3.6.1. Description of the device/technique ....................................................................................................................230 3.6.2. Material model .....................................................................................................................................................230 FRP material.......................................................................................................................................................................230 3.6.3. Element model ......................................................................................................................................................231 State of the art.....................................................................................................................................................................231

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Cross-sectional resistance in compression ........................................................................................................................232 Members under axial compression ....................................................................................................................................232 Validation of the model with numerical simulations .........................................................................................................235 3.6.4. Conclusions ..........................................................................................................................................................238 Notations .............................................................................................................................................................................239 3.6.5. References ............................................................................................................................................................240

3.7. REINFORCED CONCRETE FRAMES RETROFITED WITH ECCENTRIC BRACES ...............................................................242 3.7.1. Introduction..........................................................................................................................................................242 3.7.2. Connections..........................................................................................................................................................242 3.7.3. Performance criteria............................................................................................................................................244 3.7.4. References ............................................................................................................................................................245

3.8. REINFORCED CONCRETE STRUCTURES RETROFITTED WITH METAL SHEAR PANEL ..................................................246 3.8.1. Introduction..........................................................................................................................................................246 3.8.2. Retrofitting design method...................................................................................................................................246 The general approach.........................................................................................................................................................246 3.8.3. The study case ......................................................................................................................................................248 3.8.4. Application methodology .....................................................................................................................................248 3.8.5. The behavior of the retrofitted structures............................................................................................................249 3.8.6. References ............................................................................................................................................................251

D11 – DEVELOPMENT OF SIMPLIFIED MODELS FOR THE GLOBAL SEISMIC ANALYSIS OF HISTORICAL CONSTRUCTIONS ...................................................................................................................................................................253 4. MODELS FOR GLOBAL ANALYSIS..........................................................................................................................253

4.1. ANALYSIS METHODS..................................................................................................................................................253 4.1.1. Global analysis and modeling requirements.......................................................................................................253 4.1.2. Choice of analysis procedure ..............................................................................................................................259 4.1.3. Choice of the intervention technique ...................................................................................................................261 4.1.4. PBE Methodologies and examples ......................................................................................................................263 4.1.5. Vulnerability Analysis ..........................................................................................................................................266 4.1.6. Reference..............................................................................................................................................................269

4.2. OVERVIEW OF COLLAPSE MODES AND EVALUATION OF BEARING CAPACITY............................................................272 4.2.1. Introduction..........................................................................................................................................................272 4.2.2. Generalities ..........................................................................................................................................................272 4.2.3. Calculation models of masonry buildings for seismic design.............................................................................273 Strategies for masonry building modeling .........................................................................................................................273 Performance-based design of masonry buildings..............................................................................................................273 Computations on masonry structures.................................................................................................................................275 Modeling masonry building by rigid blocks ......................................................................................................................278 4.2.4. Ultimate limit states for masonry elements .........................................................................................................280 Masonry walls.....................................................................................................................................................................280 (i) For in-plane behaviour..................................................................................................................................................280 (ii) The case of out-of-plane ...............................................................................................................................................284 4.2.5. Collapse mechanisms for masonry floors, arches, vaults and domes ................................................................288 4.2.6. Ultimate limit state for masonry structures.........................................................................................................291 Collapse mechanisms for buildings....................................................................................................................................291 4.2.7. Collapse mechanisms for individual buildings ...................................................................................................291 4.2.8. Collapse mechanisms for complex buildings ......................................................................................................294 Romanesque churches ........................................................................................................................................................298 Gothic churches ..................................................................................................................................................................298 Renaissance churches.........................................................................................................................................................299 Byzantine churches .............................................................................................................................................................300 4.2.9. Romanesque churches..........................................................................................................................................301 4.2.10. Gothic churches...............................................................................................................................................306 4.2.11. Renaissance churches .....................................................................................................................................308 4.2.12. Byzantine churches..........................................................................................................................................308 4.2.13. Retrofitting of masonry buildings using the collapse mechanisms................................................................309 4.2.14. Conclusions .....................................................................................................................................................311 4.2.15. References .......................................................................................................................................................312

CONCLUDING REMARKS.....................................................................................................................................................315

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ANNEXES ...................................................................................................................................................................................316 LIST OF CONTRIBUTORS AND DATA SHEETS: ............................................................................................................................316

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INTRODUCTION

The activity in WP 9 is belonging to the main research part of PROHITECH Project (Part R3- Experimental and numerical research) aiming to produce the main deliverables D III - Reversible mixed technologies for seismic protection: set-up of calculation methods.

WP 9 had the mission to provide practical calculation models (or tools) for structural systems and or devices applied or developed and studied in the parallel Working Packages, WP 7 - Experimental analysis and WP 8 - Numerical analysis.

The WP9 specific deliverables are:

D10 Set-up of analytical models for special materials and special devices for the seismic structural control;

D11 Development of simplified models for the global seismic analysis of historical constructions.

These deliverables are connected to the Objective no 7 of the project (see B.1.1 in Description of scientific/technological objectives and work-plan) aiming to allow engineers to use simple and reliable tools for analyzing the behaviour of constructions provided with advanced systems for seismic protection, as well as for detailing up-grading interventions.

The calculation models, procedures and tools provided by WP 9 are intended to form the basis of the design guidelines to be developed in WP12 Development of design guidelines.

The following partners have been assigned to contribute to the achievement of tasks related that objective and deliverables D 10 and D11:

1. UNINA (PTN. N° 1) F.M. MAZZOLANI

2. B (PTN. N° 2) J-P. JASPART

3. MK (PTN. N.° 3) K. GRAMATIKOV (corresponding)

4. NA – ARC (PTN. N° 5) R. LANDOLFO

5. ROPUT (PTN. N° 7) D. DUBINA

6. ROTUB (PTN. N° 8) D. LUNGU

7. SL (PTN.N.° 9) D. BEG (corresponding)

8. TR (PTN. N° 10) G. ALTAY (ASKAR)

9. ISR (PTN. N° 11) A.V. RUTENBERG

10. EG (PTN. N° 12) M. EL ZAHABI

11. SUN (PTN. N° 14) A. MANDARA

12. UNICH (PTN. N° 16) G. DE MATTEIS

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Their contributions were materialized in 24 Datasheets on the different strengthening techniques and devices associated with different structural materials and systems. The Datasheet have been produced on the basis of a general template of following contents:

• Description of the device/technique

• Material model

• Element model

• Connections

• System model

• Analysis types

• Performance criteria

Despite the non-homogeneity of the topic of datasheets, the report tries to structure the essentials of these datasheets in three sections i.e.

I Models and performance criteria for structural elements of different material

II Models for devices and sub-systems tested in the frame of project

III Models for global analysis

The Integrated Summary Table, which precedes these sections, represents the envelope of whole WP 9 contributions.

The datasheets and their authors are presented in the Annex of this Report.

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INTEGRATED SUMMARY OF CALCULATION MODELS

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INTEGRATED SUMMARY OF CALCULATION MODELS

Material Model Element Model DEVICE MODEL System model Connection Analysis type Performance criteria UNREINFORCED CLAY BRICK MASONRY (principles are common to other masonry types)

Capacity design Linear analysis – low dissipative

Ultimate strenght associate with relevant failure mode

Composite material – linear behavior – brittle fracture Analytical formulas: uniaxial behavior,

biaxial behavior,

shear behavior

Masonry shear walls (1.1) Codes relations associated with failure modes: - Sliding (a) - Flexural (b) - Shear (c)

Physical models – Equivalent strut – confined masonry

Numerical models: Micro-model (Interface - a, Layer model - b), Macro model (Homogeneous - c)

a b c

Discontinuous modeling of masonry Discrete crack approach Smeared crack approach Interface smeared crack approach Use of joint elements

2D systems identical with elements models -unreinforced shear walls composed by piers and spandrel - Capacity of transversal walls - Capacity of longitudinal walls 3D systems can be decomposed in 2D subassamblies

Nonlinear static analisys – displacement based metodologies

(values for a, b, c, d, e – FEMA 356) Generalized Component Force-Deformation Relations Modeling

Shear deformation of panel

IO – Immediate ocupancy LS – Life savety CP – Collapse prevention Interstory drifts limits

REINFORCED CLAY BRICK MASONRY Metal sheating (3.1)

Mas

onry

bas

ed sh

ear w

alls

Masonry material model Aluminiu Steel

Composite masonry-metal shear walls External reinforcing of walls

Masonry wall (150x150x25 cm)

Steel/alluminium plate

Chemical anchors

Metal (aluminiu / steel) shear panel connected with chemical anchors or prestressed ties

2D systems - composite shear walls composed by piers and spandrel 3D systems can be decomposed in 2D subassamblies

Constitutive law - Multi-linear spring

0

5000

10000

15000

0 5 10 15 20 25 30

Displacement (mm)

Forc

e (N

)

Mechanical anchor –prestress ties Chemical anchor

Capacity design assisted by tests Capacity design: numerical analysis – linear static, nonlinear static

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FRP (2.10; 3.3) FRP σ σf,u

Ef ε

Composite FRP – masonry wallss FRP glued with epoxy resin Analytical models

Bonding structure

Failure modes

Mode 1 - Laminate/sheet end debonding; Mode 2 - Intermediate debonding, caused by flexural cracks; Mode 3 - Debonding caused by diagonal shear cracks; Mode 4 - Debonding caused by irregularities and roughness of concrete surface; Bonding length

Glued with epoxy resin Steel wire mesh SWM (zincoated or stainless steel)

Composite masonry – steel wire mesh (similar with FRP technologiy)

SWM with epoxy resin Similar with FRP

UNREINFORCED CLAY BRICK MASONRY: RIGID BLOCS ULTIMATE LIMIT ANALYSIS (4.2) - Material simplificate assumtion - rigid material with not tensile strenght

Modeling masonry elements as rigid blocs - sliding failure mode (a); - shear failure mode (b); - overturning failure mode (c).

d

a) b) c)

Unreinforced elements Assemblages of rigid blocks (composing walls) interacting through joints Ussualy 2D models (3D possible) Proposed colapse mechanism

a) b)

c) d)

e)

Joints pinned conection without friction Joints assumption: - the compression and shear failures at the joints are perfectly plastic; - hinging failure at joint does not consider the effects of local crushing.

Ultimate limits state analysis Kinematic analysis of proposed colapse mechanisms

Minimum value of the determined amplification factors determinated by minuimum total potential energy

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Material Model Element model Device model System model Connection Analysis type Performance criteria UNCONNECTED MARBLE OR LIMESTONE BLOCS’ STRUCTURE

Assemblages of rigid blocks interacting through joints (similar with ……)

- Self weight - Friction joint

Ultimate limits state analysis Kinematic analysis of proposed colapse mechanisms

Minimum value of the determined amplification factors

Linear behavior (1.2) Numerical models Failure criteria: Tensile stress Fracture toughness

Columns: compression - Axial - Eccentric (rocking effect) Archittraves (dominant shear effect accompaned by bending) Numerical models based on fracture mechanics

Pinned frames Pinned/simple suported conection Capacity design Linear static

Ultimate limit state – material strenght Overall stability

CONNECTED MARBLE OR LIMESTONE BLOCS’ STRUCTURE Marble connectors (2.3) Capacity design

Linear static – low dissipative Ulitimate limit state - Material strenght Ultimate slip in connection (elastic deformation of spring)

Schematic representation of the specimens (m: marble, c: cement mat., b: bar)

Clamped joints P-slip curves - Linear behavior – linear spring - Bilinear behavior – nonlinear spring

0

8

16

24

0 2 4 6 8System displacement, δ [mm]

Load

, P [k

N]

0

1

2

3

4

5

6

7

8

Slip

[mm

]

P-δslip-δ

First change of slope

Initiation of slip

Peak load

Slip evolution, Vmax, Vmed

Architrave connection (2.2)

Mar

ble

and

limes

tone

Semi-rigid frames

Force F Fu,fract.

Strain εε

u,clamp

Fu,clamp

Load-strain responseof clamp neck

Bilinear approximation of clamp response

Failure of spring

Nonlinear static analysis (e.g. nonlinear connector)

Material strenght Predifine slip Failure of the spring: - Fracture of the stone - Failure of the clamp

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Material Model Element Model Device model System model Connection Analysis type Performance criteria UNREINFORCED IRON

Linear behavior in tension (1.4) Ramberg-Osgood law in compression

Columns Analytical formula Cross sectional resistance Elastic verification Cross section imperfection

Member Geometric imperfection - crookedness Tension failure Compression failure Member stability Member in axial compression Member in bending (LTB) Member in bending and axial compression

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00

Lambda Bi

NB

Compression failure in thin side

Traction failure in thick side

Numerical model without FRP

2D and 3D framing – global imperfection Trusses

Usualy riveted pinned connection - tying - component method – physical model (2.1)

Rigid joints of riveted connection can be obtained

- Capacity design - Linear static - Buckling analysis - Nonlinear analysis posible

Allowable stress Limit state criteria - Strenght - Stifness - Stability

REINFORCED IRON FRP (3.6)

Iron

fram

ing

Iron + FRP Elastic behavior FRP

σ σf,u

Ef ε

Composite element Stress – strain relation

Thick side

Thin side

εi,t (σi,t) v'eq

εi,c (σi,c) σM

geq

σN

Stress Strain

FRP

Iron veq

Mechanical characteristics of a composite cross-section Analytical formula Tension failure Compression failure

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00

Lambda Bi

NB

without FRP, compression failure in thin side

without FRP, traction failure in thick side

with FRP, compression failure in thin side

with FRP, traction failure in thick side

Numerical model

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Material Model Element Model Device model System model Connection Analysis type Performance criteria UNREIFORCED TIMBER FRAMES

Capacity design Linear static – low dissipative Linear dynamic - Lateral force method - Linear time-history

Ultimate limit state Material strenght

Linear orthotropic behavior: Tension parallel to the grain Tension perpendicular to the grain Compression parallel to the grain Tension parallel to the grain Bending Shear

Linear elements Analytical formula – for beams, columns

2D and 3D Pinned frames Trusses

Pined connections Bilinear or multilinear elasto-plastic spring Gap - sliding

Nonlinear static Nonlinear dynamic

Plastic deformation Interstory drift

REIFORCED TIMBER FRAMES Compsite concrete – wood floor (3.5) Linear static – low dissipative

Linear dynamic Ultimate limit state Material strenght

Tim

ber f

ram

ing

Elastic model Analytical model – considering slip

Slip moduli Rigid diaphragm effect

2D and 3D Pinned frames

Numerical models – behaviour curves P-δ

δ

0,4Fu

Fu

F

0,7Fu

kULS

kSLS

Nonlinear static Nonlinear dynamic

Plastic deformation Interstorey drift

Material Model Element Model Device model System model Connection Analysis type Performance criteria UNREINFORCED RC FRAMES

Linear static q – factor Linear dynamic

Ultimate limit state Material strenght

Rein

forc

ed c

oncr

ete

fram

es

Uniaxial behavior (1.3)

Biaxial behavior

Columns and beams 2D or 3D moment resisting franes Rigid and semi-rigid connection (in case of pre-cast concrete)

Nonlinear static Nonlinear dynamic

Plastic deformation (rotation) Interstorey drift

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REINFORCED RC FRAMES Aluminum / Steel Panel (2.5, 2.9, 3.8) Linear static - q – factor

Linear dynamic Limit state criteria - Strenght - Rigidity - Stability

Aluminium Stress – strain relation

AW 1050A ALUMINIUM ALLOY

f02=115 MPa

fu=69 MPa

f02=20 MPa

0

20

40

60

80

100

120

140

0% 10% 20% 30% 40% 50% 60%

strain

stre

ss (M

Pa)

Not heat treated aluminiumHeat treated aluminium

Stiffned - Unstiffned Classification: compact, semi-compact, slender – Analytical formula – for strenght and stiffness

Discrete physical models – Strip model

Continous phisical models: FEM or FSM (plane stress/strain or shell elements)

2D or 3D moment resisting frames braced with shear panels (strip, FEM or FSM)

Postinstaled anchors: mechanical or chemical - shear strenght - tensile strenght

With or without infill steel frame

Full bay or partial bay type Pinned connection in frame analysis

Nonlinear static Design methodology: Equivalent rigidity and strength

Line of minumum required acceleration capacity

IO limit

Line of minimum required stiffness

0.02

0.05

0.010

0

Spe

ctra

l acc

eler

atio

n (g

)

0.15

0.2

0.25

0.3

0.35

0.1

0.45

0.5

0.4

Spectral displacement (m)LS limit

0.03 0.040.037

SS limit

0.05 0.06 0.080.07

Performance point ofthe initial structure

Line of target displacement

Desired performance point

at desired performance

=5%

=10%

=20%

=30%

Nonlinear dynamic

Plastic shear deformation of plate Interstory drift

PIN INERD (2.11) Linear static q – factor Linear dynamic

Ultimate limit state Material strenght

Steel Elastic perfect-plastic

Ramberg - Osgood

Columns and beams

Nonlinear static behavior Verbindung Typ B

0

200

400

600

800

1000

0 10 20 30 40 50Verformung [mm] (positiv wenn Platten auf Druck)

Last

[kN

]

Monotoner Druck (FEM)

Nonlinear dynamic behavior

INERD Connection "TYPE D" - Allowance for Bauschinger effect

-700

-350

0

350

700

-40 -30 -20 -10 0 10 20 30 40Displacement [mm] (positive when eye-bars in compression)

Axia

l For

ce [k

N]

Experimental ResultsFEA Cyclic ResultsFEA Monotonic Results

Analytical formulas – Design rules

δy δ lim

δ

Py

Pu

P

I

II

III Point I:Yield Strength ("y")

Point III:Ultimate Strength ("u")

2D or 3D conventional concentric braced frames

Pinned connection

With one or two eye bars

Nonlinear static Nonlinear dynamic

Plastic deformation (rotation) Interstorey drift of RC members (MRF)

- 16 -

BRB – Buckling restrained braces (2.7) Linear static q – factor Linear dynamic

Limit state criteria - Strenght - Rigidity - Stability

Steel - restrained yielding segment – most of the

elastic and all of the plastic deformations take place here - restrained non-yielding segment – an extension of the yielding segment but with enlarged area to ensure elastic response - unrestrained non-yielding segment – used to connect the BRB to other structural elements Physical models for: Elastic global analysis Nonlinear global analysis

Nonlinear dynamic analysis

Axial-resisting and flexural-resisting mechanisms

2D or 3D conventional bracing frames Configuration: concentrical, chevron, inverted V

Pinned connection (usually); semi-rigid Connection details r.c. frame structure

Design criteria - Brace connections are to be designed with sufficient overstrength

Nonlinear statci - Pushover Nonlinear dynamic - Time-history

Core plastic deformation Interstory drift

EBF – Eccentric braced frames (2.8, 3.7) Linear static q – factor Linear dynamic

Limit state criteria - Strenght - Rigidity - Stability

Steel Analytical formulas – Behavior (short, long link) Numerical models

Eccentric bracing frames configuration Horizontal or vertical link

Types of connection Pinned or semirigid connection

Nonlinear statci - Pushover Nonlinear dynamic - Time-history

Link plastic deformation Interstory drift

Steel jacketing reinforcement (3.4) Composite column Analytical formulas (design metodologies) for - increase ductility of column - increase column resistance to axial force - ductility index - axial force ratio

2D and 3D moment resisting frames Linear static

- 17 -

FRP (3.3) Linear static q – factor Linear dynamic

Ultimate limit state Material strenght

Linear behavior (fiber + matrix)

Analytical formula Flexural strengthening Changing the failure mode from shear to flexure Avoiding lap-splice failure Confinement

2D and 3D moment resisting frames Bonding structure

Failure modes

Mode 1 - Laminate/sheet end debonding; Mode 2 - Intermediate debonding, caused by flexural cracks; Mode 3 - Debonding caused by diagonal shear cracks; Mode 4 - Debonding caused by irregularities and roughness of concrete surface; Bonding length

Nonlinear static Nonlinear dynamic

Incresed plastic deformation (rotation) Interstorey drift

DISIPATIVE DEVICE Magneto-rheological device (2.6) - Reinforced concrete frames

- Steel frames - Iron frames - Timber frames

Columns Beams Braces

Frames with dampered braces Linear static for pre-design phase Ultimate limit state Strenght and rigidity demand Ultimate displacement

Stru

ctur

al ty

polo

gy

- Masonry shear walls - Reinforced concrete shear walls

Shear walls

Controlable fluid damper

Parametric and nonparametric models Mechanical model Rheological models

Wall structures with shock absorber

The dievice is pin connected into the structure

Design phase Nonlinear dynamic

Plastic deformation of members Interstorey drift Specific device design parameters (range of displacement, frecvency)

18

D10 – Set-up of analytical models for special materials and special devices for the seismic structural control

1. Models and performance criteria for structural elements of different material

A complex problem like evaluating the bearing capacity of a structure and to decide on the necessity of a structural intervention must start from the study and thorough understanding of the real nature and stress-strain behavior of materials and elements behavior. This chapter of the report treats the most common structural typologies of monumental and historical buildings and the component materials like: masonry, marble and lime-stone, iron, reinforced concrete and timber.

1.1. Masonry elements – Clay brick

This section treats especially the behavior of the masonry structures made by clay brick and cement mortar. In the Mediterranean aria exists a wide range of masonry elements in terms of pattern and also in term of component materials, like adobe, stone with lime – mortar etc. All this typologies of masonry respect, more or less, in terms of behavior the same principles.

1.1.1. Introduction

This section was prepared in accordance with data-sheet no. 9-1 “Simplified and Advanced Models for Calculation and Analysis of Masonry Shear Walls” provided by A. Dogariu, T. Nagy-Gyorgy, C. Daescu, D. Daniel, V. Stoian and D. Dubina from “Politehnica” University of Timisoara (ROPUT).

Masonry is the oldest building material (Figure 1.1-1) that still finds wide use on today building industries and remains one of the most used construction material. The most important advantage of masonry construction is its simplicity, but in the same time a lot of difficulties arise in evaluating its behavior. When a masonry building is the subject of strengthening, the strength technique cannot avoid considering the base material behavior, and modelling. The document makes a review from the analytical formula of masonry behavior, as a composite material, in different loading condition thru advanced numerical possibilities. Also it is focus on shear behavior of masonry panels only, without treating the out-of-plain behavior, and elements like arches and vaults. This problematic is treated in detail in Chapter 4 of this report.

Figure 1.1-1 Brick making in Egypt (wall painting in the tomb of Rekhmara at Thebes 1500 BC).

1.1.2. General problems of the material and element behavior

The main problem of masonry is that it is a nonhomogeneous material composed of two materials with different mechanical properties. The equivalence with a homogenous material is difficult to be done because of the dependency of masonry on several factors: properties of the materials, typology of masonry, quality of workmanship etc.

One of the main problems is the great vulnerability of the masonry to earthquake due to the lack of resistance (small tensile resistance), small deformability and low ductility having a sudden and brittle

19

failure. On another hand the small ratio between resistance and own weight of the material (the masonry elements are massive with a great mass and rigidity) attract high inertia forces.

The great variability of the masonry typology can be a great inconvenience in establishing a concise methodology to describe the characteristics of masonry behavior in terms of mechanical properties. In different parts of the world and in different historical periods masonry has known a wide application from stone elements, independent or linked with earth based material to clay brick with or without mortar. In our days the brick unit that is use for masonry elements can be classified as: solid, perforated unit, hollow unit, cellular unit, horizontally perforated unit etc. The mortar can be classified as: general purpose mortar, thin layer mortar and lightweight mortar. In the following figure (Figure 1.1-2) some of the different types of masonry elements may be observed. In the frame of PROHITECH project have been studied experimentally and numerical different masonry typologies (i.e. adobe, sale-stone with lime-mortar and clay brick). This document will focus on clay brick with the remark that the general principles presented remain the same for all the other typologies also.

Figure 1.1-2 Examples of different kinds of stone masonry, (a) rubble masonry and (b) coursed

ashlar masonry, and (c,d) possible cross sections (Lourenco, 2001)

From the following scheme (Figure 1.1-3) which shows the failure modes of a masonry structure when an earthquake occurred, it may be observe that due to the direction of the loads the masonry panel demonstrates a different behavior and different failure modes. A global analysis procedure (i.e. ultimate limit state), including main failure modes – collapse mechanism and evaluation of bearing capacity, is presented in detailed in Chapter 4 of this report.

Figure 1.1-3 Masonry structure behavior under earthquake action

From this point the masonry panel failure modes may be divided in two categories:

20

• In plane behavior

• Out-of-plane behavior

This document will focus in describing the behavior and the possibility to modeling the in-plane behavior. Subjected to in plane loads a masonry panel can fail in one of the following ways (Figure 1.1-4), depending on wall geometry and load conditions:

Figure 1.1-4 In-plane failure modes of shear panels (Marzhan, 1998)

• Sliding failure (a)

• Flexural failure (b)

• Shear failure (c)

Typical in-plane failure modes for a masonry wall with openings is shown in Figure 1.1-5:

Figure 1.1-5 Critical failure modes in a masonry wall with openings, IAEE/NICEE (2004).

- Sliding failure is defined as the horizontal movement of entire parts of the wall on a single brick layer, vapor barrier or mortar bed.

- Flexural failure, when the wall behaves as a vertical cantilever under lateral bending and, either cracking in the masonry tension zone (opening of bed joints) or crushing at the wall toe.

- Shear failure is characterized by a critical combination of principal tensile and compressive stresses as a result of applying combined shear and compression, and leads to typical diagonal cracks. In practice, two types of shear cracking can be observed, joint cracking by local sliding along the bed joint and diagonal cracking associated with cracks running through the bricks as well as the joints.

All this failure types should be considered when we try to determine the element’s resistance in case of design or check of a structure. The design codes for masonry offer for each failure type precise formulas for resistance associated with a failure mode.

21

1.1.3. Models for masonry component materials (Material model)

In case of a composite material like masonry the first step for calculation and analysis requires an exact study of the component material. Our document will describe the behavior of clay brick and cement mortar. Material test on single brick blocks and mortar specimens (Figure 1.1-6) are needed in order to establish the behavior of each component.

Figure 1.1-6 Compression tests for brick/mortar units

Usually, this test offers a behavior curve from which we can extract the load bearing capacity and deformation characteristics. These tests give us the physical models for each material. In Figure 1.1-7 the physical models for brick and mortar in case of uniaxial load are presented.

Figure 1.1-7 Behavior curves for brick and mortar

Some conclusions about material behavior can be summarized:

• The component material have higher resistance in compression than in tension;

• In general brick has higher elastic modulus and resistance than mortar;

• In comparison with brick, which have a brittle failure, the mortar has a higher ductility and admits higher deformations.

1.1.4. Models for masonry as a composite material (Element model – walls)

In this paragraph the possibilities to take in account a masonry wall subjected at in plane load will be summarized. The ways to design and analyze an element are presented in a formally ranked order from simple formulas to complex numerical approaches.

a) Design code relationship (Analytical Models)

From the practical point of view of design, the national standards offer different formulas for each failure mode. For example, the old Romanian Code for Masonry Building P2/85 and EC6 suggests simple mathematical relations (Table 1.1-1) for establishing the resistance of an element.

Table 1.1-1 Design formulas

22

P2/85 EC6

Sliding failure

Small eccentricity

0( 0.7 )iCF f

i

AT R f σµ

= + (1.1-1)

High eccentricity

00.7 iCF

i

f AT σµ

⋅ ⋅ ⋅= (1.1-2)

1 01( ) (1 )

cosRd vd p pF zu f l t αθ

= + (1.1-3)

0.07 4 1p

p

hl

α⎛ ⎞

= −⎜ ⎟⎜ ⎟⎝ ⎠

(1.1-4)

Flexural failure

0

0

1.25

1.25

c cCM

c c

c

M Ne RSTZ Z Z

S A eNA

R

= = =

=

=

(1.1-5) 2 342 ( ) 0.8 cos b

Rd d st p pz

EF zu f I h tE

θ= (1.1-6)

Shear failure

01 0.8p iCP

i p

R AT

Rσ

µ= + Φ (1.1-7) 0

3 ( )0.6cos

vd p pRd

f l tF zu

θ= (1.1-8)

The minimum value from associated resistances gives the most possible failure mode and the correspondent capacity.

Similar relations are given in most standards for masonry buildings available in the world.

This kind of approach is the easiest one, but gives information only about the resistance of the element, resistance that usually is highly under evaluated.

Some other codes offer more detailed information about masonry behavior, like constitutive laws, rigidity characteristic, deformation capacity, performance criteria etc.

The following figure (Figure 1.1-8) presents qualitatively the uniaxial behavior of the masonry compared with the component materials.

23

Figure 1.1-8 Behavior curves for masonry and his components (uniaxial loading) and simplified tri-linear stress–strain model for masonry Hemant (2007)

Based on component mechanical properties, Hilsdorf proposed a relation to determine the masonry properties:

( )0.9( )

4.1

234.5

b bt mw

bt b

m

b

m

f f ffU f f

hh

fU

αα

α

+=+

=

= −

mf - mortar compression strength

bf - brick compression strength

btf - brick tensile strength

mh - mortar joint depth

bh - brick depth

U – non-uniform stress distributing factor

b) Simplified relations for numerical analysis – considering masonry as an homogenous and isotropic material (Analytical Models)

The formulas available are determined from experimental tests on sub-assemblages (Figure 1.1-9):

Compression test Shear test

Figure 1.1-9 Usual tests on sub-assemblages

i. Uniaxial loading

Different empirical equations are suggested in scientific papers and standards as constitutive laws for masonry elements as a homogenous material (Table 1.1-2).

Table 1.1-2 Constitutive laws

Turnsek-Cacovic (1970): 1.17

6.4 5.4k k k

σ ε εσ ε ε

⎛ ⎞ ⎛ ⎞= −⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠ (1.1-9)

Sawko (1982) based on Powell-Hodgkinson experimental test:

2

2k k k

σ ε εσ ε ε

⎛ ⎞ ⎛ ⎞= −⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠ (1.1-10)

ANDIL (Italian Association of Clay Brick Producers):

EC 6 propose : 2

2 0

1

kk k k

k uk

for

for

σ ε ε ε εσ ε εσ ε ε εσ

⎛ ⎞ ⎛ ⎞= − ≤ ≤⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

= ≤ ≤

(1.1-12)

Legend:

24

0.5

3.4142* 1 1k k

σ εσ ε

⎡ ⎤⎛ ⎞⎢ ⎥= − +⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

(1.1-11) σk = maximum allowable compression strength

εk = 0.002 (characteristic strain correspondent σk )

εu = 0.003÷ 0.0045 (ultimate strain)

ii. Biaxial loading

Being a nonhomogeneous material with different component materials, masonry has a very different behavior in relation to direction of the applied load. Consequently the resistance of the element is highly dependent of the biaxial state of stress in the element.

Failure mode for different biaxial tests specimens are presented in next table (Table 1.1-3):

Table 1.1-3 Different biaxial tests Dhanasekar et al. (1985)

Many experimental works (Page, 1981) have been carried out and they suggest the follow biaxial interaction curve between the principal stresses (Figure 1.1-10).

Figure 1.1-10 Experimental interaction curves

25

Based on experimental tests a failure domain (Figure 1.1-11 – Concrete smeared cracking used by ABAQUS) used for numerical, finite element simulation can be established. Also, other types like Hill type + Rankine type composite yield surface, Hoffman type single yield surface, yield surface proposed by Dhanasekar (1986) or by Ganz (1989)

Figure 1.1-11 Theoretical interaction curves (ABAQUS)

iii. Shear loading

The most important phenomenon that governs the behavior of masonry panels is shear behavior. In order to determine the mechanical characteristics needed in analysis some easy tests (Figure 1.1-12) should be performed on “double” (a) or “triple” (b) samples. The testing set-up is presented bellow:

Figure 1.1-12 Pure shear test

Tests at different levels of normal pre-compression showed that the failure criteria have a Mohr – Coulomb shape.

26

Figure 1.1-13 Mohr – Coulomb

behavior

The Mohr – Coulomb relationship is described by the following formula:

0ult vτ τ µσ= + (1.1-13)

τ0 - ultimate tangential stress at zero level of pre compression (cohesion)

µ - friction coefficient

σv – pre compression stress

a) Test set-up b) Applied forces

Figure 1.1-14 Apparatus to obtain shear behaviour (van der Pluijm 1993)

Other more sophisticated failure criteria like Drucker–Prager–Cap modified or other models that catch the influence of normal state of stress at the ultimate shear capacity, can be used as well.

Knowing the geometry of a panel and the loads applied, the principal stress can be determined with the following relationships:

0w

VA

σ = the average compressive stress due to vertical load

w

HA

τ = the average shear stress due to lateral load H

2 2

2 2cbσ σστ

⎛ ⎞ ⎛ ⎞= + +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

0 0 (1.1-14)

2 2

2 2tbσ σστ

⎛ ⎞ ⎛ ⎞= + −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

0 0 (1.1-15) Aw – the horizontal cross section of the wall

b – the shear stress distribution factor depending on the geometry of the wall

c) Physical models for masonry infill panels – truss equivalent elements (Numerical Models)

Basic Features of Masonry Walls Modeling

It is one of the most used ways of modellation masonry bracing walls, and consists in replacing the masonry panel thru a linear brace element (Figure 1.1-15). Using this technique global analysis of the building with masonry infilled walls in both elastic and plastic domain can be performed.

27

,max minm

Sliding failureV Compression failure

Diagonal tension failure

⎧⎪= ⎨⎪⎩

Figure 1.1-15 Main characteristic of the system Constitutive Law

Values for each of the resistance Vm (Stafford Smith 1962, Mainstone 1974, Klingner & Bertero 1978 and FEMA 306) can be established from design standards and scientific literature.

Sliding failure , 0.6s

m TS ltV = (1.1-16)

Compression failure , 0m s mV l t Nτ µ= + (1.1-17)

2

0 0.04

m m

m

uN E l th

fτ

⎛ ⎞= ⎜ ⎟⎝ ⎠

=

Diagonal tension failure , cosm cr mV atf θ= , (1.1-18)

0.4

2 2

1/ 4

0.175( )

sin 24

m

m m m

m

c g m

a h d

d l h

E tE I h

λ

θλ

−=

= +

⎛ ⎞= ⎜ ⎟⎜ ⎟⎝ ⎠

Figure 1.1-16 Equivalent diagonal strut (Al Chaar, 2002)

Panagiotakos & Fardis, 1994

28

Like all the others models this one considers the masonry panel like a strut with a specify rigidity and resistance. This model has the advantage of taking into account empirically the openings by reducing the strut width. The constitutive law of the equivalent element is defining by the follow relation:

0

20 cos

m m m

m

m m

m

G t IkhE t ak

dα θ

=

= (1.1-19)

,

,max ,1.3m y ms m m

m m y

V f t l

V V

=

= ⋅ (1.1-20)

msf - shear strength according to diagonal compression test

Constitutive Law

Mostafaei & Kabeyasawa, 2004

,max minm

Sliding failureV

Compression failure⎧

= ⎨⎩

Constitutive Law

cosm w

mdu εθ

=

2 2ww w w

w

harctg d l hl

θ⎛ ⎞

= = +⎜ ⎟⎝ ⎠

,max ,max 00 , ,max ,2 ; 0.20 ( 1.33 )

1m m m

m y m m ym

V V k uk V V V

uα

αα

−= = → = =

− (1.1-21)

29

Al-Chaar, 2002

Constitutive Law

Geometrical parameters are defined:

coscolumn

column

alθ

= (1.1-22) -costan

mcolumn

column

ah

lθθ = (1.1-23)

Openings and existing infill damage are considered by reducing the diagonal strut width

2

11 2

2

0.6

306

open

red panel

AR

a aR R A

R Table FEMA

⎧ ⎛ ⎞⎪ =⎪ ⎜ ⎟⎜ ⎟= ⎨ ⎝ ⎠⎪

=⎪⎩

(1.1-24)

The presented evaluation procedures are applicable to all building structures that have been constructed with RC frames and walls that consist of infill panels constructed of solid clay brick, concrete block, and hollow clay tile masonry. In the case of old building structures the evaluation must be changed.

These assumptions are done in order to avoid dealing with the complicate behavior of masonry walls and are covering the life safety requests from the codes. The numerical analyses become easier.

This kind of supposition allow the user to perform both elastic and plastic analyzes, but without observing the state of stress distribution inside wall element or local damages, being more appropriate for global structural analysis.

d) Advanced Modeling of masonry

In the last forty years an enormous growth in the development of numerical tools for structural analysis has been achieved. Historical structures are particularly difficult to be analyzed due to the lack of data. Nevertheless, significant information can be obtained from numerical analysis.

Today, the finite element method is usually adopted to achieve sophisticated simulations of the structural behavior. A mathematical description of the material behavior, which yields the relation between the stress and strain tensor in a material point of the body, is necessary for this purpose. This mathematical description is commonly named a constitutive model and an important objective of today’s research is to obtain robust numerical tools, capable of predicting the behavior of the structure from the linear elastic stage, through cracking and degradation until total loss of strength.

Continuous modeling of masonry

The first step toward carrying out such analyses is to develop adequate constitutive models. For masonry elements, basically three approach levels have been addressed (Rots, 1991) (Figure 1.1-17):

30

• Micro-modeling – where units are represented by continuum elements whereas the behavior of the mortar joints and unit-mortar interface is lumped in discontinuous or interface elements. A complete micro-model must include all the failure mechanisms of masonry, namely, cracking of joints, sliding over one head or bed joint, cracking of the units and crushing of masonry.

In the micro-model each component of masonry – unit, mortar (simplified), and unit/mortar joint (detailed) – must be represented with different finite elements. The employment of a micro-model to analyze an entire building becomes prohibitive, since it would result in a large number of finite elements, and consequently require a lot of computer resources to run the analyses.

Two approaches can be used: the first one is the simplified or layer model, without taking into account the interface (friction law) between brick unit elements and mortar elements (Figure 1.1-17a), and the second one detailed or interface model, by introducing a normal and tangential contact surface instead of mortar layers (Figure 1.1-17b).

These kinds of detailed and simplified micro-model have very accurate results in case of suitable input data. This type of analysis is the most advanced level of numerical simulation in case of masonry elements. It is very suitable for simulating out-of-plane behavior of masonry, but for in-plane behavior this type of approach is not justified due to the high complexity compared with similar results as in easier approaches.

However if there is a high interest in observing local behavior and interaction with other elements or material this technique may be the only one that leads to coherent results.

• Macro-modeling – where an anisotropic continuum model establishes the relation between average stresses and average strains in masonry.

Units and joints are not represented anymore and the geometry of masonry constituents (units and joints) is lost (Figure 1.1-17c). An adequate macro-model must include anisotropic elastic and inelastic behavior.

Figure 1.1-17 Advances modeling approach (a) masonry sample; (b) detailed micro-modeling; (c)

simplified micro-modeling; (d) macromodeling (Lourenco, 1996)

31

This type of analysis is the most suitable form the point of view of balance between involved time and accuracy of the results. Anyway macro-modeling require an extra process, homogenization introduced by Salamon (Salamon, 1968). Homogenization of masonry step that has been widely treated in articles proposing complicated energy and deformation compatibility equations. Even so, the obtained results must be seriously calibrated after this homogenization, in order to obtain a good correlation with the experimental tests.

The homogenization process, proposed by (Pande, 1998) (Figure 1.1-18), in two steps has as results an elastic orthotropic material representing the anisotropic behavior of masonry.

[ ] 1

1 0 0 0

1 0 0 0

1 0 0 0

10 0 0 0 0

10 0 0 0 0

10 0 0 0 0

xy xz

x x x

yx yz

y y y

zyzx

z z z

xy

yz

xz

E E E

E E E

E E EE

G

G

G

ν ν

ν ν

νν−

⎡ ⎤− −⎢ ⎥

⎢ ⎥⎢ ⎥− −⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥− −⎢ ⎥= ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

Figure 1.1-18 Homogenization steps

The homogenization process described previously has many weak points as:

• it is suitable only in elastic range,

• it does not take into account the real pattern of masonry wall, the results being the same for the next figure (Figure 1.1-19):

Figure 1.1-19 Pattern of masonry wall (a) stack bond; (b) stretcher bond. (Lourenco, 1998)

Other methods of homogenization are presented below (Gang, 2006) (Table 1.1-4)

Table 1.1-4 Homogenization method exemple

Methods of Homogenization 1E (MPa) 2E (MPa) 12v 12G (MPa)

FEM, Stack bond (Anthoine, 1995) 8530 6790 0.196 2580

FEM, Running bond (Anthoine, 1995) 8620 6770 0.200 2620

Periodic Model, Stack bond 8568 6850 0.191 2594

32

Periodic Model, Running bond 8574 6809 0.197 2620

Multilayer Method (Pande et al. 1989) 8525 6906 0.208 2569

Two-step Method (Pietruszczak & Niu 1992) 9187 6588 0.215 2658

Elliptical Cylinder Model (Bati et al., 1999) 7784 6315 0.247 2556

The most modern way of homogenization is proposed by P. B. Lourenço and A. Zucchini (Lourenco, 2002) and is based on extracting from the element a basic-cell (Figure 1.1-20). Other authors have chosen different cells.

Figure 1.1-20 Basic cell (Lourenco, 2002)

For the purpose of understanding the internal deformational behavior of masonry, detailed finite element calculations were carried out for different homogeneous loading conditions (Figure 1.1-21).

Figure 1.1-21 Basic cell components and behavior (Lourenco, 2002)

Writing the simple equilibrium equation for below scheme (Figure 1.1-22) the elastic modulus of the “homogenous” material in the direction of loading can be obtained.

33

Figure 1.1-22 Basic cell stress conditions

Roberto Capozucca and Fabrizio Collini developed, based on Lourenco theory a homogenization technique for analysis of a shear wall. They studied a panel of small width s compared with the dimensions of the wall in the x-y plane.

The wall is considered to be stratified with the thickness of layer hi. The continuum is considered transversally isotropic as a result of the symmetry around the vertical axis y. The stress and strain relationships for the homogeneous continuum are evaluated considering the equivalence of energy of stratified element, Ur, with the energy of homogeneous element U0 (Capozucca, 2002).

Ur = U0

The energy of the stratified element is expressed as follows:

12 i

Tr i iV

iU dVδ ε= ∑∫

Other more simple technique for homogenization is proposed. Starting from the experimental global behavior we can extract the rigidity of the element and obtain the elastic modulus. After establishing an initial value for elastic modulus and compressive ultimate stress of the material, the numerical simulation and calibration of the model in order to obtain a good fit of the experimental results and numerical simulation can be obtained.

31

12

Kh hEI GAλ

=+

2(1 )EG

ν=

+

E

34

2u

cEf ε=

Appling a constitutive law

Discontinuous modeling of masonry (Tzamtzis, 2003)

Recently a considerable attention has also been given to rational assessment methodologies, which deal more directly with the discontinuous nature of structural masonry.

The discontinuities in continuous systems are in fact interfaces between dissimilar materials and joints or fractures in the material. A survey of the literature on finite element modeling of cracks and joints shows that two main approaches are common for a representative analysis: the discrete crack and smeared crack approach and the use of joint or interface elements.

Discrete crack approach

Discrete crack models explicitly represent the crack as a separation of nodes (Figure 1.1-23). When the stress or strain at a node, or the average in adjacent elements, exceeds a given value, the node is redefined as two nodes and the elements on either side are allowed to separate. While this produces a realistic representation of the opening crack, a coarse meshing in the finite element model may result in misrepresentation of the propagating crack tip. A more serious problem is that, changing the formulation of the finite element model changes the number of equations to be solved and broadens the bandwidth of the stiffness matrix.

Figure 1.1-23 Discrete crack

Smeared crack approach

In the smeared crack approach, cracks and joints are modeled in an average sense by appropriate modifying the material properties at the integration points of regular finite elements.

Smeared cracks are convenient when the crack orientations are not known beforehand, because the formation of a crack involves no re-meshing or new degrees of freedom. However, they have only limited ability to model sharp discontinuities and represent the topology or material behavior in the vicinity of the crack.

The smeared crack concept, based upon strain decomposition and first developed for use in concrete structures, has also been extended to the analysis of masonry elements. The method is attractive if global analysis of large-scale masonry structures is required. It does not make a distinction between individual bricks and joints, but treats masonry as an anisotropic composite such that joints and cracks are smeared out. An inherent limitation of the smeared crack approach is that discrete cracks are smeared out over an entire element and crack opening is modeled by the continuous displacement approximation functions of the conventional finite element approach (Figure 1.1-24). In view of this limitation, as well as other problems such as mesh-dependency due to tensile and compressive softening and difficulties of model calibration, smeared crack models should only be used with caution for the analysis of discontinuous structures.

35

Figure 1.1-24 Smeared crack

Interface smeared crack approach an interface smeared crack model that combines the advantages of the discrete and smeared approaches described above is proposed.

The model treats cracks discretely like joint elements, but, like smeared crack elements, it does not introduce additional degrees of freedom. Cracking is limited to element boundaries and, if the crack opening criterion is met at a boundary node, then the local element displacements are altered until stresses perpendicular to the interface are brought as close as possible to zero.

Other methods of approach

Some researchers used the crack band theory to model the tensile behavior of concrete. The fracture of concrete is represented as a band of smeared cracks over a crack band of a certain width. Micro-cracking in the band is identified with the phenomenon of strain softening, which is represented by a stress-strain relationship that preserves the fracture energy of the material.

Some investigators have proposed another approach to model discontinuities present in a system: the method of constraints. According to this approach, interface discontinuities are represented by a sequence of double nodes, one on each side of the interface. The interconnection between the double nodes is controlled to simulate the physical behavior of the interface, and the desired solution is obtained by modifying the global stiffness equations in a manner that all the interface conditions, such as compatibility and friction law, are satisfied.

Use of joint elements

All of the crack models reviewed above have only limited ability to model sharp discontinuities present in many structural systems. Joint elements are more appropriate for modeling opening and closing of discrete cracks and joints and have been used in numerous applications.

For the efficient non-linear analysis of masonry, it is necessary to consider relative slip, de-bonding and cycles of closing and opening of the interfaces.

For wall thickness tw and mortar joint thickness tm, the normal and shear stiffness required to define the material property matrix can be represented by the following expressions (Page, 1978):

wsx sy

m

tK K Gt

= = wnz sy

m

tK K Et

= =

In which E and G are the instantaneous tangent elastic and shear module at the particular value of normal and shear stress considered. The non-linear behavior of the joints can therefore be treated by assigning

36

the joint properties corresponding to the level of stress obtained from the last load step in a step-by-step loading analysis procedure.

The failure criteria of a joint depend mainly on the relative magnitudes of the normal and shear stresses present in the joint. The relationship between the normal stress in a joint and its ultimate shear strength can be obtained from tests on masonry prisms with the load inclined to the bed joints.

1.1.5. Analysis types and performance criteria

According with Eurocode 6 linear analysis are recomened respecting performance criteria in terms of limits states:

• Ultimate limit state associated with collapse or with other forms of structural failure,

o loss of equilibrium of the structure or any part of it, considered as a rigid body,

o failure by excessive deformation, rupture, or loss of stability of the structure or any part of it, including supports and foundations.

• Serviceability limit states correspond to states beyond which specified service criteria are no longer met.

o deformations or deflections which affect the appearance or effective use of the structure (including the malfunction of machines or services) or cause damage to finishes or non-structural elements,

o vibration which causes discomfort to people, damage to the building or its contents, or which limits its functional effectiveness.

1.1.6. Design assisted by testing:

In some cases there are no analytical calculation procedures and numerical simulation is either difficult due to the scatter of real material properties or does not offer accurate results. Experimental test can solve the problem. This kind of approach is based on experimental determination of a characteristic strength of the shear wall kR . This strength kR is used further in order to evaluate the necessary length of the walls on a direction “i” and at storey “j” to resist the corresponding seismic shear force.

The principle of the method is presented bellow (Table 1.1-5):

Table 1.1-5 Principle of method

, , , ,

, , ,

s i j s i j

s i j k i j

E R

R R L

<

= ⋅

, ,s i jE - total shear force induced by seismic action in “i” direction and “j” storey;

, ,s i jR - total shear wall resistance in “i” direction and “j” storey;

kR - characteristic strength of shear wall experimental determined;

,i jL - length of shear wall in “i” direction and “j” storey;

The method is applicable both for pure masonry wall and for strengthen walls (FRP, SSP – Steel Shear Plate, ASP – Aluminum Shear Plate, SWM – Steel Wire Mesh).

1.1.7. References:

“A homogenization model for stretcher bond masonry” P. Lourenço, A. Zucchini, 2002; Metodos numericos en ingenieria V - J. M. Goicolea, C. Mota Soares, M. Pastor y G. Bugeda (Eds.) SEMNI, Spain 2002

“The homogenization technique applied for analysis of shear walls with hollow bricks” Roberto Capozucca, Fabrizio Collini, 2002

37

“A micro-mechanical model for the homogenisation of masonry” A. Zucchini a,1, P.B. Lourenco, International Journal of Solids and Structures 39, February 2002;

“The elasoplastic implementation of homogenisation techniques with an extension to masonry structures “P. B. Lourenco 1995;

“Finite Element Modeling of Cracks and Joints in Discontinuous Structural Systems” A.D. Tzamtzis, P.G. Asteris, Electronic Journal of Structural Engineering, 1 (2004);

“Design of Fiber-Reinforced Polymer Materials for Seismic Rehabilitation of Infilled Concrete Structures” Ghassan K. Al-Chaar and Gregory E. Lamb, 2002;

“Biaxial Loading and Failure Behavior of Brick Triplets with Fiber-Reinforced Polymer Composite Upgrades” J.B. Berman, G.K. Al-Chaar, and P.K. Dutta, December 2002;

“The Shear Strength of Dry-Stacked Masonry Walls”, Gero Marzahn, 1998;

FEMA 356 “Seismic Rehabilitation Prestandard” Chapter7: Masonry;

EUROCODE 6 Masonry specifications;

“The modulus of elasticity of masonry“ J.J Brooks, B.H. Abu Baker, Masonry international, Vol. 12 , 1998;

ABAQUS /CAE Users Manual;

“Contribution at masonry shear wall calculation and design” – PhD These – Silviu Secula, 2003;

“Non-linear Analysis of Masonry Elements” –Dan D, S. Ianca, D. Tudor, “Politehnica” University Journal 1999;

“Modellatione numerica dei panelli murari rinforzati con elementi metallici” – Diploma These – Francesco Campitielo 2006;

“Masonry-infilled RC frames: experimental and numerical study” – F. Mazzolani, G. Della Corte, L. Fiorino, E. Barecchia, M. D’Aniello, S. D’Ambrosio, 2005.

“Finite Element Model for Masonry” Page, A. W., , Journal Str. Div., Proc. ASCE, Vol. 104, No ST8, 1978, pp. 1267-1285.

“Numerical simulation of cracking in structural masonry” Rots, J.G.; Heron, Vol. 36(2), pp. 49-63 (1991)

“Equivalent Elastic Moduli for Brick Masonry” Pande, G. N., J. X. Liang and J. Middleton; Computers and Geotechnics, 8, 243-265 (1989).

“Effective Elastic Stiffness for Periodic Masonry Structures via Eigenstrain Homogenization”, Gang Wang, Shaofan Li, Hoang-Nam Nguyen , Nichloas Sita, ASCE Journal of Materials in Civil Engineering, 2006

“The homogenisation technique applied to the analysis of shear wall built with hollow bricks” Roberto Capozucca , Fabrizio Collini, Engenharia Civil – Numero 14, 2002

“Elastic moduli of stratified rock mass”, Salamon, M.D.G., Int. J. Rock. Mech. Min. Sci., 5, 519-527 (1968).

“The biaxial compressive strength of brick masonry” Page, A.W., Proc. Intsn. Civ. Engrs., Part 2, Vol. 71, pp. 893-906 (1981)

“The influence of brick masonry infill properties on the behavior of infilled frames” Dhanasekar, M. and Page, A.W., , Proc. Intsn. Civ. Engrs., Part 2, Vol.81, pp. 593-605 (1986)

38

“Failure criteria for masonry” Ganz, H.-R., , 5th Canadian Masonry Symposium, Vancouver, Canada, pp. 65-77 (1989)

“Computational strategies for masonry structures”, P.B. Lourenco, Delft University Press, Stevinweg 1, 2628 CN Delft, The Netherlands (1996).

“The failure of brick masonry under biaxial stresses” Dhanasekar M, Page, A.W. and Kleeman P.W.,Proc. Intsn. Civ. Engrs., Part 2, 79 , p. 295-313 (1985).

“Experimental and numerical issues in the modelling of the mechanical behavior of masonry” Lourenco P.B.., Structural Analysis of historical constructions II - P. Roca, J.L. González, E. Oñate and P.B. Lourenço (Eds.) CIMNE, Barcelona (1998).

“Shear behavior of bed joints” Pluijm, R.v.d.,, Proc. 6th North American Masonry Conf., Philadelphia, U.S.A., pp. 125-136 (1993)

“A homogenization model for stretcher bond masonry” Lourenço, P.B., Zucchini, A.; Computer Methods in Structural Masonry - 5, Eds. T.G. Hughes and G.N. Pande, Computers & Geothecnics, UK, p. 60-67 (2001)

“Finite Element Modeling of Cracks and Joints in Discontinuous Structural Systems” Athanasios D. Tzamtzis, (2003).. 16th ASCE Engineering Mechanics Conference, July 16-18 2003, University of Washington, Seattle.

“The Shear Strength of Dry-Stacked Masonry Walls” Marzhan, G.; Institüte für Massivbau und Baustofftechnologie, Universität Leipzig. Lacer No.3, 1998.

“Uniaxial compressive stress–strain model for clay brick masonry” Hemant B. Kaushik, Durgesh C. Rai and Sudhir K. Jain, Current Science, vol 92 feb (2007)

“Evaluating Strength and Stiffness of Unreinforced Masonry Infill Structures” Al Chaar G, Construction Engineering Research Laboratory ERDC/CERL TR-02-1, January 2002

“Lateral stiffness of infilled frames” Stafford Smith 1962, Journal of the Structural Division ASCE 88(6), pp 183-199.

“Code Approaches to Seismic Design of Masonry-Infilled Reinforced Concrete Frames: A State-of-the-Art Review” Hemant B. Kaushik, Durgesh C. Rai and Sudhir K. Jain, Earthquake Spectra, Volume 22, No. 4, pages 961–983, November 2006; Earthquake Engineering Research Institute

“Full-scale cyclic tests of a real masonry-infilled RC building for seismic upgrading” F.M. Mazzolani, Gaetano Della Corte, L. Fiorino, E. Barecchia - March 30-31, 2007 - Prague, Czech Republic

“Supplementary note on the stiffness and strength of infilled frames” Mainstone, R. J., Current Paper CP13/74, Building Research Establishment, London, 1974.

“Seismic Response of Infilled R.C. Frames Structures” Panagiotakos T.B. and Fardis M.N., 11th World Conference on Earthquake Engineering, Acapulco, 1996, paper n.225.

"Non linear Dynamic Response Analyses of the 4-storey Infilled Structure at ELSA to 1.5 the Design Earthquake" T.B. Panagiotakos and M.N. Fardis, 1st year progress report of PREC8 project, June 1994, University of Patras, Patras, Greece.

“Seismic response of gravity load design frames with masonry infills” G Magenes, S. Pampanin, 13th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 4004

IAEE/NICEE (2004). "Guidelines for Earthquake Resistant Non-Engineered Construction". First printed by International Association for Earthquake Engineering, Tokyo, Japan. Reprinted by the National Information Center of Earthquake Engineering, IIT Kanpur, India.

39

FEMA 306: Evaluation of Earthquake Damaged Concrete and Masonry Wall Buildings , Basic Procedures Manual, Federal Emergency Management Agency, Applied Technology Council (ATC-43 Project), Washington DC, USA, 1998.

“Effect of Infill Masonry Walls on the Seismic Response of Reinforced Concrete Buildings Subjected to the 2003 Bam Earthquake Strong Motion: A Case Study of Bam Telephone Center” Mostafaei, H.; Kabeyasawa, T, Bulletin of the Earthquake Research Institute, The University of Tokyo, Vol. 79, pp. 133 - 156, 2004.

“Earthquake Resistance of Infilled Frames” Klingner, R. E., and Bertero, V. V. Journal of the Structural Division, ASCE, Vol. 104, No ST6, June, 1978, pp. 973-989.

1.2. Marble and limestone

1.2.1. Introduction

This section was prepared in accordance with data-sheet no. 9-2 “Stone – Unito Limestone” provide by L. Pavlovčič and D. Beg from University of Ljubljana, Faculty of Civil and Geodetic Engineering (SL).

Being the component material on ancient temples the study of these materials becomes an important demand in order to preserve them. It is well know that this kind of materials have a very brittle behavior govern by a weak tensile resistance. This report present some approach ways and critical opinions in order to predict material behavior and failure (i.e. sophisticated fracture analysis, simplified criteria related to tensile strength) based on different experimental tests and interpreting procedures.

In order to investigate the stone fracture resistance in general, two types of stone were experimentally examined: the Greek partner investigated the properties of Dionysos-Pentelicon marble, which is widely used for the restoration programs in Greece (reported in Vayas, 2008), while in Slovenia a typical Slovenian limestone from Lipica was tested, called Unito limestone due to its fine grained and homogeneous structure (the results presented in Pavlovcic, 2006).

1.2.2. Material properties

According to the linear fracture analysis the critical stress intensity factor SIF, named fracture toughness Kc is a very important material property for the description of stone fracture resistance is. With the series of tests the most important critical SIF KIc of the crack opening mode I was analysed (Figure 1.2-1). The importance of this concept for the linear fracture mechanics is that it overcomes the problem of sharp stress concentration (theoretically infinitely large in the case of no plasticity) in the vicinity of the crack initiation zone. On the other hand, with the fracture toughness taken as only one-dimensional property criterion, the stone fracture resistance in the complex three dimensional problem can only be roughly assessed.

As a more traditional engineering judgment of stone fracture resistance, the tensile strength ft may also be applied when the maximal principal stresses in the developed stress field close to the critical region are considered. Although this concept is not as advanced, this criterion may be treated as a considerably simplified assessment alternative.

Moreover, in order to simulate the numerically marble elements according to the elastic linear fracture analysis (see L. Pavlovčič, 2008) also Young’s modulus E and Poisson’s ratio ν of the stone are needed.

40

Figure 1.2-1 Three different crack opening modes (figure according to [4])

1.2.3. Linear analysis parameters - Young’s modulus and Poisson’s ratio

The examination of Young’s modulus and Poisson’s ratio of Unito limestone showed no significant difference of both values in tension or in compression (3% or 10%, respectively, (L. Pavlovčič, 2006)). Furthermore, compressive Young’s modulus Ec of Unito limestone in three different material directions differs only up to 7%, showing the high degree of isotropy.

When considering similarly homogeneous material (proved by compressive tests in three directions), the recommendation would be to obtain Elastic modulus and Poisson’s ratio from well defined and standardized procedure for compression tests (International Society for Rock Mechanics, 1972) (Figure 1.2-2). Moreover, from the aspect of accuracy of numerical simulation, the simplification to only compression properties (E = Ec and ν = νc) would be suggested also for more anisotropic material.

Figure 1.2-2 Compression test on cylindrical specimen

1.2.4. Tensile strength

The tensile strength may be determined either from direct tensile tests or from pure bending tests. In direct tensile tests special attention should be paid to the eccentricity of loading and load transition to the stone (Figure 1.2-3).

41

Figure 1.2-3 Tensile tests with constructed double space hinge and with glued Plexiglas plates on

each side of flat specimen

To avoid rather complicated and sensitive direct tensile tests, the pure bending tests would be recommended (Figure 1.2-4), where the tensile strength could be assessed from the tensile stresses on the lower specimen surface. Due to not uniform tensile stress field throughout the mid-span cross-section, the obtained tensile strength ft,B of Unito limestone was twice as large as determined from the direct tensile tests, which is also in agreement with Vardoulakis’ findings (Vardoulakis, 2001).

42

Figure 1.2-4 Pure bending test with a two-dimensional strain gauge glued on the bottom surface

1.2.5. Fracture toughness

In general the critical SIF is dependent on the initial crack geometry, stone dimensions and the stresses acting on the crack (notch). To consider the fracture toughness as a material characteristic, the size effect should be excluded in the way that the lower bound for KIc should be assessed. These normally require a series of tests. The stresses should be perpendicular to the notch direction.

There was an extensive experimental study conducted on Unito limestone (L. Pavlovčič, 2006), both on bending specimens of various geometry and DENT specimens in tension (Figure 1.2-5). The testing program and results are presented in (L. Pavlovčič, 2006).

a) 3P and 4P bending tests b) DENT test

Figure 1.2-5 Various tests on Unito limestone for the determination of fracture toughness KIc

As presented in (L. Pavlovčič, 2006), the fracture toughness may be determined with three following procedures:

• from the standardized procedure according to ASTM standard E 399-90 (American Society for Testing and Materials, 1997)

• from the critical crack opening displacement (COD) parameter δcrit, determined from the recorded NMOD at the maximal load

• directly from stress distribution obtained from strains measured with strain gauges

The evaluation of fracture toughness from the latter procedure turned out to be less reliable due to inaccurate strain measurement and the fact that the strain gauge close to the notch tip appeared to be located in the process zone showing already some local stone plasticity. The critical SIF of all Unito

43

limestone bending specimens evaluated according to the other two methods are presented in Figure 1.2-6.

Fracture toughness KIc determined according to ASTM

0,860,77

1,050,940,930,96

0,820,82

0,94

1,040,970,98

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

0 0,1 0,2 0,3 0,4 0,5

a/H

KIc [M

Pa*m

1/2 ]

20-5-5: 4PB-average20-5-5: 3PB-average20-5-5: 4PB20-5-5: 3PB40-20-10: 4PB40-20-10: 3PB20-20-10: 4PB11-2.5-2.5: 3PB

Fracture toughness KIc determined from δcrit

0,600,61

0,69

1,22

0,82

0,630,620,65

0,63

0,79

1,13

0,69

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

0 0,1 0,2 0,3 0,4 0,5

a/H

KIc

[MPa

*m1/

2 ]

20-5-5: 4PB-average20-5-5: 3PB-average20-5-5: 4PB20-5-5: 3PB40-20-10: 4PB40-20-10: 3PB20-20-10: 4PB11-2.5-2.5: 3PB

Figure 1.2-6 Comparison of KIc of Unito limestone according to ASTM standard and from δcrit

Results according to ASTM show surprisingly constant value of KIc with the variation of notch depth (a/H is notch depth-to-specimen height ratio). Hence, the assessed fracture toughness of Unito limestone according to ASTM would be around KIc = 1.0 MPa·m0.5. On the other hand, according to the second approach the results appeared to be size-dependent converging to the lower limiting value of KIc = 0.6 MPa·m0.5 with the increase of a/H.

It is important to note that for all performed tests the validity requirements stipulated by ASTM were not fulfilled: either size requirements or linear response condition, which is for the brittle material very rigorous (the standard was originally developed for metallic materials). Furthermore, the notch was machine cut instead of natural sharp crack obtained by fatigue cracking. On the other hand, from the perspective numerical simulations, the obtained lower limit from δcrit seems to be rather conservative, especially since in the applied recalculation of critical COD the smaller angle ϕ = 30º was considered (Figure 1.2-7), yielding higher values of KIc than in the case of ϕ = 45º (KIc,lower = 0.45 MPa·m0.5).

s

a ϕ ϕ = 30 - 45

a.re

f1.

7

mmaa

NMODCOD refcritcrit 7.1+

= (1.2-1)

sCODcrit

crit =δ (1.2-2)

Figure 1.2-7 Determination of the critical COD parameter δcrit from the measured critical NMOD at the maximal load (ϕ = 30º - 45º proposed by (Schwalbe,1995))

As the bottom line, in order to experimentally determine close to the lower limit bound of KIc for different stone materials, the suggestion would be to perform bending tests on prismatic specimens L/H/B = 20/5/5 cm and with the notch-to-specimen height ratio a/H ≥ 0.2. To obtain accurate notch shape, cutting under water jet is promising for the specimens not wider/deeper than B = 5 cm. The most transparent procedure for the evaluation of fracture toughness would be the standardized method according to ASTM standard E 399-90, disregarding some too rigorous size and linearity requirements for the stone material. The alternative procedure would be to determine KIc from the critical COD parameter δcrit, defined with the angle ϕ = 30º. This procedure probably yields conservatively low values.

44

1.2.6. Reference:

L. Pavlovčič, F. Sinur, D. Beg “Material tests on Unito limestone from Lipica”, Final report for WP7 of European project PROHITECH, Ljubljana: University of Ljubljana, Faculty of Civil and Geodetic Engineering, Chair for Metal Structures, 2006. 55 pp.

L. Pavlovčič, P. Kozlevčar, F. Sinur, D. Beg “Architrave connection tests”, Final report for WP7 of European project PROHITECH, Ljubljana: University of Ljubljana, Faculty of Civil and Geodetic Engineering, Chair for Metal Structures, 2008. 70 pp.

International Society for Rock Mechanics: “Suggested methods for determining the uniaxial compressive strength and deformability of rock materials”, 1972

I. Vardoulakis, Rosakis, S. Kourkoulis: “The building stone in monuments”, Interdisciplinary workshop, Institute of Geological & Mining Research, Greek department of ICOMOS, Technical chamber of North Aegean, November 9th -11th 2001, Athens, Mytilini

American Society for Testing and Materials: “E 399-90: Standard test method for plain-strain fracture toughness of metallic materials”, Annual Book of ASTM Standards, Vol. 03.01, Metals-Mechanical Testing; Elevated and Low-Temperature Tests; Metallography; 1997, pp. 408t-422

K.H. Schwalbe: “Introduction of δ5 as an operational definition of the CTOD and its practical use”, Fracture mechanics, Vol. 26, STP. 1256, ASTM, Philadelphia, PA, 1995, pp. 763-778

I. Vayas, S. Kourkoulis, S.-A. Papanicolopulos, A. Marinelli: “DIII-P.I-p1.4.1: Marble, Final Report for WP7 of European project PROHITECH”, National Technical University of Athens, March 2008

1.3. Concrete / Reinforced concrete

1.3.1. Materials

There is a general agreement that design (characteristic) strength is not appropriate for evaluation of existing buildings (Priestley, 1997) for two reasons. First is that use of design strength is too conservative, and the second is that the use of characteristic instead of expected strength for concrete may often lead to change of predicted failure mode from ductile flexure to brittle shear. Ideally, expected strengths of concrete and steel are to be determined experimentally. In the absence of experimental tests, different values are suggested in literature (see Table 1.3-1). In the same table are presented the ultimate strains specified in the same sources. Design codes (EC2) provide the most conservative estimates (as would be expected). However, there is an important difference between the other two "predictive" oriented sources in the case of steel strength and ultimate strain.

Table 1.3-1. Relation between characteristic and expected strength for materials, and ultimate strain limits.

EC2 Priestley FEMA 356 Concrete compression strength (fc)

fck + 8 N/mm2 (1.3 fck for C25/30)

1.5 fck 1.5 fck

Steel yield strength (fy) - 1.1 fyk 1.25 fyk Ultimate concrete strain (bending)

0.0035 0.005 0.005

Ultimate steel strain - 0.10-0.15 0.02 – compr. 0.05 - tension

where: fck – concrete characteristic (nominal) compression strength; fyk – steel characteristic yield strength.

45

Concrete strength and ultimate strain could be further enhanced by the effect of confining. However, this will seldom be the case for poorly detailed gravity load design (GLD) frames. According to Priestley (1997), concrete should be considered unconfined if the following conditions govern:

stirrups ends not bent back into the core, and spacing of stirrups in the potential plastic hinge is such that: s≥d/2 or s≥16dbl where s is the stirrups spacing, d is the effective depth of the cross section, and dbl is the diameter of the longitudinal reinforcement.

Analytical modelling of steel will be usually based on an elastic-perfectly plastic stress-strain relationship. Strain hardening may be considered for a more realistic behaviour of steel in tension. A refined modelling of steel in compression will require accounting for buckling of longitudinal reinforcement. Lower ultimate steel strains in compression in the FEMA 356 approach may be intended to account in an approximate way for the effect of reinforcement buckling.

Modelling of concrete in compression will usually consist of a parabola stress-strain relationship up to a strain of approximately 0.002, with a plastic plateau afterwards, up to the ultimate strain (0.0035 – 0.005). A more realistic modelling, especially for the case of unconfined concrete, is to consider the softening (descending) branch after the attainment of the maximum strength.

1.3.2. Modelling of elements

Modelling of nonlinear behaviour of r.c. frames may be performed in different ways, ranging from finite element models of increased complexity, to models based on macroelements representing structural members (beams and columns), or even bigger portions of a structure. Nonlinear analysis models based on macroelements for beams and columns are widely used due to reliability and computational efficiency. A variety of implementations for modelling reinforced concrete elements exist, depending on the computer code used. Several element modelling options are mentioned here.

Behaviour of moment-resisting frames is governed by the flexural response of beams and columns. One of the simplest models for flexural behaviour of beam-column is the one-component model (Figure 1.3-1a). All inelastic deformations are assumed concentrated at elements end (lumped plasticity model). The element is characterised by a bilinear or trilinear moment-rotation envelope curve, and a set of rules describing cyclic behaviour. Two one-component elements are necessary to model a column in biaxial bending. It offers a great flexibility in modelling, by allowing for such effects as stiffness and strength degradation, and pinching under cyclic loading.

A variant of one-component model is the moment-curvature based model, assuming linear variation of flexibility along the member. This model is appropriate for members with moment distribution close to the uniform one. The same limitations of the moment-rotation based one-component model apply.

The multi-spring model (see Figure 1.3-1b) is composed of an elastic line element and two multi-spring elements at each end. Each multi-spring element consists of a number of springs (fibres) representing uniaxial behaviour of concrete or steel materials. The model accounts naturally for biaxial moments and axial force (M-M-N) interaction. The multi-spring element is considered to be of zero length in establishing member force-displacement relationship (being a lumped plasticity model in effect). The force-deformation relationship of the multi-spring element itself is determined based on a plastic zone length and the Bernoulli plane section assumption.

46

(a) (b)

Figure 1.3-1. One-component model (a) and multi-spring model (b), (Li, 2002).

A distributed plasticity model is based on discretisation of cross-sections at the element ends into a number of fibres, similarly to the multi-spring model. However, a linear variation of curvature along the element is assumed, resulting in a distributed plasticity model. Like the multispring model, the fibre model accounts naturally for the interaction of biaxial moments and axial force.

The bilinear moment-rotation relationship for elements can be modelled based on the procedure described in Paulay and Priestley, 1992 (see Figure 1.3-2). A standard moment-curvature analysis is carried out for each element. For columns, axial force corresponding to gravitational loading was considered. Yield curvature yφ is determined at first yielding of reinforcement or at the attainment of 0.0015 strain in concrete. The ultimate curvature uφ is found at attainment of ultimate steel or concrete strains. The equivalent plastic hinge length can be determined as:

0.08 0.022p b yL L d f= ⋅ + ⋅ ⋅ (1-1)

where L is the shear span of the member (assumed half the clear span for most of the members), db is the diameter of the longitudinal reinforcement, and fy is the yield strength of the reinforcement.

Then, the moment-rotation relationship is obtained by integrating the curvature distribution along the element length:

/ 3y y Lθ φ= ⋅ (1-2)

( ) ( )θ θ φ φ

⋅ − ⋅= + −

0.5p pu y u y

L L LL

(1-3)

where yθ is the yield rotation and uθ is the ultimate rotation.

47

Figure 1.3-2. Equivalent curvatures and plastic hinge length for bilinear model

(Paulay and Priestley, 1992)

A slightly modified procedure can be used for constructing the trilinear moment-curvature and moment-rotation relationships (see Figure 1.3-3). Cracking curvature cφ is defined as the one corresponding to the attainment of the lower cracking moment Mc in the cross section. The ultimate curvature uφ is determined as previously at the attainment of ultimate strains in concrete or steel. With the plastic hinge length defined as in equation (1-1), the following relations are used to derive the trilinear moment-rotation relationship:

/ 3c c Lθ φ= ⋅ (1-4)

1 1 26

c c cy c y

y y y

M M MLM M M

θ φ φ⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎛ ⎞

= ⋅ ⋅ + + ⋅ − ⋅ +⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎝ ⎠ (1-5)

( ) ( )θ θ φ φ

⋅ − ⋅= + −

0.5p pu y u y

L L LL

(1-6)

M

φc

c yM

φc

cM

φy

MuMcMy

L L

φc

yφ

Lp

uφ

Figure 1.3-3. Curvature distribution along the shear span

for trilinear moment-curvature idealisation.

48

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

0 0.002 0.004 0.006

STRAIN

STR

ESS,

N/m

m2

CoreCover

Figure 1.3-4. Stress-strain models for core and cover concrete.

In the case of bilinear element modelling, a simplification often used is the assumption of an effective element flexural stiffness as a fixed ratio of the uncracked stiffness. Eurocode 8 stipulate an effective stiffness of 0.5EcIg for both beams and columns, where Ec is the concrete modulus of elasticity, and Ig is the gross moment of inertia of the element cross-section. Other sources recognize the stiffening effect of compressive axial load on columns, differentiating effective stiffness as a function of column axial load. Thus, FEMA356 specifies effective stiffness of 0.5EcIg for beams, 0.7EcIg for columns with a nondimensional axial compressive force ν≥0.5Agfc, and 0.5EcIg for columns with ν≤0.3Agfc. Paulay and Priestley (1992), recommend values of 0.35EcIg for beams, 0.8EcIg for columns with a nondimensional axial compressive force ν>0.5Agfc, and 0.6EcIg for columns with ν<0.2Agfc.

Another simplification in modelling of r.c. elements, especially when effective stiffness is used, is the assumption of empirical values of post-yielding stiffness for the moment-rotation relationship. Some commonly used values are about 1% to 3% of the secant stiffness to the yield point. FEMA356 recommends strain hardening values ranging from 0% to 10%. Sometimes higher values were found to fit well the experimental results. Thus, Dolsek and Fajfar (2002) used 10% post-yielding stiffness for beams under positive bending (bottom reinforcement in tension) and columns, and 20% for beams under negative bending. Higher values of strain hardening for beams under negative bending are intended to approximately account for the observation of increase of the flange effective width as the plastic deformations increase.

1.3.3. Beam effective width

Slab contribution to the strength and stiffness of beams could be important for the seismic assessment of r.c. frames, as it will affect the relative beams/columns strength and stiffness. This, in effect may change the plastic mechanism. However, this contribution is difficult to estimate, as it varies along the length of the member, and depends on the level of inelastic deformations, as well as presence of transverse beams and anchorage of the slab reinforcement (Paulay and Priestley, 1992). Thus, the effective flange width specified in codes and literature is only an approximate measure of the real and complex slab contribution. Several approaches for determination of effective slab width are considered in the following.

Eurocode 8 (2002) states that the effective flange width beff is drastically reduced due to local plastification effects. The effective width values provided are intended for determination of member strength (not stiffness). The following relations are suggested: for beams framing into exterior columns: Bc – in the absence of a transverse beam

4c fB h+ ⋅ – if there is a transverse beam of similar dimension

for beams framing into interior columns: the above lengths may be increased by 2hf on each side of the beam

49

where: Bc – column width, hf – slab height

Eurocode 2 (2001) states that in T beams the effective flange width, over which uniform conditions of stress can be assumed, depends on the web and flange dimensions, the type of loading, the span, the support conditions and the transverse reinforcement. Values of effective widths are intended for all limit states (strength and stiffness) and are to be based on the distance L0 between points of zero moments:

,eff eff i wB B B B= + ≤∑

with , 0 00.2 0.1 0.2eff i iB B L L= ⋅ + ⋅ ≤ ⋅ and ,eff i iB B≤

where Beff is the flange effective width on each side of the web; Bi is the half the clear distance to the next beam web; Bw is the beam web width.

FEMA 356 specifies that for flanged beams the combined stiffness and strength for flexural and axial loading shall be calculated considering a width of effective flange on each side of the web equal to the smaller of:

• the provided flange width,

• eight times the flange thickness,

• half the distance to the next web, or

• one-fifth of the span for beams.

The New Zealand seismic provisions NZS3101 consider that flange contribution to stiffness in T and L beams is typically less than the contribution to flexural strength, as a result of the moment reversals occurring across beam-column joints and the low contribution of tension flanges to flexural stiffness. Consequently, it is recommended that for load combinations including seismic actions, the effective flange contribution to the stiffness be 50% of that commonly adopted for gravity load strength design (Paulay and Priestley, 1992). The following effective widths are specified for determination of stiffness:

for T beams, Beff is the lesser of:

• Bw+ 8hf

• Bw+ Lny/2

• Lx/8

For L beams

• Bw+ 3hf

• Bw+ Lny/4

• Bw + Lx/24

where: Lx – span length of beam; Lny – clear distance to the next web.

Paulay and Priestley, (1992) recommend that in T and L beams, built integrally with the floor slabs, the longitudinal slab reinforcement placed parallel with the beam, to be considered effective in participating as beam tension (top) reinforcement. In addition to the bars placed within the web width of the beam, these should include all bars within the effective width in tension Beff, which may be assumed to be the smallest of the following:

• ¼ of the span of the beam under consideration, extending each side from the centre of the beam section, where a flange exists

50

• ½ of the span of a slab, transverse to the beam under consideration, extending each side from the centre of the beam section, where a flange exists

• ¼ of the span length of a transverse edge beam, extending each side of the centre of the section of that beams which frames into an exterior column and is thus perpendicular to the edge of the floor

Within this width Beff only those bars in the slab that can develop their tensile strength at or beyond a line of 45° from the nearest column should be relied on. At edge beams, effective anchorage of bars, in both the top and bottom of the flange must also be checked. Where no beam is provided at the edge of a slab, only those slab bars that are effectively anchored in the immediate vicinity of a column should be relied on (Beff=2 Bc).

hf

Beff

Bw Beff,2Beff,i

Lb

B1 B2

Beff

Bw (Bc)

Figure 1.3-5. Notations used for definition of effective flange width.

A comparison of the different approaches in determining beam effective widths is presented in Table 1.3-2. The same notations (see Figure 1.3-5) were used to facilitate the comparison. It can be observed that different approaches disagree on whether the effective widths should be used for determination of strength, stiffness or both. Eurocode 8 provide similar values with NZS3101, but these values are intended for strength in the first case and stiffness in the second one. Higher effective widths (and close to each other) are specified by FEMA 356 and Paulay and Priestley.

Table 1.3-2. Comparison of effective flange widths according to different approaches.

T beams L beams Remarks

EC8 Beff = BC+ Beff,1 + Beff,2

a) for beams framing into exterior columns:

Beff,i ≤ 2 hf

Beff,i = 0 in the absence of a transverse beam

b) for beams framing into interior columns:

Beff,i ≤ 4 hf

for bending resistance

51

EC2 Beff = Bw+ Beff,1 + Beff,2

Beff,i ≤ 0.5 Bi

Beff,i ≤ 0.2 Bi + 0.05 LB

Beff,i ≤ 0.1 LB

for all limit states; L0 – distance between points of zero moments; L0 assumed LB/2

FEMA 356 Beff = Bw+ Beff,1 + Beff,2

Beff,i ≤ 8 hf

Beff,i ≤ 0.5 Bi

Beff,i ≤ 0.2 LB

for both stiffness and strength

Paulay and Priestley

Beff = Bw+ Beff,1 + Beff,2

in the absence of a transverse beam: Beff = 2BC

Beff,i ≤ 0.5 Bi

Beff,i ≤ 0.25 LB – Bw/2

Beff,i ≤ 0.25 (Bi + Bw) for beams framing into exterior columns

for effective tension reinforcement (negative bending)

NZS 3101 (in Paulay and Priestley)

Beff = Bw+ Beff,1 + Beff,2

Beff,i ≤ 4 hf

Beff,i ≤ 0.25 Bi

Beff,i ≤ 0.0625 LB – Bw/2

Beff = Bw+ Beff,1

Beff,i ≤ 3 hf

Beff,i ≤ 0.25 Bi

Beff,i ≤ 0.0417 LB

for stiffness analysis; 50% of the values specified for strength design under gravity loading (flange in compression)

1.3.4. Beam-column joints

There are two major problems in the beam-column joints of GLD frames. The first one is related to the insufficient bond between the longitudinal reinforcement and the concrete core, due to relatively small depth of the columns. This is of concern especially in the interior joints, were the slip of plain top bars may be significant. If significant slip occurs, the bar will be in tension through the joint core, and the compression reinforcement at one side of the column may be actually in tension. This was shown to result in reduction of the beam ductility and strength (Hakuto et al., 1999), in addition to a reduction of the frame stiffness.

The second problem is related to the assessment of the shear behaviour of the joints, which lack transverse reinforcement. Shear failure of beam-column joint cores without transverse reinforcement is due to extensive diagonal tension cracking that may eventually lead to diagonal compression failure in the joint core (Hakuto et al., 2000). Attempts have been made to predict the shear failure of the joints by limiting the nominal stress vjh as a function of concrete compressive strength (fc), tensile strength ( cf ), or by limiting the principal compression and tensile stresses in the joint. Two mechanisms of shear resistance are traditionally considered (Paulay and Priestley, 1992): the diagonal strut mechanism and the truss mechanism. The latter is ineffective in the case of joints lacking transverse reinforcement or

52

after bond deterioration between the beam longitudinal reinforcement and the joint core. Consequently, the shear resistance of GLD frames beam-column joints will rely on the diagonal strut mechanism only (see Figure 1.3-6).

Mb1Mb2

Vc

Figure 1.3-6. Concrete diagonal strut mechanism in interior bam-column joints.

In the case of exterior beam-column joints, the extent to which the diagonal compression strut mechanism can be mobilised depends greatly on the detailing of longitudinal beam reinforcement. Longitudinal beam reinforcement bent into the joint core (see Figure 1.3-7a) will permit the diagonal compression strut to bear effectively against the bend, since the bearing stresses at the bend of the bar act in the direction of the strut. When beam reinforcement is bent away from the joint (see Figure 1.3-7b), diagonal strut in the joint can not be stabilized, and joint failure occurs at an early stage (Priestley, 1997).

(a) (b)

Figure 1.3-7. Mechanism of shear transfer in exterior beam-column joints.

The horizontal shear force acting on the joint can be written as (Hakuto et al., 2000):

1 2

1 2

b bjh c

b b

M MV Vz z

= + − (1-7)

53

where: Mb1 and Mb2 are the beam moments at the face of the joints core; zb1 and zb2 are the lever arms between the tensile forces and the centroids of compressive forces, Vc is the shear force in the column above the joint.

The nominal shear stress at the mid-depth of the column can be written as:

/jh jh jv V A= (1-8)

where Aj = bj hc is the effective cross sectional area of the joint core; bj – effective width of the joint core; hc – column depth.

The nominal axial compressive stress in the column at the mid-depth of the joint core can be written as:

/a jf N A= (1-9)

where N – axial compressive load on the column above.

Both vjh and fa stresses are nominal values, as they are not uniform over the joint core. Though the stress distribution in the joint core is not elastic, a measure of the principal tensile (pt) and compressive (pc) stresses in the joint could be derived from the Mohr's circle (compression positive):

2

2

2 2a a

c jhf fp v⎛ ⎞= + +⎜ ⎟

⎝ ⎠ (1-10)

2

2

2 2a a

t jhf fp v⎛ ⎞= − +⎜ ⎟

⎝ ⎠ (1-11)

Eurocode 8 (2002) draft provides the following formula to ensure that "the diagonal compression induced in the joint by the diagonal strut mechanism does not exceed the compressive strength of concrete in the presence of transverse tensile strains" in the case of interior joints:

1 djh cv f νη

η≤ ⋅ − (1-12)

where: 0.6 (1 / 250)cfη = ⋅ − , fc in N/mm2; νd – normalised axial force in the column above.

In the case of exterior joints, 80% of the value provided by (1-12) is required.

FEMA 356 (2000) defines the joint shear strength as:

jh cv fλ γ≤ ⋅ (1-13)

in which λ = 0.75 for lightweight aggregate concrete and 1.0 for normal weight aggregate concrete, and γ is as defined in Table 1.3-3. In addition to classification of beam-columns joints as interior or exterior, FEMA 356 distinguishes another category of knee joints.

Table 1.3-3. Values of γ for Joint Strength Calculation, for fc in N/mm2, and ρ"<0.003, FEMA 356, (2000)

Interior joint with transverse beams

Interior joint without transverse beams

Exterior joint with transverse beams

Exterior joint without transverse beams

Knee joint

1.0 0.83 0.66 0.50 0.33

54

ρ" - volumetric ratio of horizontal confinement reinforcement in the joint; knee joint = self-descriptive (with transverse beams or not).

Priestley (1997) suggested a failure model for interior joints based on the principal compression stress:

2

2 (0.45...0.5)2 2a a

c jh cf fp v f⎛ ⎞= + + ≤ ⋅⎜ ⎟

⎝ ⎠ (1-14)

where: 0.5c cp f= ⋅ for one way joints, and 0.45c cp f= ⋅ for two-way joints to allow for the effects of the biaxial joint shear.

The joint strength decreases with imposed ductility demand, according to the model in Figure 1.3-8a. Equation (1-14) can be rearranged as:

1 ajh c

c

fv pp

≤ − (1-15)

where pc takes values between 0.45 (at 0.0 plastic drift) and 0.225 (at 0.04 plastic drift) for two-way joints.

For exterior beam-column joints, the joint shear strength is expressed as a function of the principal tensile stress pt:

2

2 (0.29...0.42)2 2a a

t jh cf fp v f⎛ ⎞= − + ≤ ⋅⎜ ⎟

⎝ ⎠ (1-16)

with limiting values of 0.29t cp f= − ⋅ for beam bars bent away from the joint, and 0.42t cp f= − ⋅ for beam bars bent into the joint. The above values reduce with increasing drift demand, as in Figure 1.3-8b. Equation (1-16) can be rearranged as:

1 ajh t

t

fv pp

≤ − (1-17)

0

0.1

0.2

0.3

0.4

0.5

0 0.01 0.02 0.03 0.04 0.05

plastic drift

p c/f c

one-way jointstwo-way joints

00.05

0.10.15

0.20.25

0.30.35

0.40.45

0 0.01 0.02 0.03 0.04 0.05

joint rotation [drift]

p t/ √

f c

beam bars bentinto jointbeam bars bentaway from joint

(a) (b)

Figure 1.3-8. Strength degradation models for exterior (a), and interior (b) joints, (Priestley, 1997)

55

0

0.05

0.1

0.15

0.2

0 2 4 6 8

displacement ductility factor, µv j

h/fc

Figure 1.3-9. Model for degradation of joint strength with imposed ductility demand, Hakuto et

al., 2000

Hakuto et al. (2000) experimentally studied the shear strength of interior beam-column joints without shear reinforcement and found that the nominal joint shear stress increases almost proportional to the compressive strength of concrete. The following equation was proposed:

0.17jh cv f≤ ⋅ (1-18)

with joint shear strength degradation with increasing ductility demand as in Figure 1.3-9, Kitayama et al. (1991) suggested a limit of 0.25fc for the joint shear stress in order to prevent shear failure of interior beam-column joints after beam yielding. Also, it was found that the presence of transverse beams and slab improve the shear strength of the joint approximately 1.3 times, a limit of 0.33fc being suggested in this case. Non-dimensional column axial stress smaller than 0.5 cf⋅ was found not to affect the joint shear strength.

In the case of exterior beam column joints with plain bars anchored by 180° hooks, Pampanin et al. (2001) found that this particular joint detail may lead to premature joint degradation. The principal tensile stress limitation 0.2t cp f= ⋅ was suggested as the upper limit for first diagonal cracking, followed by "significant and sudden strength reduction without any additional source for hardening behaviour".

Figure 1.3-10. Failure mode of exterior beam column joints with 180° hooked bars, Pampanin et

al., 2001.

56

1.3.5. Shear resistance of members

Shear failure of reinforced concrete members is of brittle type therefore it is avoided in the design of new structures. The shear capacity of beams and columns of GLD frames may be insufficient due to the following reasons:

• columns often have only nominal transverse reinforcement, with spacing similar to column dimensions

• beam shear reinforcement is usually in the form of inclined bars, that do not provide a resisting mechanism at load reversal

• stirrups may not be adequately anchored with 135° hooks, their efficiency being reduced in this case

Shear capacity of reinforced concrete members is known to depend on the degree of flexural ductility in the plastic hinge. A distinction can be made between a brittle shear failure of columns before the flexural strength of the column has been reached, and ductile shear failure, where a degree of ductility develops in plastic hinges before shear failure occurs (Priestley et al., 1994).

Evaluation of shear strength by the code equations may be excessively conservative in many cases. In the following shear strength evaluation by EC8/EC2, FEMA 356, and Priestley et al. approaches are compared.

Eurocode 8 (2002) draft refers to Eurocode 2 for shear design of reinforced concrete elements in moment-resisting frames, specifying that the inclination θ in the truss method is specified to be 45°. The contribution of concrete to the shear strength is given in Eurocode 2 (2001) draft as:

( )1/ 30.18 100 0.15c l c cp wV k f b dρ σ⎡ ⎤= ⋅ ⋅ ⋅ ⋅ − ⋅ ⋅ ⋅⎣ ⎦ (1-19)

with a minimum of 0.4 0.15c ct cp wV f b dσ⎡ ⎤= ⋅ − ⋅ ⋅ ⋅⎣ ⎦ , and where: = + ≤1 200 / 2k d ; ρ =⋅sl

lw

Ab d

;

/ 0.2cp c cN A fσ = > ⋅ ; fc - concrete compressive strength; d – effective depth of the member, Asl – area of the tensile reinforcement effectively anchored, bw – cross-section width, N – axial force in the cross section, Ac – area of concrete cross-section.

The shear resistance for members with vertical shear reinforcement is taken as the lesser off:

cotsws yw

AV z fs

θ= ⋅ ⋅ ⋅ and νθ θ⋅ ⋅ ⋅=

+max cot tanw c

Rdb z fV (1-20)

Contribution of the inclined shear reinforcement is taken as the lesser off:

(cot cot ) sinswsi yw

AV z fs

θ α α= ⋅ ⋅ ⋅ + ⋅ and θ ανθ

+= ⋅ ⋅ ⋅ ⋅+max 2

cot cot1 cotRd w cV b z f (1-21)

where: Asw – cross-sectional area of the shear reinforcement, s – spacing of stirrups, fyw – yield strength of shear reinforcement, z - inner lever arm corresponding to the maximum bending moment ( 0.9z d≅ ⋅ ), θ - angle between the concrete compression struts and the main tension chord;

0.6 (1 / 250)cfν = ⋅ − ; α - angle between shear reinforcement and the main tension chord.

However, according to Eurocode 2 (2001) draft, the contribution of concrete to the member shear strength is to be disregarded if it is insufficient in resisting the shear force alone, for both beams and columns. While this approach may be a reasonable simplification for design needs, it is definitely not appropriate for evaluation purposes.

57

FEMA 356 provides the following comments on the evaluation of shear strength of members:

• Within yielding regions of components with low ductility demands and outside yielding regions for all ductility demands, calculation of design shear strength using procedures for effective elastic response such as the provisions in Chapter 11 of ACI 318 shall be permitted.

• Where the longitudinal spacing of transverse reinforcement exceeds the component effective depth measured in the direction of shear, transverse reinforcement shall be assumed ineffective in resisting shear or torsion.

• For beams and columns in which perimeter hoops are either lap-spliced or have hooks that are not adequately anchored in the concrete core, transverse reinforcement shall be assumed not more than 50% effective in regions of moderate ductility demand and shall be assumed ineffective in regions of high ductility demand.

• In the case of beams (where low ductility demands are expected), the ACI 318 applies for the contribution of concrete (with fc in N/mm2):

0.166c c wV f b d= ⋅ ⋅ ⋅ (1-22)

In the case of columns, the following equation is provided by FEMA 356 (with fc in N/mm2) for the contribution of concrete:

0.5

1 (0.8 )/( ) 0.5

cc w

c c

f NV k b hM V d f A

λ⎛ ⎞⋅⎜ ⎟= ⋅ ⋅ + ⋅ ⋅ ⋅⎜ ⎟⋅ ⋅ ⋅⎝ ⎠

(1-23)

in which k = 1.0 in regions of low ductility demand, 0.7 in regions of high ductility demand, and varies linearly between these extremes in regions of moderate ductility demand; λ = 0.75 for lightweight aggregate concrete and 1.0 for normal weight aggregate concrete; N = axial compression force (= 0 for tension force); M/V is the largest ratio of moment to shear under design loadings for the column; M/(V d) shall not be taken greater than 3 or less than 2; d is the effective depth; and Ac is the gross cross-sectional area of the column. It shall be permitted to assume d = 0.8h, where h is the dimension of the column in the direction of shear.

The steel contribution is given as:

sw ys

A f dV

s⋅ ⋅

= (1-24)

(sin cos )y ys

A f dV

sα α

⋅ ⋅= ⋅ + (1-25)

for stirrups, and inclined reinforcement, respectively.

Priestley et al. (1994) proposed a predictive model of the shear strength of the column considering it to consist of three independent components: a concrete component Vc whose magnitude depends on the level of ductility, an axial load component Vp whose magnitude depends on the column aspect ratio, and a truss component Vs whose magnitude depends on the transverse reinforcement content.

Rd c p sV V V V= + + (1-26)

with the three components evaluated as:

0.8c c gV k f A= ⋅ ⋅ ⋅ (1-27)

58

k=0.29 for member displacement ductility 1θµ ≤ (biaxial), or curvature ductility 1ϕµ ≤ ; k=0.1 for member displacement ductility 3θµ ≥ (biaxial), or curvature ductility 5ϕµ ≥ ; k varies linearly between member displacement ductility 1 and 3 (see Figure 1.3-11).

2p

h cV Pa−= (1-28)

h – the overall section depth; c – the depth of the compression zone; a = L for a cantilever column, and a = L/2 for a column in reversed bending.

cot30sw yws

A f dV

s⋅ ⋅

= ⋅ ° (1-29)

Asw – the total transverse reinforcement area per layer; fyw – the steel yield strength; s – spacing of stirrups; d – the effective depth

Figure 1.3-11. Degradation of concrete shear strength with ductility, Priestley et al., (1994)

The model of Priestley et al. (1994) was developed for column sections. The following adjustments have been proposed for evaluation Vc in the case of beams (Priestley, 1997): k=0.2 for member displacement ductility 1θµ ≤ (biaxial), or curvature ductility 1ϕµ ≤ ; k=0.05 for member displacement ductility

3θµ ≥ (biaxial), or curvature ductility 5ϕµ ≥ ; k varies linearly between member displacement ductility 1 and 3.

1.3.6. Anchorage failure

Only nominal beam bottom reinforcement at the supports is characteristic for GLD frames. Additionally, its anchorage length is insufficient for development of the bar tensile strength. Consequently, bar pullout is expected to occur at positive bending moments under seismic excitation. This will result in both a decrease of the negative beam yield moment and an increase of the deformability of the structure. Accounting for the effects of the bar pullout may be accomplished by explicitly modelling it's behaviour through an additional rotational spring at the element end (Fillipou et al, 1992, Saatcioglu et al., 1992), or by simply considering the reduced bar tensile force in deducing the beam negative moment capacity. The latter approach has the advantage of simplicity, but it fails to account for increase in deformations due to bar pullout. However, it is recommended in FEMA 356, (2000), and was used for assessment of GLD frames by Kunnath et al. (1995). This latter approach was used also in the present study.

The following formula is suggested by FEMA 356 to compute the equivalent yield strength of bars with insufficient anchorage:

59

,,

,

b avy eq y

b req

lf f

l= ⋅ (1-30)

where fy is the bar yield strength, lb,av is the available anchorage length, lb,req is the anchorage length required for full bar anchorage.

1.3.7. Rotation capacity of elements

Most of the structures experience significant inelastic deformations when subjected to moderate to strong earthquake motions. The ability of the structure, or its elements, or of the component materials to offer resistance in the inelastic domain of response is generally termed ductility (Paulay and Priestley, 1992). It includes the ability to sustain large deformations and dissipate energy by hysteretic behaviour.

Displacement ductility is widely used as a measure of the structure or element capacity and demand, being easier to measure experimentally and having clear engineering meaning. However, due to the fact that ductility is expressed as a ratio of ultimate to yield displacements, it is often more convenient to express the demands directly in ultimate or plastic displacements. For elements of moment-resisting frames, chord rotations are commonly used as the generalised displacements.

Ultimate rotation θu is defined as the rotation when significant reduction of element strength occurs (see Figure 1.3-12a), and is often considered as failure of the element, though the element may be able to sustain additional deformations at lower strengths. There are several definitions of element failure. In this study, element failure for the bilinear and trilinear one-component models was determined at the attainment of ultimate strains in steel and concrete (see chapter 1.3.2). Direct modelling of element failure, as suggested by FEMA356 (see Figure 1.3-12b) is, however, not readily available in most of the non-linear analysis programs. Therefore, the usual procedure is to consider the attainment of failure when element demands exceed the computed capacities.

My

M

θθuθy

θpl

(a) (b)

Figure 1.3-12. Definition of ultimate and plastic rotations (a), and non-linear modelling of component behaviour in FEMA356 (b).

1.3.8. References

ACI 318, (1995) "Building Code Requirements for Structural Concrete", American Concrete Institute.

Dolsek, M. and Fajfar, P. (2002) "Mathematical modelling of an infilled RC frame structure based on the results of pseudo-dynamic tests", Earthquake Engineering and Structural Dynamics, 31: 1215-1230.

Eurocode 2, (2001) "Design of concrete structures", European Committee for Standardisation (CEN), final draft.

60

Eurocode 8, (2002) "Design provisions for earthquake resistance of structures", European Committee for Standardisation (CEN), Draft No.5.

FEMA 356, (2000) "Prestandard and commentary for the seismic rehabilitation of buildings", Federal Emergency Management Agency, Washington (DC).

Filippou, F.C., D'Ambrisi, A., Issa, A., (1992) "Nonlinear static and dynamic analysis of reinforced concrete subassemblages", Report No. UCB/EERC–92/08, Earthquake Engineering Research Center, University of California, Berkeley.

Hakuto, S., Park, R., and Tanaka, H., (1999) "Effect of Deterioration of Bond of Beam Bars Passing through Interior Beam-Column Joints on Flexural Strength and Ductility", ACI Structural Journal, V.96, No.5, 858-864.

Hakuto, S., Park, R., and Tanaka, H., (2000) "Seismic Load Tests on Interior and Exterior Beam-Column Joints with Substandard Reinforcing Details", ACI Structural Journal, V.97, No.1, 11-25.

Kitayama, K., Otani, S., Aoyama, H., (1991) "Development of Design Criteria for RC Interior Beam-Column Joints,” ACI SP-123, Design of Beam- Column Joints for Seismic Resistance, pp. 97-123.

Kunnath, K., Hoffman, G., Reinhorn, A.M, and Mander, B., (1995) "Gravity-Load-Designed Reinforced Concrete Buildings – Part I: Seismic Evaluation of Existing Construction", ACI Structural Journal, V.92, No.3, 343-354.

Li, K., (2002) "CANNY 99: 3-Dimensional nonlinear static/dynamic structural analysis computer program". Technical manual and User manual.

Pamapanin, S., Calvi, G.M., Moratti, M., (2001) "Seismic response of reinforced concrete beam-column joints designed for gravity load", submitted for publication to ASCE Journal of Structural Engineering.

Paulay, T. and Priestley, M.J.N., (1992) "Seismic Design of Reinforced Concrete and Masonry Buildings", John Wiley & Sons, Inc., New York.

Priestley, M.J.N., Verma, R., and Xiao, Y., (1994) "Seismic Shear Strength Demand of Reinforced Concrete Columns", Journal of Structural Engineering, Vol. 120, No.8, 2310-2329.

Priestley, M.J.N., (1997) "Displacement-Based Seismic Assessment of Reinforced Concrete Buildings", Journal of Earthquake Engineering, Vol. 1, No.1, 157-192

Saatcioglu, M., Alsiwat, J.M., and Ozcebe, G., (1992) "Hysteretic behaviour of reinforcement slip in R/C members", Journal of structural engineering, Vol.118, No.9

1.4. Iron elements

1.4.1. Introduction

This section was prepared in accordance with data-sheet no. 9-3 “Development of design rules for cast iron columns reinforced by FRP” provided by LY Lam, DEMONCEAU Jean-François, JASPART Jean-Pierre from University of Liege (B).

The use of iron as a building material probably dates back to about the year 1800. Cast iron columns were still being made for limited use in the early 1930's though they substantially stopped to be used in any quantity after the beginning of the century of when steel took over as the main structural material.

61

1.4.2. Material model

The mechanical properties of the iron material are highly dependent on the origin and production period of the iron. They are also linked to the type of iron (cast or wrought iron). Values of the ultimate stress σi,u in compression (σi,u,c) and in tension (σi,u,t) can be found in literature. Usually, iron material possesses a relatively ductile behavior in compression, but a brittle one in tension. The ratio of the two ultimate strengths (σi,u,t/σi,u,c) may range from 0.1 to 0.2 (J. Rondal,2003).

In order to apply modern design procedures to iron elements, it is necessary to determine a nominal value of 0.2% proof stress (σι,0.2), considered as the equivalent yield stress. Following the conclusions stated in (L. Ly, 2008) for the studied irons, their full behavior can be expressed by a non linear part in compression with four parameters Ei, σi,0.2,c n and σi,u,c (Ramberg-Osgood law), and a linear part in tension with two parameters Ei and σi,u,t. Figure 1.4-1 shows that the so-defined model permits to represent with a good accuracy the behavior of iron materials if compared to experimental results (Figure 1.4-1).

,0.2,

0.002n

i i cEσ σε

σ⎛ ⎞

= + ⎜ ⎟⎜ ⎟⎝ ⎠

(1.4-1)

-800

-700

-600

-500

-400

-300

-200

-100

0

100

200

300

-11% -10% -9% -8% -7% -6% -5% -4% -3% -2% -1% 0% 1%

Espsilon (%)

Sigm

a (N

/mm

²)

BT2BT5BT3BT4Model

Compression

Tension

Model

Figure 1.4-1 Comparison of the defined analytical model for the iron behavior law to experimental

test results (L. Ly, 2008)

Given the mechanical characteristics of iron material described above, it is preferable to assume that this material can only work in the elastic domain only, especially when subjected to tensile stresses.

1.4.3. Element model

Safety approaches

The design for structural elements followed the safety approach called "allowable stresses" based on global safety factor on material strength (values ranging from 4 to 5 in the available literature). Nowadays, another safety approach is proposed and usually used: the semi-probabilistic approach based on partial safety factors (safety factors applied on the material strengths and on the actions). For cast iron, values ranging from 2.22 to 2.78 are proposed for the material safety factors and a value of about 1.4 for the action safety factors (Eurocode 0). Equivalence between the two methods can be observed; in deed, if the material safety factors from the semi-probabilistic approach are multiplied by the action safety factors, that gives values ranging from 3.1 to 3.89 which are close to global safety factors used in the allowable stresses approach. It means that there is no difference between both and we can use both for the design of structural elements.

62

In this report, the analytical procedure for the computation of iron column resistance is based on the semi-probabilistic approach used in many available documents such as Eurocodes (EC3, 1993).

In theory, formula available for the design of structural elements (with criteria on cross-section resistance and member stability) may be applied for elements.

Cross-sectional resistance

Elastic verification should be used because of the brittle behavior of the in tension.

During their life, iron elements may be affected by corrosion. The main consequence of the latter is to make the iron section thinner; procedures to estimate this effect are available in (M.R. Guerrieri, 2006). Then, a re-evaluation of slenderness of the constitutive elements of the section (b/t) should be done to ensure that there is not any risk of local buckling inside the element.

Member stability

Member in axial compression

The analytical procedure proposed for iron columns hereafter is extracted from the (J. Rondal, 2003).

Geometric imperfection

Member imperfection

Like other metallic column, cast iron column has also geometrical imperfections. An initial crookedness (δ0) (taken as the maximum deviation of the column axis from a straight line connecting the ends) can be assumed as:

0,max 750Lδ = (1.4-2)

the mean crookedness is approximately:

0,mean 1500Lδ = (1.4-3)

Cross-section imperfection

Hollow cast-iron section is frequently dissymmetrical (Figure 1.4-2). The irregular wall thickness is the result of lifting forces, dislocations and/or deflections of the casting core used for producing the hole of the member during casting in the horizontal position. The eccentricity of the hole leads to an eccentricity (g) of the load with reference to the centroid of the cross-section. The eccentricity g can be obtained by the following formula:

2

2 2i

e i

dg jd d

=− (1.4-4)

with de, the external diameter, di, the internal diameter and j calculated as follows:

min2e id dj t−= − (1.4-5)

tmin is the minimum thickness.

63

Figure 1.4-2: Cross-section imperfection in hollow cast iron column.

The size of the eccentricity (g) is difficult to evaluate, but can be estimated by (J. Rondal, 2003)

1 130 40e

gd

= ÷ (1.4-6)

Compression failure

According to the generalized column curve formulation, the ultimate stress (σult,c) of an iron column can be estimated as follows:

, 0.2,ult c c cσ χ σ= (1.4-7)

Where σ0.2,c is the 0.2 proof stress for compression and χc, the slenderness reduction factor given by:

2 2

1c

c c c

χϕ ϕ λ

=+ −

(1.4-8)

with:

21 (1 )2c c c gA

Iυϕ η λ= + + + (1.4-9)

where:

0

0.2,cc

E

σλ

σ= (1.4-10)

0

20

2( / )EE

L rπσ = (1.4-11)

The imperfection parameter (ηc) may be approximated by the value such as 0.85 (J. Rondal, 2003).

" gAIυ " is the parameter accounting for the cross-section imperfection. "A" and "I" are the cross-section

area and the moment of inertia respectively. " gAIυ " may be approximated to the value of 32/225.

Tension failure

Cast iron is relatively weak in tension and it is therefore possible that column reaches its collapse by fracture in tension on one of its sides during overall bending.

The verification on tension failure can be checked by the formula as follows:

64

, 0.2,ult t c cfσ χ σ= (1.4-12)

The strength ratio (f) is assumed equal to the ratio (0.1÷0.2) between the ultimate tensile and compressive strengths. The slenderness reduction factor (χt) is given by the formula as follows:

2 2

1t

t t cfχ

ϕ ϕ λ=

+ + (1.4-13)

where:

21 '( 1 )2t c cf gA

Iυϕ η λ= − + + + (1.4-14)

The imperfection parameter (ηc) may be approximated by the value such as 0.85 (J. Rondal, 2003).

" 'gAI

υ " is the parameter accounting for the cross-section imperfection. It may be approximated to the

value of 32/225.

Member in bending (Lateral Torsional Buckling – LTB)

No information relative to the resistance of iron elements affected by lateral torsional buckling seems available. As an alternative to the study of the actual LTB effects, it is possible to refer, for I-shape elements, to a traditional approach which consists in considering LTB as the transverse flexural buckling of the compression flange.

Member in bending and axial compression

An iron member in bending and axial compression is affected, at the same time, by buckling and by LTB (both mentioned above); so, it is possible to refer to elastic interaction criteria to combine these two phenomena.

1.4.4. Reference:

“Old industrial buildings: the cast-iron column problem”, J. Rondal and K.J.R. Rasmussen, International Colloquium on Stability and Ductility of Steel Structures, Akademiai Hiado, Budapest, 2002.

“Investigation, appraisal, and reuse, of a cast-iron structural frame”, M.N. Bussell and M.J. Robinson, Ordinary Meeting, The structural Engineer, 3 February 1998.

“Assessment of the load bearing capacity of old cast iron columns”, R. Käpplein, Fourth International Colloquium on Structural Stability, Istanbul, Sept. 16-20, 1991.

“Untersuchung und Beurteilung alter Gubkonstruktionen”, R. Käpplein, Stahlbau 6, June 1997.

“Appraisal of existing ferrous metal structures”, J. Blanchard, M. Bussell, A. Marsden and D. Lewis, Stahlbau 6, June 1997.

“On the strength of cast iron columns”, J. Rondal and K.J.R Rasmussen, Research report N°R829.

“Appraisal of existing iron and steel structures”, M. Bussell, SCI publication 138, ISBN 1 85942 009 5, 1997.

“Historical structural steelwork handbook”, W. Bates, The British constructional steelwork association, ISBN 0 85073 015 5, 4th impression April 1991.

“Etude du flambement plan de poutres colonnes en acier à section non symétrique”, S. Cescotto, S. Gilson, A. Plumier and J. Rondal, Publication du CRIF, Mai 1983.

65

“Columns – a treatise on the strength and design of compression members”, E. H. Salmon, Oxford Technical Publications, 1921.

“Résistance des matériaux – Tome 1”, A. Morin, Librairie de L. Hachette et Cie, 1862.

“Résistance des matériaux – Tome 2”, A. Morin, Librairie de L. Hachette et Cie, 1862.

“Design of cast iron columns with explicit calculation of tension fracture capacity”, J. Rondal and K.J.R. Rasmussen, Eurosteel 2005, 4th European conference on steel and composite structures, Maastricht, The Netherlands.

“Structural appraisal of iron-framed textile mills”, T. Swailes and J. Marsh, ICE design and practice guide, 1998.

“Assessment of the seismic performance of the iron roofing structure of the Umberto I Gallery in Naples”, R. Landolfo, O. Mammana and F. Portioli.

“Influence of atmospheric corrosion on the XIX century iron structures: assessment of damage for Umberto I Gallery in Naples”, M.R. Guerrieri, G. Di Lorenzo and R. Landolfo, 2006

“Historical development of iron and steel in buildings”, ESDEP lecture 1B.4.3.

"Studi Preliminari finalizzati alla redazione di Istruzioni per Interventi di Consolidamento Statico di Structture Metalliche mediante l'utilizzo di Compositi Fibrorinforzatti", Commissione incaricata di formulare pareri in material di normativa tecnica relative alle costruzoni, CNR-DT 202/2005.

"Eurocode 3: Design of Steel Structures, Part 1.1: General Rules and Rules for Building, prEN-1993", European Committee for Standardisation, Brussels.

"Tests on iron elements", Demonceau Jean-François, Jaspart Jean-Pierre, Prohitech WP7, 2006.

1.5. Timber elements

1.5.1. Introduction

This section was prepared in accordance with data-sheet no. 9-4 “Models for materials and elements: timber” provided by Gülay Altay and Ali Bozer from Bogazici University of Istambul (TR).

Timber is an efficient building material with regards to its mechanical properties. When compared to its weight the strength is high. The strength weight ratio is even higher than steel. However, considering its beneficial properties, timber is still not widely used in construction. One of the main reasons for this is that timber is a highly complex material. This section made an overview of models for material, depending on moisture content, creep, duration of load, models for timber element, system – frames model, connection and analysis types.

1.5.2. Models for material

Mechanically wood exhibits an orthotropic behavior that is it has independent mechanical properties in the directions of three perpendicular axes. The longitudinal axis is parallel to the grain; the radial axis is normal to the growth rings and perpendicular to the grain in the radial direction; and the tangential axis is perpendicular to the grain but tangent to the growth rings. Twelve constants are needed to describe the elastic behavior of wood: three modulus of elasticity E, three shear modulus G and six Poisson’s ratio µ. However, engineering models consider mechanical properties in two directions, such as stiffness or strength, between the respective values parallel and transverse to the grain direction. Strength and stiffness parameters of the timber can be determined with a series of tests for various types of action effects. These action effects include:

1. Tension parallel to the grain

66

2. Tension perpendicular to the grain

3. Compression parallel to the grain

4. Tension parallel to the grain

5. Bending

6. Shear

Moreover, the mechanical properties of timber are strongly dependent on moisture content. A structural timber member is, depending on its exposure to moisture, associated with one of three service classes. Dry condition is in Class 1 and wet condition is in Class 3. In EN 1995-1-1:2004 service classes are defined as:

• Service class 1 is characterized by a moisture content in the materials corresponding to a temperature of 20°C and the relative humidity of the surrounding air only exceeding 65 % for a few weeks per year.

• Service class 2 is characterized by a moisture content in the materials corresponding to a temperature of 20°C and the relative humidity of the surrounding air only exceeding 85 % for a few weeks per year.

• Service class 3 is characterized by climatic conditions leading to higher moisture contents than in service class 2.

Furthermore, wood exhibits a pronounced time dependent deformation behavior in terms of creep. Creep of wood is also influenced by the state of moisture whether it is constant or varying.

The duration of load is also an important factor in determining the load that the member can safely carry. The constant stress that a wood member can sustain is approximately an exponential function of time to failure. For a member that continuously carries a load for a long period, the load required to produce failure is much less than that determined from strength properties. For example, a wood member under the continuous action of bending stress for 10 years may carry only %60 of the load required to produce failure in the same specimen loaded in standard bending strength test of only a few minutes duration. Conversely, if the duration of load is very short, the load carrying capacity may be higher than determined from strength properties.

In EN 1995-1-1:2004 the load-duration classes are determined by the duration of a constant load acting to the structure. If the duration of characteristic load exceeds 10 years, it is defined as permanent load. A typical example of a permanent load is self-weight. If the duration of characteristic load is 6 months to 10 years, it is defined as long-term load. A typical example of a long-term load is storage. When the duration of characteristic load is 1 week to 6 months, it is defined as medium-term load as in the case of imposed floor loads or snow loads. If the duration of characteristic load is less than 1 week, it is defined as short-term load as in the case of snow and wind loads.

For determining fundamental mechanical properties straight-grained wood is used, however because of natural growth characteristics of trees, wood products may have knots and localized slope of grain. Natural defects such as pitch pockets may occur as a result of biological and climatic elements influencing the living tree. These wood characteristics must be taken into account in assessing actual properties of timber members.

To account for the problems associated with wood, characteristic value of a strength property is modified in Eurocode 5 Part 1.1. The design value Xd (EN 1995-1-1:2004) of a strength property can be calculated as:

67

M

kd

XkX

γmod= (1.5-1)

where:

Xk - is the characteristic value of a strength property;

Mγ - is the partial factor for a material property which is given in EN 1995-1-1:2004 – Table 2.3. This partial factor is associated with the problems of inhomogeneous material and imperfections such as grain deviation and knots.

kmod - is a modification factor taking into account the effect of the duration of load and moisture content and is given in EN 1995-1-1:2004 – Table 3.1

The design member stiffness property Ed or Gd can be calculated as: (EN 1995-1-1:2004)

Mdef

meand k

EE

γ)1( += (1.5-2)

Mdef

meand k

GG

γ)1( += (1.5-3)

where:

Ed - is the mean value of modulus of elasticity

Gd - is the mean value of shear modulus

kdef - is a factor for the evaluation of creep deformation taking into account the relevant service class

Table 1.5-1 Recommended partial factors Mγ for material properties and resistances (EN 1995-1-1:2004)

Table 1.5-2 Values of kmod (EN 1995-1-1:2004)

68

Table 1.5-3 Values of kdef for timber and wood-based materials (EN 1995-1-1:2004)

69

1.5.3. Models for Elements

Structural analysis of timber frames is done in the same way as in frames built with other materials. Once a model is constructed the timber components and joints are designed to resist the calculated loads. However, within the components of a timber structure such as walls, frames, floors, roof systems and connection elements actual load distribution is not well defined due to complexity of the material. Thus, a designer is bound to some simplifications and assumptions.

Assessment of timber elements can be realized by using linear material models, however if the internal forces are able to be redistributed by sufficiently ductile connection members than elastic-plastic methods can be used to determine internal forces in the members. Beams and columns can be modeled with line elements with 6 degrees of freedom per node. Linear shell elements can be used to represent roof and floor diaphragms.

1.5.4. Connections

In most cases connection members do not provide necessary rigidity or strength to provide a rigid connection, so internal forces of the members can be calculated by taking in to account the deformation of the connections. The influence of these deformations in the connections can be considered by either macro-modeling or micro-modeling of the joint. In-macro modeling global joint behavior is examined with no emphasis to underlying principles such as properties of the individual elements like fasteners and wood. In this case parameters for rotational spring elements can be extracted from the cyclic experiments of single connections. In this respect bilinear or multilinear elasto-plastic springs are sufficient to model the hysteretic behavior of the joint. Translational slip at joints can be modeled with gap elements. In micro-modeling a more mechanics based approach is followed and all the respective elements in the connection are modeled with regards to their linear and nonlinear material properties. A micro-model should include three basic energy dissipation modes in the connection. These modes are the friction between beams and columns; bending of dowel type fasteners; and dowel bearing behavior of wood. When there is no means of macro-modeling or micro-modeling, connections can be assumed rotationally stiff if their deformation has no significant effect upon the distribution of member forces and

70

moments. Otherwise, connection can be generally assumed to be rotationally pinned. Translational slip at the joints may be disregarded for the strength verification unless it significantly affects the distribution of internal forces and moments.

Connection between deck and beams can be modeled as pinned, however this assumption neglects the additional friction damping from deformation in the deck to beam connections. The general approach to model this mechanism is to add %2 equivalent viscous damping ratio. To account for the energy dissipation characteristics of other structural and non-structural elements, the additional viscous damping should be in the range of %1-5 of critical damping (A. Heiduschke, 2006). For linear models, mass and stiffness proportional damping coefficients for the Rayleigh damping can be determined using the first and second mode frequencies. However, as the stiffness of the system continuously changes in non-linear analysis stiffness proportional damping may lead to unrealistically large damping forces since the initial stiffness is used to calculate the stiffness-proportional damping terms.

Experimental studies carried out at Bogazici University, described in data-sheet, have shown a trilinear moment-rotation graph for the used connection

y = 32.273x

y = 2.9006x + 0.7662

y = 13.361x + 0.2967

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Rotation (rad)

Mom

ent (

kNm

)

Figure 1.5-1 Moment-Rotation Graph

1.5.5. System model

In a frame analysis, the system lines should coincide with the member center-line. If not, influence of the eccentricity in terms of moments should be taken into account. To model the eccentricities, fictitious beam elements or spring elements can be used. The stiffness of the fictitious beam elements or spring elements should correspond to that of the actual connection.

Member forces and moments are also influenced by the support eccentricities and the stiffness of the supporting structure. Thus, it is important to include these factors into model.

1.5.6. Analysis type

Most timber buildings have natural periods of vibration in the range of 0.06-0.8 sec. This is within the range of typical earthquakes, on the other hand wind spectrum contains much higher periods. Therefore, a static model can be sufficient for wind loads but a dynamic analysis should be utilized for earthquake cases (G. Foliente, 1998).

1.5.7. Reference:

BS EN 1995-1-1:2004 “Eurocode 5: Design of Timber Structures – Part 1.1: General-Common rules and rules for buildings”, BSI 389 Chiswick High road, London (2004)

71

Heiduschke A, Kasal B. and Haller P. “Analysis of wood-composite laminated frames under dynamic loads-analytical models and model validation. Part 1: connection model”, Prog. Struct. Engng. Mater. 8, 103-110 (2006)

Heiduschke A, Kasal B. and Haller P. “Analysis of wood-composite laminated frames under dynamic loads-analytical models and model validation. Part 2: frame model”, Prog. Struct. Engng. Mater. 8, 111-119 (2006)

Foliente G. C. “Design of timber structures subjected to extreme loads”, Prog. Struct. Engng. Mater. 3, 236-244 (1998)

Foliente G. C. “Design of timber structures subjected to extreme loads”, Prog. Struct. Engng. Mater. 3, 236-244 (1998)

Ayoub A. “Seismic analysis of wood building structures”, Engineering Structures. 29, 213-223 (2007)

Gupta R. “System behavior of wood truss assemblies”, Prog. Struct. Engng. Mater. 7, 183-193 (2005)

72

2. Models and performance criteria for structural elements of different material

2.1. Riveted connection

2.1.1. Introduction

This section was prepared in accordance with data-sheet no. 9-5 “Riveted connection” provided by M. D’Aniello, L. Fiorino, F. Portioli, R. Landolfo from University of Naples “Federico II”, Department of Construction and Mathematical Methods in Architecture, Naples, Italy (NA-ARC).

Connections between metal parts are required in most applications being a critical part of every design. The joining of parts by cylindrical fasteners passing through holes has been use extensively a long history. For the connection of iron members rivets were traditionally used. Such connections are treated in the next paragraph of this report from the hand calculation using component method to numerical and experimental validation of method.

2.1.2. Hand made calculation models

The analysis of riveted shear connections is similar to the one of bolted connections. Hence, the response of riveted connections can be schematized by means of simplified hand made calculations based on the so called “component method”. The application of the component method requires three basic steps: listing of the joint components, evaluation of force–deflection diagram of each individual component, in terms of initial stiffness, strength and deformation capacity, and assembly of the components with a view to evaluate the whole joint behaviour. The stiffness, the resistance are assembled separately for simplicity. As shown in Figure 2.1-1, the rivet connections may be dismantled into the following components: plate in tension, rivets in shear, and rivets in bearing.

Figure 2.1-1 Definition of each component of connection.

The components are in this case in series. Hence the total deformation stiffness ktot of the connection may be predicted according to Eq. (2.1-1):

, , , ,

1 1 1 1 1 1

tot t p b p s b c t ck k k k k k= + + + + (2.1-1)

Where kt,p and kt,c are the stiffness of the plate and of the cover plate, respectively. In addition, ks is rivets’ shear stiffness and kb,p and kb,c are the rivet-to-plate and rivet-to-cover plate bearing stiffness,

73

respectively. Each contribution reported in Eq. (2.1-1) is given by European design practice (see ENV 1993-1-1, 1998). In particular, the deformation stiffness of the component plate in tension may be predicted as:

Kt=EA/L (2.1-2)

where A is the plate area and L its length. The initial stiffness of the component bolt in shear may be approximated as

2

16

16 b ubs

M

n d fkEd

= (2.1-3)

where d is the nominal diameter of the rivets; dM16 is the nominal diameter of an M16 rivet; fub is the ultimate tensile strength of the rivets; nb is the number of rivets. The initial stiffness of the component rivet/plate in bearing is calculated in the format:

, ,, ,

, ,

24b j k b b t ub j k s

b j k

F n k k dfkE E

βδ

= = (2.1-4)

where Fb,j,k is the force in the component j,k in bearing, E is the modulus of elasticity, b,j,k is the deformation of the component j,k in bearing, kb =kb1 is but kb ≤ kb2; kb1 = 0:25eb/d + 0.5 but kb1 ≤ 1.25; and kb2 ≤ 0:25pb/d + 0.375 but kb2 ≤ 1.25; and kt = 1.5tj/dM16 but kt ≤ 2.5.

The prediction of strength of the riveted connection can be calculated in accordance to Eurocode 3 part 1-8, as the minimum strength of the ones related to each possible failure mechanism of shear connection.

In riveted shear connections, the following basic types of failure modes usually occur:

• rivet shear failure (Figure 2.1-2);

• yield in bearing of both steel plates (a) or yield in bearing of thinner plates only (b) (Figure 2.1-3);

• tearing of the steel plate in net section;

• shearing of the steel plate;

• plastic bending of steel plate in asymmetric lap joints.

The shear resistance of rivets can be calculated according to the following expression:

0, 6

0,

2

r vn n f AurF

V RdM

γ= (2.1-5)

Where nr and nv are the number of rivets and the number of shear planes, respectively.

Figure 2.1-2 Rivet shear failure.

74

Initial rivet position Final rivet position

Figure 2.1-3. Bearing failure.

The calculation of the strength due to bearing failure (Figure 2.1-3) is related on the triaxial nature of the actual stress in the material (Hertz Contact Stress), resulting in high allowable values for the contact stress. The calculation formula links the bearing capacity to the projected rivet shank area normal to the load direction by means some coefficients related to the mechanical and geometrical properties of the shear connection. In detail, referring to EC3 part 1-8, the bearing resistance should be calculated as follows:

, 1b Rd b uF k f dtα= (2.1-6)

where fu is the material ultimate stress of the thinner plate, d is the diameter of the rivet and t is the thickness of the thinner connected plate. Moreover, b is a parameter depending on the geometry of the shear connection and it should be distinguished for the two main direction of the splice. In fact, it is the smallest of αd ; fub/fu or 1.0 in the direction of load transfer. While, perpendicularly to the direction of

load transfer it is 1

3d

o

ed

α = for end rivets. For inner rivets it should be calculated as 1 13 4d

o

pd

α = − .

Finally, the factor k1 should be calculated as follows:

12min 2.8 1.7;2.5o

ked

=⎧ ⎫

−⎨ ⎬⎩ ⎭

for edge rivets;

12min 1.4 1.7;2.5o

kpd

=⎧ ⎫

−⎨ ⎬⎩ ⎭

for inner rivets;

In addition, for clarity sake, the symbols previously cited are shown in Figure 2.1-4 and listed as follows:

• do is the hole diameter for a rivet;

• e1 is the end distance from the centre of a fastener hole to the adjacent end of any part, measured in the direction of load transfer,

• e2 is the edge distance from the centre of a fastener hole to the adjacent edge of any part, measured at right angles to the direction of load transfer

• p1 is the spacing between centres of fasteners in a line in the direction of load transfer;

• p2 is the spacing measured perpendicular to the load transfer direction between adjacent lines of fasteners.

75

Figure 2.1-4. Symbols for end and edge distances and spacing of fasteners.

It is should be noting that in case of a group of fasteners the connection resistance may be taken as the sum of the design bearing resistances Fb,Rd of the individual fasteners provided that the design shear resistance Fv,Rd of each individual fastener is greater than or equal to the design bearing resistance Fb,Rd . Otherwise the design resistance of a group of fasteners should be taken as the number of fasteners multiplied by the smallest design resistance of any of the individual fasteners.

Another typical mechanism of shear connection is the block tearing that consists of failure in shear at the row of rivets along the shear face of the hole group accompanied by tensile rupture along the line of rivets holes on the tension face of the rivet group (Figure 2.1-5). The tearing resistance can be calculated as:

, ,

2

ueff l Rd

net

M

f AV

γ= (2.1-7)

The Eq. (7) does not include stress concentration factors, and local yielding may occur around the holes. Stress concentration factors are required if fatigue is a concern. Moreover, the total net area is used if multiple fasteners are used in the connection.

Figure 2.1-5. Block tearing failure.

Another similar failure mechanism is the shear tear out at edge of plate (Figure 2.1-6). Generally speaking, the shearing plate failure occurs in case of rivet excessively close to the free plate edge. Therefore it is normally controlled by specifying minimum edge distances. However, since an edge distance greater than 1.5d is commonly used, this mechanism can be considered avoided in shear connections with ordinary geometry.

76

Figure 2.1-6. Shear tear out at edge of plate failure.

The plastic bending of connected plates can be considered as possible essentially for asymmetric lap shear connections. In fact, the offset in a lap connection creates a moment equal to approximately M=Ft/2. This bending moment can cause complex deformations and stresses in the connection that affect the overall connection strength. In most cases this offset moment is neglected and a suitable factor of safety is used. However, the secondary bending effect is most pronounced in a splice with only a single fastener in the direction of the applied load (Fisher & Yoshida 1969, Shoukry & Haisch 1970). In such a joint the fastener is not only subjected to single shear, but a secondary tensile component may be present as well. Furthermore, the plate material in the direct vicinity of the splice is subjected to high bending stresses due to the load eccentricity. Hence, the bending tended to decrease slightly the ultimate strength of short connections. The shear strength of longer asymmetric lap joints seems to be less affected by the effects of bending. However, in case of significant bending moment the net section capacity should be calculated as the one corresponding to the plastic capacity due to the contemporary presence of an axial force equal to the shear force and the relevant bending moment.

Figure 2.1-7. Yielding due to secondary bending.

Finally, since in case of long splices the actual stress distribution is far from being uniform, significant stress concentration at splices ends are easily recognized. For these reason, the final strength of connection is lesser than the commonly calculated value. Hence, according to EC3 part 1-8, if the distance Lj between the centres of the end fasteners in a joint, measured in the direction of force transfer (see Figure 2.1-8), is larger than 15 d, the design shear resistance Fv,Rd of all the fasteners should be reduced by multiplying it by a reduction factor Lf, given by:

15

1200Lf

fL d

dβ

−= − but 0.75≤βLf≤1 (2.1-8)

77

Figure 2.1-8. The distance between the centres of the end fasteners in a long joint.

2.1.3. Numerical vs. Hand made calculation

Figure 2.1-9 shows the modelling response (D’Aniello et al. 2007, 2008a) in term of slip resistance vs. relative in-plane displacement of the unsymmetrical specimen U16-10-1 (referring to relevant Section of WP7 report) in case of finite element calculation (developed in ABAQUS ver. 6.5) and hand-made calculation. From numerical analyses, it seems that the influence of bending is most pronounced. In fact the plate material near the splice is subjected to high bending stresses due to the eccentricity of the load. However, this has little influence on the load capacity, since the material will strain-harden and cause yielding on the gross area of the connected plate, as it can be observed comparing the joint capacity to the hand calculation. In fact, the simplified approach explained in the previous Section allows properly predicting the initial stiffness and the shear capacity of the connection.

0

10

20

30

40

50

60

70

80

0 5 10 15Displacement [mm]

Shea

r For

ce [k

N]

Numerical Model

hand calculated stiffness

hand calculated strength

Figure 2.1-9. Numerical vs. hand made calculation.

2.1.4. Experimental vs. predicted shear strength

The key mechanical parameter of shear connections is its shear resistance, which is the maximum load (Fu) provided by connection. In Table 2.1-1 Experimental vs. predicted shear strength and relevant failure mechanisms.Table 2.1-1, the average measured and the calculated shear capacities of the tested specimens (referring to relevant Section of WP7 report) are compared with their actual failure modes (D’Aniello et al. 2008b). In particular, the theoretical shear capacities of the examined connections have been calculated assuming the average experimental values of the strength of materials (see the relevant part in the WP7) and considering the partial safety factor γm2 equal to 1. As it can be observed, the experimental values referred to the rivet failure are usually larger than the predicted ones. This seems to be mainly due to the large variability of yield strength of the material constituting the rivets. This aspect is evident in case of specimen U22-12-2, where the experimental evidence showed a tearing failure having a value close to the calculated one, but, on the contrary, the predicted strength suggested a rivet shear collapse.

Table 2.1-1 Experimental vs. predicted shear strength and relevant failure mechanisms.

Specimen Fu

(kN) Experimental failure mechanism

Fv,Rd

(kN) Ft,Rd

(kN) Fb,Rb

(kN) Theoretical failure mechanism

U16-10-1 78.33 Rivet shear failure 57.27 280.8 151.84 Rivet shear failure

U16-10-2 152.66 Plate plastic bending 114.5 280.8 151.84 Rivet shear failure

78

and rivet shear failure

U22-12-2 278.66 Plate plastic bending and tearing of the steel plate in net section

216.56 299.52 363.78 Rivet shear failure

S16-10-1 137.00 Rivet shear failure and yield in bearing of inner plate

114.5 280.8 151.84 Rivet shear failure

S22-12-4 298.50 Tearing of the steel plate in net section 866.26 299.52 727.56 Tearing of the steel plate

in net section

2.1.5. References

ABAQUS, Inc. User’s Manual. ABAQUS Standard V6.5. ABAQUS, Inc.; 2005.

D’Aniello M., Fiorino L., Landolfo R., (2007). “Riveted connections in historical metal structures: analysis and testing”. XXI C.T.A. Conference, Catania (Italy) 1-3 October.

D’Aniello M., Fiorino L., Landolfo R., (2008a). “Structural performance of rivetted connections in historical metal structures. SAHC’08 VI international conference on structural analysis of historical constructions evaluating safety and significance Bath, UK 2, 3, 4 JULY 2008.

D’Aniello M., Fiorino L., Portioli F., Landolfo R., (2008b). “Analysis and modelling of rivetted connections in historical metal structures”. 5th European Conference on Steel and Composite Structures, Graz (Austria) 3-5 September. (To be published)

Fisher J. W. & Yoshida N. (1969) “Large Bolted and Riveted Shingle Splices,” Journal of the Structural Division, ASCE, Vol. 96, ST9, September.

prNV-1993-1-8. Eurocode 3: design of steel structures. Part 1.8—design of joints.

Shoukry Z. & Haisch W. T. (1970). “Bolted Connections with Varied Hole Diameters,”Journal of the Structural Division, ASCE, Vol. 96, ST6, June.

2.2. Architrave connection

2.2.1. Introduction

This section was prepared in accordance with data-sheet no. 9-6 “Architrave connection” provide by L. Pavlovčič and D. Beg from University of Ljubljana, Faculty of Civil and Geodetic Engineering (SL).

In this paragraph it is summarized the experimental program with the main findings and the numerical simulation, based on different failure criteria, carried out in order to calibrate critical values for each criteria. A nonlinear spring model is proposed for represent the connection behaviour in case o large scale ancient temple with columns and architraves.

2.2.2. Basic concept

In ancient temples the architrave beams placed on the columns are connected to each other with metallic clamps of double T-shape (Figure 2.1-8), which provide the structural integrity in the case of seismic events. To perform the capacity design of such connections, the clamps should be designed strong enough to keep architrave in the position in the case of horizontal actions and at the same time with deformations the clamps should absorb the seismic energy. However, in the case of tremendous seismic impacts the clamp should fail before the stone suffered any damage. Since the material properties and

79

hence capacity of metallic clamps is easy to define, the major problem is to assess the fracture resistance of stone for the selected shape of mortise and clamp dimensions. To design the clamp as the weakest part of the connection, the web of the clamp can be modelled in a dog-bone shape (see Figure 2.2-2a) with lower tensile resistance as is the fracture resistance of the stone.

Figure 2.2-1 Titanium clamps used in the architrave blocks at the north-east corner of Parthenon The obtained fracture toughness and tensile strength of the stone from one-dimensional problems were then applied as fracture criteria for the connection capacity assessment with the use of linear FEA (Pavlovcic, 2008). These results were compared with the results of numerous tests, carried out on 1:3 scaled models with stone blocks from Unito limestone and stainless steel clamps of various shapes – (Pavlovcic, 2008a). All these results serve for a general design of architrave connection on different levels:

As an example how to perform similar tests on scaled models with the use of the actual stone and clamps of architraves. Together with these tests some selected material tests should be also performed, when fracture properties of this stone are not already thoroughly investigated and known. The test results on the Unito limestone might offer the reference values only roughly due to varying characteristics of stone in general.

The test results in the scope of PROHITECH project already offer some important information and guidelines for the selection and design of clamps.

The numerical analysis shows the possibility of relatively simple linear FE simulations based on linear fracture mechanics. For this purpose different fracture criteria are discussed and clear examples are given, how to apply a selected one parameter criterion in such a complex three-dimensional problem.

An idea is also given, how to model architrave connection and clamps, in numerical simulation of the large scale model of an ancient temple or its part.

80

(a) (b)

Figure 2.2-2 Metallic T-clamps with dog-bone web, used in the present restoration program of the Acropolis in Athens (a) and former corroded ones (b)

Detail information on performance of different material tests and architrave connection tests are given in Pavlovcic, 2006 and Pavlovcic, 2008a, respectively. This section summarizes some crucial results from architrave connection tests and numerical simulation and gives the idea for macro modelling. Nevertheless, for the proper design of architrave connection in an extensive and demanding restoration program, at least some of the tests should be performed with the material in observation, in order to obtain the reference case for the calibration of numerical model and the reference values to derive calibration factors for different criteria used for the capacity assessment.

2.2.3. Architrave connection tests with main results

Test description

The scaled model of architrave connection consists of a single stone block from Unito limestone (Figure 2.2-3), with stainless steel clamp embedded in cut mortise and fixed with cement mortar in-fill. Two shapes of clamps were investigated:

• T-shaped clamps as originally used in ancient temples and in the restoration practice (see Figure 2.2-2)

• Π-shaped clamps with a threaded hook (see Figure 2.2-3), possibly used where the originally cut mortise is damaged and minimal acceptable intervention would be to drill a hole in the flange bottom only.

The studied parameters of T-clamp and mortise geometry were clamp/slot length L, flange width b/B, slot depth d and clamp embedment elevation d1. In the case of Π-clamps the studied parameters were clamp/slot length L, the depth of the clamp hook D, clamp diameter φ, slot depth d and the type of fixation in the hole (with cement mortar or glued in). The width of the stone block was also varied in order to check the possible effect of side boundary conditions. The specimen was subjected either to monotonic tensile loading (static or with fast loading) or cyclic loading in tension or tension-compression with different loading protocol. The shear loading was not investigated, since it is presumed that such loading is restricted by dowels between architrave and columns. The whole testing program comprised 46 tests and is summarized in Data-sheet no. 9-6, with clamp and mortise geometry and denotations depicted in Figure 2.2-3 and Figure 2.2-4

All details of test set-up, loading protocols, accompanying material tests and test results are presented in the test report Pavlovcic, 2008.

81

dL

- 15

15L

B

10

AA

A - A:

W = 250

120 120

A =

300

250

For T-clamps:

dL

- 55 L

+2

CC

C - C:

250

(248- )/2 (248- )/2

300

250

D +

5

+ 2φ

15

BB/2 B/2

7.5

7.5

+ 2

φ

φ

φ φ

For Π-clamps:

Figure 2.2-3 Stone block dimensions with mortise position and geometry

L - T

T =

15

L

T = 10

B

8

4

b = B-10

AA

A - A:

T-clamps: -clamps:

B - B:

φ

D

φ

dd

D

or:

dDd

d = 0

+ 2

D +

5

3.5

3.5

33

φ

1

1

L - 1

5T

= 1

5L

+ 2

BB

φ

Lc

φ

+ 2

φ

B/2 B/2

φB

(13

- )/2φ

ff

w

wt =

wt =

f

w= T

Figure 2.2-4 Mortise and clamp dimensions and denotations of varying parameters

Test results with main findings

The most important test results may be summarized in the following:

82

- Failure modes were similar for the T-clamp and Π-clamp tests showing the tendency to occur in conical shape (clear picture only in the case of wider stone blocks or for the shortest clamps due to too narrow stone blocks). By T-clamps the critical crack starting edge was observed as the bottom edge of mortise flange with the crack propagation towards the stone surface under 45-60º regarding loading direction. By Π-clamps the critical crack starting edge was along the clamp hook on the pressure contact side.

Both tests on wider stone blocks did not yield any larger connection capacity, proving that the selected size of the stone blocks was not decisive for failure. The stone resistance is obviously influenced by the crack initiation rather than the crack propagation.

- The length of both clamps is very important parameter, since the capacity is increased by 80% when T-clamp mortise web (Lw = L – Tf) is increased from 35 to 75 mm and in the case of Π-clamps even by 53% for smaller length increase (Lw = 55 to 75 mm). It is very important to note, that by T-clamps the main capacity increase occurred from Lw = 35 to 55 mm (from 21.5 to 35.5 kN), showing that in the architrave connections it is necessary to consider a certain minimal distance of the clamp flange to the stone surface in order to avoid a sever boundary effect. Observed from the tests on scaled specimens such minimal length would be Lw = 55 mm (165 mm on full-scale model). The numerical simulation show the limit length as Lw = 35-40 mm.

- Slot depth is also very important for T-clamps, increasing the capacity by 60% for d = 50 mm instead of 20 mm. On the other hand, the variation of mortise depth for Π-clamps has almost no impact on the stone capacity.

- Embedment elevation of T-clamp (d1 = 20 mm above the mortise bottom) does not contribute to any enhancement, but to the stone resistance reduction by 35%. This means that the favourable smaller direct pressure of T-clamp to the bottom inner mortise edge is not as relevant as unfavourable bending effect around that edge, which is increased with higher clamp elevation d1.

- T-clamp flange width variation yielded more controversial results: with the increase of the mortise flange width from B = 50 mm to 60 mm the load capacity decreases by 29% and for B = 70 mm the resistance is then by 7% increased compared to B = 60 mm. The reason for this not monotonic curve might be in the contradiction of two opposite effects: the beneficial effect of the larger pressure contacts in the case of wider flanges and the unfavourable effect of the wider flange mortise, which increases the mortise and clamp flange flexibility as well as the lever arm from the vertical mortise corner to the force resultant, which results in higher moment in the vertical mortise corner.

- The depth of Π-clamp hook is influential parameter, increasing the stone resistance by 22% with the hook depth D = 100 mm instead of 70 mm.

− Π-clamp diameter surprisingly appeared not to have any important influence on the connection capacity: the tests with φ = 10 mm accidentally possess even by 5% lower resistance than the tests with φ = 8 mm, which probably appeared due to material property scatter. However, certain minimal clamp diameter is necessary in order to avoid the pull-out of the clamp, which occurred in the case of the first φ = 8 mm test.

- The clamp fixation by gluing the Π-clamp with 8 mm diameter does not significantly increase the stone capacity (by 10%), but protects the clamp pull-out as long as the adhesion between the glue and the stone is sufficient (after failure the gluing mass remained connected to the clamp and not to the stone).

- The loading speed by T-clamp monotonic tests appeared not to be important: fast loading of v = 5 mm/s with failure within 0.2 s, simulating the effect of the seismic stroke more properly, yield by 8% lower capacities than monotonic static tests with v = 0.008 mm/s. In the case of Π-clamps the capacity is even strongly increased (by 59%), since the fast loading probably prevents the intention of clamp pull-

83

out and consequently contribute to smaller pressure concentration than in the case of slower load introduction, where the higher pressure contacts may be established around the upper part of clamp-to-stone contact (the region of the clamp crook).

- Also in the case of cyclic loading compared to the identical monotonic tests, the ultimate resistance is not severely influenced: the capacity of T-clamp connection decreased by 15% at the most, while in the case of Π-clamps the capacity is even increased by 21%. It is interesting that the cyclic loading in tension-compression, expected in the seismic event (due to plastic clamp elongation), decreased the capacity only by 9% compared to the monotonic tests. Nevertheless, to be on the safe side in the case of a real seismic event, the clamp should be designed with the consideration of presumable 20% reduction of capacity obtained in static monotonic loading condition.

- Load versus surface stone displacement curves of all tests show non-linear response, with different scale of non-linearity. Displacement are taken as the average measurement of both “bridge” transducers. However, the ultimate stone displacements (K displacements at the failure load Fu) appeared to be fairly comparable among different tests – see Table 2.2-1. The mean values vary only from 0.020 to 0.040 mm and for monotonic T-clamp tests even from 0.025 to 0.036 mm. The mean value of all T-clamp or all Π-clamp tests are almost the same (0.031 or 0.029, respectively), which is a surprise due to different action of T- or Π-clamps within the stone. As a common average failure measure, the surface stone displacement UK,u = 0.030 mm can be assessed. However, such a measure can be useful when performing tests or for non-linear FEA, but hardly applicable as a consistent criterion in a linear FE analysis, due to different scale of non-linearity.

Table 2.2-1 Ultimate surface stone displacements UK-av,u (average of both K1 and K2 measurements across the flange mortise)

T-clamp specimens UK-av,u [mm]

UK-av,u

- mean

[mm]

Π-clamp specimens UK-av,u [mm]

UK-av,u

- mean

[mm]

T55-50-30/D20-s

0.033 (s1)

0.027 (s2)

0.033 (s3)

0.031 Π55-50-30/D70-φ10-s 0.028 (s1)

0.0334 (s2) 0.031

T75-50-30/D20-s 0.025 (s1)

0.042 (s2) 0.033 Π75-50-30/D70-φ10-s

0.023 (s1)

0.041 (s2) 0.032

T35-50-30/D20-s 0.046 (s1)

0.024 (s2) 0.035 Π55-12-10/D70-φ10-s

0.038 (s2)

0.043 (s3) 0.040

T55-60-30/D20-s 0.028 (s1)

0.0251 (s2) 0.027 Π55-50-30/D100-φ10-s

0.033 (s1)

0.020 (s3) 0.027

T55-70-30/D20-s 0.023 (s1)

0.037 (s2) 0.030 Π55-50-30/D70-φ8-s

0.0205 (s1)

0.046 (s2) 0.033

T55-50-20/D20-s 0.033 (s1)

0.031 (s2) 0.032 Π55-50-30/D70-φ8-fixed-s

0.012 (s1)

0.033 (s2) 0.023

T55-50-50/D20-s 0.026 (s1)

0.024 (s2) 0.025 Π55-50-30/D70-φ10-sf

0.017 (sf1)

0.022 (sf2) 0.020

84

T55-50-50/D20-d1-20-s

0.032 (s1)

0.030 (s3) 0.031 Π55-50-30/D70-φ10-c

0.025 (c1)

0.029 (c2) 0.027

T55-50-30/D20-w500-s

0.032 (s1)

0.040 (s2) 0.036

T55-50-30/D20-sf 0.043 (sf1)

0.021 (sf2) 0.032

T55-50-30/D20-cI-

0.0192 (1)

0.0282 (2) 0.024

T55-50-30/D20-cII-

0.023 (1)

0.032 (2) 0.027

T55-50-30/D20-c-comp

0.031 (1)

0.0073 (2) 0.031 (0.019)

NOTES: 1 – The second peak with Fu after restoring the capacity 2 – The peak load of the last cycle is taken 3 – The peak load of 4th cycle, although Fu in the third cycle (result seems not to be consistent) 4 – Taken at the first peak load, although at the Fu it would be UK-av,u = 0.076 5 – At the ultimate load due to clamp pull-out and not due to stone failure

The numbers in italic designate more remarkable difference between two identical tests.

T-clamp monotonic tests: UK-av,u = 0.025–0.036 (mean) or 0.021–0.046 (all); UK-av,u,mean = 0.031

Π-clamp monotonic tests: UK-av,u = 0.020–0.040 (mean) or 0.012–0.046 (all); UK-av,u,mean = 0.029

2.2.4. Numerical simulation with applied fracture criteria

Numerical models

The linear fracture analysis was carried out by finite element (FEA) code ABAQUS – Hibbit, 2007. Figure 2.2-5 depicts FE model consisting of stone block, T- or Π-clamp and cement mortar in-fill. The specimens were modelled with three-dimensional elements (C3D4 and C3D8R). All mortar-to-stone contact surfaces were connected as tied. Clamp-to-mortar contacts were established as “hard” contact in the normal direction: in the case of Π-clamps between all surface-to-surface contacts and in the case of T-clamps only between both pressure contact surfaces, while the other T-clamp-to-mortar surfaces were not connected.

(a) (b)

Figure 2.2-5 Numerical model for T-clamp (a) and Π-clamp connection (b)

For the calculation of stress intensity factor (SIF), different edges were tested the initiation of crack and the critical crack appeared to be as depicted in Figure 2.2-6. The crack extension direction in T-clamp

85

models was selected under 45º angle regarding mortise bottom and no remarkable sensitivity of SIF on the limited variation of this angle was observed. On the other hand, for Π-clamp model it turned out that the proper crack extension direction may vary between 0º and 45º angle regarding the direction of loading (Z axis), and trial is needed to obtain the most critical angle. The calculation of SIF in this case appeared to be very sensitive on the angle selection. All the details of FE modelling are presented in Pavlovcic, 2006. The most of the static monotonic tests were simulated.

a) T-clamp model – crack 1 b) Π-clamp model

Figure 2.2-6 Definition of critical crack for T- and Π-clamp model with crack extansion direction

Different fracture criteria

Fracture toughness and tensile strength

The entire testing program of the Unito limestone (reported in Pavlovcic, 2006) was mainly aimed at determining a simple one parameter criterion for the stone fracture resistance, which may be regarded as a material property. The critical stress intensity factor, i.e. fracture toughness KIc was successfully determined with two procedures. As a more engineering and simplified criterion for fracture resistance assessment may be tensile strength ft of the stone (see Pavlovcic, 2008b).

Nevertheless, it should be kept in mind that both measures KIc and ft are only one-dimensional criteria, derived from “one-dimensional problem”, while in architrave connection the problem is much more complex, since the stress field is three dimensional and the crack propagation is space orientated. Therefore, the one-dimensional criteria may be applicable only as a simplified assumption.

Different criteria for FEA capacity determination

The stress intensity factor KI was calculated in each node of predefined crack in linear dependency of the load increment. Figure 2.2-7a shows the SIF-F results for the basic T-clamp model (T55-50-30/D20) in each node of crack 1. There is a question of SIF definition, which may be taken as the reference one for the capacity determination. The following was considered for the subsequent analysis (see Figure 2.2-7b):

• The average SIF in nodes on the width of the flange clamp - x = [0, 15] mm, where x = 0 is taken at the web-to-flange mortise corner.

• The maximum value of SIF (i.e. at x = 0) – this measure is due to the local character not very stable and it is expected that the initiation of the crack in one point does not already lead to stone failure.

• The minimum value taken at x = 15 mm (the end of the clamp flange).

86

SIF in nodes - T55-50-30/D20

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 5 10 15 20 25 30 35 40 45

F [kN]

KI

[MP*

m0.

5 ]x = 0x = 2.7 mmx = 5.4 mmx = 8.3 mmx = 11.4 mmx = 15.0 mmx = 17.2 mmx = 20.0 mm

x = 0 - at web-to-flange mortise corner

Selected SIF - T55-50-30/D20

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 5 10 15 20 25 30 35 40 45

F [kN]

KI

[MP*

m0.

5 ]

SIF - max (x = 0)SIF - average onx = [0, 15] mmSIF - min (x = 15 mm)

FuFEA = 9.0 15.1 36.8

FuTEST = 35.5 kN

KIc,x=15 = 0.96

KIc,aver. = 2.35

KIc,max = 3.95

KIc =

a) SIF in nodes of the crack 1 b) Three different SIF and capacity determination

Figure 2.2-7 Determination of FEA capacity FuFEA from KIc

for three different definitions of calculated SIF and the calibration of KIc from test capacity Fu

TEST for different SIF definitions

From the selected SIF curve the model capacity may be obtained based on the reference critical SIF KIc = 1.0 MPa·m1/2, as can be seen in Figure 2.2-7b. The results show fairly good agreement when taking the minimum SIF (at x = 15 mm) as the relevant criterion, while the calculated capacity is remarkably underestimated when considering the average or maximum value of SIF. However, the average value of SIF seems to be the most natural and also reliable, since the local effects are mitigated. The reasons for the capacity underestimation in this case might be in the following:

• In the case of architrave connections there is more complex three dimensional stress field and not clearly defined critical crack with its propagation direction than in the case of simple fracture bending tests with the clear maximal principle stress field perpendicular to the crack extension direction.

• Due to its space and complex nature, the local initiation of the crack probably does not instantaneously lead to the stone fracture. Moreover, the space stress field may act favourably.

• The reference critical SIF KIc = 1.0 MPa·m1/2 was chosen as the possible lower limiting value. To recall the large scatter in the KIc results for different specimen geometry and size effects, the actual critical SIF in the situation of architrave connection may also be much higher.

• In FEA the mortise is modelled with geometrically sharp edges, while at the fabrication of the mortise in the real stone the edges can never be perfectly sharp, which leads to a larger notch effect in the case of FEA and consequently to smaller capacities.

For the sake of the relative comparison between FEA and test capacities, the reference critical SIF KIc can be calibrated from the measured average capacity of both T55-50-30/D20-s models - Fu

TEST = 35.5 kN (see Figure 2.2-7b):

• for the average SIF on the range x = [0, 15] mm KIc,aver. = 2.35 MPa·m1/2,

• for the maximal SIF KIc,max = 3.95 MPa·m1/2,

• for the minimal SIF (at x = 15 mm) KIc,x=15 = 0.96 MPa·m1/2.

All three calibrated KIc values (average, max and min) are presented in Figure 2.2-8, where critical SIF is plotted along crack 1 of the basic model T55-50-30/D20 at the force equal to the test capacity Fu

TEST = 35.5 kN. Along with this curve for crack opening mode I, in the same figure also the critical SIF for crack opening modes II and III (seeFigure 2.2-9) are plotted along crack 1 together with the equivalent critical SIF Keq.c, which can be calculated as follows:

87

222. IIIcIIcIcceq KKKK ++= . (2.2-1)

The SIF for mode II can be neglected, while fracture mode III slightly contribute to the stone fracture and the equivalent critical SIF Keq.c is then by 8% increased regarding KIc. However, since the shape of KIc and Keq,c curves remains the same and the calibrated average critical SIF (KIc,aver. = 2.35 MPa·m1/2) is anyway remarkably higher than the reference value KIc = 1.0 MPa·m1/2, for the T-clamp models the calibrated KIc instead of Keq.c may be simply considered for the fracture criterion.

In the case of Π-clamp models, the selected crack propagation direction is important for the calculated values of KI, KII and KIII. In the case of higher crack propagation direction angles, the second crack opening mode becomes even more critical than the first one (KII > KI). Therefore, for the Π-clamp models Keq.c is more properly considered as the fracture criterion.

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

0 2 4 6 8 10 12 14 16 18 20

Crack 1 - x [mm]

Kc

[MP*

m0.

5 ]

K.IK.IIK.IIIK.eq

KIc,aver. = 2.35

Keq.c,aver. = 2.53

KIIc,aver. = 0.01

KIIIc,aver. = -0.91

KIc,min = 0.96

KIc,max = 3.95

Keq.c,max = 4.21

Keq.c,min = 1.11

Keq.c = (KIc2 + KIIc

2 + KIIIc2)0.5

Figure 2.2-8 Different critical SIF along crack 1 (for fracture mode I, II, III and equivalent value)

calculated at the average test capacity FuTEST = 35.5 kN (model T55-50-30/D20)

Figure 2.2-9 Three different crack opening modes (Gross, 2006)

As the alternative criterion to the SIF criteria, the tensile principle stresses along the relevant crack may be compared with the tensile strength of the stone. Figure 2.2-10 shows the maximal principle stresses along crack 1 of the basic model T55-50-30/D20 at force equal to the test capacity Fu

TEST = 35.5 kN. The average critical tensile principal stresses σIc, aver., determined at the test capacity Fu

TEST, turned out to be 3 times larger that tensile strength from bending tests ft,B and 6.4 times larger that tensile strength from direct tensile tests ft,T. Especially when compared to ft,B, the calibration factors for σIc, aver.(3.0), σIc,

max (4.0) and σIc, min (1.6) are fairly of the similar scale as in the case of KIc or Keq.c. Figure 2.2-11 shows the contour plot of maximal principle stresses in the vertical cross-section of the basic model T55-50-30/D20 at the load step Fu

TEST = 35.5 kN. The maximum value σIc,MAX = 86.0 MPa resulted a few

88

milimeters under the mortise bottom. Therefore, the calibration factor for the critical principle stress at that region would be even larger: σIc,MAX / ft,B = 86.0/13.3 = 6.5.

0

10

20

30

40

50

60

0 5 10 15 20Crack 1 - x [mm]

σIc

[N

/mm

2 ]σIc,aver. = 39.5 = 3.0*ft,B = 6.4*ft,T

ft,B = 13.3

ft,T = 6.2

σIc,max = 53.5 = 4.0*ft,B = 8.6*ft,T

σIc,min = 21.7 = 1.6*ft,B = 3.5*ft,T

Figure 2.2-10 Maximal principle stress σI along the crack 1 calculated at the test capacity Fu

TEST = 35.5 kN (model T55-50-30/D20)

Figure 2.2-11 Maximal principle stresses σI at the critical cross-section of T55-50-30/D20 model at the load step Fu

TEST = 35.5 kN

Calibrated critical values for different criteria In the previous sub-chapter the calibrated critical values for different criteria were derived for the basic model T55-50-30/D20. Table 2.2-2 and Table 2.2-3 present the calibrated critical values for all considered criteria, derived for each calculated T- and Π-clamp model from the measured test capacity in the same way as presented in Figure 2.2-7. For Π-clamp models the relevant criteria are based only on Keq and σIc. In both tables also the average and the minimum values are extracted.

Table 2.2-2: Calibrated critical values derived for different T-clamp models (values in MPa·m0.5 and MPa)

T-clamp models KIc,aver. (on [0, 15]) KIc,max

KIc,min (at x = 15)

Keq.c,aver. (on [0, 15])

σIc,aver. (on [0, 15]) Bt

averIc

f ,

,σ

Tt

averIc

f ,

,σ

89

T55-50-30/D20 2.35 3.96 0.97 2.53 39.5 3.0 6.4

T35-50-30/D20 1.65 2.69 0.72 1.76 28.3 2.1 4.6

T75-50-30/D20 2.45 4.20 0.96 2.86 40.7 3.1 6.6

T55-50-20/D20 2.23 3.68 0.93 3.79 36.9 2.8 5.9

T55-50-50/D20 2.42 4.22 0.91 2.63 40.5 3.0 6.5

T55-60-30/D20 1.73 (1.56*) 3.02 0.81

(0.51*) 3.09 (2.79*)

29.4 (27.1*) 2.2 (2.0*) 4.7 (4.4*)

T55-70-30/D20 2.04 (1.56*) 3.27 0.99

(0.45*) 3.30 (2.55*)

34.7 (28.1*) 2.6 (2.1*) 5.6 (4.5*)

Average 2.12 (2.03*) 3.58 0.90

(0.78*) 2.85 (2.70*)

35.7 (34.4*) 2.7 (2.6*) 5.8 (5.6*)

Min. (without T35) 1.73 (1.56*) 3.02 0.81

(0.45*) 2.53 29.4 (27.1*) 2.2 (2.0*) 4.7 (4.4*)

*Values calculated on the actual clamp width: [0, 20], [0, 25] or at x = 20, 25 mm.

With italic the minimal (conservative) values are denoted.

Table 2.2-3: Calibrated critical values derived for different Π-clamp models (values in MPa·m0.5 and MPa)

Π-clamp models Keq.c,aver. (on [0, 70]) Keq.c,max

Keq.c,min (at x = 70)

σIc,aver. (on [0, 70])

Bt

averIc

f ,

,σ

Tt

averIc

f ,

,σ

Π55-50-30/D70-φ10 0.56 2.08 0.12 14.1 1.1 2.3

Π55-50-30/D100-φ10 0.66 (0.48*) 2.49 0.05 (0.05*) 16.9 (12.2*) 1.3 (0.9*) 2.7 (2.0*)

Π55-50-30/D70-φ8 0.92 2.54 0.17 26.3 2.0 4.2

Π75-50-30/D70-φ10 0.84 3.12 0.16 20.1 1.5 3.2

Average 0.75 (0.70*) 2.56 0.13 19.3 (18.2*) 1.5 (1.4*) 3.1 (2.9*)

Min. (without *) 0.56 2.08 0.05 14.1 1.1 2.3

*Values calculated on the actual clamp hook depth: [0, 100] or at x = 100 mm.

With italic the minimal (conservative) values are denoted.

FEA capacities compared to test results

Figure 2.2-12 to Figure 2.2-14 show the capacity comparison for T-clamp models in dependency of varying parameters: web length L, slot depth d and mortise flange width B. Some additional FE calculations were carried out, in order to dense and to extend the range of parameters L and d. Figure 2.2-15 shows the capacity comparison for different Π-clamp models, with the crack propagation direction simply selected as 0º for the sake of clear comparison. However, with this angle the lowest capacity is not guaranteed. For T-clamp models five already presented criteria were considered (KIc,aver., KIc,max, KIc,min(x=15), Keq.c,aver., σIc,aver., averaging on the same flange width - [0, 15] mm) and for Π-clamp models the following three criteria: Keq.c,aver., Keq.c-max or σIc-aver. (averaging on the same hook depth for all specimens - [0, 70] mm). The considered calibration factors were derived from the basic T- and Π-clamp model.

90

The detailed analysis of the results is presented in Pavlovcic, 2006. As the bottom line it can be concluded that the linear FE simulation of T-clamp models was fairly successful when the results are relatively compared to each other. The connection capacities in the absolute sense can also be satisfactory assessed, when the calibrated critical values for each criterion are adopted. The calibration could be justified due to the complexity of three-dimensional connection problem in comparison with one-dimensional problems used for the determination of single material properties KIc and ft. The selection of the fracture criterion is not particularly decisive. Hence, the alternative criterion based on the average tensile principle stresses σIc,aver. and stone tensile strength ft could also be promising, avoiding more advanced concepts of linear fracture mechanics (SIF calculation with the critical crack definition). On the other hand, the simulation of Π-clamp models is more demanding and a special attention should be paid to the selection of the most critical crack propagation direction.

Fu (L) - TL-50-30/D20-s

16.4

35.5

16.4

35.5

16.3

35.3

42.4

16.7

35.5

16.7

21.5

38.835.5

8.3

30.7

37.239.1

7.5

31.6

36.6

38.0

12.2

28.6

38.7

8.8

30.9

37.2

38.935.6

9.8

30.0

37.7

39.7

0

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120 140 160

Web length - L [mm]

Fu [

kN]

Tests - averageFEA - K.Ic-aver.=2.35FEA - K.Ic-max=3.96FEA - K.Ic(x=15)=0.96FEA - K.eq.c-av.=2.53FEA - S.Ic-av.=39.5

-39.6%

+9.2%-13.5%

+4.8%+4.7%

-13.0%

-15.6%

+6.0%

-18.9%

+9.5%-10.8%

+3.2%

Figure 2.2-12 Capacity comparison between test and FEA (considering different criteria - KIc,aver.,

KIc,max, KIc,min(x=15), Keq.c,aver., σIc,aver.) in dependency of the web length L of T-clamp models

Fu (d) - T55-50-d/D20-s

48.1

42.0

26.3

35.5

43.3

40.8

39.4

32.7

35.5

27.7

41.4

39.438.833.4

35.5

28.3

44.240.4

31.1

35.3

27.3

42.6

40.439.0

32.6

35.5

28.0

42.9

41.039.2

32.6

35.6

28.2

0

10

20

30

40

50

60

15 20 25 30 35 40 45 50 55 60 65 70 75

Slot depth - d [mm]

Fu [

kN]

Tests - averageFEA - K.Ic-aver.=2.35FEA - K.Ic-max=3.96FEA - K.Ic(x=15)=0.96FEA - K.eq.c-av.=2.53FEA - S.Ic-av.=39.5

-25.9%

+18.3

-21.8%

+15.1%+13.8%

-21.1%-20.7%

+15.3%

-22.7%

+25.2%

-20.3% +11.0%

Figure 2.2-13 Capacity comparison between test and FEA (considering different criteria - KIc,aver.,

KIc,max, KIc,min(x=15), Keq.c,aver., σIc,aver.) in dependency of the slot depth d of T-clamp models

91

Fu (B) - T55-B-30/D20-s

25.3

35.5

27.9

34.335.5

32.133.2

35.5

33.8

29.9

35.3

26.9

34.435.5

32.234.035.5

31.7

0

5

10

15

20

25

30

35

40

45 50 55 60 65 70 75

Mortiese flange width - B [mm]

Fu [

kN]

Tests - averageFEA - K.Ic-aver.=2.35FEA - K.Ic-max=3.96FEA - K.Ic(x=15)=0.96FEA - K.eq.c-av.=2.53FEA - S.Ic-av.=39.5

-28.7%

-21.5%

-3.2%

-9.5%-9.4%

-3.1%

-4.2%

-10.7%

-15.3%

-4.9%

-6.4%

-23.1%

NOTE: For all cases the average values calculated on X = [0, 15] mm of the crack

Figure 2.2-14 Capacity comparison between test and FEA (considering different criteria - KIc,aver.,

KIc,max, KIc,min(x=15), Keq.c,aver., σIc,aver.) in dependency of the mortise flange width B of T-clamp models

Fu from different Keq.c and σIc

31.733.4

38.7

48.5

31.7

20.1

32.534.0 32.432.3

27.331.7 31.7

17.9

32.334.0

0.0

10.0

20.0

30.0

40.0

50.0

60.0

Pi55-50-30/D70-fi10 Pi75-50-30/D70-fi10 Pi55-50-30/D70-fi8 Pi55-50-30/D100-fi10

Different specimens: Π -models

Fu [k

N]

Test - averageKeq.c-aver.[0,70] = 0.56Keq.c-max = 2.08S.Ic-aver. = 14.1 (1.1*f.tB)

NOTE: Averaging on [0, 70] mm

Figure 2.2-15 Capacity determination for different Π-clamp models regarding different criteria (Keq.c,aver., Keq.c-max, σIc,aver.) with appropriate calibration factors derived from the basic model Pi55-

50-30/D70-fi10

92

Different Π specimens - FEA: Keq (F = 42 kN)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Crack 1 - x [mm]

Keq

[M

Pa*m

0.5 ]

Pi55-50-30/D70-fi10Pi75-50-30/D70-fi10Pi55-50-30/D70-fi8Pi55-50-30/D100-fi10SIF-average (fi10)SIF-average (L75)SIF-average (fi8)SIF-aver.-100 mm (D100)SIF-aver.-70 mm (D100)

Crack propagation direction: 0º angle

Keq = (KI2 + KII

2 + KIII2)0.5

Different Π specimens - FEA: σI (F = 42 kN)

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Crack 1 - x [mm]

σ I [

MPa

]

Pi55-50-30/D70-fi10Pi75-50-30/D70-fi10Pi55-50-30/D70-fi8Pi55-50-30/D100-fi10SIF-average (fi10)SIF-average (L75)SIF-average (fi8)SIF-aver.-100 mm (D100)SIF-aver.-70 mm (D100)

Crack propagation direction: 0º angle

a) b)

Figure 2.2-16 : Comparison of Keq (a) and σI (b) along the crack 1 for four different Π-clamp models at an arbitrary load step F = 42 kN

Capacity scaling factor for full-scale architrave connection

All presented test and FEA results were obtained on 1:3 scaled models. The question is, which scaling factor to adopt for the capacity assessment of full-scale architrave connection. Due to the manufacturing reasons of scaled specimens, only the main mortise and clamp dimensions were scaled by factor 3, while the voids between clamp and stone as well as the clamp flange thickness remained proportionally larger. Figure 2.2-17 shows the original mortise and clamp geometry, from which the basic model T55-50-30/D20 was scaled and adjusted.

165

2519

0

140

515

120

AA

70

A - A:

60

5

1010

10

10

20

5 5

Figure 2.2-17 Original full-scale geometry of the architrave connection used for the basic scaled

model T55-50-30/D20

Since the determined FEA capacities are proportional to the 1/Ki (higher the calculated SIF at the selected load increment, the lower capacity), the necessary capacity scaling factor nC might be derived on the basis of the SIF units as follows:

2/32

2

2

,

,

)()/(/

LL

L

LLscalefull

scaled

scaledu

scalefulluC n

nn

mnmnNmmN

KK

FF

n ==⋅⋅⋅

⋅===−

− , (2.2-2)

93

where nL is length scale factor. For the adopted length scale factor nL = 3, the capacity scaling factor should hence amount nc = 33/2 = 5.2. To verify this analytical assumption, two additional basic T-clamp models were calculated: the one consistently enlarged by nL = 10 (the same model, where all dimensions were considered in cm instead of mm, the loading in kN instead of N and hence the elastic modulus was defined as E = 7450 kN/cm2 instead of 74500 N/mm2) and the other as the original full-scale model (nL = 3), with the mortise and clamp dimensions depicted in Figure 2.2-17. In Table 2.2-4 the capacities of all three models are compared (determined on the basis of scaled average critical SIF - KIc,aver. = 2.35 MPa·m1/2) and the obtained capacity scaling factors are compared with the derived ones.

Table 2.2-4: Capacity scaling factors for 10-times and 3-times enlarged T55-50-30/D20 model

Models nL FU-FEA [kN] nc = FU / FU,basic nc = nL3/2

T55-50-30/D20 (basic) 1 35.5 1 1

10-times larger 10 1124.5 31.68 31.62

Original model (Figure 2.2-17) 3 212.7 6.0 5.2

The results show, that the obtained capacity scaling factor for consistently 10 times enlarged model is practically the same as the derived one, while for the original model obtained nc = 6.0 is by 15% larger than derived one, showing that proportionally narrower voids and hence proportionally more stiff stone contribute to the additional capacity. Nevertheless, when investigating the architrave connections on the scaled models, as a general recommendation the derived capacity scaling factor nc = nL

3/2 could be adopted.

2.2.5. Large scale modelling of ancient temples with columns and architraves

Within the PROHITECH project the shaking table tests were performed on large scale models consisting of a few columns and architraves. For the subsequent numerical simulation as well as for any other numerical modelling of the architrave connections on the macro scale, the idea for the simplification is to replace the inserted clamp with a non-linear spring acting in the longitudinal clamp direction. The stiffness of spring may be determined according to tensile behaviour of the clamp neck obtained from the accompanying tensile tests. Presumed may be either non-linear force-strain relation or simplified bilinear response as illustrated inFigure 2.2-18. The failure of such spring may be determined considering the more critical of two criteria: either as the rupture of clamp neck at Fu,clamp or by fracture of the stone at the ultimate load Fu,fract for the simulated architrave connection - Figure 2.2-18. As discussed in the previous chapters, the main problem is the determination of the stone fracture resistance. As a rough estimation of fracture capacity of architrave connection made of e.g. Dionysos-Pentelicon marble, the relation between fracture material tests on Unito limestone and this marble could be taken into account at the extrapolation of the test results obtained on architrave connection from Unito limestone to the case of marble connections.

94

Force F Fu,fract.

Strain εε

u,clamp

Fu,clamp

Load-strain responseof clamp neck

Bilinear approximation of clamp response

Failure of spring

Figure 2.2-18 Non-linear spring response with failure criteria Fu,fract. < Fu,clamp

2.2.6. References:

I. Vayas, S. Kourkoulis, S.-A. Papanicolopulos, A. Marinelli: “DIII-P.I-p1.4.1: Marble, Final Report for WP7 of European project PROHITECH”, National Technical University of Athens, March 2008

L. Pavlovčič, F. Sinur, D. Beg: “Material tests on Unito limestone from Lipica”, Final report for WP7 of European project PROHITECH, Ljubljana: University of Ljubljana, Faculty of Civil and Geodetic Engineering, Chair for Metal Structures, 2006. 55 pp.

L. Pavlovčič, F. Sinur, D. Beg: „Workpackage 8: Devices – Architrave connection”, Final report for WP8 of European project PROHITECH, Ljubljana: University of Ljubljana, Faculty of Civil and Geodetic Engineering, Chair for Metal Structures, 2008. 25 pp.

L. Pavlovčič, P. Kozlevčar, F. Sinur, D. Beg: “Architrave connection tests”, Final report for WP7 of European project PROHITECH, Ljubljana: University of Ljubljana, Faculty of Civil and Geodetic Engineering, Chair for Metal Structures, 2008. 70 pp.

Hibbit, Karlsson & Sorensen, Inc.: ABAQUS, Version 6.7, 2007

L. Pavlovčič, D. Beg: “PROCHITECH WP9 – Calculation models: Stone – Unito limestone”, University of Ljubljana, Faculty of Civil and Geodetic Engineering, Chair for Metal Structures, 2008. 7 pp.

American Society for Testing and Materials: “E 399-90: Standard test method for plain-strain fracture toughness of metallic materials”, Annual Book of ASTM Standards, Vol. 03.01, Metals-Mechanical Testing; Elevated and Low-Temperature Tests; Metallography; 1997, pp. 408t-422

D. Gross, T. Seeling: “Fracture Mechanics; With an Introduction to Micromechanics”, Springer-Verlag, Berlin Heidelberg, 2006

2.3. Anchors in marble

2.3.1. Introduction

This section was prepared in accordance with data-sheet no. 9-7 “Anchors in marble” provided by Ioannis Vayas, Aikaterini Marinelli, Stavros Kourkoulis, Stefanos-Aldo Papanicolopulos from National Technical University of Athens, Greece (GR).

The most dedicated problem in preserving the structural integrity and stability of ancient temples, made of multi-fragmented structural members, is to assure the joining of his cracked elements, columns and

95

architraves. This section proposed a practical design methodology based on a bilinear behavior model of anchor with two design criterion.

2.3.2. Basic concept

The problem of restoring and conserving an ancient monument is an extremely complicated multidisciplinary scientific task and a series of problems are to be considered and solved before a final decision is reached (Kourkoulis, 2006) . These problems vary from elementary ones, as for example the strength and deformability of the materials used, to rather complex ones, such as the preservation of the structural system, the determination of the minimum possible intervention, the reversibility of the interventions and of course their durability. Archaeologists, architects and engineers collaborate in order to meet the final target, the extension of the life of the monument. The decisions made are usually a compromise between various, and often contradictory, points of view. The structural stability is among the most important problems confronted by the experts working for the restoration of a monument. The determination of the reinforcement required for joining together multi-fragmented structural members is a prerequisite for the correct solution of the problem of the structural stability.

Especially for the structural restoration of the monuments of the Acropolis of Athens a pioneer method was developed, already from the early seventies, based on the use of titanium bars in combination with suitable cement mortar. The method permitted the reduction of the interventions on the authentic material in comparison to older approaches and became the reference point for scientists studying the structural behaviour of a series of classic monuments in Greece (Kourkoulis, 2006; Zambas, 1986, Zambas, 1989). In general the aim of the restoration of fractured or cracked structural members is either to reach their initial load-bearing capacity or to reach the capacity corresponding to the maximum load that is expected to be applied on the member after the restoration of the monument is completed (taking into account all possible future interventions). A part of this approach for the calculation of the reinforcement required for joining together multifragmented architraves of the Parthenon colonnades, is evaluated within PROHITECH project both experimentally and numerically.

For the development of these connections for the restoration of the integrity of structural elements of ancient stone temples, it is imperative, among others, to understand the reasons of the “pull-out” phenomenon, namely of the gradual or abrupt removal of the reinforcing bars from the body of the structural member, without prior failure of neither the marble nor the bars. An analytic solution is not yet available and in this context a combined experimental and numerical analysis was undertaken (Prohitech, WP7; Prohitech, WP8; Kourkoulis, 2008, Marinelli, 2008) in an effort to enlighten the failure mechanisms activated during the phenomenon.

With the aim to protect original members, the main criterion adopted for the design of the connections is to exclude failure of the connected marble pieces but also to minimize the number and the dimensions of reinforcement bars required. In this context, the actual resistance of the “marble - cementitious material - reinforcement bar” system had to be determined against pull-out.

96

c

b

m

Figure 2.3-1 Schematic representation of the specimens (m: marble, c: cement mat., b: bar)

2.3.3. Summary experimental results

The main experimental part included 9 series of pull-out tests on prismatic specimens made from Dionysos marble, in which threaded metallic bars were planted in drilled holes (Prohitech, WP7). The adhesion between the marble and the bar was achieved using suitable cementitious material (Figure 2.3-2). The external diameter of the bars was kept constant and equal to 12 mm. To the thread depth h, three different values were attributed: 1.75, 1.25, 0.75mm. For the thread pitch, the values 2, 3, 4mm were selected (Figure 2.3-3). The experimental set-up and results are presented in detail in Prohitech, WP7.

Figure 2.3-2 Specimen preparation procedure

Figure 2.3-3 Geometric characteristics of the reinforcement bar

The predominant failure mode was the pure pull-out in the form of the separation of the marble - mortar interface. Results from a typical pull-out experiment are summarized in Figure 2.3-4, where the variation of the load P and the relative slip s between marble and reinforcement bar are plotted against the loading frame’s displacement δ.

97

0

8

16

24

0 2 4 6 8System displacement, δ [mm]

Load

, P [k

N]

0

1

2

3

4

5

6

7

8

Slip

[mm

]

P-δslip-δ

First change of slope

Initiation of slip

Peak load

Slip evolution, Vmax, Vmed

Figure 2.3-4 P-δ and Slip-δ curves for a typical pull-out test

The P-slip curves for all specimens are available as well as the experimentally derived shear stresses at characteristic states during testing such as the start of the slip, the reach of the maximum load (capacity limit state) and the reach of 1mm slip (considered as a performance limit) (Zambas, 1989) . It seems that the role of the thread’s geometry is quite critical since the denser pitches exhibit satisfactory performance for any thread depth while on the other hand the medium depth guarantees a significant load carrying capacity. Practically, these results support the selection of a thread’s geometry as close as possible to the metric one. In any case though, the specimen preparation conditions and possible material imperfections influence significantly the pull-out behavior.

In brief, the effect of the thread’s geometry becomes obvious in Figure 2.3-5, where the mean value of the pull-out force has been plotted against the thread’s pitch for all 9 test series. The pull-out force generally decreases with the increase of the pitch, especially for the medium thread depth.

0

15

30

45

1 2 3 4Thread pitch [mm]

Pmax

[kN

]

D:10.5D:9.5D:8.5

Figure 2.3-5 The dependence of the pull-out force from the thread pitch and depth

The P-slip curves for the each testing category are plotted for all three identical performed tests (specimen group No 4, Figure 2.3-6).The significant scattering of results is obvious, attributed either to the unpredicted and uncontrollable differences in the specimen preparation procedure or to the inhomogeneous material properties.

98

0

15

30

45

0 0.5 1 1.5 2

s [mm]

P [k

N]

Figure 2.3-6 Experimental load – slip curves (Specimen category 4)

2.3.4. A design criterion based on the experimental results

In order to practically evaluate the pull-out behavior in terms of the slip and the load carrying capacity, a performance based criterion allowing for a predefined amount of slip is introduced (Figure 2.3-7). The assumption proposed is based on this behavior description in terms of the residual strength following a bilinear law.

0

10

20

30

0 1 2 3 4 5 6

Slip, s [mm]

Load

,P [k

N]

Figure 2.3-7 Introduction of a design criterion based on the residual strength at s=1mm

In order to implement the performance based criterion previously mentioned, some observations are necessary:

• For the pitches equal to 2 and 3mm the load at first slip is almost equal to the load at s=1mm and much lower than Pmax (Figure 2.3-8a)

99

• For the pitch equal to 4mm the load at s=1mm is greater than the load at first slip and less than Pmax but comparable to it. In this second case, the residual strength may be greater but refers to a lower load level anyway (Figure 2.3-8b).

Two bilinear behavior models are proposed for the description of the connection’s behavior: an increase of the slip under constant load is assumed for a dense pitch whereas for the coarse one the load increases linearly (Figure 2.3-8). This approach is repeated for all categories of tests and the simplified model is created either by adopting the average load values mS (Figure 2.3-8a) or by calculating the characteristic ones for each group of identical specimens through the formula K m s sS S kσ= − × , considering the 95% fractal of the normal distribution, where σs is the standard deviation and ks a coefficient equal to 1,64 for the above mentioned assumptions (Figure 2.3-9b). When taking into account the standard deviation of each category the results become more reliable and the differences between them are less pronounced. The conclusions are consistent with the preliminary ones meaning that the dense pitch has less variance and satisfactory performance for any thread depth while the medium depth guarantees a significant load carrying capacity.

The need for further parametric study of the phenomenon necessitates, also, numerical analysis. Based on the results of the experimental work, an axisymmetric model is developed simulating the geometry of the specimens and the testing conditions. Design guidelines referring to geometry variations and different anchorage lengths could be formed based to relevant parametric analyses.

0

5

10

15

20

25

0 0.2 0.4 0.6 0.8 1 1.2

Slip, s [mm]

Load

, P [k

N]

(a)

100

0

4

8

12

16

20

0 0.2 0.4 0.6 0.8 1 1.2

Slip, s [mm]

Load

, P [k

N]

Figure 2.3-8 P-slip curve and bilinear behaviour model for (a) p=4mm, Dint=10.5mm

(b) p=3mm, Dint=8.5mm

0

5

10

15

20

25

30

0 0.2 0.4 0.6 0.8 1Slip, s [mm]

Load

, P [k

N]

D10.5, p2 D10.5, p3

D10.5, p4 D9.5, p2

D9.5, p3 D8.5, p2

D8.5, p3 D8.5, p4

(a)

101

0

4

8

12

16

20

0 0.2 0.4 0.6 0.8 1

Slip, s [mm]

Load

, P [k

N]

D10.5, p2 D10.5, p3

D10.5, p4 D9.5, p2

D9.5, p3 D8.5, p2

D8.5, p3 D8.5, p4

Figure 2.3-9 Bilinear behaviour models for all test categories, derived by (a) adopting average load values (b) calculating the characteristic ones

2.3.5. Practical implementation of the design criterion

Such design criteria for the cases of dense and coarse thread pitches derived experimentally and the corresponding ones that can be formed by numerical results, can be used for primary and practical numerical analyses in a larger scale. The connection of marble pieces through reinorcement bars can be realized by the use of suitable springs replacing actual detailed connectors at their positions. The selection of appropriate parameters characterizing each spring between suitable start and end positions can lead to a description of the unified system’s macroscopic behavior.

Spring elements can couple a force with a relative displacement and can be linear or nonlinear. Linear spring behavior is described by specifying a constant spring stiffness (force per relative displacement). Nonlinear spring behavior is implemented by giving pairs of force–relative displacement values. These values should be given in ascending order of relative displacement and should be provided over a sufficiently wide range of relative displacement values so that the behavior is defined correctly. The P-slip bilinear law representing the pull-out phenomenon of the reinforcement bar, derived after experimental or numerical results, can therefore be introduced as the spring force–relative displacement relationship.

(b)

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Figure 2.3-10 Indicative modelling of connecting two pieces by the use of spring

2.3.6. Conclusions

A design criterion was proposed in the present study regarding the pull-out of threaded metallic bars from prismatic marble bodies. The criterion was proposed in accordance to the results of a series of experiments in which the influence of the geometrical characteristics of the thread on the pull-out force was quantified. The experimental study was adjusted to the needs of the restoration project of the Parthenon Temple on the Acropolis of Athens where the bars are attached to the marble with the aid of a suitable cementitious material injected in a whole of slightly higher diameter compared to that of the bar. The experimental technique used was partly improvised since the respective standards do not cover the case studied, where two interfaces appear, namely marble – cement and cement - metal.

Results of preliminary experiments indicated the anchoring length for which failure is restricted systematically at the marble - cement interface, since the target of any restoring effort is the protection of the authentic material (in this case marble). Therefore the specific length was used for the preparation of the specimens and the parameter “anchoring length” was excluded from the present study.

Two bilinear behavior models were introduced for the description of the connection’s behavior according to the experimental findings: that of slip increasing under constant load (valid for the denser pitches) and that of linearly increasing load versus slip (valid for the coarser pitches). The conclusions obtained using these models indicate that the denser pitches exhibit satisfactory performance for any thread depth while on the other hand the medium depth guarantees a significant load carrying capacity.

For the needs of the further parametric analysis of the problem a numerical model was designed for which the failure (debonding of the “mortar-marble” interface) was described by the successive failure of elements caused by the progressive degradation of the stiffness of the material due to damage. It was proved that the overall load-slip curve cannot be described in terms of a uniquely calibrated model.

For general practical purposes, it is convenient to use the developed design criteria for primary numerical analyses in a larger scale. The P-slip bilinear law representing the pull-out phenomenon of the reinforcement bar, derived after experimental or numerical results, can therefore be introduced in the model as the spring force–relative displacement relationship.

2.3.7. References:

S. K. Kourkoulis, E. Ganniari-Papageorgiou, M. Mentzini Experimental and numerical evaluation of a new method for joining together fragmented structural members, 2006

Zambas C., Ioannidou, M. & Papanikolaou, A. 1986. The use of titanium reinforcements for the restoration of marble architectural members of Acropolis Monuments. Proc. IIC Congress on Case Studies in the Conservation of Stone and Wall Paintings: 138-143. Bologna: The International Institute for Conservation of Historic and Artistic Works.

Zambas, C. 1989. Structural problems of the restoration of the Parthenon, Vol. 2a, Athens: Committee for the Preservation of the Acropolis Monuments.

Zambas, C. 1994. Structural problems of the restoration of the Parthenon, Vol. 3b, Athens: Committee for the Preservation of the Acropolis Monuments

PROHITECH: WP7 Final Deliverable for Anchors in marble (D-III, Part 1 §2.3), March 2008.

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PROHITECH: WP8 Final Deliverable for Anchors in marble (D-III, Part 2 §3.3), March 2008.

Kourkoulis S.K., Papanicolopulos S.-A., Marinelli A., Vayas I., Restaurierung antiker Tempel: Experimentelle Untersuchungen zum Ausziehverhalten von Verankerungen im Marmor, Bautechnik 85 Heft 2, pp. 109-119, 2008.

Marinelli A., Papanicolopulos S.-A., Kourkoulis S.K., Vayas I., The Pull-out Problem in restoring marble fragments: a design criterion based on experimental results, Strain, 2008 (accepted for publication).

2.4. Post-installed anchors in concrete

2.4.1. Introduction

This section was prepared in accordance with data-sheet no. 9-8 “Reinforced concrete” provided by Dan Lungu, Cristian Arion from Technical University of Civil Engineering Bucharest, Romania (RO-TUB).

An important issue in case of rehabilitation is the connection between the existing building and the added elements. This may be done by using pre-installed anchors in order to obtain the transfer of forces between existing and added members. The section treats all the types, materials and specific design rules for this type of anchors.

2.4.2. Design of post-installed anchors

The post-installed anchors are designed for the smooth transfer of force at the joint surface between the existing concrete structure and newly added reinforcement member. As shown in Figure 2.4-1, one end of the anchor main component or anchor rebar is embedded and fixed in the existing concrete, and the other end is connected to the added reinforcement member.

Figure 2.4-1 Example of using post-installed anchor

Post-installed anchors can be grouped into two main types:

• the mechanical anchor and

• the adhesive anchor.

A close-up detail of point A in Figure 2.4-1 is shown in Figure 2.4-2

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Figure 2.4-2 Details and description of an post-instaled anchor

Generally, the anchors cannot be used when the existing structure has extremely low-strength concrete, or when there are other defects such as rock pockets that could reduce anchor performance.

• Post-installed anchor: Generic term for methods where anchors or anchor rebars are embedded by drilling into existing concrete, for adding seismic shear walls or wing walls.

• Adhesive anchor: Post-installed anchors where adhesive capsules are inserted into holes drilled in existing concrete, and then the adhesive is mixed to harden and fix the anchor rebar.

• Mechanical anchor: Post-installed anchors that are installed into holes drilled in existing concrete, and its resisting mechanism fixes the anchor to the concrete.

2.4.3. Types and methods of post-installed anchors

The types of post-installed anchors are: the mechanical anchor and the adhesive anchor.

Types of post-installed anchors

Post-installed anchors are installed by drilling a hole into the existing concrete structure, then inserting the anchor or anchor rebar and fixing it to the concrete. Anchors can be divided into two types by fixing method: mechanical anchors and adhesive anchors. Figure 2.4-3 shows the different types of post-installed anchors.

Drive extension expanding type Drive pin type

Drive in end-cone type

Improved type Drive pin type Conventional type

Drive in expansion type

Drive-in type

Sleeve type

Threaded bolt with cone type

Mechanical anchor

Drive-in flush-mount type Expansion end type

Threaded bar with nut and cone

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Double cone type Horizontal expansion type

Wedge type

Other mechanical anchors

Organic type Capsule type

Non-organic type

Mix-at-site type Injection type

Cartridge type

Rotation impact type

Adhesive anchors

Type according to capsule use

Drive-in type

Figure 2.4-3Types of post-installed anchors

The post-installed anchors are used in seismic retrofitting:

• for adding RC walls or steel reinforcement frames to existing concrete frames,

• for connecting the added wall thickness to the existing wall to function as a single structure, or when adding concrete thickness to beams and columns.

Post-installed anchors used in seismic retrofitting are usually designed based on their shear strength. Therefore, effective anchors are those that do not cause a loss of concrete near the joint surface between the existing concrete structure and the added portion.

The post-installed anchor method are divided into mechanical anchors and adhesive anchors by the method of anchoring in the drilled hole. These anchors are outlined below.

Mechanical anchor

An example of a mechanical anchor is shown in Figure 2.4-4. Mechanical anchors are fixed by inserting them into the hole, and then applying impact or tension, which makes the end, expand and become mechanically fixed to the concrete wall inside the drilled hole. The fixing mechanism is usually a wedge at the end of the anchor. Therefore, to achieve sufficient anchoring strength, the end section must be sufficiently expanded.

Figure 2.4-4 Example of a mechanical anchor

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Adhesive anchor

An example of an adhesive anchor is shown inFigure 2.4-5. As shown, capsule type adhesive anchors are divided into the rotation impact type and the drive-in type, according to the method of installation. With both types, the capsule is inserted into the hole in the concrete. With the rotation impact type anchor, the tip of the anchor rebar is cut at a 45-degree angle on one side, and is installed by rotating and applying impact. With the drive-in type anchor, the tip of the rebar is cut flat and is manually driven into the hole, such as with a hammer. These processes mix the adhesive in the hole and fix the anchor. The fixing mechanism of this type of anchor, as shown in Figure 2.4-5, is the effect of adhesion between the surface of the anchor rebar and the rough texture inside the concrete hole. To obtain sufficient anchoring strength, it is necessary to thoroughly remove all dust remaining in the hole caused by drilling.

Figure 2.4-5 Example of an adhesive anchor

2.4.4. Material, shape and dimensions of post-installed anchors

Materials

Some of the major materials that are used in mechanical anchors is presented in Table 2.4-1.

The material for connection rebars and anchor rebars is presented in Table 2.4-2.

Base materials used in the adhesives of capsule type adhesive anchors are organic resins; such as epoxy acrylate, polyester, epoxy and vinyl urethane type resins.

Shape and dimensions

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The outer diameters, minimum lengths and embedded depths of mechanical anchors are shown in Table 2.4-3. Examples of connection rebars that can be combined with these anchors are shown in Table 2.4-4.

Table 2.4-1 Materials for mechanical anchor components

JIS Number Specification items Code

G3123 Smooth steel bar ＳＧＤ２９０－Ｄ

ＳＧＤ４００－Ｄ

G3507 Cold rolled carbon steel wire ＳＷＲＣＨ８Ｒ

ＳＷＲＣＨ１０Ｒ

G3539 Cold rolled carbon steel wire ＳＷＣＨ８Ｒ

ＳＷＣＨ１０Ｒ

G4804 Sulfur and sulfur combined free-cutting steel

ＳＵＭ２２

ＳＵＭ２３

Table 2.4-2 Materials for connection rebar and anchor rebar

JIS Number Specification items Code

G3112 Steel rod for use in reinforced concrete

ＳＤ２９５Ａ

ＳＤ３４５

Table 2.4-3 Outer diameters and embedded depths of mechanical anchors

Main component of anchor

Outer diameter da (mm) Embedded depth Effective embedded depth

φ13

φ16

φ19

φ22

More than 5da More than 4da

da: outer diameter of anchor main component

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Table 2.4-4 Applicability of mechanical anchors and connection rebar

Main component of anchor Applicability of connection rebar

Outer diameter da (mm) Nominal size db Nominal thread size

φ13 D10 W3/8

φ16 D10 W3/8

φ19 D13 W1/2

φ22 D16 W5/8

The anchor rebars used in the rotation and impact type adhesive anchors (capsule type), have their inserted end cut at a 45-degree angle, as shown in Figure 2.4-6. An example of the relations between embedded depth and minimum length is shown in Table 2.4-5. Furthermore, when using an anchor with a nut at the head, the threaded anchor rebar should have more than two ridges exposed above the nut.

Table 2.4-5 Embedded depth and anchorage length of adhesive anchor (anchor rebar)

Anchor rebar

Nominal size db

Embedded depth l Effective anchorage depth in the added wall

Effective embedded depth

Total length

D13

D16

D19

D22

More than 8da When using in RC wall reinforcement:

More than 20da (with nut)

More than 30da (without nut)

When using in braced reinforcement:

More than 6da (with nut)

Effective embedded depth (le)

le = l – da

Total length (ld)

ld = l + ln + height of nut

(in case of anchor with nut)

Figure 2.4-6 Dimensions of anchor rebar and shape at the tip

2.4.5. Design strength

The adhesive performance of adhesive anchors is the adhesive strength between concrete and anchor rebars. Furthermore, the adhesive strength is the adhesive strength against pullout force (τa).

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The yield strength of anchor rebars shall be the same as the yield strength of the connection rebars mentioned above.

The design strength of post-installed anchors shall be the smallest value among material strength and the strengths of resistance mechanisms calculated according to the material strengths.

To calculate the design strength for post-installed anchors, calculation formulas according to the various expected modes of failure are presented below. The smallest value obtained from the various calculations shall be the design strength.

Shear capacity Qa: Shear force that each anchor could resist at the joint surface, which is the smaller value of either Qa1 dependent on the shear capacity of the steel, or Qa2 dependent on the bearing capacity of concrete.

The shear capacity of post-installed anchors that are fixed in concrete members depends on the shear failure type of the steel material at the shear plane, and the type of bearing failure of concrete adjacent to the steel. These failures are related to the effective embedded depths of post-installed anchors into the concrete. That is, when the effective embedded depth of the post-installed anchor is sufficient, the shear capacity is dependent on the yield strength of the steel member. However, when the effective embedded depth is small, the shear capacity becomes dependent on the type of failure where the anchor is pulled out of the concrete.

Among the calculations for the shear capacity of stud connectors that are installed to transfer shear force in a composite beam, between steel beams and RC slab, a formula has been proposed that incorporates a factor considered to be effective in evaluating the bearing strength of the concrete. By taking these proposed formulas into consideration, the method for calculating the shear capacity of post-installed anchors was based on the results of previous tests on this type of anchor. Therefore, the shear capacity of an anchor at the joint surface is to be the smaller value of either Qa1, which is dependent on the shear capacity of steel, or Qa2, which is dependent on the bearing capacity of concrete.

For calculating Qa1, the following were considered: the tensile strength of the steel material is approximately 1.3 to 1.4 times the yield strength in general; the formula is based on the yield strength of steel; and that this incorporates the method that expands shear capacity, which is obtained from the yield conditions, into tensile strength. A factor 0.7 was thus obtained, and this corresponds to the factor 0.7 indicated in the friction equation.

For calculating Qa2, the pullout type of failure from insufficient effective embedded depth of post-installed anchors into the concrete was considered. Therefore, a factor of 0.3 for mechanical anchors with effective embedded depths that are less than 7da, and a factor of 0.4 for the same with effective embedded depths that are more than 7da and for adhesive anchors were obtained.

With adhesive anchors that have deeper effective embedded depths, the shear capacity is stable as shear deformation increases, and the load approaches the tensile strength of steel after showing large deformation. On the other hand, with mechanical anchors that have shallow effective embedded depths, shear deformation tends to be large from the early stage of loading, and eventually reaches maximum capacity when the anchor is pulled out. When adding a seismic shear wall to an existing RC framework, the shear capacity at the joint surface of this shear wall is calculated by adding the total shear capacities of anchors, which are embedded at the joint surface, and the shear capacity and punching shear capacity of the column. The upper limit of Qa is decided by comparing the shear deformation, obtained from the test on a single anchor, with the measured shear deformation obtained at the joint surface under maximum strength, from the test on reinforced seismic shear wall. The values for τ (= Qa / sae) in this document are: 245 N/mm2 for anchors with effective embedded depths le that are less than 7da, and 295 N/mm2 for anchors with le that are less than 7da.

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For the improved type of drive-in expansion mechanical anchors, where the main component is driven in, when the protruding length l2 from the joint surface is more than 5da, the shear capacity calculated at the joint surface is to be regarded as shear capacity Qa. For other mechanical anchors, when the protruding length l2 from the joint surface is less than 5da, the shear capacity shall be the minimum value in the calculated shear strengths within the range from the joint surface up to 5da.

Mechanical anchor, when 4da ≤ le < 7da

1 2min( , )a a aQ Q Q= (2.4-1)

1 0.7a m y s eQ aσ= i (2.4-2)

2 0.3a c B s eQ E aσ= i i (2.4-3)

However, τ (Qa / sae) should be less than 245 N/mm2.

Mechanical anchor, when le ≥ 7da

1 2min( , )a a aQ Q Q= (2.4-4)

1 0.7a m y s eQ aσ= i (2.4-5)

2 0.4a c B s eQ E aσ= i i (2.4-6))

However, τ (Qa / sae) should be less than 295 N/mm2.

Adhesive anchor, when le ≥ 7da

1 2min( , )a a aQ Q Q= (2.4-7)

1 0.7a m y s eQ aσ= i (2.4-8)

2 0.4a c B s eQ E aσ= i i (2.4-9)

However, τ (Qa / sae) should be less than 295 N/mm2.

where,

• σB: Compressive strength of existing concrete. In principle, core compression tests shall be performed and if the value is greater than the design strength Fc, then the σB value that was used in seismic evaluation is to be used. (N/mm2)

• Ec: Young’s modulus calculated from σB. If Young’s modulus is clarified by measuring the strain during the core compression test, then this value is to be used. (N/mm2)

Tensile capacity Ta: Tensile force that an anchor could resist at the joint surface. For mechanical anchors, this shall be the smallest value of either Ta1 dependent on the yield strength of steel, or Ta2 dependent on the cone failure of concrete. For adhesive anchors, this shall be the smallest value among three values, which is the above two values and Ta3 dependent on adhesive strength.

When tensile forces act on post-installed anchors that are fixed in concrete, the resisting mechanism of a mechanical anchor and adhesive anchor is different. Mechanical anchors transfer the tensile force acting on the anchor to the concrete through the wedge effect of the expanded section. With adhesive anchors, the adhesive embeds into the concrete surface texture of the drilled hole as it hardens. Therefore, the anchorage mechanism, which depends on the shear resistance of the concrete or hardened adhesive at this surface, is to be the adhesive force between the anchor rebar and concrete. However, the type of failure is basically either failure of the steel connection rebars and anchor, or failure of anchorage

111

concrete. Therefore, to obtain the tensile capacity of a post-installed anchor, it is necessary to indicate the calculation formulas and perform calculations according to these types of failure. The smallest value is then taken to be the tensile capacity of the anchor.

To obtain the tensile forces of mechanical anchors, values according to the types of failure under Ta1, which is dependent on steel, and Ta2, which is dependent on concrete, are to be compared. Tensile capacity Ta1 is calculated by obtaining the smallest tensile capacity at the steel portions where shear force is transferred, such as the connection rebar, anchor main component, and anchor expansion mechanism. Ta2 is obtained as the tensile capacity under which the strength is transferred from the expanded portion of the anchor to the concrete and causes pullout cone failure of the concrete.

With adhesive anchors, the tensile capacity is obtained as the smallest value among the three calculations for: Ta2, which is calculated from the pullout cone failure of concrete, similar to mechanical anchors, and Ta3, which is calculated as being dependent on the adhesive strength, together with Ta1, which is calculated as being dependent on the strength of the steel. From the tests, it was observed that when the effective embedded depth of the anchor rebars into concrete was approximately ten times the diameter of the anchor rebar, the pullout cone type failures became more significant than adhesive type failures.

The formula for the adhesive strength τa obtained according to the compressive strength of concrete is shown, under the condition that quality control of adhesive anchors and related material strengths are secured. The factor 0.23 in Equations 2.4-12 and 2.4-15 comes from the original formula under the MKS unit with a factor of 0.75, which was converted to SI units.

Mechanical anchor

1 2min( , )a a aT T T= (2.4-10)

1 min( , )a m y e y oT a aσ σ= i i (2.4-11)

1 0.23a B cT Aσ= i (2.4-12)

Adhesive anchor

1 2 3min( , , )a a a aT T T T= (2.4-13)

1a y oT aσ= i (2.4-14)

2 0.23a B cT Aσ= i (2.4-15)

3a a a eT d lτ π= i i i (2.4-16)

10 ( / 21)a Bτ σ= (2.4-17)

2.4.6. Applying post-installed anchors in low-strength concrete

When there is a need to use post-installed anchors in low-strength concrete, the engineer should take full responsibility when deciding whether to use such anchors in the design. Then, it is necessary to fully consider the edge distance, pitch, the diameter and embedded depths of the anchors.

Shear capacity

When the concrete strength (σB) is approximately 10 N/mm2, the shear capacity of adhesive anchors is evaluated according to the shear capacity calculation formula indicated by this chapter.

The upper limit for shear capacity is to be according to the shear displacement (δ = 20 mm), and was specified as τ = 295 N/mm2. The D19 anchor satisfies this value, but the D22 anchor will be less than

112

this value. Therefore, with low concrete strength (σB), such as 10 N/mm2, it is desirable to use anchors of relatively narrow diameter of less than D19.

Tensile capacity

When σB is approximately 10 N/mm2, the tensile capacity of adhesive anchors could be largely obtained by the tensile capacity calculation formula in this chapter. However, for a test piece with an anchor edge distance of 4.55da, similar to the shear capacity, some tensile capacities obtained from the tensile capacity calculation formula indicated by this chapter could become over-estimated. Therefore, care is needed.

Figure 2.4-7 Mechanical anchors

Figure 2.4-8 Relation between shear test results of headed stud connectors and calculation formula

(Qa2)

113

Figure 2.4-9 Shear test of connections that use post-installed anchors

Figure 2.4-10 Efecctive horizontal projected area Ac of a post-installed anchor

2.4.7. Structural design in the case of shear RC wall

Common provisions

114

At portions that assure the yield strength of rebars in the wall against tensile forces, the anchors that are installed should be adhesive anchors. The effective embedded depth le should be more than 10da.

The diameter, pitch (longitudinal spacing) and arrangement of post-installed anchors are as follows (see Figure 2.4-11).

pitch (more than 7.5ｄa and less than300mm) pitch(more than 7.5ｄa and less than 300mm)

(a) double bar arrangement (b) staggered bar arrangement

Figure 2.4-11 Spacing and arrangement of post-installed anchors

• Diameter da of anchor bar: More than 13 mm, less than 22 mm

• Pitch: More than 7.5da, less than 300 mm

• Gage (transverse spacing): More than 5.5da for double row arrangement, more than 4da for staggered arrangement

• End distance: More than 5da, but less than the pitch

• Edge distance: More than 2.5da, and to be installed inside of the main rebars (see Figure 2.4-12) For anchors used in added walls and steel reinforcement frames, sufficient rebars should be arranged around anchors and anchor rebars to prevent splitting (see Figure 2.4-13).

Figure 2.4-12 Arrangement of post-installed

anchors Figure 2.4-13 Example of spiral hoop installed

to prevent splitting

In principle, all columns and beams that are connected to the added walls should have post-installed anchors embedded.

Mechanical anchors

115

The connection rebar that will be anchored into the added wall should be a deformed steel bar, and the effective anchorage depth should be more than 30da in principle. However, when there is a hook or nut at the head of the anchor, this should be more than 20da.

The effective embedded depth of the main component of the anchor le should be more than 4da.

Adhesive anchors

The anchor rebar that will be anchored into the added wall should be a deformed steel bar with a nut attached to the head, and the effective anchorage depth should be more than 20da. The effective embedded depth of the anchor rebar le should be more than 7da.

There is little test information available for reference on using mechanical anchors in steel reinforcement frames. Therefore, headed anchors should be used, and the embedded depth into connection mortar should be more than 6da. Other items should be according to the provision above, but it is desirable for the effective embedded depth to be more than 7da. For headed anchors, the type that is threaded with a nut attached at the anchor head could be used, and the type with the head integrated as one piece could be considered as well (Figure 2.4-14).

Figure 2.4-14 Outline of headed anchors

An example of a post-installed anchor arrangement for use in added seismic shear walls is shown in Figure 2.4-15 An example of calculating the minimum wall thickness is shown in Table 2.4-6.

116

bar arrangement of added seismic wall (example)

*1 post-installed anchorage

reinforcing bars

*2 mortar injected part

*3 reinforcement for preventing splitting

examples of single bar arrangement examples of staggered bar arrangement

Figure 2.4-15 Arrangement of rebars around post-installed anchors in added seismic shear walls

Table 2.4-6 Minimum wall thickness for installing added walls in the transverse direction of the beam

minimum wall diameter of anchor

wall reinforcement single staggered double

remarks

Ｄ10 150 210 240

Ｄ13 150 220 240 16φ

Ｄ16 160 220 250

Ｄ10 150 230 260 19φ

Ｄ13 160 240 260

Error! Objects cannot be created from editing field codes.

main bar (column, beam - Ｄ22)

Stirrup Ｄ10

cover thickness

Beam 30mm

wall 20mm

Ｄ16 170 240 270

22φ Ｄ10 160 250 280

117

2.4.8. References:

AIJ Structural Design Guideline for Reinforced Concrete Buildings, published by the Architectural Institute of Japan, 1994

AIJ Design Guidelines for Earthquake Resistant RC Buildings Based on Inelastic Displacement Concept, published by the Arch. Institute of Japan, 1999

Japanese Standard for Seismic Evaluation of Existing Reinforced Concrete Buildings, 2001

Japanese Technical Manual for Evaluation and Seismic Retrofitting of Existing Reinforced Concrete Buildings, 2001

2.5. Pure aluminium shear panels

2.5.1. Introduction

This section was prepared in accordance with data-sheet no. 9-9 “Calculation models for pure aluminium shear panels” provided by G. De Matteis, S. Panico, G. Brando, A. Formisano, F.M. Mazzolani from Faculty of Architecture, University of Chieti / Pescara “G. D'Annunzio”, Italy (UNICH) and Engineering Faculty, Department of Structural Analysis and Design, University of Naples “Federico II”, Italy (UNINA).

This section makes a description of the technique presenting possibilities to model the panel depending on geometry of the panel and the analysis procedure.

2.5.2. Description of the device

Pure Aluminium Shear Panels (PASPs) consist of stiffened shear plates made of heat treated aluminium alloys characterised by low yield strength and high ductility (such as AW 1050A alloy). They may be used as special hysteretic dissipative devices for passive seismic protection. Such a system is studied at the Department of Structural Analysis and Design (DAPS) of the University of Naples “Federico II” (Figure 2.5-1).

Ｄ13 160 250 290

Ｄ16 170 260 290

Figure 2.5-1 PASPs system testing lay-out.

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Differently by Japanese system denoted as LYSWs (Low Yield Shear Walls) (Nakagawa et al., 1996), where Low Yield Strength (LYS) steel is used, aluminium alloys characterised by a very high degree of purity (99.50% of aluminium) are instead used in the PAPSs system, whose employment is suggested for the scarce availability on the market of low yield strength steel (De Matteis et al, 2003).

This device can be directly or indirectly bolted to the members of a framed structure. If they are adequately stiffened, shear panels may allow a pure shear dissipative mechanism with shear plastic deformations developing before the occurrence of buckling phenomena.

The system described on this document was not yet used on real structures but only tests on pinned steel frame have been carried out (Figure 2.5-2) (De Matteis et al., 2006a, b).

Panel type F

(b/t=50)

Welded stiffeners

PURE ALUMINIUM SHEAR PANELCONFIGURATION TYPE F

-50

-40

-30

-20

-10

0

10

20

30

40

50

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06shear strain (mm/mm)

shea

r str

ess

(MPa

)

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 500 1000 1500 2000 2500 3000 3500time (s)

shea

r str

ain

(mm

/mm

)

Panel type B

(b/t=100)

Welded stiffeners

PURE ALUMINIUM SHEAR PANELCONFIGURATION TYPE B

-40

-30

-20

-10

0

10

20

30

40

50

-0.15 -0.12 -0.09 -0.06 -0.03 0 0.03 0.06 0.09shear strain (mm/mm)

shea

r str

ess

(MPa

)

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 800 1600 2400 3200 4000 4800 5600 6400time (s)

shea

r str

ain

(mm

/mm

)

Panel type G

(b/t=50 and 25)

Welded stiffeners

PURE ALUMINIUM SHEAR PANELCONFIGURATION TYPE G

-50

-40

-30

-20

-10

0

10

20

30

40

50

-0.12 -0.09 -0.06 -0.03 0 0.03 0.06 0.09shear strain (mm/mm)

shea

r str

ess

(MPa

)

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 1000 2000 3000 4000 5000 600time (s)

shea

r str

ain

(mm

/mm

)

Panel type H

(b/t=50)

Bolted steel stiffeners

PURE ALUMINIUM SHEAR PANELCONFIGURATION TYPE H

-50

-40

-30

-20

-10

0

10

20

30

40

50

60

-0.15 -0.12 -0.09 -0.06 -0.03 0 0.03 0.06 0.09 0.12 0.15shear strain (mm/mm)

shea

r str

ess

(MPa

)

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0 1000 2000 3000 4000 5000 6000 7000 8000 900time (s)

shea

r str

ain

(mm

/mm

)

Figure 2.5-2. Cyclic behaviour of some tested shear panels.

Design provisions for PASPs as dissipative device are not yet codified but the guidelines used to design the tested specimens are available in Eurocode 9 (2003).

Considering the fact that the better cyclic performance of dissipative stiffened shear panels is obtained by preventing them from buckling, their modelling for structural analysis consist of ribbed plates in shear. However, more advanced calculations and their validation by testing are needed for the design of BRB itself.

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2.5.3. Material model

The proposed pure aluminium shear panel is fabricated by the wrought aluminium alloy EN-AW 1050A, which is a commercial material with a degree of purity of 99.50%, whose chemical composition is provided in Table 2.5-1. To improve its mechanical feature, the panel, after the fabrication, is subjected to a heat treatment, favouring the increase of material ductility and the reduction of yielding stress. Details of heat treatment are listed in Table 2.5-2.

Table 2.5-1 Chemical composition and mechanical properties of the adopted aluminium alloy 1050A H24.

Mechanical properties

Tensile Strength (MPa)

Yield strength (0.2% offset, MPa)

Elongation on 5cm (%)

70-100 30-70 20-40

Commercial denomination: Aluminium 99.50%

Impurities: 0.02%Cu, 0.40%Fe, 0.31%Si, 0.07%Zn, 0.02%Tl, 0.02%other

Table 2.5-2. Cycle of heat treatment of the aluminium alloy.

No. Phase

Temperature (ºC)

Exposure time (hours)

Brinell’s index

initial environment / 69

1 150 4 68

2 230 4 67

3 280 4 44

4 330 4 35

In Figure 2.5-3, the comparison of the tensile curves related to the adopted materials before and after heat treatment is shown.

AW 1050A ALUMINIUM ALLOY

f02=115 MPa

fu=69 MPa

f02=20 MPa

0

20

40

60

80

100

120

140

0% 10% 20% 30% 40% 50% 60%

strain

stre

ss (M

Pa)

Not heat treated aluminiumHeat treated aluminium

f0.2 (Nmm-2) fu (Nmm-2) εu(%) E(Nmm-2) E/f0.2 α = fu/f0.2

_________________________________________________________________________________

20 69 45 70000 3286 3.45

120

Figure 2.5-3 Stress-strain relationship aluminium alloy used for panel and mechanical properties.

Ramberg-Osgood plastic model with high hardening can be used for nonlinear static (pushover) analysis, while Wen hysteretic model can be used to approximately reproduce the cyclic behaviour of material (Wen, 1976) (Figure 2.5-4).

-60

-40

-20

0

20

40

60

-15 -10 -5 0 5 10 15Displacement (mm)

Forc

e (k

N)

exp=0,35k=80yield=38ratio=0,015

Figure 2.5-4 Testing system and cyclic response of aluminium alloy used for panel and Wen’s

hysteretic model.

2.5.4. System model

Shear panels can be classified as (Astaneh-Asl, 2001) (Figure 2.5-5):

• compact, if they reach plastic collapse without suffer of shear buckling phenomena;

• semi-compact, when they buckle while developing shear plastic deformation;

• slender, if they buckle in the elastic phase.

a. Compact shear panel b. Non-Compact and Slender shear panel

Figure 2.5-5 Shear resisting mechanisms: a. “shear yielding”, b. “tension field” action.

In compact shear panels, the aluminium plate is expected to collapse for ultimate shear stress before buckling. Therefore in the analysis, the compact shear walls can be modeled using full shell elements and isotropic material. The shear force V acting on the cross section of the wall can be calculated by assuming a uniform distribution of the shear stress. This applied shear force represents the demand on the panel and should be less than or equal to shear capacity of the panel Vu.

In slender and semi-compact shear panels, aluminium plates are expected to buckle along compressive diagonals before (slender) or after (semi-compact) that yielding stress has been reached. After buckling, the tension field action of the tension diagonal becomes the primary mechanism to resist shear force in the panel. This behaviour should be considered in the analysis by modeling shear panels using shell elements that can buckle. If the analysis software does not have the capability to consider the buckling of shells, to simulate the buckling of compression diagonal the shear walls can be modeled using full shell elements and anisotropic material. Using anisotropic materials enables the analyst to assign different

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moduli of elasticity and shear moduli to three principal directions of the wall such that the compression diagonal will have much less stiffness and will attract much less shear in proportion to its buckling capacity than the tension diagonal. The shear force V acting on the cross section of the wall can be calculated by adding up the shear in the shell elements. This applied shear force represents the demand on the wall and should be less than or equal to shear capacity of the wall.

The processing time is an important aspect when performing numerical analysis of complex structures. For this reason, it is necessary to also consider simplified models reproducing the global effect of shear panels in terms of strength, stiffness and dissipative behaviour. With reference to slender shear panels, several studies have been already carried out demonstrating the effectiveness of the so called strip model to interpret the actual behaviour of the system (Driver et al., 1998, Lubell et al., 2000, Rezai et al., 2000).

Figure 2.5-6 Modeling of slender shear panels by strip model.

The strip model can be easily extended and applied to compact and semi-compact panels as well, taking into account the contributing effect of compression principal stresses also, therefore using a double series of strips oriented according to both tension and compression diagonals with different axial stiffness and strength. When the effect of flexural interaction between the shear plate and the boundary members is negligible, a further simplification allows the adoption of two truss members only, connecting the opposite corners of the frame mesh according to the X-bracing model (Figure 2.5-7). Mechanical features of the diagonal trusses, namely the section area and the material yield strength, may be determined by equating the shear behaviour of the panel under consideration with that provided by the equivalent diagonal members in terms of stiffness, elastic strength and post elastic behaviour. The same simplified model can be also assumed in case of different shear panel configurations - namely partial bay type, pillar type or bracing type (Figure 2.5-8)– by relating the above relationships to the panel depth (h) to storey height (H) ratio.

Full bay type

γy γu γ

α

β

γ

122

Partial bay type

Figure 2.5-7 X-bracing model for compact and semi-compact shear panels.

Full bay type Partial bay type Bracing type Pillar type

Figure 2.5-8 Typical arrangements for shear panels.

A further simplification in the modelling may be obtained by considering shear panel as an added damping and stiffening device, which acts together primary framed structure to globally form a parallel combined (dual) system, where the primary structure exhibits elastic deformations only under moderate earthquakes, while it becomes a useful supplementary energy dissipation system for medium and high intensity earthquakes, developing plastic hinges in beams and columns (Figure 2.5-9). The hysteretic properties of shear panel, i.e. maximum hardening ratio (τmax/τ02 with τ02=f02/ 3 ), secant shear stiffness (Gsec) and equivalent viscous damping factor (ζeq), can be calculated for each shear strain ∆γ by experimental cyclic curves according to relationships 1 of Figure 2.5-10. At moment, the available experimental data are related to the four tested shear panels shown in Figure 2 and relative results in terms of the above hysteretic properties are shown in Figure 2.5-11.

Composite (dual) system Shear Panels (SP)

Med

ium

Earth

quak

e in

tens

ity le

vel

Hig

hLo

w

Steel Frame (SF)

Figure 2.5-9 Modelling of SF-SP combined systems.

123

γτ

πζ

γτ

∆∆=

=

∆⋅∆=

sec

41

81

G

EE

E

S

Deq

d

(1)

Figure 2.5-10 Definition of hysteretic properties of shear panel device: dissipated energy (Ed), equivalent viscous damping ratio (eq ) and secant shear stiffness (Gsec).

0

1

2

3

4

0% 4% 8% 12% 16% 20% 24% 28%shear strain ∆γ

τ max

/ τ02

AW 1050A-Panel type BAW 1050A-Panel type FAW 1050A-Panel type GAW 1050A-Panel type H

0

1

2

3

4

5

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77cycles

τ max

/ τ02

AW 1050A-Panel type BAW 1050A-Panel type FAW 1050A-Panel type GAW 1050A-Panel type H

0

2000

4000

6000

8000

10000

12000

14000

16000

0% 4% 8% 12% 16% 20% 24% 28%shear strain ∆γ

Gse

c (M

pa)

AW 1050A-Panel type BAW 1050A-Panel type FAW 1050A-Panel type GAW 1050A-Panel type H

0

2000

4000

6000

8000

10000

12000

14000

16000

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77cycles

Gse

c(M

pa)

AW 1050A-Panel type BAW 1050A-Panel type FAW 1050A-Panel type GAW 1050A-Panel type H

0%

5%

10%

15%

20%

25%

30%

35%

0% 4% 8% 12% 16% 20% 24% 28%shear strain ∆γ

ζ eq

AW 1050A-Panel type BAW 1050A-Panel type FAW 1050A-Panel type GAW 1050A-Panel type H

0%

5%

10%

15%

20%

25%

30%

35%

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77cycles

ζ eq

AW 1050A-Panel type BAW 1050A-Panel type FAW 1050A-Panel type GAW 1050A-Panel type H

Figure 2.5-11 Hysteretic properties of tested panels (interpolation curves).

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2.5.5. Analysis procedure

Procedures suitable for numerical analysis and design of framed structures equipped with steel shear panels are available in TIPS report (Astaneh-Asl, 2001), where the author tentatively proposed the values listed in the Table 2.5-3.

Table 2.5-3 Proposed Design Coefficients and Factors for Steel Shear Wall Seismic-force-resisting systems.

This document suggests force-reduction factors R similar to eccentrically braced frames and special moment frames (R=8) given by ICC (2000). Any design provision is given for steel shear walls in the European Code (Eurocode 8, 2003). As far as pure aluminium shear panels are concerned, they are still in experimental phase but some numerical analyses on steel frame-compact pure aluminium shear panels combined systems demonstrated that the contribution provided by aluminium shear panels is rather significant, allowing a remarkable improvement of the seismic performance of the structure in terms of stiffness, strength and ductility, with the possibility to strongly limit the damage occurring in the members of moment resisting frames (De Matteis et al., 2004).

The obtained outcomes established that the optimal steel frame-aluminium shear panels dual system for frames designed to both gravity load only and seismic loads correspond to a shear panel strength equal to 75% and 50% of the global seismic strength, respectively. Owing to very low strength and high ductility of pure aluminium, the q-factor value, which is representative of the global dissipative capacity of the system and defined as the ratio between the elastic spectral acceleration corresponding to the collapse of the frame and the one related to first plastic deformation in the panels, reaches a value until to 14. A similar result shows that in such a dual system the q-factor of the frame (about 6) and the shear panel one (about 8) can be added up.

2.5.6. References

Astaneh-Asl, A. (2001). “Seismic Behavior and Design of Steel Shear Walls”. Steel TIPS report, Structural Steel Educational Council, Moraga, CA.

De Matteis, G., Mazzolani, F.M., Panico, S., (2004). “Seismic protection of steel buildings by pure aluminium shear panels”. Proc. Of 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada, August 1-6, 2004, Paper No. 2704.

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De Matteis, G., Panico S., Mazzolani, F.M., (2006a). “Experimental study on pure aluminium shear panels with different stiffener types”. Proceedings of the 5th STESSA Conference (Behaviour of Steel Structures in Seismic Areas), Yokohama, Japan.

De Matteis, G., Panico, S., Mazzolani, F.M., (2006b). “Experimental tests on stiffened aluminium shear panels”. Proc. of XI International Conference, Metal Structures, Rzeszów, Polonia, June 21-23.

Driver, R.G., Kulak, Elwi A.E., Kennedy, D.J.L., (1998). “FE and simplified models of steel plate shear wall”. Journal of Structural Engineer, ASCE, vol. 124, No. 2: 112-120.

Eurocode 8 (2003). "Design of structures for earthquake resistance. Part 1: General rules, seismic actions and rules for buildings". December, 2003. CEN - European Committee for Standardization.

Eurocode 9 (2003). "Design of aluminium structures. Part 1-1: General Structural Rules". CEN - European Committee for Standardization.

ICC, (2000). "The International Building Code, IBC-2000". International Code Council, Falls Church, VA.

Lubell, S., Prion, H.G.L., Ventura, C.E., Rezai, M., (2000). “Unstiffened steel plate shear wall performance under cyclic loading”. Journal of structural engineering, 126(4): 453-460.

Nakagawa, S., Kihara, H., Torii, S., Nakata, Y., Matsuoka, Y., Fyjisawa, K., et al. “Hysteretic behaviour of low yield strength steel panel shear walls: experimental investigation”. Proc. of the 11th WCEE, Elsevier, CD-ROM, Paper No. 171.

Rezai, M., Ventura, C.E., Prion, H.G.L. (2000). “Numerical investigation of thin unstiffened steel plate shear walls”. Proceedings 12th World Conference on Earthquake Engineering.

Wen, Y.K., (1976). “Method for Random Vibration of Hysteretic Systems,” Journal of the EngineeringMechanics Division, ASCE, Vol. 102, No. EM2.

2.6. Magnetorheological devices

This section was prepared in accordance with data-sheet no. 9-10 “Analytical and numerical models for magnetorheological device” prepared by A. Mandara, F. Ramundo, G. Spina form Second University of Naples, Italy (SUN). This section present an innovative device based on magnetisable particles with a controllable force at exposure to a magnetic field. In this section presented parametric and non-parametric models available in the literature.

2.6.1. Description of the device

Magnetorheological dampers (MRD) are semi-active control devices that use special fluids to provide controllable force. They represent one of the best examples of smart devices, due to their ability to dissipate energy and their low power requirements. As shown in literature, they proved to be effective in semi-active control applications in civil structures, thanks to their special characteristics: fully controllable reaction force in dynamic range, simple mechanics and low power supply.

They are based on the use of magnetorheological fluids, which are suspension of micron-sized magnetizable particles in an appropriate carrier liquid, able to reversibly change from free flowing, linear viscous liquids to semisolids having a controllable yield strength (100 kPa order) in milliseconds when exposed to a magnetic field.

126

Figure 2.6-1Organization of micron-sized particles in the fluid under a magnetic field.

Magnetorheological devices can be implemented in structural control strategies like mass dampers (MD), in their passive, semi-active and active versions. Semi-active MD combine the best features of both active and passive systems, as they are essentially stable, require a minimum amount of external energy and have the potential to perform very close to active systems. Since the energy dissipated by MD does not depend on the relative motion of parts of the structure, it can be relatively easily implemented and installed on both new and existing structures.

A number of experimental studies have been conducted to evaluate the usefulness of MR dampers for vibration reduction under wind and earthquakes. Dyke et al. (1996a,b, 1998), Jansen and Dyke (2000), Spencer et al. (1996b), and Yi and Dyke (2000) used MR dampers to reduce the seismic vibration of model building structures. Spencer et al. (2000), Ramallo et al. (2001) and Yoshioka et al. (2001) incorporated an MR damper with a base isolation system such that the isolation system would be effective under both strong and moderate earthquakes. Johnson et al. (2001a,b) employed the MR damper to reduce wind-induced stay cable vibration. The experimental results indicate that the MR damper is quite effective for a wide class of applications.

2.6.2. Device models

Different techniques have been developed to model the behaviour of the controllable fluid (CF) dampers. Basically, two types of models have been investigated: non-parametric and parametric models. Ehrgott and Masri (1992) presented a nonparametric approach to model a small Controllable Fluid damper that operates under shear mode by assuming that the damper force could be written in terms of Chebychev polynomials. Chang and Roschke (1998) developed a neuralnetwork model to emulate the dynamic behavior of MR dampers. However, the non-parametric damper models are quite complicated. Stanway et al. (1987) proposed a simple mechanical model, the Bingham model (Figure 2.6-2), in which a Coulomb friction element is placed in parallel with a dashpot.

127

Figure 2.6-2 Mechanical model of MRD based on Bingham theory.

Figure 2.6-3 Stress – deformation velocity diagram for MRF Bingham model..

0 ( ) sgn( )Hτ τ γ η γ•

= +

0ττ ≤ 0=•γ

0ττ ≥ 0γ•

≠

(2.6-1)

Where τ0 represents the shear strenght; γ is the velocity of angular deformation; H is the amplitude of the magnetic field and η is the plastic viscosity coefficient, which is magnetic field independent. This is a quasi-static model that is not sufficient to describe the dynamic behavior of MR dampers, especially the nonlinear force-velocity behavior. As a direct extension of the Bingham plasticity model, an idealized mechanical model was proposed by Stanway et al. (1987). This model is shown in Figure 2.6-3. In this model, a Coulomb friction element is placed in parallel with two springs and a linear viscous damper. The Bingham plasticity model is intrinsically the same as the quasi- static models developed by Stanway et al. (1987). Therefore the MR damper force-displacement behavior is reasonably modeled; however, the nonlinear force-velocity behavior is not captured (Spencer et al. 1997a).

128

Figure 2.6-4 Stress – deformation velocity diagram for MRF Bingham model..

Gamoto and Filisko (1991) extended the Bingham model and developed a viscoelastic-plastic model. The model consists of a Bingham model in series with a standard model of a linear solid model. Kamath and Wereley (1996), Makris et al. (1996), and Wereley et al. (1998) developed parametric models to characterize MR dampers. Dyke et al. (1996a,b), Spencer et al. (1997a) proposed a phenomenological model for MR dampers based on the Bouc-Wen hysteresis model, then developed by the same researchers (Yang et al.,2001.). This model is the better of those proposed because it has a very good approximation of the dynamic behaviour of the MRF dampers. The schematic of the model is illustrated in Figure 2.6-5. The Bouc-Wen model whose versatility was utilized to describe a wide variety of hysteretic behavior.

Figure 2.6-5 Rheological model for MR proposed by Spencer et al. (1997 and Yang et al (2001).

For this model the total reaction force of the device is:

)()()( 0110100 xxkycxxkyxkyxczF −+⋅=−+−+⎟⎠⎞

⎜⎝⎛ −+⋅=

•••α (2.6-2)

where z and y are governed by:

( ) ( )yxAzyxzzyxz nn −+−−−−= − βγ 1

( ) yxkxczcc

y −+++

= 0010

1 α (2.6-3)

where c0 is the high velocity viscous damping coefficient, c1 is the low velocity viscous damping coefficient, k0 and k1 are the high and low velocity stiffness, x0 is the initial displacement of the spring k1.

129

Because the shear stress depends on the current input, α can be assumed as function of the current i. Moreover c0, and c1 also result function of current input as confirmed by experimental studies.

Assuming for α, c0 e c1 third order polinomial expression, we obtain:

151141683268707116566)( 23 ++−= iiiiα

45774116413761545407437097)( 230 ++−= iiiic

27916304878864053341839363108)( 231 −++−= iiiic

(2.6-4)

The other parameters for the model proposed by Spencer are reported in table 1. They are referred to an experimental studies conducted on a MR Damper realized with fluid from LORD corporation (Figure 2.6-6).

Table 2.6-1 parameters for the identification of the model proposed by Spencer et al.(1997) and Yang et al(2001).

130

Figure 2.6-6 Comparison between the experimentally-obtained and predicted responses using the

simple Bouc-Wen model proposed by Spencer et al. (1997) Yang et al (2001): (a) force vs. time; (b) force vs. displacement; and (c) force vs. velocity.

Figure 2.6-7 Scheme of the MagnetoRheological Damper produced by Lord Corporation used for

the model proposed by Spencer at al. (1997) and Yang et al(2001)..

2.6.3. References:

Aiken, I.D., and Kelly, J.M., (1990). Earthquake simulator testing and analytical studies of two energy-absorbing systems for multistory structures. Report No. UCB/EERC-90/03, University of California, Berkeley, CA.

Carlson, J.D., (1994). The Promise of Controllable Fluids. Proc. of Actuator 94 (H. Borgmann and K. Lenz, Eds.), AXON Technologie Consult GmbH, 266-270.

Carlson, J.D., and Spencer Jr., B.F., (1996a). Magneto-rheological fluid dampers: scalability and design issues for application to dynamic hazard mitigation. Proc. 2nd Workshop on Structural Control: Next Generation of Intelligent Structures, Hong Kong, China, pp. 99–109.

Carlson, J.D., and Spencer Jr., B.F., (1996b). Magneto-rheological fluid dampers for semi-active seismic control.” Proc. 3rd International Conference on Motion and for semi-active seismic control.”

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Proc. 3rd International Conference on Motion and Vibration Control, vol. 3, Chiba, Japan, pp. 35–40.

Carlson, J.D., and Weiss, K.D., (1994). A growing attraction to magnetic fluids. Machine Design, Aug. 8, pp. 61–66.

Carlson, J.D., Catanzarite, D.N. and St Clair, K.A., (1996). Commercial Magneto-Rheological Fluid Devices. Proceedings 5th Int. Conf. on ER Fluids, MR Suspensions and Associated Technology, W. Bullough, Ed., World Scientific, Singapore, pp. 20–28.

Christenson, R.E., and Spencer Jr., B.F., (1999a). Coupled Building Control Using ‘Smart’ Dampers. Proc. 13th ASCE Engineering Mechanics Division Conference, Baltimore, Maryland, CD-ROM (6 pages), June 13-16, 1999.

Christenson, R.E., Spencer Jr., B.F., and Johnson, E.A., (1999b). Coupled Building Control using Active and Smart Damping Strategies. B.H.V. Topping and B. Kumar (eds.), Optimization and Control in Civil and Structural Engineering, Civil-Comp Press, 187-195.

Christenson, R.E., Spencer Jr., B.F., and Johnson, E.A., (2000a). Coupled Building Control using ‘Smart’ Damping Strategies. Proc. SPIE Smart Structures and NDE Symposia, Newport Beach, CA, CD-ROM (9 pages), March 6-9, 2000.

Christenson, R.E., Spencer Jr., B.F., Hori, N., and Seto, K., (2000b). Experimental Verifi-cation of Coupled Building Control. Fourteenth Engineering Mechanics Conference, American Society of Civil Engineers, Austin, Texas, May 21-24, 2000.

Constantinou MC, Symans MD, (1993). Experimental study of seismic response of buildings with supplemental fluid dampers. Journal of Structural Design of Tall Buildings 2:93–132.

Dyke SJ, Spencer BF Jr, Sain MK, Carlson JD., (1997). An experimental study of magnetorheological dampers for seismic hazard mitigation. Proceedings of Structures Congress XV, Portland, OR, 1358–62.

Dyke SJ, Spencer BF Jr, Sain MK, Carlson JD., (1996). Experimental verification of semi-active structural control strategies using acceleration feedback. Proceedings of Third International Conference on Motion and Vibration Control, Vol. III, Chiba, Japan, 291–6.

Dyke SJ, Spencer Jr BF., (1996). Seismic response control using multiple MR dampers. Proceedings of the 2nd International Workshop on Structural Control, Hong Kong, 163–173.

Dyke, S.J. Spencer Jr., B.F., Quast, P., Sain, M.K., and Kaspari Jr., D.C. (1994a). Experimental Verification of Acceleration Feedback Control Strategies for MDOF Structures. Proc. of the 2nd Int. Conf. on Comp. Mech., Athens, Greece, June 13-15.

Dyke, S.J., and Spencer Jr., B.F., (1997). A comparison of semi-active control strategies for the MR damper. Proc. of the IASTED International Conf., Intelligent Information System, The Bahamas.

Dyke, S.J., Spencer Jr., B.F., Jr.,Sain, M.K., and Carlson, J.D., (1996a). Modeling and control of magnetorheological dampers for seismic response reduction. Smart Mat. and Struct., 5:565–575.

Dyke, S.J., Spencer Jr., B.F., Quast, P., and Sain, M.K., (1995). The Role of Control-Structure Interaction in Protective System Design. Journal of Engineering Mechanics, ASCE, 121 (2), 322-338.

Dyke, S.J., Spencer Jr., B.F., Quast, P., Kaspari Jr., D.C., and Sain, M.K., (1994b). Experimental Verification of Acceleration Feedback Control Strategies for an Active Tendon System. NCEER Technical Report NCEER-94-024.

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Dyke, S.J., Spencer Jr., B.F., Quast, P., Kaspari Jr., D.C., and Sain, M.K., (1996b). Implementation of an Active Mass Driver Using Acceleration Feedback Control, Microcomputers in Civil Engineering: Special Issue on Active and Hybrid Structural Control, 11, 304-323

Dyke, S.J., Spencer Jr., B.F., Quast, P., Sain, M.K., Kaspari, Jr., D.C., and Soong, T.T., (1995). Acceleration feedback control of MDOF structures. J. Engrg. Mech., ASCE, 122(9):907–918.

Dyke, S.J., Spencer Jr., B.F., Sain, M.K. and Carlson, J.D., (1996b). Modeling and control of magnetorheological dampers for seismic response reduction. Smart Mat. and Struct., 5, pp. 565-575.

Dyke, S.J., Spencer Jr., B.F., Sain, M.K. and Carlson, J.D., (1998). An experimental study of MR dampers for seismic protection, Smart Mat. and Struct., 7, pp. 693-703.

Gavin HP, Hanson RD, Filisko FE., (1996a). Electrorheological dampers, part 1: analysis and design. J of Applied Mechanics, ASME;63(9):669–75.

Gavin HP, Hanson RD, Filisko FE.,(1996b). Electrorheological dampers, part 2: testing and modeling. J of Applied Mechanics, ASME;63(9):676–82.

Hagedorn, P., (1988). Active Vibration Damping in Large Flexible Structures, Proc. 17th Int. Congr. Theor. Appl. Mech., Grenoble, France, 83-100 , August 21-27, 1988.

Housner, G., Soong, T.T. and Masri, S.F., (1994a). Second generation on active structural control in civil engineering. Proc. 1st World Conf. on Struct. Control, pp. FA2:3-18, Pasadena, CA.

Housner, G.W. et al., (1997). Structural control: past, present, and future. J. Engrg. Mech., ASCE, 123:897–971.

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2.7. Steel buckling restrained braces

2.7.1. Introduction

This section was prepared in accordance with two data-sheets no. 9-11 “Analytical and numerical models for steel buckling restrained braces”” prepared by A. Stratan, S. Bordea, D. Dubina from Politehnica University of Timisoara, Romania (ROPUT) and no. 9-12 “Design methods for buckling restrained braces” prepared by M. D’Aniello, G. Della Corte and F. M. Mazzolani from University of Naples “Federico II” (UNINA).

This section makes a short description of material model, element model and axial and flexural resisting mechanisms, global analysis procedure and acceptance criteria.

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2.7.2. Description of the device/technique

Buckling restrained braces (BRB) are characterised by their ability to prevent local and overall buckling of the brace in compression, and are also referred as "unbonded brace". Inelastic cyclic response of standard braces is characterised by buckling under compression forces which leads to strength and stiffness degradation, and highly non-symmetric response. In contrast, buckling restrained braces have a stable hysteretic response, providing a stable and effective seismic resistant element (Ko and Field, n.d.). Most of the BRBs developed to date are proprietary, but their principle of operation is similar (Uang et al., 2004). A typical BRB consist of a steel core encased in a steel tube filled with mortar or concrete. A layer of unbonding material or a small air gap is provided between the steel core and the mortar in order to minimise the transfer of axial forces from the steel core to the mortar and steel tube during elongation and contraction of the steel core, and also allows for its expansion when in compression (Black et al., 2002, Clark et al., 1999).

Figure 2.7-1. The conceptual scheme of a buckling restrained brace, and characteristic force-displacement relationship (Clark et al., 1999).

A comprehensive review of past research on buckling-restrained systems at the component, subassemblage, and frame levels is available in Uang et al., 2004 and Uang and Nakashima, 2004.

BRB frames were used extensively in Japan after the 1995 Hyogoken-Nanbu earthquake, and gained acceptance in United States a few years after the 1994 Northridge earthquake (Uang et al., 2004).

Applications of BRBs for seismic retrofit existing reinforced concrete and steel structures lacking seismic design are available in Brown et al., 2001, D’Aniello et al., 2006, Black et al., 2002.

(a) Wallace F. Bennett Federal Building -

(b) Building 5, HP Corvallis Campus -

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Federal General Services Administration, Salt Lake City, Utah, USA.

Hewlett-Packard, Corvallis, Oregon, USA

Figure 2.7-2. Application of BRBs for seismic retrofit of reinforced concrete (a) and steel (b) structure, Black et al., 2002.

Design provisions for BRB steel frames are available in AISC 2005a and NEHRP 2003. A design guide is available as well (Lopez and Sabelli, 2004).

Considering the fact that steel core of a BRB is prevented from buckling, modelling of a BRB for structural analysis simplifies to modelling of a plate in tension. However, more advanced calculations and their validation by testing is required for the design of BRB itself, as a system composed of the steel core, unbonding material, and buckling-restraining mechanism.

Buckling restrained braces are the effective solution to the problem of the limited ductility of classic concentric bracing, thanks to the avoidance of global compression buckling. BRBs are characterized by the ability of bracing elements to deform inelastically in compression as well as in tension.

Traditional brace, buckled out in compression BRB, unbuckled in compression

forc

e

fo

rce

Displacement Displacement

Hysteresis loop-poor nonlinear behaviour Hysteresis loop-excellent nonlinear behaviour

Figure 2.7-3 Traditional brace vs buckling restrained brace. This behaviour is achieved through limiting buckling of the steel core within the bracing elements. The axial strength is decoupled from the flexural buckling resistance; in fact, the axial load is confined to the steel core, while the buckling restraining mechanism resists overall brace buckling and restrains high-mode steel core buckling (rippling).

As shown Figure 2.7-3, BRBs are characterized by a stable hysteretic behaviour and, differently from traditional braces, they permit an independent design of stiffness, strength and ductility properties.

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2.7.3. Material model

The active component of buckling restrained braces is the steel core. Steel is a well established structural material. Properties of steel for elastic analysis are available in design codes, such as Eurocode 3 (2003). Simple plastic models with hardening can be used for nonlinear static (pushover) analysis. Various models of steel are available for cyclic response needed in time-history analysis. Practical options are dependent on the particular software package used. As an example, Opensees (Mazzoni et al., n.d.) offers the following models for steel material:

• Steel01 - offering a bilinear model with kinematic hardening and optional isotropic hardening

• Steel02 and Steel03 - Giuffré-Menegotto-Pinto model with isotropic strain hardening

Considering that the active component of BRBs (the steel core) is subjected to axial deformations only and is precluded from buckling, material model can be used directly for characterisation of element response. However, the most straightforward approach is to model directly the element response.

2.7.4. Element model

• The steel core of atypical BRB is composed of three segments (Uang et al., 2004, see Figure 2.7-4):

• restrained yielding segment – most of the elastic and all of the plastic deformations take place here

• restrained non-yielding segment – an extension of the yielding segment but with enlarged area to ensure elastic response

• unrestrained non-yielding segment – used to connect the BRB to other structural elements

Elastic global analysis

In an elastic analysis, a BRB can be modelled using an elastic truss element (when a pinned connection is used, or when stiffness of a rigid connection is neglected in analysis) or a frame element. Taking into account the variation of cross-section of the BRB described above, variation of core cross-sectional area should be accounted for in analysis. Some authors suggested approximating brace stiffness to the one of the yielding segment alone, as most of the elastic deformations and all of the plastic ones are concentrated here (Clark et al., 1999).

Figure 2.7-4. Details of a typical BRB (Uang et al., 2004)

The design axial strength of a BRB can be written as (in Eurocode 3 notation, adapted from AISC 2005a):

140

0

ysc scysc

M

f AP

γ⋅

= (2.7-1)

where:

yscf - specified minimum yield stress of the steel core, or actual yield stress of the steel core as determined from a coupon test, N/mm2

scA - net area of steel core, mm2

0Mγ - partial safety factor ( 0 1.1Mγ = )

Nonlinear static analysis

When modelling a BRB for a nonlinear static analysis, two factors are to be accounted for in addition to the initial stiffness. The first one is the compression-strength adjustment factor, β, reflecting higher strength in compression in comparison with the strength in tension. The second one is the tension strength adjustment factor, ω, accounting for strain hardening (AISC 2005b). Both factors are intended for computation of maximum forces in tension Tmax and in compression Pmax that can be developed by the BRB, for design of connections and beams and columns. Yield strength in tension Ty is determined as (using Eurocode notations):

y ov ysc scT f Aγ= ⋅ ⋅ (2.7-2)

where: Ty – yield strength in tension of the BRB

ovγ - material overstrength factor, to account for the possibility that the actual yield strength of steel is higher than the nominal yield strength

Up to date, design provisions for buckling restrained braces require that brace design be based on qualifying tests (AISC 2005a, NEHRP 2003). Therefore, yscf is determined directly from tensile tests, and material overstrength factor ovγ need not be considered. A simple bilinear model based on the above consideration is shown in Figure 2.7-5. This force-displacement relationship can be incorporated in a nonlinear truss element in order to obtain a complete model of a BRB for a pushover analysis.

Figure 2.7-5. Bilinear modelling of BRB (AISC 2005b)

Nonlinear dynamic analysis

Considering stable hysteretic response that should be proved by BRB experimentally, a simple hysteretic model with hardening can be used, based on the bilinear model from Figure 2.7-5. More complicated

141

models were used by others. Black et al., (2002) used a Bouc-Wen hysteretic model to approximate the macroscopic behaviour of BRBs. Though most of the parameters were determined from geometrical and physical characteristics of the brace, experimental data was needed in order completely define the Bouc-Wen model. The same authors showed that simple bilinear models are satisfactory in representing BRB nonlinear response for global structural analysis.

Figure 2.7-6. Experimental vs. Bouc-Wen model hysteretic curves for a BRB (Black et al., 2002)

Tremblay et al. (2004) compared seismic response of BRB frames where BRBs were modelled using modified Ramberg-Osgood and bilinear hysteretic relationships. Four simulated and six historical ground motion time histories were used. The use of the bilinear model generally resulted in underestimation of storey drifts and overestimation of brace forces in comparison to the more exact Ramberg-Osgood model.

Axial – resisting and flexural - resisting mechanism

The basic principle characterizing the BRB response is based on the possibility of decoupling of the axial-resisting and flexural-resisting mechanisms in the compression field. In fact, the steel core plate has to resist axial stresses, while a sleeve, which may be of steel, concrete or composite, provides buckling resistance.

Figure 2.7-7 shows the parts which constitute a common BRB. It is possible to divide the core into three zones: the yielding zone, that has a reduced cross section area within the zone of lateral restrain provided by the sleeve (zone C); the transition zones, which have a larger area than the one of the yielding zone,

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and similarly restrained (zone B); the connection zones, which extend beyond the sleeve and connect to the frame by means of gusset plates (zone A).

Figure 2.7-7 . Schematic view of a typical BRB element (Sabelli & Lopez 2005).

Assuming that local buckling does not occur along the steel core, the global stability of BRBs can be estimated directly from the Euler theory of buckling. Figure 2.7-8a shows the schematic of a BRB in compression, while Figure 2.7-8b and Figure 2.7-8c show the distributed forces on the steel core and the retaining tube in their deformed configuration (Black et al. 2002).

The unknown distributed load shown in Figure 2.7-8b is the transverse reaction of the outer tube along the inner steel core. Following the system of axis shown in Figure 2.7-8, the equilibrium of the inner steel core in its deformed configuration is given by:

+ =4 2

4 2( ) ( )

- ( )i id y x d y x

E I N q xdx dx

(2.7-3)

where Ii is the second moment of area of the inner core and q(x) is the distributed reaction of the outer tube. Therefore, because the deflection of the inner core is the same as that of the retaining unit, the equilibrium of the outer tube in its deformed configuration is given by (Black et al. 2002):

=4

4( )

( )o od y x

E I q xdx

(2.7-4)

a)

NN

b)

N N

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c) Figure 2.7-8 (a) BRB under axial loading, (b) distributed load along the inner core at its deformed

configuration, (c) distributed load along the outer tube (Black et al. 2002).

Using Eqs. (2.8-3) and (2.8-4) a homogenous Euler equation is obtained:

+ =+

4 2

4 2( ) ( )

0o oi i

d y x N d y xE I E Idx dx

(2.7-5)

For a brace with length L, Eq. (2.8-5) yields the critical buckling load of the brace:

( )( )π

= = +2

2cr e o oi iN N E I E IKL

(2.7-6)

where KL is the effective (or equivalent) length (K = 1 for pinned ends and K = 0.5 for fixed ends). Since the bending rigidity of the inner steel core, EiIi, is two to three orders of magnitude smaller than the bending rigidity of the encasing mortar/outer tube, EoIo , Eq. (2.8-6) simplifies to (Black et al. 2002):

( )π

= ≈2

2tube

cr eEI

N NKL

(2.7-7)

where E and Itube are the Young’s modulus and moment of inertia of the outer tube, respectively. The flexural resistance of the encasing mortar has been neglected. Therefore, Equation (2.8-7) indicates that the critical load of the unbonded brace is merely the Euler buckling load of the outer tube. Accordingly, the global stability of the brace is ensured when the Euler buckling load of the tube, Ncr, exceeds the yielding load of the core, Ny=fyAcore .

Therefore, referring to Eq. (2.8-7), the required stiffness of the steel sleeve in order to prevent the BRB from a global flexural buckling is given by (Watanabe et al. 1988):

( )π

= ⋅2

max2tube

N KLI FS

E (2.7-8)

FS being a safety factor which considers imperfections.

The lateral strength of the BRB device is closely related to the lateral stiffness of the support element. Chen (2002) suggested that the nominal limit strength in compression Nmax, sustained by the outer retaining tube, can be calculated according to the following relationship:

δ=

+max01

E

E

NN

N M (2.7-9)

where NE is the Euler buckling load of the restraining unit, δ0 is an initial crookedness, usually assumed equal to L/1000 and M is the bending moment at midlength of the lateral restraining unit. Then re-arraging Eq. (2.8-9) the maximum moment Mmax can be written as:

144

δ= max 0

maxmax1- E

NM

N N (2.7-10)

Introducing the yielding moment of the encasing member My, the stiffening criterion (Xie 2005) can be written as follows:

<max yM M (2.7-11)

Based on Eqs. (2.8-10) and (2.8-11), according to Xie (2005), the overall buckling criterion can be expressed as:

δ>

⎛ ⎞⎜ ⎟⎝ ⎠

011- y

Em

n L (2.7-12)

in which:

= yE En N N and =y y ym M N L (2.7-13)

where nE and my are non-dimensional parameters corresponding to the flexural stiffness EItube and moment strength My of the restraining member, respectively.

When some gaps between steel cores and encasing members are designed, the stiffening criterion expressed in Eq. (2.8-12) can be modified into the following expression:

δ +>

⎛ ⎞⎜ ⎟⎝ ⎠

011- y

E

sm

n L (2.7-14)

in which s is the size of the gap (which usually varies from 0.7 to 3.5 mm).

In order to properly confine the BRB’s inelastic deformations inside the restraining tube, the cross sectional area (Ac) of the energy dissipation core segment (Lc) is smaller than the one of the end joint regions (Lj).

Lwp

b)

Lb/2

Figure 2.7-9 (a) Dimensions of theoretical total BRB length (node-to-node length); (b) Dimensions of theoretical effective length of end connections (Tsai et al.2004a,b).

node node

Lj/2 LcLt/2 Lt/2 Lj/2

145

Figure 2.7-10. Profile of steel core member in BRB.

A schematic configuration of a BRB in the frame is illustrated in Figure 2.7-8a, in which Lc and Lwp represent the core length and the node-to-node length, respectively. Between the end and the core segment, a transition region can be deviced as illustrated in Figure 2.7-10 It is confirmed by tests (Lin et al. 2004, Tsai & Huang 2002) that the effective stiffness, Ke of the BRB, considering the variation of cross sectional area along the length of the brace, can be accurately predicted by:

=+ +2 2

cj te

c c cj t t j j t

EA A AK

A A L A A L A A L (2.7-15)

which simply combines axial stiffness of three axial springs connected in series.

According to Tsai et al. 2004, the relationship between the brace overall strain (εwp) and the inter-story drift θ can be approximated as:

θ φε ⋅=

sin22wp (2.7-16)

where φ is the angle between the brace and the horizontal beam as illustrated in Figure 2.7-11. The strain-to-drift ratio versus the beam angle φ relationship given by (2.8-16) is plotted in Figure 2.7-12.

Introducing the ratio between the core length and the node-to-node length:

α = c

wp

LL

(2.7-17)

δ∆=δcosφ

H

θ

φ

Figure 2.7-11 Brace deformation vs inter-story drift angle (Tsai et al.2004a,b).

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εwp/θ(1/rad)

δ ∆=δcosφ

Hθ

φ

0.6

0.5

0.4

0.3

0.2

0.1

010 20 30 40 50 60 70 80 90

φ(rad) Figure 2.7-12 Brace strain to story drift ratio vs brace angle relationship (Tsai et al.2004a,b).

the following upper bound to the BRB core strain (εc ) can be defined: ε

εα

≤ wpc (2.7-18)

Since the elastic strain outside the core segment is relatively small compared to the inelastic core strain, from Eqs. 2.8-16 through 2.8-18, it can be found that if the inter-story drift demand is 0.02 radians, then the peak core strain would be close to 0.02 for a BRB having a length aspect ratio α = 0.5 and oriented in a 45 degree angle.

A significant aspect of BRBs is their hardening behaviour, which includes both isotropic and kinematic components. Tests typically result in hysteretic loops having nearly ideal bilinear hysteretic shapes, with moderate kinematic and isotropic hardening evident.

The following Equation may be applied when estimating the maximum compressive strength possibly developed in a BRB (Tsai et al. 2004b):

β= Ω ⋅ Ω ⋅ ⋅max yhN N (2.7-19)

where Ny = Acfy is the nominal yield strength of the core section, Ω and Ωh take into account the possible material over-strength and strain hardening factors of the core steel, respectively, and the bonding factor β represents the imperfect unbonding, i.e. the fact that the peak compressive strength is somewhat greater than the peak tensile strength observed during large deformation cycles.

2.7.5. Connections

Detailing and design of connections between BRBs and the existing structure is highly dependent on the particular type of structure to be strengthened (steel, r.c. or masonry). Two examples of connections between a BRB system and an existing r.c. frame structure are shown in Figure 2.7-13. The first one consists in an external steel frame (beams, columns and BRBs) attached to the existing r.c. frame (Brown et al., 2001). The second one is a suggested detail for connecting braces to existing r.c. frames, consisting in a gusset plate bolted to the r.c. beam-to-column joint by means of bolts passing through holes drilled in the r.c. members (Maheri and Sahebi, 1997, in D’Aniello et al., 2006).

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(a) (b)

Figure 2.7-13. Connection between an exterior BRB system and the existing r.c. structure Brown et al., 2001 (a), and suggested detail for brace connection to existing r.c frame, Maheri and Sahebi,

1997, in D’Aniello et al, 2006 (b)

Brace connections are to be designed with sufficient overstrength with respect to the brace, in order to keep it free of damage. AISC 2005a requires the brace connection (in new steel BRB frames) to be designed for a force equal to 1.1 times the adjusted brace strength in compression Pmax (see Figure 2.7-5).

2.7.6. System model

Beams and columns of the existing structure have to be designed for the maximum forces that adjoining braces are able to develop (AISC 2005a).

Bracing configurations in which braces intersect in a floor are unavailable in the case of BRB frames. Some possible brace arrangements in the case of BRB frames are shown in Figure 2.7-14 (Calado et al., 2006).

(a)

(c)

(b)

(d)

Figure 2.7-14. Possible brace arrangements in the case of BRB frames (Calado et al., 2006)

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In concentrically braced frames, V-brace configurations are characterised by significant demands on the beam after the compression brace buckles. Buckling restrained braces do not lose strength due to buckling, and there is only a small difference between tension and compression brace capacities. Therefore, demands on the beam are much reduced in comparison with conventional braced frames. However, beam deflects vertically due to the unbalanced load caused by compression brace overstrength (AISC 2005b, see Figure 2.7-15). The beam should have sufficient strength to permit yielding of both braces. Additionally, NEHRP Recommended provisions (FEMA, 2003) limit deflections of the beam in this configuration to L/240 (where L is the beam span) under the combination of gravitational loads and the unbalanced load due to braces.

Figure 2.7-15. Post-yield change in deformation mode for V BRB frames (AISC 2005b)

Due to these special requirements, in the case of strengthening of existing structures, BRB configurations may be preferred that do not have the adverse effect of V-brace arrangement, such as the ones shown in Figure 2.7-14a and Figure 2.7-14d.

2.7.7. Analysis types

Procedures suitable for static equivalent global analysis of BRB frames are available in AISC 2005 and FEMA 2003. Both of these documents suggest force-reduction factors R similar to eccentrically braced frames (R=8). In European practice, behaviour factors q=6 are specified for eccentrically braced frames (Eurocode 8, 2003), and can be suggested for BRB frames as well. However, equivalent static procedure is believed to be suitable for new steel BRB frames. Application of this procedure for strengthening of existing structures may be inappropriate, therefore pushover and nonlinear time-history analyses are believed to be better suited for this case.

2.7.8. Performance criteria

Performance criteria for BRBs are generally difficult to be defined; in fact, BRBs are usually manufactured rather than built. That is, they are typically made by a specialty manufacturer, rather than by a contractor or steel fabricator (although such a method of producing them is possible). Specifications should address the furnishing of the braces, including the associated brace-design calculations and quality-control procedures, and the documentation of successful tests that qualify the furnished braces for use in the project.

AISC/SEAOC Recommended Provisions for Buckling-Restrained Braced Frames (2001) requires that experimental tests have to be carried out to provide assurance that certain failure modes do not limit the performance of BRBs. In particular, two types of brace tests are required by the Recommended Provisions. The first is a uniaxial test in which braces are loaded axially and cycled through displacements based on the design story drift until they have dissipated a sufficient amount of energy.

149

The second type of brace test is called a sub-assemblage test. In this test braces are loaded axially while the end connections are rotated to simulate the conditions to be expected when braces are employed in a frame. Rotations can be imposed in a number of ways:

1) Braces can be loaded on an eccentric path, so that a rotational deformation proportional to the axial deformation is imposed (Figure 2.7-16a).

2) a constant rotational deformation can be maintained while the brace is cycled axially (Figure 2.7-16b).

3) a column-brace assembly can be tested (Figure 2.7-16c).

4) finally, a full frame can be tested (Figure 2.7-16d).

The sub-assemblage test is of great importance because it is intended to verify that the brace-end rotational demands imposed by frame action will not compromise the performance of the brace.

Generally speaking, it is possible to fix the range of structural effectiveness of this device in terms of interstory drift ratio. The experimental and numerical experiences presented in literature usually suggest that common values of interstory drift are between 1 to 2.5%.

a) Eccentric Loading of Brace, b) Loading of Brace with constant imposed rotation

c) Loading of Brace and Column d) Loading of Braced Frame

Figure 2.7-16. Sub-assemblage tests according to AISC/SEAOC Recommended Provisions for BRB Frames.

Since energy input by a strong earthquake is expected to be greatly dissipated by these devices, BRBs should yield far before that structural damage could occur in other members.

In case of the design of BRBs for seismic upgrading of RC structures, the performance criteria of this device depend on the RC lateral displacement response. RC frames generally yield for an interstory-drift of about 1%, while the performance criterion for Collapse Prevention corresponds to 2.5% for a seismic event with a 10% probability of exceedance in 50 years (10/50).

Then, assuming a brace ductility capacity in the range of µ=εmax/εy=4÷8, BRBs should be designed to yield for an interstory-drift of 0.25% (obtained by dividing an interstory drift of 1% per the ductility capacity µ ) in a 10/50 seismic event. In this way, the maximum displacement demand corresponds to the first RC damaging. While, in case of a 2/50 seismic event (i.e. with a 2% probability of exceedance in 50 years), it seems conservative to not exceed twice the ductility capacity considered for a life safety design.

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In Table 2.7-1 some indicative values of core plastic deformation ratio εmax/εy that may be appropriate to a performance based design are reported. The symbols IO, LS and CP are in place of Immediate Occupancy, Life Safety and Collapse Prevention, respectively.

Table 2.7-1 Acceptance Criteria for BRBs

Core Plastic deformation (εmax/εy)

IO LS CP

0.5 4 8

2.7.9. References

Clark, P., Aiken, I., Kasai, K., Ko, E., and Kimura, I. (1999), “Design Procedures for Buildings Incorporating Hysteretic Damping Devices,” Proceedings 68th Annual Convention, pp. 355–371, Structural Engineers Association of California, Sacramento, CA.

Ko, E., and Field, C. (n.d.) "The Unbonded Brace™: From research to Californian practice". http://www.arup.com/DOWNLOADBANK/download172.pdf

Uang, C-M., Nakashima, M. and Tsai, K-C. (2004). "Research and application of buckling-restrained braced frames". Steel Structures, vol. 4 (2004): 301-313.

Black, C., Makris, N., and Aiken, I. (2002). "Component Testing, Stability Analysis and Characterization of Buckling-Restrained Unbonded BracesTM". PEER Report 2002/08. Pacific Earthquake Engineering Research Center, College of Engineering, University of California, Berkeley.

Uang, C.M. and Nakashima, M. (2004). "Steel Buckling-Restrained Braced Frames". Earthquake Engineering: From Engineering Seismology to Performance-Based Engineering, Chapter 16, Y. Bozorgnia and V.V. Bertero, (eds.) CRC Press, Boca Raton, FL.

Brown, A. P., Aiken, I. D., Jafarzadeh, F. J. (2001). "Buckling Restrained Braces Provide the Key to the Seismic Retrofit of the Wallace F. Bennett Federal Building". Modern Steel Construction, August, 2001.

D’Aniello, M., Della Corte G. and Mazzolani, F.M. (2006). "Seismic upgrading of RC buildings by buckling restrained braces: Experimental results vs numerical modeling". STESSA 2006 – Mazzolani & Wada (eds), Taylor & Francis Group, London, ISBN 0-415-40824-5.

AISC (2005a). "Seismic provisions for structural steel buildings". American Institute of Steel Construction, Chicago, IL.

AISC (2005b). "Commentary on seismic provisions for structural steel buildings". American Institute of Steel Construction, Chicago, IL.

FEMA (2003). "NEHRP recommended provisions for seismic regulations of buildings and other structures". FEMA 450, Federal Emergency Management Agency, Washington, DC.

Lopez, W.A. and Sabelli, R. (2004). "Seismic design of buckling-restrained braced frames". Steel Tips, Structural Steel Educational Council, Moraga, CA.

Eurocode 3 (2003). "Design of steel structures. Part 1-1: General Rules and Rules for Buildings". CEN - European Committee for Standardization.

Mazzoni, S., McKenna, F., Fenves, G.L. (n.d.) "Open System for Earthquake Engineering Simulation. User manual for OpenSees version 1.7.0". Pacific Earthquake Engineering Research Center, University of California, Berkeley. accessed 2006 at http://opensees.berkeley.edu/

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Tremblay, R., Poncet, L., Bolduc, P., Neville, R. and DeVall, R. (2004). "Testing and design of buckling restrained braces for Canadian application". 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada, August 1-6, 2004, Paper No. 2893.

D’Aniello, M., Della Corte, G., Mazzolani, F.M. (2006). "Buckling restrained braces as solution for seismic upgrading of existing RC structures". PROHITECH Datasheet n. 01.06.01.01, WP6, University of Naples Federico II, Italy.

Calado, L., Proença, J.M., Panão, A., NsieriE., Rutenbrg, A., Levy, R., (2006). "Buckling-Restained Braces". PROHITECH datasheet for WP5: innovative materials and techniques.

Eurocode 8 (2003). "Design of structures for earthquake resistance. Part 1: General rules, seismic actions and rules for buildings". December, 2003. CEN - European Committee for Standardization.

AISC/SEAOC (2001). “Recommended Provisions for Buckling-Restrained Braced Frames,” American Institute of Steel Construction/Structural Engineers Association of California Task Groupr.

Black C., Makris N., Aiken I., (2002). Component testing, stability analysis and characterization of buckling restrained braces. PEER Report 2002/08, Pacific Earthquake Engineering Research Center, University of California at Berkeley.

Chen C.H., (2002). Recent advances of seismic design of steel building in Taiwan. International training programs for seismic design of building structures, Taiwan

D’Aniello, M., Della Corte, G. & Mazzolani, F.M., (2006). Seismic Upgrading of RC Buildings by Steel Eccentric Braces: Experimental Results vs Numerical Modeling. Proceedings of the STESSA Conference, Yokohama, Japan, 14-17 August.

Della Corte, G., Mazzolani, F.M., (2006). Full scale tests of advanced seismic upgrading techniques for RC Buildings. Proceedings of the 2nd fib Congress, Naples, Italy, 5-8 June.

Fahnestock L.A., Sause R. & Ricles J.M., (2003). Analytical and experimental studies on buckling restrained braced composite frames. Proceedings of the International workshop on Steel and Concrete Composite Construction (IWSCCC-2003), October, 8-9, Taipei, pp. 177-188.

FEMA 356 (2000). Prestandard and commentary for the Seismic Rehabilitation of Buildings. Building seismic safety Council for the Federal Emergency Management Agency, Washington.

Iwata M., Kato, T. & Wada, A., (2000). “Buckling-restrained braces as hysteretic dampers,” Proceedings of Third International Conference on Behavior of Steel Structures in Seismic Areas (STESSA 2000), Montreal, Canada, pp.33-38.

Mazzolani, F.M., “Seismic upgrading of RC buildings by advanced techniques. The ILVA-IDEM research project”. POLIMETRICA Publisher, Italy 2006.

Mazzolani, F.M., Della Corte, G. & Faggiano, B., (2004). Seismic Upgrading of RC Buildings by means of Advanced Te-chinques: the ILVA-IDEM Project, Proceedings of the 13th World Conference on Earthquake Engineering, Canada.

Mochizuki S., Murata Y., Andou N. & Takahashi S., (1979). Experimental study on buckling of unbonded braces under axial forces: Parts 1 and 2. Summaries of technical papers of annual meeting. Architectural Institute of Japan;.p.1623–6

Mochizuki S., Murata Y., Andou N. & Takahashi S., (1980). Experimental study on buckling of unbonded braces under axial forces: Part 3. Summaries of technical papers of annual meeting. Architectural Institute of Japan; p. 1913–4

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Mochizuki S., Murata Y., Andou N. & Takahashi S., (1982). Experimental study on buckling of unbonded braces under axial forces: Part 4. Summaries of technical papers of annual meeting. Architectural Institute of Japan; p. 2263–4

Sabelli R., Mahin S. & Chang C., (2003). Seismic demands on steel braced frame buildings with buckling-restrained braces. Engineering Structures, Vol. 25 (5).

Sabelli R., Aiken I., (2004). U.S. building-code provisions for buckling-restrained braced frames: basis and development. Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, Canada, CD-ROM: paper no. 1828.

Sabelli R., Lopez W., (2005). Design of Buckling Restrained Braced frames.

Tsai K.C., Huang Y.C., (2002). Experimental responses of large scale BRB frames. Report No. CEER/R91-03, Center for Earthquake Engineering Research.

Tsai, K.C., Lai, J.W., Hwang, Y.C., Lin, S.L. & Weng, Y.T., (2004,a). Research and application of double-core buckling restrained braces in Taiwan. Proceedings of the 13th World Conference on Earthquake Engineering, Canada.

Tsai, K.C., Weng, Y.T., Lin, S.L. & Goel, S., (2004,b). Pseudo-dynamic test of a full-scale CFT/BRB frame: Part1-Performance Based Design. Proceedings of the 13th World Conference on Earthquake Engineering, Canada.

Tremblay R., Poncet L., Bolduc P., Neville R. & De Vall R., (2004). Testing and Design of Buckling Restrained Braces for Canadian Application. Proceedings of the 13th World Conference on Earthquake Engineering, Canada.

Wada A., Nakashima M., (2004). From infancy to maturity of buckling restrained braces research. Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, Canada, CD-ROM: paper no. 1732.

Wakabayashi M., Nakamura T., Katagihara A., Yogoyama H. & Morisono T., (1973). Experimental study on the elastoplastic behavior of braces enclosed by precast concrete panels under horizontal cyclic loading—Parts 1 & 2. Summaries of technical papers of annual meeting, vol. 10. Architectural Institute of Japan, Structural Engineering Section; p. 1041–4

Wakabayashi M., Nakamura T., Katagihara A., Yogoyama H. & Morisono T., (1973). Experimental study on the elastoplastic behavior of braces enclosed by precast concrete panels under horizontal cyclic loading—Parts 1 & 2. Summaries of technical papers of annual meeting, vol. 6. Kinki Branch of the Architectural Institute of Japan; p. 121–8

Watanabe A., Hitomi Y., Saeki E., Wada A. & Fujimoto M., (1988). Properties of brace encased in buckling-restraining concrete and steel tube. In: Proc. of ninth world conf. on earthquake eng, vol. IV. p. 719–24.

2.8. EBF – Eccentric braced frames

This section was prepared in accordance with data-sheets no. 9-13 “Design methods for eccentric braces” prepared by M. D’Aniello, G. Della Corte and F. M. Mazzolani from University of Naples “Federico II” (UNINA).

This section makes a description of the technique and reviews the analytical available methods.

2.8.1. Description of EB technique

The eccentric braced frame (EBF) is a hybrid lateral force-resisting system. In fact, it can be considered as the superposition of two different framing systems: the moment-resisting frame and the concentrically braced frame. EBFs can combine the main advantages of each conventional framing system and

153

minimize their respective disadvantages, as well (Bruneau, Uang & Whittaker, 1998). In general, EBFs possess high elastic stiffness, stable inelastic response under cyclic lateral loading, and excellent ductility and energy dissipation capacity.

The key distinguishing feature of an EBF is that at least one end of each brace is connected to isolate a segment of beam called “link”. EBF arrangements, usually adopted, are shown in Figure 2.8-1.

Figure 2.8-1EBF configurations

In each framing scheme of Figure 2.8-1 the links are identified by a bold segment. The four EBF arrangements here presented are usually named as split-K-braced frame, D-braced frame, V-braced and finally inverted-Y-braced frame.

In eccentric braced frames (EBFs), forces are transferred to the brace members through bending and shear forces developed in the ductile steel link. The link is designed to yield and dissipate energy while preventing buckling of the brace members. As it is well known, the inelastic behaviour of a link is significantly influenced by its length. The shorter is the link length, the greater is the influence of shear forces on the inelastic performance. In particular, shear yielding is very ductile with an inelastic capacity considerably in excess of that predicted by the web shear area.

Research on the behaviour of EBFs started in the second mid-1970s (Roeder & Popov 1977, Roeder & Popov 1978) and continued up today. All these studies confirmed the reliability of EBFs to resist horizontal actions.

Shear links in eccentrically braced frames have been studied for new buildings (Kasai & Popov 1983, Popov & Malley 1983, Hjelmstad & Popov 1986, Ricles & Popov 1987, Engelhardt & Popov 1989), but their use is now also becoming aviable method to retrofit RC structures and for protecting bridges. Two examples of bridge retrofitting are Richmond San Rafael Bridge (Itani 1997) and the use of shear links in the tower of the new San Francisco-Oakland Bay suspension cable bridge (Nader et al. 2002)

In RC frames, the concrete beams are incapable to perform as a ductile link for the steel bracing system that is inserted in the frame bays. Hence, the need to adopt a Y-inverted bracing configuration, with a vertical steel link, can be easily recognized. Moreover, bolted connections at the link ends are required, what could have the advantage to permit replacement of the dissipative members (links) after a damaging earthquake.

An example of seismic retrofitting of RC structures by means of EBF systems has been developed within the ILVA-IDEM project (Mazzolani, 2006), where EBFs have been applied for seismic upgrading of an existing two-story RC structure, which has been subjected to pushover test [1]. The geometry of the RC structure, that has been equipped with the EBFs and then tested, is shown in Figure 2.8-2.

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Figure 2.8-2Geometry of tested RC structure in the ILVA-IDEM project

This experimental investigation on removable bolted links demonstrated the technological feasibility of the solution. Performance of short removable links and possibility to be easily replaced makes them attractive for retrofitting RC structures. Figure 2.8-3 highlights the plastic deformation occurred in links during the test and testifies the large local ductility that this system can guarantee.

155

a) b)

Figure 2.8-3 Link shear hinging(a); halfway stage of experimental test (b).

2.8.2. Analytical methods for the design of EB

The main purpose in the design of EBFs is to restrict the inelastic action to the links and to keep the framing around the links in the elastic range by making them able to sustain the maximum forces that the links can develop. Design using this strategy should ensure that the links act as ductile seismic fuses and preserve the integrity of the whole frame. For this reason, the other components of the framing system (such as diagonal braces, columns and link connections) should be designed for the forces generated by the full yielding and strainhardening of dissipative links. To do this it is important to clarify the distribution of internal actions in a EBF system and define a relationship between frame shear force and link shear force. This relationship depends only on the EBF configuration; in fact, it is the same if the link response is elastic or plastic. The design actions in links can be calculated using equilibrium concepts. For example in a split-K-braced EBF (shown in Figure 2.8-4), assuming that the moment at the center of the link is equal to zero, the link shear force V can be expressed as:

F HVL⋅= (2.8-1)

where F is the lateral force, H is the interstory height and L is the bay length.

Figure 2.8-4 Design action in link for a split-K-braced EBF configuration.

In case of an inverted-Y-braced EBF (Figure 2.8-5), assuming that the moment at the brace connections is equal to zero (i.e. in case of pinned braces), the link shear force V can be expressed as:

V F= (2.8-2)

156

where F is again the lateral force.

Figure 2.8-5. Design action in link for an inverted-Y-braced EBF configuration.

The link inelastic performance essentially depends on its length and crosssection properties. For a given cross-section, the link length controls the yielding mechanism and the ultimate failure mode. Short links are mainly dominated by a shear mechanism, instead flexure controls link response for long links. Moreover, intermediate links are characterized by a M-V interaction.

Assuming perfect plasticity, no flexural-shear interaction and equal link end moments, the theoretical dividing point between a short link (governed by shear) and a long link (governed by flexure) is a length of e= 2Mp/Vp where the plastic bending moment M =Z⋅fy (in which Z is the plastic modulus and fy is the

value of steel yielding stress) and V =0.55⋅fy (d - 2tf ) (in which d is the depth of the cross section and tw is the web thickness). A large number of experimental activities (such as Kasai & Popov 1986, Hjelmstad & Popov 1983, Foutch 1989) indicate that the assumption of no M-V interaction is reasonable, but an assumption of perfect plasticity is not correct. In fact, substantial strain hardening occurs in shear links. According to tests performed on American wide-flange steel profiles, the average ultimate link shear forces reach the value of 1.5Vp. One implication of this strain hardening is that both shear and moment yielding occur over a wide range of link lengths. In case of shear links, end moments substantially greater than Mp can be developed. In fact, shorter is the link, greater the bending moment

will be in order to necessarily have V= 2Me. The large end moments, combined with the significant strain gradient that occurs in links, lead to very large flange strains, which in case of steel built up sections can prompt the flange welds failure. Kasai and Popov (1986) estimated that the maximum link end moments can be assumed 1.2 Mp . Thus, from link static of Figg. 4 and 5, if the end moments are

limited to 1.2 Mp and the link shear is assumed to reach 1.5Vp, the limiting link length is

2 (1.2 )1.6

1.5p p

p p

M Me

V V⋅

= =⋅

(2.8-3)

Then the following equations can be used to classify the link mechanical response:

Shear (short) links: e≤ 1.6Mp/Vp (3)

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Intermediate links: 1.6Mp/Vp<e< 2.5Mp/Vp (2.8-4)

Flexure (long) links: e≥ 2.5Mp/Vp

The ultimate failure modes of short and long links are quite different. In particular, inelastic web shear buckling is the ultimate failure mode of short links. This buckling mode can be delayed by adding web stiffeners (Figure 2.8-6).

Hjelmstad & Popov (1983) developed several cyclic tests in order to relate the web stiffeners spacing to link energy dissipation, and Kasai & Popov (1986) subsequently developed simple rules to relate stiffeners spacing and maximum link inelastic rotation γ up to the web buckling. Starting from the consideration that the link web buckling modes are very similar to the ones of plates under shear loading, they applied the plastic plate shear buckling theory to relate the stiffeners spacing to the maximum deformation angle of a shear link. In fact, the theoretical plastic buckling shear stress τb was obtained

starting from the elastic buckling solution τE and can be expressed as:

b Eτ η τ= i (2.8-5)

where η is a plastic reduction factor, that is a function of plate strain hardening history and was

experimentally derived, while the elastic buckling shear stress τE can be expressed as:

22

2

1( )12(1 )E s

E Kπτ αν β

⎛ ⎞= ⎜ ⎟− ⎝ ⎠i (2.8-6)

in which ν is the Poisson ratio, ks is a plate buckling coefficient, which is a function of the aspect ratio α and the boundary conditions, that are assumed in this case as clamped end conditions. In particular the aspect ratio is equal to α = a b, where a is the stiffener spacing and b is the web panel height, while β is

the web panel height-to-thickness ratio that is equal to β = b tw , where tw is the web thickness. The

secant shear modulus Gs (Gerard 1948 and 1962) for the shear link was defined as:

sG τγ

= (2.8-7)

in which γ is the maximum shear deformation angle attained at the point of web buckling, which has to

be experimentally measured, and τ is the corresponding shear stress approximately defined as

w = /A Vτ , where V is the shear force and Αw is the web area.

It was found that there is a linear relationship between η and the ratio Gs/G in which G is the elastic

shear modulus given by G=E/2(1+ )ν , where E is the Young’s modulus and =0.3ν . Hence, this relationship is expressed by:

3.7 /sG Gη = (2.8-8)

Substituting Eqs. (2.9-7) and (2.9-8) into Eq. (2.9-5) with bτ τ= at an incipient buckling stage it results:

3.7 bb EG

ττ τγ

= (2.8-9)

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Eq. 2.9-9 can be rearranged leading to:

3.7 Eb G

τγ γ= = (2.8-10)

Then using 2.9-6 and 2.9-10 gives: 2

18.7 ( )b sKγ αβ

⎛ ⎞= ⎜ ⎟⎝ ⎠i (2.8-11)

Furthermore, instead of using the parameter β it is more convenient to approximate it by a beam depth to

web thickness ratio d/tw . In addition, since it has been pointed out that the web stiffeners are effective in reducing the possibility of lateral torsional buckling (Hjelmstad & Popov 1983), a maximum spacing of a/d=1 is adopted. Considering these factors, for the range of γ from 0.03 to 0.09 rad, Eq.2.9-11 can be conservately approximated as :

5 Bw w

a d Ct t

+ = (2.8-12)

where the constant CB is equal to 56, 38, and 29, respectively for γ equal to 0.03, 0.06 and 0.09 rad. Thus rearranging Eq. (13), it was possible to draw the following simple expressions for each required link deformation capacity (Kasai & Popov 1986):

29 / 5wa t d= − for 0.09radγ = (2.8-13)

38 / 5wa t d= − for 0.06radγ = (2.8-14)

56 / 5wa t d= − for 0.03radγ < (2.8-15)

where a is the distance between equally spaced stiffeners, d is the link depth and tw is the web thickness. In order to study the effect of inelastic web buckling in links, Popov & Engelhardt (1988) reported the results of two series of cyclic tests on both stiffened and unstiffened isolated links. In the first series, fifteen full-size shear links were subjected to equal end moments to simulate the performance of a typical link in a split-K-braced frame. In this case, the unstiffened links showed severe web buckling shortly after yielding, hence their load-carrying capacity rapidly reduced.

a) inelastic response of stiffened short link b) inelastic response of unstiffened short link

Figure 2.8-6 Plastic deformation of short links.

The specimens provided with stiffeners equally spaced on both link side according to Eq. (2.9-13) showed a significant improvement in performance, achieving large inelastic rotations with full rounded hysteretic loops, confirming a plastic rotation capacity of about 0.10 rad under cyclic excitation and 0.20

159

rad under monotonic loading. Moreover, links with stiffeners on only one side have been tested and their performance was adequate in shear links for beams of moderate depth, i.e. link depth up to 24in or 600mm. In the second series, shear links were subjected to unequal end moments in order to simulate the performance of links located next to a column. In fact, in this configuration the typical ratio of elastic end moments can be on the order of 2 to 4 or more. If steel behaved as a perfectly plastic material, the equalization of link end moments could occur if the link is loaded to its ultimate state. However, because of steel strain hardening, this end moment equalization may not occur. The tests conducted on links with unequal end moments permitted to understand that:

• For very short links, i.e. e≤Mp/Vp, unequal end moments remain unequal hroughout the loading history up to link failure. The ultimate link end moment at the column face is significantly larger than the predicted equalized moment. As link length increases, the ultimate link end moments tend to equalize. In particular, when link length is about e≥1.3Mp/Vp , full equalization of end moments can occur.

• The initial unequal end moments have little effect on the plastic rotation capacity and on the overall hysteretic behaviour.

• Interaction between bending moment and shear force can be neglected when predicting the yield limit state of a link. In fact, even in the presence of high shear force, the full plastic moment can be assumed rather than a reduced value based on flanges only. This result is very important because contradicts the predictions from plastic theory, but it is confirmed by experimental tests. Moreover neglecting M-V interaction simplifies the analysis and design of shear links.

These results are very important because they permit to calculate the forces generated by the fully yield and strain hardened links. In fact, for links adjacent to columns, the ultimate link end moments can be taken as:

/ 2a b ultM M V e= = i for 1.3 / 1.6 /p p p pM V e M V≤ ≤ (2.8-16)

a pM M= ; b ult pM V e M= −i for 1.3 /p pe M V≤ (2.8-17)

where Ma and Mb are the link end moments at the column face and at the opposite end of the link. For links not adjacent to columns, the ultimate moments given by Eq. (2.9-16) are appropriate for links of any length.

Steel links are subjected to high levels of shear forces and bending moments in the active link regions. In the analysis of the performance of links, elastic and inelastic deformations of both the shear and flexural behaviours have to be taken into consideration. Few researchers attempted to develop link models for the dynamic inelastic analysis of EBFs (Ricles & Popov 1994, Ramadan & Ghobarah 1995). Ramadan & Ghobarah modelled the link as a linear beam element with six nonlinear rotational and translational springs at each end.

Three rotational bilinear springs were used to represent the flexural inelastic behavior of the plastic hinge at the link end represented by the multilinear function shown in Figure 2.8-7a. Three translational bilinear springs were used to represent the inelastic shear behavior of the link web represented by the multilinear function shown in Figure 2.8-7b.

Under the effect of cyclic loading, moment yielding obeys the kinematic hardening rule while shear yielding follows a combination of both isotropic and kinematic hardening. For the shear spring, a special function was derived to account for the upper bound of the shear capacity (Ramadan & Ghobarah 1995).

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The function determines the maximum attainable shear force capacity after a certain amount of plastic action. This function has the following form:

( )101 0.8 1 spV V e−⎡ ⎤= + −⎣ ⎦ (2.8-18)

where Vp is the initial shear yield strength and S is the accumulated strain in the shear spring.

Figure 2.8-7 a) Flexural inelastic behavior of link plastic hinge; b) Shear inelastic behavior of link

plastic hinge

2.8.3. References:

Bruneau M., Uang C.M., Whittaker A., (1998). “Ductile design of Steel

Structures“, McGraw- Hill

Della Corte G., D’Aniello M., Barecchia E., Mazzolani F.M. (2006) “Experimental

tests and analysis of short links for eccentric bracing of RC buildings”.

Engineering Structures (Submitted for publication).

Engelhardt M.D, Popov E.P,, (1989). On Design of Eccentrically Braced Frames. Earthquake Spectra, vol.5, No.3, 495-511.

Engelhardt M.D, Popov E.P,, (1992). Experimental performance of long links in eccentrically braced frames. Journal of Structural Engineering, Vol.188, No.11:3067-3088.

Ghobarah A., Elfath A.H., (2001). Rehabilitation of a reinforced concrete frame using eccentric steel bracing. Engineering Structures, vol. 23, 745–755

Hjelmstad K.D., Popov E.P., (1983). Cyclic Behavior and Design of Link Beams. Journal of Structural Engineering, vol.109, No. 10, 2387-2403,.

Itani A, Douglas B.M. & ElFass S., (1998). Cyclic behavior of shear links in retrofitted Richmond-SanRafael Bridge towers. Proceedings of the First World Congress on Structural Engineering – San Francisco, Paper No. T155-3, Elsevier Science Ltd.

Kasai K., Popov E.P,. (1986a). General Behavior of WF Steel Shear Link Beams. Journal of Structural Engineering, vol.112, No. 2, 362-382, 1986

Kasai K., Popov E.P., (1986b). Cyclic Web Buckling Control for Shear Link Beams. Journal of Structural Engineering, vol.112, No. 3, 505-523.

Malley J.O., Popov E.P., (1984). Shear Links in Eccentrically Braced Frames. Journal of Structural Engineering, vol.110, No. 9, 2275-2295.

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Mazzolani, F.M., “Seismic upgrading of RC buildings by advanced techniques. The ILVA-IDEM research project”. POLIMETRICA Publisher, Italy 2006.

Mc Daniel, C. C., Uang, C. & Seible, F., (2003). Cyclic Testing of Built-Up Steel Shear Links for the new Bay Bridge. Journal of Structural Engineering, vol. 129, No 6.

Nader M., Lopez-Jara J. & Mibelli, C., (2002). Seismic Design Strategy of the New San Francisco-Oakland Bay Bridge Self-Anchored Suspension Span, Proceedings of the Third National Seismic Conference & Workshop on Bridges & Highways, MCEER Publications, State University of New York, Buffalo, NY.

Popov E.P., Engelhardt M.D., (1988). Seismic Eccentrically Braced Frames. Journal of Construction and Steel Research, (10) 321-354.

Popov E.P., Malley J.O., (1983) Design of links and beam-to-column connections for eccentrically braced steel frames. Report No. EERC 83-03.

Berkeley (CA): Earthquake Engineering Research Center, University of California. Ramadan T, Ghobarah A., (1995). Analytical model for shear–link behavior. J Struct Engng, ASCE, 121(11):1574–80.

2.9. Metal shear panel

2.9.1. Introduction

This section was prepared in accordance with data-sheets no. 9-14 “Metal shear panels for seismic upgrading of existing buildings” prepared by G. De Matteis, A. Formisano, S. Panico, F. M. Mazzolani from University of Chieti/Pescara “G. d’Annunzio” (UNICH) and University of Naples “Federico II”, Italy (UNINA).

This section makes a description of the technique, interpreting models like frame system and shear panel system and the numerical models.

2.9.2. Description of the device/technique

Seismic upgrading of RC buildings represents a topic of remarkable interest in the field of structural engineering. In this framework, among solutions based on the introduction of new structural components, metal shear panels can be profitable used. These devices, which are obtained by inserting a metallic panel inside a frame composed by steel beams and columns, are characterised by a low erection cost and high speed of installation. The use of such a kind of system seems to be very interesting, since the insertion of shear panels within existing structures could represent an effective way to increase their strength, stiffness and energy dissipation capacity, making them able to withstand seismic actions. Lightness, versatile ductility, strength and stiffness, architectural function as complementary or substitutive cladding elements of the existing ones, little flexural interaction with beams and columns are few of the important advantages that make metal panel systems competing of others conventional and innovative existing systems in the seismic retrofitting field.

Metal shear panels can be categorised into two different typologies, namely compact and slender shear panels (De Matteis et al., 2003 a, b). For seismic retrofitting purposes of existing buildings, the use of slender shear panels results to be more appropriate than compact ones due to both easier fabrication and lesser weight, other than the valuable structural contribution that they are able to provide. Slender panels can be conformed according to two different structural configurations (Astaneh-Asl, 2001). The first one, which may be defined as standard (Figure 2.9-1a), is based on the use of pin-jointed steel frames: in such a case the only seismic-resistant system is represented by the shear wall, while the remaining part of the structure must be designed in order to carry gravity loads only. The second solution, which leads

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to the adoption of a dual system (Figure 2.9-1b), is based on coupling steel plate shear walls with moment resisting frames. Therefore, the external frame has to be intended as primary structure, which participates significantly to the absorption of the horizontal forces, providing an additional contribution to the lateral strength ensured by shear walls.

In both cases, the connection between shear panels and the members of the surrounding frames can be realized by using bolts or by welding the panel to appropriate plates preventively fixed to the beam and column members.

Figure 2.9-1 Shear walls configurations: a) standard system; b) dual system

Comparing the current system with the traditional steel lateral load resisting systems (concentric or eccentric bracings), it has to be observed that the former is easily compatible with openings, either by the insertion of opportune stiffening elements surrounding the open surface or by using two separate steel shear walls connected among them through the floors beams (Astaneh-Asl and Zhao, 2002).

2.9.3. Interpreting models

The frame system

In order to define the behaviour of slender shear walls, the structural analogy existing with the behaviour of a stiffened girder may be applied (Timler, 2000). In fact, the columns where the shear plates are anchored can be compared to the beam flanges, the shear plate to the web of a girder and the horizontal beams placed at each level can be considered as the transversal stiffeners of the web girder. Nevertheless, the above analogy may be limited by a different stiffness ratio between the single parts of the system. In particular, a reduced flexural stiffness of the shear wall columns could cause a significant modification of the tension field inclination angle, avoiding that the resisting mechanism is activated on the whole panel surface. To this purpose, Kuhn et al. (Thorburn et al., 1983) established the minimum value of the second moment of area of columns in order to avoid their excessive deformation under the loads transferred by the shear plate:

L

ht0,00307I4s

c ≥ (2.9-1)

This problem is not relevant for the intermediate beams of shear walls. In fact they are subjected on both sides to a stress state induced by shear plates which have the same intensity but opposite sign, hence they do not produce any effect (Figure 2.9-2).

STEEL PLATE SHEAR WALL

1.1. PINNED FRAME

1.2. MOMENT RESISTING FRAME

a) b)

STEEL PLATE SHEAR WALL

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Figure 2.9-2 Effect of the tension field mechanism on the intermediate beam of a steel plate shear wall

On the contrary, upper and lower beams of a shear wall must possess a sufficient flexural stiffness in order to absorb the stresses developed by the shear panels. With regard to columns, their stiffness is an important parameter for both the force distribution within the panel and the definition of the global system flexibility. This is due to two separate effects: the flexural deformation of columns, which depends on the applied cross-section, and the horizontal forces generated by the tension field developed into the panel.

The shear panel system

Among proposed theoretical methods for interpreting the behaviour of slender shear panels, the PFI model (Sabour-Ghomi and Roberts, 1991) allows the application of the following simplified relationships to determine the stiffness (Kw) and the ultimate strength (Fwu):

⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅+⋅⋅=

2sin2Θσ

τtbF tycrwu ;

dtb

Esin2Θσ2

Gτ

2sin2Θστ

Ktycr

tycr

w⋅

⋅⋅+

⋅+= (2.9-2)

where2

2

2

cr dt

)ν(112Eπkτ ⎟

⎠⎞

⎜⎝⎛⋅

−⋅⋅⋅= is the critical shear stress and the plate factor k is a coefficient

depending on both the a=b/d ratio and the boundary conditions of the panel.

In particular, when the slenderness ratio b/t of the applied shear plate is quite large, the pre-critical behaviour of the panel can be neglected assuming τcr = 0. In addition, also the relationship related to the evaluation of the panel stiffness can be simplified, obtaining the following expression:

d4

tLEK⋅

⋅⋅= (2.9-3)

where L is the shear plate width.

A more refined method to define the shear panel behaviour in the post-critical field is provided by the Strip Model (Thorburn et al., 1983), which interprets the behaviour of the plate by means of inclined strips having the same panel thickness t and a cross-section As given by the following expression:

( ) tn

sinαhcosαLA ss ⋅⋅+⋅= (2.9-4)

where n is the number of stripes (at minimum equal to ten), in which the panel is subdivided and α represents their inclination angle corresponding to the diagonal tension field inclination. Such a method can be simply implemented by means of commercial finite element programs, like the SAP 2000 (CSI, 2003), modelling the stripes as trusses able to develop tensile plastic hinges (Figure 5).

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Figure 2.9-3 Modelling of the shear panel by means of Sap 2000 (strip model theory)

2.9.4. References:

Astaneh-Asl, A. (2001). “Seismic Behavior and Design of Steel Shear Walls”. Steel TIPS Report, Structural Steel Educational Council, Moraga, CA.

Astaneh-Asl, A., Zhao, Q., (2002). “Cyclic behaviour of traditional and an innovative composite shear wall”. Report No. UCB-Steel-01/2002, Department of Civil and Env. Engineering, University of California, Berkeley.

Computer and Structures, Inc., (2003). “SAP 2000 Non linear Version 8.23”. Berkeley, California, USA.

De Matteis, G., Mistakidis, E.S., (2003). “Seismic retrofitting of moment resisting frames using low yield steel panels as shear walls”. Proceedings of the 4th International Conference on Behaviour of Steel Structures in Seismic Areas (STESSA 2003), Naples, pp. 677-682.

De Matteis, G., Landolfo, R., Mazzolani, F. M. (2003a). “Seismic response of MR steel frames with low-yield steel shear panels”. Journal of Structural Engineering, 25.

De Matteis, G., Mazzolani, F. M., Panico, S. (2003b). “Steel bracings and shear panels as hysteretic dissipative systems for passive control of MR steel frame”. Costruzioni Metalliche, 6.

De Matteis, G., Formisano, A., Panico, S., Calderoni, B., Mazzolani, F. M., (2006). “Metal shear panels”. Seismic upgrading of RC buildings by advanced techniques – The ILVA-IDEM Research Project, Mazzolani, F. M. co-ordinator & editor, Polimetrica International Scientific Publisher, Monza, pp. 361-449.

Formisano, A., De Matteis, G., Panico, S., Calderoni, B., Mazzolani, F.M., (2006). “Full-scale experimental study on the seismic upgrading of an existing RC frame by means of slender steel shear panels”. Proceedings of the International Conference on Metal Structures (ICMS ‘06), Poiana Brasov, September 16-18, pp. 609-617.

Hibbitt, Karlsson, Sorensen, Inc., (2004). “ABAQUS/Standard, v. 6.4”, Patwtucket, USA.

Mazzolani, F.M., co-ordinator & editor, (2006). “Seismic upgrading of RC buildings by advanced techniques – The ILVA-IDEM Research Project”. Polimetrica International Scientific Publisher, Monza.

Sabouri-Ghomi, S., Roberts, T. M. (1991). “Nonlinear Dynamic Analysis of Thin Steel Plate Shear Walls”. Computers & Structures, Vol. 39., No. 1/2, pp. 121-127.

Thorburn, L. J., Kulak, G. L., Montgomery, C. J. (1983). “Analysis of Steel Plate Shear Walls”. Struct. Eng. Rep No. 107, Dept. of Civ. Engrg., University of Alberta, Edmonton, Alta., Canada.

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Timler, P. A. (2000). “Design Evolution and State-of-the-Art Development of Steel Plate Shear Wall Construction in North America”. Proc. of the 69th Annual SEAOC Convention, Vancouver, British Columbia, Canada, pp. 197-208.

2.10. FRP – Fiber reinforced polimers

2.10.1. Introduction

This section was prepared in accordance with data-sheets no. 9-15 “Design methods for fiber reinforced polymers material” prepared by E. Barecchia, G. Della Corte, F. M. Mazzolani from University of Naples “Federico II”, Italy (UNINA).

This section make a description of the FRP available systems and make an compressive review of application advantage from flexural strengthening, avoiding lap-splice failure, confinement effect, failure modes of the connection and performance criteria.

2.10.2. Description of the FPR device/technique

Fiber Reinforced Polymers (FRP) are constituted by continuous reinforcing fibres with polymeric matrix. They are composite materials with a prevalent linear elastic behaviour up to failure. They are widely used for strengthening of civil structures with particular reference to the reinforced concrete (RC) structures. There are several advantages of using FRPs: high mechanical properties, lightweight, resistance to corrosion, etc. FRP are available in several geometries from laminates, used for strengthening of members with regular surfaces, to bi-directional fabrics easily adaptable to the shape of the member to be strengthened. FRP materials are also suitable in the applications where the aesthetic appearance of the original structures needs to be preserved (buildings of historic or artistic interest) or where strengthening with traditional techniques can not be effectively employed.

Composite materials are characterized by two materials having physical and mechanical properties quite different: the polymer matrix and the reinforcing fibres. The mechanical behaviour of composite materials is related to several characteristics such as the geometry and dimensions, the fibre orientation with respect to the loading direction and fibre concentration (volume fraction). FRP systems suitable for external strengthening of structures may be classified as follows:

• Pre-cured: Manufactured in various shapes by pultrusion or lamination and directly bonded to the structural member to be strengthened;

• Wet lay-up: Manufactured as FRP sheets or fabrics, and bonded to the support with resins at the job site;

• Pre-preg: Manufactured with unidirectional or multidirectional fiber sheets or fabrics pre-impregnated at the manufacturing plant with partially polymerized resin. They may be bonded to the member to be strengthened with (or without) the use of additional resins.

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Figure 2.10-1 FRP composition.

2.10.3. Analytical methods for the design of FRP General principles

In composite materials, fibres provide both loading carrying capacity and stiffness to the composite while the matrix is necessary to ensure sharing of the load among fibres. Most commons FRP materials are made of fibres with high strength properties, while their strain at failure is lower than that of the matrix.

Figure 2.10-2 shows typical stress-strain relationship for fiber, matrix, and the resulting composite material. The resulting FRP material has lower stiffness than fibres and fails at the same strain, εf,max, of the fibres themselves. In fact, beyond such ultimate strain, load sharing from fibres to the matrix is prevented.

Figure 2.10-2 Stress-strain relationship of fibres, matrix and composite system

Stress-strain relationship of fibres, matrix and composite system The FRP strengthening system shall be located in areas where tensile stresses are to be carried out. The compressive loading capacity of the FRP must be neglected in each phase of the design procedure. A strengthening application shall be designed such that deterioration over the design service life of the strengthened structure does not impair its performance below the intended level. Environmental conditions as well as the expected maintenance program need to be carefully addressed.

Design with FRP composites shall be carried out both in terms of serviceability limit state (SLS) and ultimate limit state (ULS), as defined by most common design building code. Structures and structural members strengthened with FRP shall be designed to have design strength, Rd, at all sections at least

167

equal to the required strength, Ed, calculated for the factored load and forces in each loading combination.

The design values (Rd) are obtained from the characteristic values (Rk) through appropriate partial factors (γ) different for each limit state as further indicated and the η conversion factor accounting for special design problems:

1d kR Rη

γ= (2.10-1)

The partial safety factors are:

1. γm for materials and products (it depends on the type of the materials);

2. γRd for resistance models (it depends on the resistance model such as bending, shear/torsion, confinement);

The η conversion factor takes into account the environmental effects such as the damage of resins due to the alkaline effects, the effects of moisture absorption, the effects of temperature on the viscous response of both resin and composite, the exposure to freeze and thermal cycles, the ultraviolet radiations causing a certain degree of brittleness and surface erosion.

Figure 2.10-3 Typical application of FRP in strengthening.

Flexural strengthening

Flexural strengthening is necessary for structural members subjected to a bending moment larger than the corresponding flexural capacity. The strengthening in bending may be carried out by applying one or more laminates or one or more sheets to the tension side of the member to be strengthened.

Flexural design at ULS of FRP strengthened members requires that both flexural capacity, MRd, and factored ultimate moment, MSd, satisfy the following equation:

Sd RdM M ≤ (2.10-2)

ULS analysis of RC members strengthened with FRP relies on the following fundamental hypotheses:

• Plain section remain plane;

• Perfect bond between FRP and concrete;

• Concrete does not react in tension.

• Constitutive laws for concrete and steel are accounted for according to the current building code.

• FRP is considered a linear-elastic material up to failure.

The bending reinforcement may be applied out both on columns and beams. Recent experimental tests (Della Corte et al, 2004, 2005 a, b, c) proposed an example of seismic strengthening of an existing gravity load designed RC structure by means of column bending reinforcement. Starting from a damaged

168

RC structure, previously tested in the original condition, the rehabilitation operation consisted in the application of pre-preg lamina along the columns of the structure, and in the application of transversal wet lay-up sheets (Figure 2.10-4).

Thanks to this type of reinforcement, the structure exhibited a beam-type collapse mechanism (in the first test the structure developed a column type mechanism) and an increase of strength (about 80%), stiffness (about 6 times) and maximum top displacement capacity (more than 100%). Further information on the experimental activity can be found in Mazzolani (2006).

Figure 2.10-4 Seismic rehabilitation of columns (Della Corte et all.)

In general, FRP can be used in the seismic field for favouring the most ductile failure mechanisms such as by eliminating brittle shear failures and forcing the formation of ductile flexural plastic hinges in the beam or in the beam-to-column joint. Some recent experimental tests carried out on half-scale laboratory models of interior beam-to-column joints of RC frame structures showed appreciable increase in strength (up to 53%) and ductility (up to 42%) of joints Mosallam (2000). El-Amoury and Ghobarah (2002) present experimental results of tests carried out on plain RC and G-FRP reinforced RC beam-column joints, showing the possibility to avoid the shear failure of the joint through the externally bonded composite reinforcement and forcing the plastic hinge to form by flexure at the beam end.

Figure 2.10-5 The tests setup and the retrofitting schemes carried out by El Amoury and Gobarah

One of the (few) analytical studies of FRP-strengthened beam-to-column joints is reported by Parvin and Granata (2000), who developed numerical finite element models of exterior beam-to-column joints reinforced by using FRPmaterials and compared them with the response of an un-reinforced control specimen. The reinforcement was supposed to be both in the longitudinal and transverse directions of both beam and column, with a fiber wrap placed at the corner deviations in order to absorb peeling stresses. Results showed an increase in the moment capacity of up to 37%. Prota et al. (2003, 2004) carried out physical tests on joints reinforced using near surface mounted (NSM) FRP round bars passing through the joint and, thus, integrating the shear-induced tensile strength of the concrete in the joint. Both monotonic and cyclic tests were performed, again showing promising results in terms of both strength and ductility capacity improvement. The possibility to control the local failure mode of RC

169

structural members is testified also by the experimental and numerical results of Lee et al. (2004). These tests show that C-FRP wrapping can produce an increase of the member shear strength large enough to allow plastic hinging in bending.

Avoiding lap-splice failure

Extensive experimental results on the effects of FRP wrapping of RC rectangular columns with lap-splices of existing longitudinal bars are reported in Bousias et al. (2004). Their study includes variation of parameters such as the type of bar, the length of splices, the number of FRP wrapping layers, the longitudinal length of the FRP wrapping, in addition to the bond properties of the bars. The Authors indicate that there was no appreciable improvement of the response in case of smoothed bars with hooked ends, independent of the examined parameter values. In case of straight ribbed bars, the increase of the number of C-FRP layers (from 2 to 5 layers) slightly improved the effectiveness of the wrapping, but the improvement effectiveness was not commensurate to the number of C-FRP plies and the effects were also strongly dependent on the length of the existing steel reinforcement lap-splices. In particular, the Authors indicate that the adverse effects of short lap-splices cannot be fully removed by the FRP-wrapping technique if the lap splicing is as short as 15 bar-diameters.

Analogous results were obtained by Yalçin et al. (2004), who conducted tests on RC columns with a rectangular cross section wrapped in the plastic hinge zone with C-FRP sheets. The Authors suggest that wet-lay-up C-FRP sheets do not provide the required confinement stress improving the bond-slip response in case of lap splices of longitudinal straight bars. Contrary, this technique was effective in case of continuous longitudinal bars.

Figure 2.10-6 Comparison between RC columns with and without C-FRP wrapping layers (Yalçin

et al, 2004).

Results of static cyclic tests on hollow square-section bridge piers (1:4 scaled), strengthened with both FRP wrapping and additional longitudinal FRP reinforcement are given in Pavese et al. (2004). It is indicated that, in case of usual lap splices of existing longitudinal steel reinforcement at the base of the pier, FRP wrapping does not provide a large enough increase of confinement able to guarantee the transfer of the tensile forces in the cross section through the lapped steel bars. In this case, additional longitudinal FRP reinforcement is required. However, the basic problem of the foundation-anchoring of this newly added reinforcement must still be solved, in such that it proves to be effective under large tensile forces, but keeping the simplicity of the plain FRP system.

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Figure 2.10-7 Comparison between several hollow square-section in the unreiforced and

strengthened configurations (Pavese et al., 2004).

Schlick and Breña (2004) presented an experimental study on the use of FRP for wrapping the plastic hinge region of bridge columns with a circular cross section. The Authors indicate that FRP jackets, fabricated with a wet-lay-up procedure, changed the failure mode of the tested specimens from a nonductile lap-splice failure at the base to a ductile flexural plastic hinge failure mode. Besides, the confining pressure of the FRP jackets increased the lateral bending strength between 19% and 40%, meanwhile maintaining the integrity of the column by avoiding the longitudinal bar buckling at large lateral displacements.

Figure 2.10-8 Experimental specimens tested by Schlick and Breña (2004).

The possibility of using FRP wrapping for improving the inelastic response of plastic hinges of circular-section RC columns, with lap-splices of longitudinal bars, is also indicated by the experimental results obtained by Chung et al. (2004), who tested bridge piers in a 1:2.5 scale.

Confinement

Appropriate confinement of reinforced concrete members may improve their structural performance. Confinement of RC member with FRP is necessary for structural members subjected to concentric or slightly eccentric axial loads larger than the corresponding axial capacity. In particular, it allows the increase of the following:

• Ultimate capacity and strain for members under concentric or slightly eccentric axial loads.

171

• Ductility and capacity under combined bending and axial load, when FRP reinforcements are present with fibres lying along the longitudinal axis of the member.

Confinement of RC members can be realized with FRP sheets placed along the member perimeter both as continuous or discontinuous external wrapping. The increase of axial capacity and ultimate strain of FRP-confined concrete depends on the applied confinement pressure. The latter is a function of the member cross section and FRP stiffness. FRP-confined members (FRP is linear-elastic up to failure), unlike steel confined members (steel has an elastic-plastic behaviour), exert a lateral pressure that increases with the transversal expansion of the confined members. Failure of RC confined member is attained by fiber rupture.

Design at ULS of FRP confined members requires that both factored design axial load, NSd, and factored axial capacity, NRcc,d, satisfy the following Equation:

N Sd ≤ N Rcc,d (2.10-3)

For non-slender FRP confined members, the factored axial capacity can be calculated as follows:

,1

Rcc d c cc s ydRd

N A f A fλ

= ⋅ ⋅ + ⋅ (2.10-4)

where the partial factor or γRd shall be taken equal to 1.10; Ac and fccd represent member cross-sectional area and design strength of confined concrete; As and fyd represent area and yield design strength of existing steel reinforcement, respectively.

The design strength, fccd, of confined concrete shall be evaluated as follows: 2/3

1,1 2.6 effccd

cd cd

fff f

⎛ ⎞= + ⋅⎜ ⎟

⎝ ⎠ (2.10-5)

where fcd is the design strength of unconfined concrete as per the current building code, and f1,eff is the effective confinement lateral pressure. The effective confinement lateral pressure, f1,eff, is a function of member cross section and FRP configuration as indicated in the following Equation:

1, 1eff efff k f= ⋅ (2.10-6)

where keff is a coefficient of efficiency (≤1), defined as the ratio between the volume, Vc,eff, of the effectively confined concrete and the volume, Vc, of the concrete member neglecting the area of existing internal steel reinforcement. The confinement lateral pressure shall be evaluated as follows:

1 ,12 f f fd ridf Eρ ε= ⋅ ⋅ ⋅ (2.10-7)

where ρf is the geometric strengthening ratio as a function of section shape (circular or rectangular) and FRP configuration (continuous or discontinuous wrapping), Ef is Young modulus of elasticity of the FRP in the direction of fibres, and εfd,rid is a reduced FRP design strain.

In the seismic upgrading, the confinement, enhances the section ductility of RC columns. Recent experimental test conducted by Pantelides et al (2000) clearly showed the benefits of the column confinement for the ductility of the column. In particular a real bridge column has been first tested both in the original condition and after the reinforcement. The benefits of the composite reinforcement in the plastic hinge region include providing confinement of the core, and prevention of the concrete cover from spalling off which provides the longitudinal reinforcement with lateral stability. Comparing the performance of the as-built column and the retrofitted one, it can be seen that the FRP composite retrofit significantly increased the ductile capacity, and allowed the column to achieve a higher lateral load capacity while maintaining a significant gravity load.

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2.10.4. Masonry reinforcement

There are several techniques that are commonly used for strengthening the masonry walls and the choice of the suitable technique depends on some reasons such as the type of masonry, the geometry of the wall, the type of stresses which the wall would be subjected to and the required level of upgrading.

Several conventional rehabilitation techniques for masonry walls were stated by Drysdale et al (1999). Also, Abrams had surveyed some seismic rehabilitation techniques for masonry walls. El-Hefnawy et al (2004) investigated the effect of using ferrocement overlays to upgrade the vertical load carrying capacity of concrete masonry brick walls. They tested eight 1000 mm square walls and concluded that the structural performance of the concrete masonry brick walls is greatly enhanced by the use of ferrocement overlays.

On the other hand, Mosalam (2004) conducted an experimental and theoretical study to compare the structural response of unreinforced masonry walls with and without retrofit on one side using GFRP laminates. Six walls were tested using ASTM diagonal tension standard test procedure.

The study showed that the application of GFRP laminates on only one side of a triple-wythe wall prevented brittle failure and may potentially improve the inplane seismic response of the unreinforced masonry walls.

Other researchers carried out an experimental study concerning strengthening of unreinforced clay brick masonry walls subjected to diagonal in plane and out of plane actions by using conventional steel mesh or FRP laminates. They concluded that the use of 0.02 % of FRP or 0.13 % of steel mesh can enhance the ultimate capacity of out of plane loaded walls by more than 8 folds, while, the use of 0.02 % of FRP and 0.2 % of steel mesh, increased the ultimate capacity of the in plane ultimate capacity by 30 % and 50 %, respectively.

Hadad et al investigated the effectiveness of the FRP laminates glued to the surface of clay brick masonry walls with openings. A total of nine plain and strengthened half scale walls were tested under combined vertical and lateral loads. They demonstrated that the FRP laminates are very effective in significantly increasing the strength and deformation ability.

Others presented an experimental program which consisted of four unreinforced masonry wall panels 1600 x 1600 mm tested under diagonal loads. Three of these four walls were strengthened with GFRP rods at the horizontal mortar joints or horizontal and vertical joints. The results showed that, by using the aforementioned techniques, the shear strength of unreinforced masonry walls was significantly increased.

Khafaga et al (2004) have investigated the behaviour of concrete and clay brick unreinforced masonry walls with square or rectangular openings under uniform verticals loads. Four techniques were used for strengthening: steel frame around the openings, ferrocement overlays, ordinary plastering and GFRP laminates. To achieve the aim of the current study, an experimental program consisting of testing fifteen wall panels 1200 by 1200 mm under uniform vertical load was conducted. The type of strengthening technique, the type of brick units and the presence & geometry of the opening are the main key variables studied in the current research. The following figures shown the fundamental types of FRP applications on URM.

2.10.5. Connections

When strengthening reinforced concrete members with FRP composites, the role of bond between concrete and FRP is of great relevance due to the brittleness of the failure mechanism by debonding (loss of adhesion). According to the capacity design criterion, such a failure mechanism shall not precede

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flexural or shear failure of the strengthened member. The loss of adhesion between FRP and concrete may concern both laminates or sheets applied to reinforced concrete beams as flexural and/or shear strengthening. As shown in Figure 2.10-7, debonding may take place within the adhesive, between concrete and adhesive, in the concrete itself, or within the FRP reinforcement (e.g. at the inteface between two adjacent layers bonded each other) with different fiber inclination angles. When proper installation is performed, because the adhesive strength is typically much higher than the concrete tensile strength, debonding always takes place within the concrete itself with the removal of a layer of material, whose thickness may range from few millimetres to the whole concrete cover.

Figure 2.10-9 Debonding between FRP and concrete

Debonding failure modes for laminates or sheets used for flexural strengthening may be classified in the following four categories, schematically represented in Figure 2.10-8.

• Mode 1 - Laminate/sheet end debonding;

• Mode 2 - Intermediate debonding, caused by flexural cracks;

• Mode 3 - Debonding caused by diagonal shear cracks;

• Mode 4 - Debonding caused by irregularities and roughness of concrete surface;

Figure 2.10-10 FRP flexural strengthening: debonding failure modes

To mitigate the risk of occurrence of the remaining failure modes, recommendations on both support control and preparation must be followed. Before any flexural and shear design can take place, the evaluation of the maximum force that may be transferred from the concrete to the FRP, as well as the evaluation of shear and normal stresses at the concrete-FRP interface is required. The former is necessary when designing at ULS; the latter when designing at SLS. With reference to a typical bond test as represented in Figure 2.10-9, the ultimate value of the force transferred to the FRP system prior to debonding depends on the length, lb, of the bonded area. The optimal bonded length, le, is defined as the length that, if exceeded, there would be no increase in the force transferred between concrete and FRP.

174

Figure 2.10-11 Maximum force transferred between FRP and concrete.

The optimal bonded length, le , may be estimated as follows:

2f f

ectm

E tI

f⋅

= (2.10-8)

where Ef and tf are Young modulus of elasticity and thickness of FRP, respectively, and fctm is the average tensile strength of the concrete.

2.10.6. Pefrormance criteria

The primary aim of the confinement is the enhancement of the flexural ductility. Columns with insufficient internal stirrup reinforcement cannot sustain large non-elastic rotations in the plastic hinge region. FRP confinements are suited to increase the flexural ductility of such supporting elements. Tests on circular columns retrofitted with FRP clearly indicated that they are able to increase the ductility more effectively than conventional steel jackets. The reason is the linear-elastic behaviour of the FRP confinement. In the case of seismic actions, the linear-elastic behaviour of FRP avoid no cumulative damage of member sections. Successive cycles cause similar hoop strains. The load transfer from the steel reinforcement into the concrete leads to the formation of micro-cracks in the concrete that will reduce the bond between steel and concrete. Retrofitting with FRP jackets, and with prestressed FRP systems in particular, enhances this bond.

2.10.7. References:

ACI 440 M (2005): “Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Unreinforced Masonry Structures”, Draft of the State-of-the Art Report on externally bonded Fiber Reinforced Plastic (FRP) Reinforcement for Masonry Structures.

ACI 440.1R-01 (2001):”Guide for the design and construction of concrete reinforced with FRP bars”, ACI committee report ISBN 0-87031-C32-1.

ACI 530-95 / ASCE 4-95 / TMS 402-95 (1995):”Building Code requirements for masonry structures”.

ACI Committee 440 (1996). State-of-the-art report on FRP for concrete structures, ACI440R-96, Manual of Concrete Practice, American Concrete Institute, Farmington Hills, MI.

ACI Committee 530, (1990), “State-of-The-Art Report on Ferrocement “, ACI Manual of Concrete Practice, Part 5.

Concrete Society Technical Report 55 (2000). Design guidance for strengthening concrete structures using fibre composites materials. The Concrete Society, Crowthorne, UK.

Della Corte, G.; Barecchia, E.; Mazzolani, F.M., (2004). “Seismic upgrading of existing RC structures using FRP: a GLD study case. Proceedings of the First International Conference on Innovative Materials and Technologies for Construction and Restoration (IMTCR), Lecce, Italy.

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Della Corte, G.; Barecchia, E.; Mazzolani, F.M., (2005a). “Seismic upgrading of RC structures by means of composite materials: a state-of-the-art review,” Proceedings of the COST C12 Final Conference: Improving building’s structural quality by new technologies, Innsbruck, Austria.

Della Corte, G.; Barecchia, E.; Mazzolani, F.M., (2005b). “Seismic upgrading of RC buildings by FRP: full scale tests of a real structure,” Journal of Materials in Civil Engineering, ASCE, accepted for publication.

Della Corte, G.; Barecchia, E.; Mazzolani, F.M., (2005c). “Seismic strengthening of RC buildings by means of FRP: physical testing of an existing structure,” Proceedings of the 4th Middle East Symposium on Structural Composites for Infrastructure Applications, Alexandria, Egypt.

Drydale, G.; Hamid, A. and Baker, L., “Masonry Structures Behavior and Design”, second edition, the masonry society, Boulder, Colordo, 1999.

El-Hefnawy, A.A., Sabrah, T.B. and Hodhod, O.A., “Upgrading Load Bearing Walls Using Ferrocement Overlays”, International Conference: Future Vision and Challenges for Urban Development, Cairo, Egypt, December, 2004.

FEMA 356, (2000). “Prestandard and Commentary for the Seismic Rehabilitation of Buildings” Washington D.C., Federal Emergency Management Agency, November.

fib (CEB-FIP), (2001). Bulletin n.14 (Task Group 9.3), “Externally bonded FRP reinforcement for RC structures”, Sprint-Digital-Druck, Stuttgard.

Fyfe E.R., Duane J. Gee Peter Milligan (1998). Composite materials for rehabilitation of civil structures and seismic applications. Proceedings of the Second International Conference on Composites in Infrastructure, Eds.: Saadatmanesh and M.R. Ehsni, Tucson, AZ.

Mazzolani F.M., co-ordinator & editor (2006). The ILVA-IDEM research Project – Seismic upgrading of RC buildings by advanced techniques, Polimetrica International Scientific Publisher..

Mosalam, K.M., “Retrofitting of Unreinforced Masonry Walls Using Glass Fiber Reinforced Polymer Laminates”, International Conference: Future Vision and Challenges for Urban Development, Cairo, Egypt, December, 2004.

Park, R.; Paulay, T., 1975. “Reinforced Concrete Structures”. New York, John Wiley & Sons.

Popovics S. (1973). Numerical approach to the complete stress-strain relation for concrete. Cement and Concrete Research, 3(5), 583-599.

Priestley, M.J.N.; Seible, F., (1995). “Design of seismic retrofit measures for concrete and masonry structures”. Construction and Building Materials, V. 9, No. 6, pp. 365-377.

Spoelstra M.R., Monti G. (1999). FRP confined concrete model. Journal of Composites for Construction, ASCE, 3(3), 143-150.

Taljsten B. (2003). Strengthening concrete beams for shear with CFRP sheet. Construction and Building Materials, 17, 15-26.

Triantafillou, T.C., (2001). “Seismic retrofitting of structures with fibre-reinforced polymers”. Progress in Structural Engineering and Materials, V.3, No.1, pp. 57-65.

Tumialan J.G., Morbin A., Nanni A., and Modena C., “Shear Strengthening of Masonry Walls with FRP Composites,” COMPOSITES 2001 Convention and Trade Show, Composites Fabricators Association, Tampa, FL, October 3-6, 2001, 6 pp. CD-ROM.

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2.11. PIN INERD

2.11.1. Introduction

This section was prepared in accordance with data-sheets no. 9-16 “PIN INERD connections for braced frames” prepared by I. Vayas, P. Thanopoulos from National Technical University of Athens (GR).

It is presented the principle of the device and a detailed design methodology together with analysis type and acceptance criteria.

2.11.2. Description of the device/technique

According to the current European seismic rules (Eurocode 8, 2004), “concentric braced frames shall be designed so that yielding of the diagonals in tension will take place before failure of the connections and before yielding or buckling of the beams or columns” and that “in frames with diagonal bracings, only the tension diagonals shall be taken into account”. The former condition leads to high connection costs for conventional braced frames, the latter indicates that the compression braces, almost half of the total, are considered, as inactive due to buckling.

However, Eurocode 8 leaves the door open for the development of innovative dissipative connections, as it states that “The overstrength condition for connections need not apply if the connections are designed to contribute significantly to the energy dissipation capability inherent to the chosen q-factor and if the effects of such connections on the behaviour of the structure are assessed”. The hereafter presented INERD connections fall into the above category and are therefore weaker than the connected members, exhibiting inelastic deformations and dissipating energy during seismic loading.

The INERD pin connections consist of two external eye-bars welded or bolted to the adjacent member (column for X-braces, beam for V or eccentric braces), one or two internal eye-bars welded or bolted to the brace and a pin running through the eye-bars, as indicatively shown in Figure 2.11-1. Inelastic deformations and energy dissipation concentrate in the pins. The pin cross section is not round in order to avoid twist around its axis during cyclic loading. Accordingly, two pin cross sections may be selected: a) either rectangular, where the pin is bent around its small side (in order to avoid possible lateral buckling), or b) rectangular with rounded edges, where the pin is bent around its large side.

Figure 2.11-1 Pin INERD connection with one or two internal eye-bars

Braced frames with INERD-connections exhibit the following benefits compared to conventional steel frames:

• Better compliance with the seismic design criteria.

• Protection of compression braces against buckling.

• Activation of all braces, either in compression or in tension, even at large storey drifts.

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• Limitation of inelastic action and damage in small parts of the structure that may be easily replaced.

• Avoidance of brittle fracture and/or low-cycle fatigue.

• Possibility for easy inexpensive repair after very strong earthquakes, if required.

• Reduction of overall structural costs for the same performance level.

The design of a multi-storey steel-concrete composite building with INERD connections has been approved for construction in Kalamata, Greece. Its erection will follow in the near future.

2.11.3. Behavior of INERD connections

The behaviour of the INERD connections has been extensively studied experimentally and numerically. Figure 2.11-2 shows the connection response, for two internal eye-bars, under monotonic loading as derived by FEM analysis by means of the ABAQUS programme, version 6.4. The pin behaves initially as a beam under four-point bending. After the formation of two plastic hinges under the loading points, the beam becomes theoretically a mechanism. However, the external eye-bars provide a “clamping” effect to the pin which is higher for thicker external eye-bars. The load can thus be further increased, up to the formation of two additional plastic hinges at the supports. At that point, assigned as yield point, the system becomes a plastic mechanism and only strain hardening may contribute to any further load increase. The behaviour is similar for one internal eye-bar, the difference being that the pin system behaves initially as a three-point bending beam.

Verbindung Typ B

0

200

400

600

800

1000

0 10 20 30 40 50Verformung [mm] (positiv wenn Platten auf Druck)

Last

[kN

]

Monotoner Druck (FEM)

Figure 2.11-2 Connection response under monotonic loading (two internal eye-bars)

Figure 2.11-3 shows the connection response under cyclic loading. Slip type response occurs due to hole ovalisation in the eye-bars and transverse deformations of the thinner eye-bars

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INERD Connection "TYPE D" - Allowance for Bauschinger effect

-700

-350

0

350

700

-40 -30 -20 -10 0 10 20 30 40Displacement [mm] (positive when eye-bars in compression)

Axi

al F

orce

[kN

]

Experimental ResultsFEA Cyclic ResultsFEA Monotonic Results

Figure 2.11-3 Connection response under cyclic loading

2.11.4. Design reules for the INERD connection

By means of engineering models and comparison with the results of the parametric studies, simple formulae appropriate for practical use were derived, which allow for the correct prediction of the connection response and calculation of its properties. The design formulae for the connection are based on a trilinear approximation for the force vs. deformation law of the connection (Figure 2.11-4).

δy δlim

δ

Py

Pu

P

I

II

III Point I:Yield Strength ("y")

Point III:Ultimate Strength ("u")

Figure 2.11-4 Axial force vs. deformation for the design of INERD connections.

Yield strength and yield deformation

The yield strength may be determined from:

2,y1,ynom,y P;PminP = (2.11-1)

I,red

plel1,y a

M2P −⋅

= , where yplplel fW85,0M ⋅⋅=− and ared,I = a – 0,5h

aM2

kP plpin2,y

⋅⋅= , where 2,1)h/b(1,01k1,1 pin ≤⋅+=≤

179

The yield deformation is equal to:

( )ααδ 436

lEI

M5,1 2plel

y −⋅⋅⋅⋅= −, where α = a/l

Ultimate strength and deformation capacity

The ultimate strength may be determined from:

II,red

upinnom,u a

M4kP ⋅⋅= (2.11-2)

where

midpl,uu fWM ⋅=

( )yufymid ff5,0ff −⋅⋅+= λ , ( ) ( )[ ] 10where,h2ha f2

f ≤λ≤⋅−=λ

( )[ ]22II

2pl,u 5,0hbW ΙΙΙΙΙΙΙ βχββ −⋅+−⋅⋅= , ( )2

midy ff1−=χ

The deformation capacity may be given as: a8,0u ⋅=δ

The knowledge of the above values is sufficient for practical applications. However, if more refined analysis is required, values at an intermediate point II (see Figure 2.11-4) may be used. PII is equal to the mean value of Py and Pu, whereas IIδ is equal to 4-times yδ .

Characteristic and design values

By appropriate statistical evaluation of experimental and numerical results safety factors were determined. The characteristic values may be derived from the nominal ones by application of these factors as following:

My

nom,yRk,y

PP

γ= , where 05,1My =γ (2.11-3)

Mu

nom,uRk,u

PP

γ= , where 10,1Mu =γ (2.11-4)

The design values are determined from the characteristic ones, by application of the safety factor 0,10M =γ , in accordance to EC3 as following:

0M

Rk,yRd,y

PP

γ= and

0M

Rk,uRd,u

PP

γ=

Detailing rules

• Thickness of external plates > 0,75 – 1,0 times the pin height

• Thickness of the internal plates > 0,5 times the thickness of the external ones

• Allowance for holes in the eye-bars < 2 mm.

• Distance a > pin height

Design criteria

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The connections should be sized so that

• Yielding of the pins is avoided under frequent earthquakes

• Failure of the pins is avoided under rare earthquakes

2.11.5. Capacity design criteria

In frames with INERD connections, the pins are supposed to be the dissipative elements. Therefore all adjacent elements (eye-bars, welds, braces etc.) shall be designed according to capacity design criteria. They shall be designed accordingly with forces equal to the ultimate pin strength, duly increased by a capacity design factor, which was derived from statistical evaluation of experimental and numerical results. The capacity design forces are equal to:

Rd,ucapcap,u PP ⋅γ= , where 3,1cap =γ (2.11-5)

2.11.6. System model

The system model for linear analysis and design, as applied in practical applications, does not differ from that for conventional braced frames. Due to their high stiffness in the elastic range, there is no need to introduce special elements for the connections. Figure 2.11-5 shows models for different buildings.

3,2 m3,2 m

3,4 m3,4 m3,4 m3,4 m3,4 m

6 m 6 m 6 m

3,4 m

20,4 m

7,5 m 7,5 m 7,5 m 7,5 m

31,5 m

3,5 m3,5 m3,2 m

9,6 m

5 m 5 m 5 m5 m 5 m

3,5 m3,5 m3,5 m3,5 m3,5 m3,5 m3,5 m

Figure 2.11-5 Analysis models for braced frames with INERD connections.

For non-linear static analyses, the connections may be represented by non-linear springs at brace ends. The characteristics of the springs may be derived in accordance with the expressions given in par. 2.17-3.

2.11.7. Analysis types

All possible types of global analysis proposed by Eurocode 8 may be employed. For linear analysis, a behaviour factor q = 6 may be used. The design values of the connections for non-linear analyses may be determined according to clause 3. It is recommended to size the connections in accordance to the relevant demand as determined by the global analysis, in order to allow energy dissipation in as many as possible pins.

2.11.8. Performance criteria

Due to the high deformation capacity of the pins, large inter-storey drifts may be accommodated. However, it is recommended to use the same limit values as for moment resisting frames, in order to limit second order effects and damages to non-structural elements.

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2.11.9. References:

Calado L. and Ferreira J. INERD Connections, Technical Report, IST Lisbon, 2004

Castiglioni C, Crespi A., Brescianini J. and Lazzarotto L. INERD Connections, Technical Report, Politecnico Milano, 2004

Vayas I., Thanopoulos P. and Dasiou M. INERD Connections, Technical Report, NTU Athens, 2004

Vayas, I., Thanopoulos, P.: Innovative Dissipative (INERD) Pin Connections for Seismic Resistant Braced Frames, International Journal of Steel Structures Vol 5, No. 5 (2005), 453-464

Vayas, I. Thanopoulos, P, Castiglioni, C., Plumier, A., Calado, L.: Behaviour of Seismic Resistant Braced Frames with Innovative Dissipative (INERD) Connections, EUROSTEEL 2005, Maastricht, 5.2-25 – 5.2-32, 2005

Vayas I. and Thanopoulos P.: Seismic resistant braced frames with dissipative (INERD) connections, Proceedings of the 5th conference on Behaviour of steel structures in seismic areas (STESSA), Yokohama, Japan, 2006, Mazzolani and Wada eds., p. 801 – 806, Taylor & Francis Group, London.

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3. Models and performance criteria for sub-systems

3.1. Masonry walls strengthening with metal based techniques

3.1.1. Introduction

This section was prepared in accordance with data-sheet no. 9-1 “Simplified and Advanced Models for Calculation and Analysis of Masonry Shear Walls” provided by A. Dogariu, T. Nagy-Gyorgy, C. Daescu, D. Daniel, V. Stoian and D. Dubina from “Politehnica” University of Timisoara (ROPUT).

3.1.2. Basic concept

Two strengthening solutions were proposed and investigated within the research program. The solutions use steel (SSP) or aluminium (ASP) sheeting plates (see Figure 3.1-1), and steel wire mesh (SWM), respectively (Figure 3.1-3).

CHEMICAL ANCHOR

METALL SHEATING

MASONRY WALL

PRESTRESSED TIE

METALL SHEATING

MASONRY WALL

Figure 3.1-1 Proposed solution

Connection of the metal sheets plates to the masonry wall is realized in two ways: chemical anchors (CA) and prestressed ties (PT), placed at 200-250 mm. The wire mesh is glued using epoxy resin. Both systems can be applied on one side or both sides of the panel. It is expected that the system with metallic elements on both sides to perform better, but it isn’t always possible due to architectural reasons.

Such a type of solution can be successfully applied in case of masonry walls, but it is not appropriate in case of masonry vaults and arches.

Figure 3.1-2 Weak area on masonry façade and location of SP or WM

Observing the behavior of a masonry wall with openings it is easy to identify the weak regions that need strengthening with metal plates (SP) or wire mesh (WM) (Figure 3.1-2).

The application technology is rather simple. In the case of metallic plates they must be previously drilled. Afterwards the plate is placed on the wall, anchor holes are drilled in the masonry wall through

183

the plate holes. The dust is blown away from the holes, followed by injection of epoxy resin and fixing of chemical anchors (Figure 3.1-3). Prestressed ties are applied similarly, but no resin is used, and the ties are tightened using a torque control wrench.

Figure 3.1-3 Wire mesh geometry and texture and chemical anchor

The mesh is produced either as galvanized steel or stainless steel bidirectional fabric. Spacing of the mesh is between 0.05 and 16 mm, while wire diameter is between 0.03 and 3.0 mm. Tensile strength reaches 650-700 N/mm2, while elongation is about 45-55% in the case of stainless steel wires. For galvanized steel wire, tensile strength is usually in the range of 400-515 N/mm2.

Application of wire mesh (Figure 3.1-3) requires a previous preparation of the walls to obtain a smooth surface. The preparation of resin is similar to the one used for Fiber Reinforced Polymers (FRP). The resin is applied in two steps: a fluid layer is applied first, and after it is dried, a second thick fluid layer is applied to embed the mesh. For large surfaces the mesh should be fixed to the wall with nails in order to keep plain its surface. It is important to mention that, by heating the resin layer, the wire mesh can be removed.

In order to validate the two solutions, an experimental program was carried out. It included:

• Material tests;

• Preliminary tests on 500 x 500 mm specimens;

• Full scale tests on 1500 x 1500 mm specimens, both under monotonic and cyclic loading.

3.1.3. Design assisted by testing (see Chapter 1)

In some cases there are no analytical calculation procedures and numerical simulation is either difficult due to the scatter of real material properties or does not offer accurate results. Experimental test can solve the problem. This kind of approach is based on experimental determination of a characteristic strength of the shear wall kR . This strength kR is used further in order to evaluate the necessary length of the walls on a direction “i” and at storey “j” to resist the corresponding seismic shear force. The principle of the method is presented bellow (Table 1.1-5):

Table 3.1-1 Principle of method

, , , ,

, , ,

s i j s i j

s i j k i j

E R

R R L

<

= ⋅

, ,s i jE - total shear force induced by seismic action in “i” direction and “j” storey;

, ,s i jR - total shear wall resistance in “i” direction and “j” storey;

kR - characteristic strength of shear wall experimental determined;

,i jL - length of shear wall in “i” direction and “j” storey;

The method is applicable both for pure masonry wall and for strengthen walls (FRP, SSP – Steel Shear Plate, ASP – Aluminum Shear Plate, SWM – Steel Wire Mesh).

184

3.1.4. Analytical calibration

Some simple numerical calculations have been performed to determine the thickness of steel shear plate in order to obtain a rational behaviour. On this purpose, three preliminary design criteria expressed in terms of stiffness, stability and strength have been used.

First material tests were performed in order to establish strength and stiffness parameters. They are summarized in Table 3.1-2

Table 3.1-2. Summary of material tests

Elastic modulus of masonry

Compression test on brick

Compression test on mortar Masonry component

Tension test on mortar

Tensile test on wire Steel wire mesh

Tensile test on mesh

Connectors Tensile test on ties

Tensile test on steel plates

Tensile test on aluminum plates

First criterion is used to obtain comparable stiffness of the metallic sheeting plates with masonry panel, in order to provide a uniform distribution of stresses between wall and sheeting. To evaluate the rigidity of the wall and sheeting plate the following formulas have been used:

mv

eff

gm

effm

GAh

IEh

k+

= 3

1 (3.1-1)

where km = stiffness of masonry panel; heff = effective wall height; Em = longitudinal elastic modulus of masonry; Ig = moment of inertia; Av = shear area; and Gm = transversal elastic modulus of masonry;

sv

effplate

GAh

k 1= (3.1-2)

where kplate = stiffness of steel plate; heff = height of plate; Av = shear area, and Gs = transversal elastic modulus of steel (Astaneh-Asl, 2001).

Considering known all material parameters and by equating the two relations, a 2.16 mm thickness demand for the steel sheeting was obtained.

Second condition follows to obtain a compact plate in order to prevent local buckling and assure dissipation of energy through plastic bearing work in connecting points only.

To establish the “non-compact” behaviour domain the following criterion was used:

yw

v

wyw

v

FHK

th

FHK 37.110.1 ≥≥ (3.1-3)

185

where Kv = plate buckling coefficient; H= horizontal load of the panel; Fyw = yielding stress of steel; h = distance between connectors (imposed by masonry texture); and tw = steel plate thickness.

From equation (3), the compactness criterion results as 27.2≥wt (mm).

A more complex methodology, to evaluate the resistance of each component of the system, proposed by the producer of chemical anchor can be used. Three components govern the behaviour of the chemical connection, e.g. the matrix (masonry with epoxy resin), steel anchor and steel plates. It is believed that the most desirable failure mode is the bearing of the steel hole (e.g. in the connecting points). In order to obtain this failure mode, the bearing resistance should be less than the minimum between the shear resistance of connector and crushing resistance of matrix.

),min( conectormasonrybearing NNN ≤ (3.1-4)

For chemical anchors, the design methodology suggested by producer (Hilti-Catalogue, 2005) has been adapted for masonry matrix e.g.

VARVBVcRdcRd fffVV ,0

,, ⋅⋅⋅= β (3.1-5)

where VRd,c = matrix edge resistance; VRd,c0 = basic matrix edge resistance; fBV = matrix strength

influence; fβV = load direction influence; and fAR,V = spacing and edge coefficient.

Two cases were considered: ø8 and ø10 connector diameter. Corresponding plate thickness amounted to 2.20 and 2.48 mm.

It was decided to use a 3 mm thickness steel plate of S235 grade when applied on one side and 2 mm thickness plate of S235 grade when applied on both sides. Alternatively, 5 mm aluminium plates were used (99.5% Al 1050 H14 - Rp0.2%=105 N/mm2).

3.1.5. Experimental calibration

Because of the inherent approximations in design assumptions and the poor accuracy of analytical approach based on available formulas, it was decided to perform a series of test on small specimens in order to validate and calibrate the proposed techniques. The tests on small specimens are summarized in Table 3.1-3

Table 3.1-3. Tests on small specimens

Preliminary Masonry panel

ø8 Chemical anchor (CA)

ø10

ø10 – 0% Connection

Prestressed ties (PT) ø10 – 100%

Steel wire mesh (SWM)

Chemical anchor Diagonal tension test Steel shear panel (SSP)

Prestressed ties

Some tests were carried out on unreinforced masonry panels (brick unit strength of 10 N/mm2 and mortar strength of 13 N/mm2) to obtain reference values.

Connection tests

186

Connection tests were performed in order to establish the connector diameter and to assess the influence of prestress level of steel ties. The experimental set-up is presented in Figure 3.1-4. Chemical anchors

Chemical anchors ø8 and ø10 diameters gr.5.8 have been tested. The failure mode for ø8 was the shear of connector and for ø10 the shear of connector and crushing of masonry. For the large specimen tests, an ø10 connector was chosen, due to the more efficient behaviour and resistance.

Figure 3.1-4 Experimental set-up and testing machine for connectors

Prestressed ties Two prestressing levels have been applied for the ø10 ties gr.5.8 (i.e. snug tightened ties (0% prestress) and full prestress (100%)). The failure mode was shear of ties, masonry specimens remaining almost intact. It was noted that the prestress level increases the resistance of connection due to confinement of masonry. In comparison with chemical anchors, prestressed ties lead more resistant and more rigid specimens.

System tests

Tests on systems was carried out in order to validate the analytical assumption in case of shear plates and to choose a proper steel wire mesh. The experimental set-up on small specimens and a sample test on unreinforced masonry panel are presented in the Figure 3.1-5.

MasonryPanel

Metallicelement

Load

Load

Figure 3.1-5 Experimental set-up for split test

Steel shear plates S235 grade of 2 mm thickness on both sides and 3 mm thickness on one side, connected with chemical anchors and prestressed ties were tested.

Steel wire mesh (SWM)

187

There are no analytical procedures to design the steel wire mesh reinforced masonry, therefore calibration was based on experimental test. The purpose of tests was to select the appropriate resin and wire mesh to be applied on large specimens. In the first step six types of wire mesh were tested.

Compared to FRP technique a thicker fluid resin was selected. In order not to change too many parameters and based on the experimental results, the following wire meshes were chosen: zinc coated (ZC) 0.4x1.0 (D x W), stainless steel (SS) 0.4x0.5 and 0.4x1.0.

The failure modes are shown in Figure 3.1-6.

• WM3 – sudden wire mesh rupture simultaneous with masonry crack – strength improvement (weak WM)

• WM5 – debounding of wire mesh, rupture in resin – strength improvement, energy dissipation due to the successive debounding (strong WM)

• WM6 – wire mesh yield – improvement of resistance and ductility (optimal).

Based on these observations, the stainless steel wire mesh 0.4x1.0 was chosen to be applied on large specimens.

a) b)

c)

Figure 3.1-6 Failure mode for SMW on both sides a) ZC 0.4x1.0 b) SS 0.4x0.5 and c) SS 0.4x1.0

3.1.6. Numerical approaches

The existing masonry walls may be modell following the procedure described in Chapter 1 of this report. The connection between connector and masonry was simplified in sequence of node to node internal constraints (Figure 3.1-7) and by using a nonlinear spring element with a multi-linear behavior (Figure

188

3.1-8 – determined experimentally). Although in reality the steel connector is infilled in masonry wall, the implemented ABAQUS model doesn’t respect the physical situation.

Figure 3.1-7 Modelling strategy for the connection

0

5000

10000

15000

0 5 10 15 20 25 30

Displacement (mm)

Forc

e (N

)

Figure 3.1-8 Constitutive laws of the spring elements. F = shear force in the plane of masonry wall

at the base of the connector; d = displacement of the base of the steel connector in the plane of masonry wall.

3.1.7. Reference

Astaneh-Asl, A. 2001. Seismic Behaviour and Design of Steel Shear Walls, Steel TIPS, USA (2001).

IAEE/NICEE (2004). Guidelines for Earthquake Resistant Non-Engineered Construction, First printed by Interna-tional Association for Earthquake Engineering, Tokyo, Ja-pan. Reprinted by the National Information Center of Earthquake Engineering, IIT Kanpur, India.

Hilti-Catalogue (2005), Design Manual, Anchor Technology, (2005)

D. Dubina, A. Dogariu, A. Stratan, V. Stoian, T. Nagy-Gyorgy, D. Dan, C. Daescu – Masonry wall strenghtening with inovative metal based techniques – International Conference on Steel and Composite Structures ICSCS07, Manchester, UK, 2007

A. Dogariu, A. Stratan, D. Dubina, T. Gyorgy-Nagy, C. Daescu, V. Stoian – Strengthening of masonry walls by innovative metal based techniques – COST 26 – Urban Habitat Construction Under Catrastrophic Events –Proceedings of Workshop in Prague, 2007

Campitiello F. , Dogariu A., De Matteis G., Dubina D. WP8: NUMERICAL ANALISYS “Masonry shear walls strengthened with metal sheathing: FEM modeling”

189

D. Dubina, V. Stoian, A. Dogariu, T. Nagy-Gyorgy, A. Stratan, C. Daescu, D. Diaconu, WP 7 EXPERIMENTAL ANALYSIS

3.2. Confined masonry

3.2.1. Introduction

This section was prepared in accordance with data-sheet no. 9-17 “Models for global analysis” provided by Mazzolani F., from University of Naples “Federico II”, Italy. The report presents some aspects regarding the masonry-infill walls, proposals for in-plane stiffness and strength evaluation of these structural elements, with or without openings, and an example of application in a case study.

3.2.2. General

The observation of damage caused by past earthquakes clearly indicates that the effect of infill walls on the seismic behaviour of framed structures is particularly significant when they are in tight contact with their bounding frames.

Even if they are usually considered as “non-structural” elements, the infill walls can positively or negatively condition both local and global seismic response of framed structures. In fact, in case of infill walls in tight contact with their confining frames on all four sides and being regularly distributed both in plan and elevation (“regular” infills), they significantly increase shear strength and stiffness. This effect plays an essential role especially in the case of framed structures mainly designed for vertical loads, in which the horizontal seismic actions can be resisted by overstrength (Figure 3.2-1).

Contrary, when infills present an “irregular” configuration (partial infill frame, irregularity in plan and/or elevation) their presence often negatively modifies the seismic response of framed structures, even if they are designed according to seismic criteria. In fact, in these cases frame-to-infill interactions can lead to undesired structural performance, such as brittle shear failures of RC columns, torsional effects, weak-story mechanisms (Figure 3.2-2). In addition, since the cyclic response of masonry infill frames is characterized by a pinched hysteretic shape, with stiffness and strength degradation, a reduced energy dissipation capacity is usually associated to this structural typology.

Figure 3.2-1 Positive effects of infills on seismic response: major damage to the unreinforced

masonry infill walls and moderate damage in RC frames

190

Efforts have been made in the last few decades to better understand the behaviour of infilled frames under horizontal monotonic and cyclic (seismic) actions. A synthetic literature review can be found in Shing and Mehrabi (2002). Despite of consistent progress in this field, the analysis of the lateral behaviour of infilled frames still remains a complex problem. Difficulties basically derive from complex phenomena of frame-to-infill interaction, which depends on numerous factors like mechanical and geometrical properties of frames and infills, detailing, presence of openings, existing infill damage. In addition, the prediction of the lateral response of this type of structures is complicated by a large variability of mechanical properties of infills, which usually are not submitted to quality controls because they are not considered as structural elements. In addition, the lateral response of masonry infilled RC framed structures is characterized by strong strength degradation after the infill collapse. Therefore, specific procedures should be used for their seismic performance assessment (Dolsek and Fajfar, 2004).

If the infill wall is to be considered in the analysis and design stages, a modelling problem arises because of the many possible failure modes that need to be evaluated with a high degree of uncertainty. It is generally accepted that under lateral loads the infill wall acts as a diagonal strut connecting the two loaded corners. Following principles of capacity design, undesirable modes of failure in the surrounding frame or in the masonry walls can be avoided while plastic deformations are deliberately induced in special parts of the structure.

(a) Shear failures of RC columns for short column effect due to partial tight fit infill walls

(b) Torsional effects due to infills irregular in plan

191

(c) Soft story mechanism due to infills irregular in elevation

Figure 3.2-2 Undesired effects due to “irregular” infill walls

In recent years, different techniques have been developed for both seismic repairing and strengthening of masonry infill walls. Among the most interesting techniques, those based on the use of composite fiber reinforced polymers (FRP) are very attractive, because of the well known advantages of FRP materials (e.g. lightness and simplicity of installation, no sensitivity to corrosion). Epoxy bonded FRPs (in the form of sheets, strips or bars) have been proposed for infill walls (Ehsani et al., 1999, Garevski et al., 2004). Corresponding analytical design methods are also being developed (Triantafillou, 1998; Galati et al. 2005), starting from methodologies typically applied for seismic strengthening of un-reinforced masonry load-bearing walls.

3.2.3. In-plane stiffness evaluation of masonry-infill walls

Great efforts have been invested, both analytically and experimentally, to better understand and estimate the composite behaviour of masonry-infilled frames. Polyakov (1960), Stafford-Smith (1962, 1966), Stafford-Smith and Carter (1969), Fiorato et al. (1970), Mainstone (1971), Klingner and Bertero (1976, 1978), Bertero and Brokken (1983), Zarnic and Tomazevic (1985), Dhanasekar et al. (1985), Schmidt (1989), Dawe and Seah (1989), Mander et al. (1993), Mehrabi et al. (1994, 1996), Mosalam et al. (1997), Buonopane and White (1999), Flanagan and Bennett (1999) to mention just a few, formed the basis for understanding and predicting infilled frame in-plane behaviour. Their experimental testing of infilled frames under lateral loads resulted in specimen deformation shapes similar to the one illustrated in Figure 3.2-3.

Figure 3.2-3 In-plane response (deformation shape) of masonry-infill walls

192

Generally, during testing of the masonry-infilled specimens two different behavioural phases may be individuated:

- masonry-infill wall acts as a composite cantilever;

- masonry-infill wall acts as a compressive masonry strut.

At a low lateral load level, masonry-infill walls act as a monolithic load resisting system. Under the assumptions of full contact between masonry panels and bounding frames (Mehrabi et al. 1994.), proposed the use of a composite vertical cantilever model to estimate the initial stiffness of an infilled frame:

13

*3

−

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

+⋅⋅

=IE

hltG

hk

cwww

wt ( 3.2-1)

where:

hw is the masonry-infill panel height;

tw is the masonry-infill panel thickness;

lw is the masonry-infill panel length;

h is the frame height;

Gw is the shear modulus of masonry-infill panel;

Ec is the Young’s modulus of concrete;

I* is the second moment of area of composite cantilever, which may be evaluated through the following relationship:

1222*

32ww

c

wvpp

ltEElA

II⋅

⋅+⋅

+= ( 3.2-2)

where:

Ip is the second moment of area of the column cross-section;

Ap is the area of the column cross-section;

H is the frame length;

Ewv is the Young’s modulus of masonry-infill panel in the vertical direction.

As the load increases, diagonal cracks developed in the centre of the panel, and gaps formed between the frame and the infill in the nonloaded diagonal corners of the specimens, while full contact was observed in the two loaded diagonal corners. This behaviour lead to a simplification in infilled frame analysis by replacing the masonry infill with an equivalent compressive masonry strut (Figure 3.2-4).

The equivalent masonry strut of width (bw), with same net thickness and mechanical properties (such as the modulus of elasticity Ew) as the infill itself, is assumed to be pinned at both ends to the confining frame.

Different approaches for the evaluation of the equivalent width have been presented in various references (Holmes, 1961; Stafford-Smith, 1966; Mainstone and Weeks, 1970; Kadir, 1974; Mainstone, 1974; Klingner and Bertero, 1976 and 1978; Dawe and Seah, 1989; Paulay and Priestley, 1992; Bertoldi et al. 1993; Fardis and Calvi, 1994; Flanagan et al., 1994; Saneinejad and Hobbs, 1995; Mehrabi et al., 1994; Penelis and Kappos, 1997).

193

Figure 3.2-4 Equivalent compressive masonry strut

An of most adopted approaches is that presented by Klingner and Bertero (1976, 1978) which have assumed for the evaluation of the strut width (bw) the following relationship:

( )[ ] ww dhb 175.0 4.0−⋅= λ ( 3.2-3)

where:

dw is the equivalent masonry strut length;

λ is the relative flexural stiffness of the infill to that of the columns of the confining frame.

The dimensionless relative stiffness parameter (λ) may be evaluated using the equation determined by Stafford-Smith (1966) on the bases of analogy to a beam on elastic foundation:

( )4

42sin

wpc

ww

hIEtE

⋅⋅⋅⋅

=θ

λ ( 3.2-4)

where:

θ is the angle between the diagonal and horizontal of the infill.

3.2.4. In-plane strength evaluation of masonry-infill walls

In-plane strength predictions of masonry-infilled frames are a complex, statically indeterminate problem. The strength of a composite-infilled frame system is not simply the summation of the infill properties plus those of the frame. On the basis of experimental observations, one can identify three main failure mechanisms of infilled frames:

a) Corner crushing mode (Figure 3.2-5a).

b) Sliding shear mode (Figure 3.2-5b);

c) Diagonal cracking mode (Figure 3.2-5c);

194

(a) Corner crushing mode

(b) Sliding shear mode

(c) Diagonal cracking mode

Figure 3.2-5 In-plane failure modes of masonry-infill walls

The corner crushing mode represents crushing of the infill in at least one of its loaded corners. This failure mode is usually associated with infill having weak masonry blocks surrounded by a frame with weak joints and strong members.

The sliding shear mode represents horizontal sliding shear failure through bed joints of a masonry infill. This failure mode is associated with infill built with weak mortar joints and frame with strong members and joints. The occurrence of this failure mode causes what is known as the knee brace effect on the frame.

The diagonal cracking mode in the form of a crack connecting the two loaded corners is associated with frames with weak joints and strong members, and infill with strong blocks and mortar joints.

195

Following the limit states design philosophy, the smallest value obtained from all of these possible failure modes will control the shear capacity of the wall (R), as defined by the following relation:

Error! Objects cannot be created from editing field codes. ( 3.2-5)

in which RC, RS and RD are the strengths associate to corner crushing mode, sliding shear mode, diagonal cracking mode, respectively.

Applying the diagonal equivalent masonry strut theory, the wall strength associate to corner crushing failure (RC) may be obtained as follows:

θθ cos⋅⋅⋅= − wwwC tdfR ( 3.2-6)

where:

fw-θ is the ultimate compressive strength of the masonry strut;

bw is the strut width;

tw is the masonry-infill panel thickness;

θ is the angle between the diagonal and horizontal of the infill.

The ultimate compressive strength of the masonry strut (fw-θ) may be evaluated using the following equation:

αθθ /−− = ww Ef ( 3.2-7)

where:

[ ]θθθθαθ424 sin)cos(sin 2cos25.1/ +⋅+⋅=− wvw fE ( 3.2-8)

is the Young’s modulus of the masonry strut;

wvwv fE '/=α ( 3.2-9)

Ewv is the Young’s modulus of masonry-infill panel in the vertical direction.

fwv is the ultimate compressive strength of masonry-infill panel in the vertical (perpendicular to the bed joint) direction.

The strut width (bw) may be evaluated according different approaches, as above illustrated methods, or using following relationship Galati et al. (2005):

θαα

cos)1( wcc

wh

b⋅−

= ( 3.2-10)

where:

4.0)2.0(2

≤⋅

+=

whw

pcpjc ft

MMα ( 3.2-11)

is the ratio between the column-wall contact length and the column height;

hw is the masonry-infill panel height;

Mpj is the minimum of the plastic moment capacity of the column, the beam or the connection, referred to as the plastic moment capacity of the joint;

Mpc is the column plastic moment capacity;

196

fwh is the ultimate compressive strength of masonry-infill panel in the horizontal (parallel to the bed joint) direction.

The wall strength associate to sliding failure (RS) may be evaluated as the minimum of the failure criteria based on Mohr-Coulomb’s theory or on the Turnšek-Čačovič’s theory (RT-C) (Turnšek et al., 1970) taking into account the results obtained in (Stafford-Smith et al., 1966).

CTCMS RRR −−= ,min ( 3.2-12)

in which:

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−+= −

−ww

CM

w

wwuCM tl

Rlh

fR 2.08.0µ ( 3.2-13)

is the wall strength associate to the failure criteria based on Mohr-Coulomb’s theory;

ww

CM

ws

w

w

wwwsCM tlR

flh

tlfR⋅

⋅−

+⋅⋅= −− 5.1

2.08.01 ( 3.2-14)

is the wall strength associate to the failure criteria based on Turnšek-Čačovič’s theory;

where:

fwu is the cohesive strength of masonry-infill panel in the horizontal (parallel to the bed joint) direction;

fws is the is the shear resistance determined by diagonal compression test in accordance with ASTM E519-02 (ASTM 2002);

µ is the coefficient of friction of masonry-infill panel in the horizontal (parallel to the bed joint) direction;

lw is the masonry-infill panel length;

The wall strength associate to sliding failure (RD) according to the relationship proposed by Stafford-Smith et al. (1966) may be obtained as:

6.0wwws

Dtlf

R⋅⋅

= ( 3.2-15)

3.2.5. Infill with openings

Infill walls may have window and door openings. Fiorato et al. (1970) have found that the reduction of the load resistance of an infilled frame is not proportional to the reduction of the cross-sectional area of an infill, owing to openings. In their tests, openings that reduced the horizontal cross-sectional area of an infill by 50% led to a strength reduction of about 20–28% only.

Mosalam et al. (1997) have confirmed this observation. In their study, they tested two two-bay steel frames infilled with concrete block masonry that had window and door openings. One specimen had symmetric window openings with one opening in each bay, and the other had a window in one bay and a door in the other. These openings reduced the horizontal cross-sectional area of an infill by about 17%. Their study has shown that the presence of openings led to a lower initial stiffness, but a more ductile behaviour. The maximum load resistance of the frame with symmetric window openings was almost the same as that without openings. However, the presence of a door opening reduced the load resistance by about 20%. They have observed that crack patterns were affected by the openings. Cracks tended to initiate at the corners of the openings and propagate towards the loaded corners, as opposed to the initiation of a horizontal crack at mid-height that propagated towards the loaded corners in a solid infill (diagonal cracking mode).

197

An approach to account for the effect of openings in the masonry panel consists to assume a equivalent strut which act in the same manner as for the fully infilled frame (Figure 3.2-6) and having an reduced equivalent strut width (b’w,red):

wredw bb ⋅= ρ, ( 3.2-16)

where:

ρ is the reduction factor to account for the loss in strength and stiffness due to the opening, usually expressed as function of area of the openings and area of the fully (without openings) infill panel;

bw is the equivalent strut width of the fully infilled frame.

This type of approach is a simplification in order to compute the global structural capacity. In fact, the reduction the strut width to account the presence of openings does not generally represent the stress distributions likely to occur. Local effects due to an opening should be considered by either modelling the perforated panel with finite elements or using struts to accurately represent possible stress fields.

The presence of openings in the masonry panel may be takes into account by subdividing each masonry panel including windows in sub-panels. According to this approach, sub-panels effective in resisting lateral forces may be considered to be those included between two subsequent panel holes, besides to those adjacent to the RC columns. The masonry-infill panel length (lw) is the actual width measured from hole to hole or from hole to column, while the “effective” height (hw,eff) may be defined according to different criteria (Figure 3.2-7).

Figure 3.2-6 Equivalent compressive masonry strut for a masonry-infill walls with openings

198

Figure 3.2-7 Effective masonry-infill sub-panels

3.2.6. Application to the case study

In order to investigate about the possibility to analytically predict the observed behavior, a back-analysis of the building response has been started.

For the purpose of the computation, values of basic mechanical properties of masonry panels, concrete and steel have been assumed as follows:

- average compression strength parallel to the holes: in the range (4.3 – 9.5) MPa for brick masonry of the building in the original condition (test #1), (5.0 – 11.5) MPa for brick masonry used for the repairing (test #2), (1.3 – 2.0) MPa for light concrete masonry (both test #1 and test #2);

- average compression strength perpendicular to the holes: in the range (2.2 – 4.8) MPa for brick masonry of the building in the original condition (test #1), (4.8 – 5.8) MPa for brick masonry used for the repairing (test #2), (0.7 – 1.0) MPa for light concrete masonry; these values are obtained as 50% of the compression strength parallel to the holes, according to FEMA (1999);

- average Young’s modulus of elasticity: in the range (2365 – 5225) MPa for brick masonry of the building in the original condition (test #1), (2750 – 6325) MPa for brick masonry used for the repairing (test #2), (715 – 1100) MPa for light concrete masonry;

- average cylindrical strength of concrete in compression: 28 MPa;

- average Young’s modulus of concrete: ( )0.3c c22 10 30E f GPa= ≅ (CEN 2005a);

- average yield strength of steel: 480 MPa.

The ranges of expected average values of properties for masonry panels have been established on the basis of a few compression tests carried out on the tile blocks, while assuming reasonable conservative values for the mortar strength (average compression strength = 2.5 MPa) and using literature or code recommendations for relating the block and mortar strength to the masonry panels strength (Paulay and Priestley 1992, CEN 2005b, Italian Ministry of Public Works, 1987). Further diagonal compression tests on masonry panels, with and without FRP strengthening, have been planned to be carried out as future development, in order to confirm these assumptions. All the remaining mechanical properties or parameters needed for computing shear strength of masonry panels, such as, for example, the value of shear strength defined by ASTM E519-02 (ASTM 2002), the cohesive strength at the bed mortar joints, the coefficient of friction, have been assumed according to the suggestions given in Galati et al. (2005), whose guidelines have been strictly applied. Values of strength of concrete and steel are assumed on the basis of information provided by original design drawings, considering knowledge of similar structures

199

located close to the tested building and also using information coming from in-situ non-destructive testing of concrete.

Each masonry panel including windows has been subdivided in sub-panels, using the same scheme adopted for describing experimental results. Sub-panels effective in resisting lateral forces are considered to be those included between two subsequent panel holes, besides to those adjacent to the RC columns. The width of the panel is the actual width measured from hole to hole or from hole to column, while the “effective” height has been defined according to the criteria suggested by Dolce (1991). Namely, the effective height is computed summing up two contributions: the average height h’w shown in Figure 3.2-8a and b) an additional term taking into account the flexibility of the remaining part of the masonry panel. The latter contribution is assumed equal to 0.33lw(hw-h’w)/h’w, where hw is the total panel height and lw is the panel width (Figure 3.2-8a). Then, the effective height is hw,eff = h’w + 0.33l(hw - h’w)/ h’w.

The contribution of the FRP strengthening system to the shear resistance of the panels is computed using the characteristic tensile strength of FRP rods. Other parameters needed for the computation of the shear strength, such as the debonding reduction factor and the parameter accounting for the orientation angle of the fibers with respect to the direction of the failure surface opening, are assumed according to the suggestions given in Galati et al. (2005). An exception has been made for the environment reduction factor, which has been set equal to 1.00 because the application and the test were carried out in a short time.

With reference to the masonry properties coming from the empirical relationship suggested by Paulay and Priestley (1992), the results of the strength computation for the original un-strengthened panels are summarized in Tabel 3.2-1. It can be noticed that the diagonal tension cracking strength (RD) is always larger than the shear sliding strength (RS), but the ratio RD / RS ranges from 1.16 to 1.46 with four cases (sub-panels #3 to #6) exhibiting a percentage difference between RD and RS smaller than or close to 25%. The largest discrepancy between the observed failure mode and the analytical prediction is noted for the panel #2, where crushing at the corner of the panel was first observed, followed by shear sliding at the interface with the first floor beam and, subsequently, by diagonal tension cracking. The predicted failure load for masonry crushing is appreciably larger than the prediction associated to the other two failure modes. The corner crushing of masonry had an important role in determining the behaviour of the corresponding adjacent column, which suffered significant shear effects.

Table 3.2-2 is similar to Table 3.2-1, but showing the prediction of shear strength for the strengthened infill walls. As it can be noted from the comparison between RD and RS, the strengthening of infills strongly increased the strength associated with the diagonal cracking mode, with the ratios RD / RS ranging from 2.77 to 3.45. Consequently, there is in this case good confidence that the sliding shear failure mode should occur.

(a) Effective height of panels.

200

(b) Simplified structural model of the staircase.

Figure 3.2-8 Simplified analytical models.

Table 3.2-1 Computation of shear strength of unstrengthened infill walls (building in the original condition).

Infill

panel #

Corner crushing

RC (kN)

Shear sliding

RS (kN)

Diagonal cracking

RD (kN) RD / RS

Predicted failure mode

Observed failure mode

1 513 44 57 1.31 S D

2 552 87 128 1.46 S C & S & D

3 556 40 46 1.16 S D

4 561 42 50 1.18 S S & D

5 558 46 58 1.24 S S & D

6 556 48 61 1.26 S S & D

(1) C: Corner crushing failure; S: Shear sliding failure; D: Diagonal cracking failure

Table 3.2-2 Computation of shear strength of strengthened infill walls (repaired building).

Infill panel #

Corner crushing

RC (kN)

Shear sliding

RS (kN)

Diagonal cracking

RD (kN) RD / RS

Predicted failure mode

Observed failure mode

1 1409 44 137 3.14 S S

2 1494 87 242 2.77 S C & S

3 1517 40 138 3.45 S S

4 1528 42 141 3.36 S S

5 1521 46 156 3.37 S S

6 1515 48 160 3.32 S S & D

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(1) C: Corner crushing failure; S: Shear sliding failure; D: Diagonal cracking failure

Furthermore, after computing the shear strength of masonry infill panels, an attempt has been made to analytically reproduce the response observed for the whole building. The aim is to get an insight into the distribution of base shear among the different lateral-force resisting elements. The following components have been considered as contributing to the lateral stiffness and strength:

1) the RC columns

2) the staircase structure

3) the perimeter masonry panels (cladding panels parallel to the load direction)

4) the internal masonry panels (partition walls parallel to the load direction)

The contribution to the lateral stiffness and strength of masonry panels has been evaluated by considering two models: composite cantilever model (Mehrabi 1994), for lower lateral load level, and equivalent masonry strut model (Klingner and Bertero 1976, 1978 and Stafford-Smith 1966), for higher lateral load level. In addition, in the analytical model, it is assumed that masonry panels are characterized by a negative post-peak stiffness, equal to 5% of the initial stiffness. Eventually, a residual strength equal to 10% of the peak value is assumed.

The contribution of the staircase structure to the total stiffness and strength of the building has been estimated by schematizing the inclined RC slabs as additional diagonal struts. The simplified model is shown in Figure 3.2-8b (Della Corte et al. 2008). The inclined RC slabs constituting the staircase have been treated as beam-column elements, having the cross-section of the slab. The flexural response in the vertical planes parallel to the loading direction has been neglected, while the elastic restraining effect coming from the bending about the strong axis has been considered (rotational springs shown in Figure 3.2-8b). Elementary mechanics of the system shown in Figure 3.2-8b can be easily studied in order to obtain the contribution of the staircase to the stiffness and strength of the whole system. The first non linear event in the staircase is yielding of the inclined strut subject to tension. After this yielding, a residual stiffness is exhibited by the staircase, which may be easily computed using the same structural scheme of Figure 3.2-8b, but removing the tension strut. The ultimate strength of the staircase sub-structure is then reached when columns supporting the half pace reach flexural yielding at their ends. Since the secondary stiffness (after yielding of the inclined elements) resulted to be a relatively small percentage of the initial stiffness, it has been neglected and an elastic-perfectly plastic model has been assumed for the staircase, using the initial elastic stiffness and the total strength.

The RC column contribution is estimated assuming that they are fixed at the ends and subject to relative transverse displacements. An effective moment of inertia equal to 20% of the gross cross section property has been used, in order to take account of cracking and bar slips (Elwood and Eberhard, 2006). Besides, an effective column height has been assumed, smaller than the clear column length, because of the need to consider column-panel interaction. The effective height of columns has been assumed to be equal to the effective height used for computing the stiffness and strength of panels. The columns’ contribution to the total strength is estimated assuming plastic hinge formation at each column end and locating plastic hinges at a distance from the effective column ends equal to one half of the column depths. A different approach was required for the column adjacent to the panel #2, which failed mainly by shear because of masonry crushing at the corner. In this case, the eccentricity of the equivalent diagonal strut, suggested by FEMA (2000) and discussed by Al-Chaar (2002), has been first computed, thus determining the presumed length of the portion of column subject to strong shear forces. This length resulted in a value of about 700 mm, which is in good accordance with the experimental observation of the length of column subject to strong shear damage. Henceforth, the stiffness of the column has been

202

computed by considering the series composition of the flexural and shear flexibilities relevant to the portion of the column having a length equal to 700 mm. Eventually, the coefficient 0.2 has been applied to the total stiffness for considering concrete cracking and bar slipping.

Results of the analytical computation of the building response during the initial part of test #1 are highlighted in Figure 3.2-9a and here compared with the experimental results. Three analytical curves are reported, corresponding to three different hypotheses on the strength of the masonry panels: Paulay and Priestley (1992), CEN (2005b), Italian Ministry of Public Works (1987). The force-deformation relationships analytically derived for each of the resisting components of the building are also reported in Figure 3.2-9a, with reference to the upper curve (i.e. the curve obtained using masonry properties computed according to Paulay and Priestley (1992)). It is seen that the analytical model results are quite close to the experimental response and the agreement can be considered very good if the simplicity of the analytical model is considered.

The analytical simulation of the response obtained with the test #2 is more difficult to be obtained, because of strength and stiffness degradation occurred in the RC members after test #1. For the sake of simplicity, it has been assumed that the staircase structure does not contribute anymore to the lateral response, while the column contribution has been degraded with empirical degradation factors equal to 0.8 for the strength and 0.5 or the stiffness. The analytical results are reported in Figure 3.2-9b, again with reference to the three different models for computing the strength of masonry panels. Analytical results are also in this case in good agreement with the experimental ones.

Based on the analytical models that more closely represents the response of the building during the two tests, the contribution of the different components to the stiffness and strength of the whole building can be estimated.

Namely, the ratios between the analytical peak strength of each resisting component and the analytical peak strength of the whole building, for the test #1, are as follows: columns = 46%, staircase = 40%, masonry panels = 20%. As far as the stiffness is concerned the following percentage distribution is obtained: columns = 17%, staircase = 41%, masonry panels = 42%. Furthermore, the distribution of shear strength and stiffness between perimeter cladding panels and interior partition panels is as follows: interior panels = 25%, cladding panels = 75%, for strength; interior panels = 21% cladding panels = 79%, for stiffness.

Figure 3.2-9c emphasizes the contribution from the different components to the total building response, using the analytical predictions obtained with the Eurocode 6 suggestion for the masonry mechanical properties. Namely, starting from the response of the degraded columns, relevant to test #2, the contribution of (i) claddings (test #2), (ii) partitions and (iii) staircase has been subsequently added. The curve resulting from this summation is lower than the prediction relevant to test #1, because of degradation of concrete columns from test #1 to test #2.

It is apparent that the distribution of stiffness and strength among the different components cannot be generalized to every situation, because the percentage influence of both the staircase and masonry panels depends upon the number of RC columns, i.e. upon the plan area of the building. This is just a case illustrating that the contribution may be large and it could be appropriate to be taken into account, in order to get a correct picture of the seismic response for small-to-medium inter-story drift angles.

203

0

500

1000

1500

2000

2500

3000

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 51st floor displacement (cm)

Bas

e Sh

ear (

kN)

Experimental

Paulay&Priestley

Eurocode 6

Italian Code

Claddings

ColumnsStaircase

Partitions

(a) Analytical vs. experimental results: test #1.

0

200

400

600

800

1000

1200

1400

0 1 2 3 4 5 6 7 8 9 101st floor displacement (cm)

Bas

e Sh

ear (

kN)

Experimental

Paulay&Priestley

Eurocode 6

Italian codeCladdings

Columns

(b) Analytical vs. experimental results: test #2.

0

500

1000

1500

2000

2500

3000

0 1 2 3 4 5

1st floor displacement (cm)

Bas

e Sh

ear (

kN)

Staircase

Partitions

CladdingsOnly columns

(test #2)Masonry properties

according to Eurocode 6

Test #1Column degradation

from test #1 to test #2

(c) Contribution of different components to the observed

response.

Figure 3.2-9 Analytical model vs. experimental results

204

3.2.7. References

Al-Chaar, G. (2002). “Evaluating strength and stiffness of unreinforced masonry infill structures.” US Army Corps of Engineers, Engineer Research and Development Center, ERDC/CERL TR-02-1.

American Society for Testing and Materials (ASTM) (2002). “Standard test method for diagonal tension (shear) in masonry assemblage.” ASTM E519-02. West Conshohocken, PA.

Bertero VV & Brokken S. “Infills in seismic resistant building”. Journal of Structural Engineering (ASCE) 1983: 109(6): 1337–1361.

Bertoldi, S. H., Decanini, L. D., & Gavarini, C., “Telai tamponati soggetti ad azioni sismiche, un modello semplicato: confronto sperimentale e numerico", Atti del 6o Convegno Nazionale ANIDIS, vol. 2, pp. 815824, Perugia, 13-5 Ottobre 1993.

Buonopane SG & White RN. “Pseudodynamic testing of masonry infilled reinforced concrete frame”. Journal of Structural Engineering (ASCE) 1999: 125(6): 578–589.

European Committee for Standardization (CEN). (2005a). “Eurocode 2 – Design of concrete structures – Part 1-1: General rules and rules for buildings.” EN1992-1-1, Bruxelles.

European Committee for Standardization (CEN). (2005b). “Eurocode 6 – Design of masonry structures – Part 1-1: General rules for reinforced and un-reinforced masonry structures.” EN1996-1-1, Bruxelles.

Dawe JL & Seah CK. “Behaviour of masonry infilled steel frames”. Journal of the Canadian Society of Civil Engineering 1989: 16: 865–876.

Della Corte G., Fiorino L., Mazzolani F.M. (2007). Lateral loading tests on a real RC building including masonry infill panels with and without FRP strengthening. Journal of Materials in Civil Engineering, ASCE, accepted for publication.

Dhanasekar M, Page AW & Kleeman PW. “The behaviour of brick masonry under biaxial stress with particular reference to infilled frames”. Proceedings of the 7th International Conference on Brick Masonry, Melbourne, Australia, 1985:815–824.

Dolce, M. (1991). “Schematisation and modelling of masonry buildings subjected to seismic actions.” L’Industria delle Costruzioni, December, Rome, (in Italian).

Dolsek, M, Fajfar, P. (2004). “Inelastic spectra for infilled reinforced concrete frames”. Earthquake Engineering and Structural Dynamics; 33:1395–1416.

Ehsani, M.R., Saadatmanesh, H., Velazquez-Dimas, J.I. (1999). “Behavior of retrofitted URM walls under simulated earthquake loading.” J. Compos. Constr., 3(3), 134-142.

Elwood, K.J., Eberhard, M.O. (2006). “Effective stiffness of reinforced concrete columns.” Pacific Earthquake Engineering Research Center, Research digest No. 2006-1, March.

Fardis, M. N., & Calvi, M. G., “Effects of infills on the global response of reinforced concrete frames", Proc. of the 10th European Conference on Earthquake Engineering, vol. 4, pp. 2893-2898, Vienna, 1994.

Federal Emergency Management Agency (FEMA). (1999). “Evaluation of earthquake damaged concrete and masonry wall buildings - Basic procedures manual.” Rep. No. 306, Washington, D.C.

Federal Emergency Management Agency (FEMA). (2000). “Prestandard and commentary for the seismic rehabilitation of buildings.” Rep. No. 356, Washington, D.C.

205

Fiorato AE, Sozen MA & Gamble WL. “An investigation of the interaction of reinforced concrete frames with masonry filler walls”. Report UILU-ENG-70-100. Department of Civil Engineering, University of Illinois, Urbana-Champaign IL, USA. 1970.

Flanagan RD & Bennett RM. “In-plane behaviour of structural clay tile infilled frames”. Journal of Structural Engineering (ASCE) 1999: 125(6): 590–599.

Flanagan, R. D., Tenbus, M. A., & Bennet, R. M., “Numerical modelling of clay tile infills", Proc. from the NCEER Workshop on Seismic Response of Masonry Infills-Report NCEER-94-0004, pp. 1/63-68, March 1, 1994.

Galati, N., Garbin, E., Nanni, A. (2005). “Design guidelines for the strengthening of unreinforced masonry structures using fiber reinforced polymers (FRP) systems.” Final draft report. University of Missouri-Rolla. Rolla, MO.

Garevski, M., Hristovski, V., Talaganov, K., Stojmanovska, M. (2004). “Experimental investigations of 1/3-scale RC frame with infill walls building structures.” Proc., 13th World Conference on Earthquake Engineering, Vancouver, Canada, Paper No. 772.

Holmes, M., Steel frames with brickwork and concrete infilling", Proc. Of the Institution of Civil Engineers, part 2, vol. 19, pp. 473-478, London, 1961.

Italian Ministry of Public Works (1987). “Technical standard for the design, execution, verification and structural rehabilitation of masonry buildings.” November, 20th.

Kadir, M. R. A., “The structural behaviour of masonry infill panels in framed structures", PhD Thesis, University of Edinburgh, 1974.

Klingner, R.E., and V. Bertero, “Infilled Frames in Earthquake-Resistant Construction”, Report No. EERC 76-32, Earthquake Engineering Research Center, University of California, Berkeley, December 1976.

Klingner, R.E., and V. Bertero, “Earthquake Resistance of Infilled Frames,” Journal of the Structural Division, ASCE, Vol. 104, June 1978.

Mainstone, R. J., “On the Stiffness and Strength of Infilled Frames,” Proceedings of the Institution of Civil Engineers, 1971.

Mainstone, R. J., “Supplementary note on the stiffness and strength of infilled frames", Current Paper CP13/74, Building Research Establishment, London, 1974.

Mainstone, R. J., & Weeks, G. A., “The influence of bounding frame on the racking stiffness and strength of brick walls", Proc. of the 2nd International Brick Masonry Conference, pp. 165-171, Stoke-on-Trent, 1970.

Mander JB, Nair B, Wojtkowski K & Ma J. “An experimental study on the seismic performance of brick-infilled steel frames with and without retrofit”. Report NCEER-93-0001; National Center for Earthquake Engineering Research, State University of New York, Buffalo, NY, USA 1993.

Mehrabi AB, Shing PB, Schuller MP & Noland JL. “Performance of masonry-infilled r/c frames under in-plane lateral loads”. Report CU/SR-94–6; Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder CO, USA. 1994.

Mehrabi AB, Shing PB, Schuller MP & Noland JL. “Experimental evaluation of masonry-infilled RC frames”. Journal of Structural Engineering (ASCE) 1996: 122(3): 228–237.

Mosalam KM, White RN & Gergely P. “Static response of infilled frames using quasi-static experimentation”. Journal of Structural Engineering (ASCE) 1997: 123(11): 1462–1469.

206

Paulay, T., & Priestley, M. J. N., “Seismic design of reinforced concrete and masonry buildings", John Wiley & Sons, New York, 1992.

Penelis, G. G., & Kappos, A. J., “Earthquake-resistant concrete structures", E & FN Spon, London, 1997.

Polyakov, S.V., “On “The Interaction Between Masonry Filler Walls and Enclosing Frame When Loaded In The Plane Of The Wall,” Translations in Earthquake Engineering Research Institute, 1960.

Saneinejad, A., & Hobbs, B., “Inelastic design of infilled frames", Journal of Structural Engineering, vol. 121, n. 4, pp. 634-650, 1995.

Shing P.B. and Mehrabi A.B. (2002). “Behavior and analysis of masonry-infilled frames,” Prog. Struct. Engng. Mater., 4, 320-331

Schmidt T. “Experiments on the nonlinear behaviour of masonry infilled reinforced concrete frames”. Darmstadt Concrete, Annual Journal on Concrete and Concrete Structures. 1989: 4: 185–194.

Stafford-Smith, B., “Lateral Stiffness of Infilled Frames,” Journal of the Structural Division, ASCE, Vol. 88, December 1962.

Stafford-Smith, B., “Behavior of Square Infilled Frames,” Journal of the Structural Division, ASCE, Vol. 92, February 1966.

Stafford-Smith, B., and C. Carter, “A Method of Analysis for Infilled Frames,” Proceedings of the Institution of Civil Engineers, Vol. 44, 1969.

Triantafillou, T.C. (1998). “Strengthening of masonry structures using epoxy-bonded FRP laminates.” J. Compos. Constr., 2(2), 96-104.

Turnsek V. e Cacovic F. (1970). “Some Experimental Results on the Strength of Brick Masonry Walls”, Proc.,2nd International Brick Masonry Conference, Stock on Trent, 1970.

Zarnic R & Tomazevic M. Study of the behaviour of masonry infilled reinforced concrete frames subjected to seismic loading. Proceedings of the 7th International Conference on Brick Masonry, Australia. 1985: 1315–1325.

3.3. Masonry walls strengthening with FRP composites

3.3.1. Introduction

This section was prepared in accordance with data-sheet no. 9-18 “Review of design recommendations for the evaluation of in-plane shear capacity of masonry walls strengthened with FRP composites” provided by Nagy-Gyorgy T, Daescu C, Florut C., Stoian V. l. from Politehnica University of Timisoara, Romania (ROPUT), respectively in accordance with data-sheet no. 9-17 “models for global analysis”, provided by Mazzolani F. et al. from University of Naples “Federico II”, Italy (UNINA).

The report presents main design aspects regarding the strengthening of the masonry walls for in-plane actions, using FRP composite materials.

3.3.2. Generalities

Recent earthquakes have shown the vulnerability of Un-Reinforced Masonry (URM) buildings, which has led to increasingly demand for techniques to upgrade URM buildings over the last few decades. Fiber Reinforced Plastic (FRP) composites can provide an upgrading alternative for URM buildings.

Several researchers have investigated the effect of FRP as upgrading material for URM walls. Ehsani (1999) increased the out-of-plane resistance of URM walls, during static cyclic tests, as much as 32

207

times the weight of the wall using FRP composites. The increase in out-of-plane resistance of URM walls has been demonstrated by Hamilton (2001) and Hamoush (2002) under monotonic, and by Albert (2001) under static cyclic loading. However, the increase in the in-plane lateral resistance of the retrofitted URM has proved to be less significant than the increase in the out-of-plane resistance. Schwegler (1994) increased the in-plane lateral resistance of URM walls, during static cyclic tests, by a factor of 1.3 by using carbon FRP plates. The enhancement factors in the in-plane lateral resistance ranged from 2 under dynamic loading (Badoux, 2002) to 3 under static cyclic (Abrams, 2001) loading.

In addition, the FRP upgrading technique could increase the lateral drift. In case of upgrading for out-of plane failure, drifts as much as 2.5% was reached (Badoux, 2002). These high drifts have been consistently proved by others. Nevertheless, the improvement in the in-plane lateral drift of the retrofitted URM is to a certain degree controversial. Schwegler (1994) increased the lateral in-plane drift of the retrofitted URM by a factor of 3; while, Abrams (2001) indicated that the FRP has no effect on the lateral drift of URM walls. Holberg (2002) achieved a lateral drift of 1.7%. This high level of lateral drift was achieved by using a ductile connection between the retrofitted URM and its footing. Moreover, this ductile connection increased the ductility and energy dissipation of such a system of retrofitted URM. However, in some cases drift was limited to 0.6% due to the eccentricity caused by this connection, which resulted in out-of-plane failure.

The influence of upgrading URM walls on one face was investigated by Schwegler (1994). It was found that the lateral resistance and ductility of a wall upgraded on one face only was not significantly lower than a wall upgraded on both faces. In addition, no out-of-plane deformations were observed for URM wall upgraded on one face only.

Although FRP experimentally demonstrates high efficiency in increasing the lateral resistance of URM walls, no rational design model is developed for such a system. Many researchers have designed the retrofitted URM based on force equilibrium, strain compatibility, and using Bernoulli-Navier hypothesis.

3.3.3. In-plane shear capacity evaluation of unreinforced masonry walls strengthened with FRP composites

In the Triantafillou (1998) approach, based on the Eurocode 6 format, the analysis and design of reinforced masonry in shear is typically based on the assumption that the total contribution to shear capacity is given as the sum of two terms, similarly to reinforced concrete.

Consider the case of a masonry wall of length l and thickness t, subjected to in-plane shear VRd with axial force NRd (Figure 3.3-1). The wall is reinforced with horizontal epoxy-bonded FRP laminates with area fraction equal to ρh, defined as the total cross-sectional area of horizontally placed FRP divided by the corresponding area of the wall, and possibly with vertical laminates too, to account for other effects (e.g. bending). The FRP laminates have Young's modulus Efrp, ultimate tensile strain εfrp,u and partial safety factor γfrp, and the masonry has ultimate compressive strain εM,u and characteristic compressive strength fk.

208

Figure 3.3-1 FRP-strengthened masonry wall subjected to in-plane shear with axial force

(Triantafillou, 1998)

The first term, VRd1, accounts primarily for the contribution of uncracked masonry, while the second term, VRd2, accounts for the effect of shear reinforcement, which is usually modeled by the well-known truss analogy. The total shear capacity, VRd, of reinforced masonry is given as follows:

M

k2Rd1RdRd

dtf30VVVγ

⋅⋅⋅≤+= . ( 3.3-1)

where

M

vkRd

dtfVγ

⋅⋅=1 ( 3.3-2)

and d is the effective depth.

The contribution of FRP reinforcement to shear capacity is more difficult to quantify. One assumption made here is that the contribution of vertical FRP reinforcement, which provides mainly a dowel action effect, is negligible. This can be justified by the high flexibility of the laminates, in combination with their local debonding in the vicinity of shear cracks. The only shear resistance mechanism left is associated with the action of horizontal laminates, which can be modeled in analogy to the action of either stirrups or shear FRP reinforcement in concrete beams. Adopting the classical truss analogy, as presented above in the case of concrete structures, the contribution of horizontal FRP to shear capacity is given as follows:

ltE70V efrpfrphfrp

2Rd ,. ερ

γ= ( 3.3-3)

where εfrp,e is an effective FRP strain, the only unknown yet to be determined for completing the analysis on FRP contribution to shear capacity.

Finally, the shear capacity of masonry strengthened with FRP laminates as:

MuM

efrph

frpk

vk

k

Rd

k

vko

Mk

Rd 25070f

fltf

N40ff80

ltfV

γεε

ωγγ

..,.min.

,

,max, ≤+⎟⎟⎠

⎞⎜⎜⎝

⎛+= ( 3.3-4)

where

209

hk

frpuMh f

Eρ

εω ,= ( 3.3-5)

εfrp,e is given by an expression in a function of ρhEfrp ,

3.3.4. In-plane strength evaluation of masonry-infill walls strengthened with FRP systems

According to the design methodology developed by Galati et al. (2005) the strengths associate to corner crushing mode (R’C), sliding shear mode (R’S) and diagonal cracking mode (R’D) of a masonry-infill wall strengthened with FRP systems may be calculated as follows:

CFRPC RMFR ⋅=' ( 3.3-6)

FRPSS RRR +=' ( 3.3-7)

FRPDD RRR +=' ( 3.3-8)

in which:

RC, RS and RD are the strengths associate to corner crushing mode, sliding shear mode, diagonal cracking mode of the unstrengthened masonry-infill wall, respectively;

MFFRP is a magnification factor;

RFRP is the shear resistance provided by the FRP system.

The magnification factor (MFFRP) may be determined from experimental test results. Galati et al. (2005) give the values of magnification factors for different FRP systems (GGRP, FRP laminates and FRP structural repointing) and masonry types (concrete and clay).

The shear resistance provided by the FRP system (RFRP) may be determined as: *

, fuEmfvFRP fCkAkR ⋅⋅⋅⋅= ϖ ( 3.3-9)

where:

Af is the total area of FRP reinforcement perpendicular to the shear crack;

kv,ϖ is a parameter which takes into account the orientation angle of the fibers with respect to the direction of the failure surface opening and should be determined from experimental test results. This coefficient is provided by Galati et al. (2005) as function of FRP system (Glass Grid Reinforced Polymer (GGRP), FRP laminates, near surface mounted (NSM) FRP bars not in the bed joints and FRP structural repointing), strengthening layout (one side or both sides), adhesive type (polyurea, epoxy, LMCG) and masonry types (concrete and clay);

km is a reduction factor which takes into account the debonding of FRP in flexure or shear. Galati et al. (2005) summarize the values of km for different FRP systems (GGRP, FRP laminates and NSM FRP bars) and adhesive type (polyurea, epoxy, LMCG).

CE is the environment reduction factor, which may be obtained as function of fiber type (carbon, glass and aramid) and exposure condition (interior exposition, exterior exposition and aggressive environment);

f*fu is the guaranteed tensile strength of FRP provided by the manufactures.

3.3.5. References

Abrams, D. P., and Lynch, J. M. (2001). “Flexural behavior of retrofitted masonry piers.” KEERC-MAE Joint Sem. On Risk Mitigation for Regions of Moderate Seismicity, Illinois.

210

Albert, M. L., Elwi, A. E., and Cheng, J. J. R. (2001). “Strengthening of unreinforced masonry walls using FRPs.” J. Comp. for Constr., ASCE, 5 (2), 76.

Badoux, M., Elgwady, M. A., and Lestuzzi, P. (2002). “Earthquake simulator tests on unreinforced masonry walls before and after upgrading with composites.” 12th ECEE, London, Paper No. 862.

Bakis, E. C., Bank, C. L., Brown, V. L. et al. (2002). “Fiber-reinforced polymer composites for construction- State-of the-art review.” J. Comp for Constr, ASCE, 6(2), 73.

Eurocode 8 (1994). “Design provisions for earthquake resistance of structures.” Comite Euro-International du Béton, Lausanne, Switzerland.

Ehsani, M. R., Saadatmanesh, H., Velazquez-Dimas, J. I. (1999). “Behavior of retrofitted URM walls under simulated earthquake loading.” J. Comp. for Constr., ASCE, 3(3), 134.

ElGawady, A. M., Badoux, M., and Lestuzzi, P. (2003). “Experimental dynamic tests on URM walls.” Response of Structures to Extreme Loading, Toronto.

Elgwady, M. A., Lestuzzi, P., Badoux, M. (2002). “Dynamic in-plane behavior of URM wall upgraded with composites.” 3rd ICCI, San Francisco.

Galati, N., Garbin, E., Nanni, A. (2005). “Design guidelines for the strengthening of unreinforced masonry structures using fiber reinforced polymers (FRP) systems.” Final draft report. University of Missouri-Rolla. Rolla, MO.

Hamilton III, H. R., and Dolan, C. W, (2001), “Flexural capacity of glass FRP strengthened concrete masonry walls.” J. Comp. for Constr., ASCE, 5(3), 170.

Hamoush, A. S., McGinley, W. M., Mlakar, P., Scott, D., and Murray, K. (2001). “Out-of-plane strengthening of masonry walls with reinforced composites.” J. Comp. for Constr., ASCE, 5(3), 139.

Holberg, M., and Hamilton, R., (2002). “Strengthening URM with GFRP composites and ductile connections.” Earth. Spec., 18(1), 63.

Kehoe, B. E., (1996). “Performance of retrofitted unreinforced masonry buildings.” 11th WCEE, Acapulco, Mexico, Paper No. 1417.

Paulay, T. and Priestley, M. J. N., Seismic Design of Reinforced Concrete and Masonry Buildings. John Wiley and Sons, Inc., New York, 1992

Schwegler, G., (1994). “Masonry construction strengthened with fiber composites in seismically endangered zones.” 10th ECEE, Vienna, 2299.

Taghdi, M. (2000). “Seismic retrofit of low-rise masonry and concrete walls by steel strips.” PhD dissertation, Department of Civil Engineering, University of Ottawa, Ottawa, Canada.

Triantafillou, C. (1998). “Strengthening of masonry structures using epoxy-bonded FRP laminates.” J. Comp. for Constr., ASCE, 2(2), 96.

Velazquez-Dimas, J. I.; and Ehsani, M. R., (2000). “Modeling out-of-plane behavior of URM walls upgraded with fibercomposites.” J. Comp. for Constr., ASCE, 4(4), 172.

3.4. Reinforced concrete structures retroffited with steel jacketing

211

3.4.1. Introduction

This section was prepared in accordance with data-sheet no. 9-8 “Calculation models”, provided by Dan Lungu and Cristian Arion, from Technical University of Civil Engineering Bucharest, Romania. The report presents some design methodologies for strengthening reinforced concrete columns with different techniques in order to increase the ductility and the axial load bearing capacity.

3.4.2. Example of reinforcement calculation to increase ductility of a column

1) Properties of the column

Acting axial force (N) = 1412 kN (σ0 = 3.9 N/mm2)

Concrete strength (Fc1) = 17.7 N/mm2

Main reinforcement: 4-D25 (SD35)

at = 2028 mm2

Pt = 0.56%

Hoop reinforcement: 2–9φ at 300-mm pitch (SR24)

Pw = 0.07%

Figure 3.4-1 Properties of the column

2) Strength of the column before retrofitting

Ultimate flexural strength (Mu):

kN5934.2/2712QmkN712mmN10712

)7.17600600

1014121(6001014125.0600)49343(20288.0

)FDb

N1(DN5.0Da8.0M

mu

26

33

1cytu

=×=⋅=⋅×=

×××−×××+×+××=

⋅⋅−⋅+⋅⋅= σ

Ultimate shear strength (Qsu):

212

kN593QkN432QkN432N432000

4816009.31.02941007.085.012.055/120

)7.1718(56.0053.0

jb1.0P85.012.0)dQ/(M

)F18(P053.0Q

musu

223.0

0wysw1c

23.0t

su

=<===

××⎭⎬⎫

⎩⎨⎧

×+××++

+××=

⋅⋅⎭⎬⎫

⎩⎨⎧

+⋅++⋅

+=

−

σσ

Therefore, the failure mode is the shear failure type.

3) Target performance

When the estimated ductility index of the structure after reinforcement is F = 2.5, and when the estimated ductility factor is µ = 3.0, the following is obtained:

5.259.2)0.305.01(75.0

10.32)05.01(75.0

12F >=

×+−×=

µ+−µ

= OK

Therefore, this is appropriate.

When the column is densely reinforced, the required shear strength of the column (reqQsu) will be as follows:

kN712593)9.010

0.3(Q)9.010µ(Q musureq =×+=+=

However, when carbon fiber sheets are wrapped for reinforcement, the required shear strength will be as follows:

kN712593)9.010

0.3(Q)9.010

(Q musureq =×+=+= µ

4) Steel jacketing reinforcement

Figure 3.4-2 Steel jacketing reinforcement

Web reinforcement ratio of existing column Pw=2×0.64/(66×30) = 0.00065

Web reinforcement ratio with steel plate Pw2=2×0.6/66=0.018 → 0.012

Pt(%) after reinforcement Pt=20.28×100/(66×66) = 0.47%

Ultimate flexural strength (Mu) after reinforcement

213

mkN801mmN10801

)7.17660660

1014121(6601014125.066039220288.0

)FDb

N1(DN5.0Da8.0M

26

33

1c2222ytu

⋅=⋅×=××

×−××××+×××=

⋅⋅−⋅+⋅⋅⋅= σ

Flexural capacity (Qmu)

kNMQ columheadumu 6304.2/)801712()/hM( 0base)u(column )( =+=+=

Required shear capacity (reqQsu)

kN756630)9.0103(Q)9.0

10(Q musureq =×+=+= µ

(Qsu)

OKkN756QkN901N901000

6606608.06606601014121.0259012.085.0

12.061/120)7.1718(47.0053.0

Db8.0Db

N1.0P85.012.0)dQ/(M

)F18(P053.0Q

sureq

323.0

2222

wyw1c

23.0t

su

∴=>==

×××⎭⎬⎫

⎩⎨⎧

×××+×+

++××=

⋅⋅⋅⎭⎬⎫

⎩⎨⎧

⋅+⋅+

+⋅+= σ

5) Carbon fiber sheet jacketing

Three layers of carbon fiber sheets are to be wrapped.

Amount applied 300 g/m2

Calculated thickness of the sheets 0.167 mm

Tensile strength σf = 35000 kgf/cm2

Young’s modulus Efd = 2.34 × 106 kgf/cm2

Figure 3.4-3 Carbon fiber sheet jacketing

Design tensile strength of carbon fiber sheet (σfd)

σfd=min(Efd x εfd , (2/3)σf)=min(2.30×105×0.7×10-2, (2/3)×3430)

=min(1610, 2290)=1610N/mm2

214

Web reinforcement ratio with carbon fiber sheet (Pwf)

Pwf=0.167×3×2/600=0.00167

Qsu

OKkNQkNN

......./

).(..

Db..PP..)dQ/(M

)F(P.Q

sureq

.

fdfwwywc

.t

su

∴=>==

×××⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

×+×+×++

+××=

⋅⋅⋅⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+⋅+⋅++⋅

+=

712737737000

60060080931016100016702940007085012055120

717185600530

8010850120

180530

230

01

230σσσ

3.4.3. Example of reinforcement calculation to increase column resistance to axial force

1) Properties of the column

Acting axial force (N) = 3727 kN (σ0 = 10.4 N/mm2)

Concrete strength (Fc1) = 17.7 N/mm2

Main reinforcement: 4-D25 (SD35)

at = 2028 mm2

Hoop reinforcement: 2–9φ at 300-mm pitch (SR24)

Ultimate strength when loaded at the center (Nmax)

Nmax=b x D x Fc + ag x σy =600×600×17.7 + 4056×294 = 7564000N = 7564kN

Figure 3.4-4 Properties of the column

2) Strength of column before retrofitting

Ultimate flexural strength (Mu)

kN5364.2/2643Qm643kNmmN10643

)7.176006004.07564000

37270007564000(7.1760012.060039220288.0

)FD0.4bN

NN(FDb12.0Dσa8.0M

mu

6

3

cmax

maxc

2ytu

=×=⋅=⋅×=

×××−−×××+×××=

⋅⋅−−×⋅⋅+⋅⋅=

215

Ultimate shear strength (Qsu)

kN536QkN550QkN550550000

48160081.02941007.085.012.055/120

)7.1718(56.0053.0

jb1.0P85.012.0)dQ/(M

)F18(P053.0Q

musu

223.0

0wysw1c

23.0t

su

=>===

××⎭⎬⎫

⎩⎨⎧

×+××++

+××=

⋅⋅⎭⎬⎫

⎩⎨⎧

+⋅++⋅

+=

−

σσ

Therefore, the failure mode of the column is flexural type, but with low allowance.

3) Target performance

Improve the column performance to produce the flexural failure mode that can secure a ductility index of F = 1.27 and satisfy the limit value in axial force ratio.

4) Steel jacketing reinforcement (see Figure 3.4-2)

a) Study of the axial force ratio

Current axial force ratio (η)

η=N/ b x D x Fc= 3727×103/ (600×600×17.7)=0.585 > 0.40

(Because the spacing of the hoop reinforcement is 300 mm)

Therefore, reinforcement is required.

Limit value of axial force ratio after reinforcement (ηH)

70.075.0201259

6602940.020/P40.0 H2wy2wH =→=×××+=⋅+= ηση

η=0.585 < ηH=0.70

Therefore, this is appropriate.

b) Verifying the flexural failure mode

Flexural strength when the axial forces are balanced (Qmu)

Column head

Mu=0.8atxσyxD+0.12xbxD2xFc=0.8×2028×392×600+0.12×6003×17.7

=840×106Nmm=840kNm

Column base

Mu=0.8atxσyxD+0.12xbxD22xFc=0.8×2028×392×660+0.12×6603×17.7

=1030×106Nmm=1030kNm

Qmu=(840+1030)/2.4=779kN

Ultimate shear strength (Qsu)

The equivalent web reinforcement ratio with steel plates: 2 × 9 / 660 = 0.027

216

Therefore, the total amount of hoop reinforcement shall be 0.012.

Pt(%) after reinforcement Pt=2028×100 / (660×660)=0.47 %

Assumed axial force (N) N=0.4×600×600×17.7=2550×103N

OKkN779kN992N10992

6606608.06606601025501.0259012.085.0

12.061/120)7.1718(47.0053.0

Db8.01.0PP85.012.0)dQ/(M

)F18(P053.0Q

3

323.0

2202wy2wwyw1c

23.0t

su

∴>=×=

×××⎭⎬⎫

⎩⎨⎧

×××+×+

++××=

⋅⋅⋅⎭⎬⎫

⎩⎨⎧

+⋅+⋅++⋅

+= σσσ

3.4.4. References

AIJ Structural Design Guideline for Reinforced Concrete Buildings, published by the Architectural Institute of Japan, 1994

AIJ Design Guidelines for Earthquake Resistant RC Buildings Based on Inelastic Displacement Concept, published by the Arch. Institute of Japan, 1999

Japanese Standard for Seismic Evaluation of Existing Reinforced Concrete Buildings, 2001

Japanese Technical Manual for Evaluation and Seismic Retrofitting of Existing Reinforced Concrete Buildings, 2001

3.5. Timber composite floor

3.5.1. Introduction

This section was prepared in accordance with data-sheet no. 9-19 “Composite timber-concrete-steel system” provided by L. Calado, J. Proença and A. Panão, from Instituto Superior Técnico, Portugal. The report presents a technique for strengthening timber floor structures using a concrete slab that produces a diaphragm effect reducing deformations and damages during earthquakes.

3.5.2. Description of Device / Technique

The connection between timber beams and concrete slab is achieved using steel devices composed by two parts bolted together around the beam. A connector welded to the upper part joins device and concrete. The device – beam interface may include rubber strips preventing damages, allowing reversibility and accommodation of devices to ancient timber beams with different shapes.

Previously, experimental tests performed at Laboratório de Estruturas e Resistência dos Materiais at Instituto Superior Técnico and numerical simulations were presented and analysed in order to evaluate the system performance and feasibility. Firstly, push-out tests discussed the connection behaviour in terms of load – slip relationships. Afterwards, beam tests analysed the beam behaviour using load – mid-span deflection relationships. Subsequently, device and beam numerical models are assembled in Abaqus, analysed and compared with experimental results.

Finally, a simple and practical design model for the composite timber – concrete system considering slip was studied and will be presented in this datasheet.

3.5.3. Material Model

The composite timber-concrete-steel system comprises the following materials: timber, concrete, steel and rubber.

217

Timber can be modelled as an elastic and isotropic material. Since it is a brittle material, it is possible to stop the analysis when the maximum bending strength is obtained. In the analysis should be introduced the mean value of modulus of elasticity (Etm), the Poisson’s ratio (νt) and the mean value of bending strength (ftm). During the study of this system, bending tests were performed on samples of pine wood allowing the determination of the modulus of elasticity and also of the maximum bending strength, shown in Table 3.5-1.

Table 3.5-1 Properties of timber. Etm [GPa] 11,83

νt 0,3

ftm [MPa] 27,60

Steel can also be modelled as elastic and isotropic material, whose elasticity modulus (Es) and Poisson’s ratio (νs) are shown in Table 3.5-2.

Table 3.5-2 Properties of steel. Es [GPa] 210

νs 0,3

The rubber can be modelled as a hyperelastic material. Hyperelasticity refers to materials which exhibit elastic behaviour after large strain, as illustrated in Figure 3.5-1. Also, these materials are usually nearly incompressible. The hyperelastic model provides a strain energy potential to describe the material behaviour. Since it is assumed that the response of the material is isotropic, the strain energy potentials are expressed in terms of strain invariants or principal stretch ratios. In this case, for the strain energy potential, it can be used a reduced polynomial form of second order. The coefficients where obtained in Abaqus during previous studies (Esposito, 2006). Table 3.5-3 shows the obtained coefficients: C10 and C20 describe the shear behaviour and D1 and D2 the compressive behaviour.

ε

σ

Figure 3.5-1 Non linear stress-strain relation for rubber

Table 3.5-3 Properties of rubber. C10 C20 D1 D2

Rubber 0,56137 0,00229 0,00 0,00

Concrete can be modelled using an isotropic elastic model and a concrete damaged plasticity model. The elastic model allows introducing the modulus of elasticity and the Poison’s ratio. The concrete damaged model is used to limit the tension and the compression in concrete reproducing the behaviour on Figure 3.5-2. The model adopted for concrete can be a linear one in order to reduce the time of the analysis.

218

After reaching the characteristic compressive strength or the average tension strength, the stress in the slab does not increase. The limit chosen can be the characteristic compressive strength since, up till this limit, concrete has behaviour similar to elastic.

Ecm

εεct

fck

σc

fctm

εc

Figure 3.5-2 Linear stress – strain relation used for concrete.

During this study and to determine the exact characteristics of the material, compression tests were performed on cubes and cylinders. Determining the characteristic strength of concrete, it was obtained the modulus of elasticity and the average tension strength for each group of tests. Afterwards, the average of both was calculated. Accordingly, Table 3.5-4 shows the characteristic compressive strength (fck), the mean tension strength (fctm), the modulus of elasticity (Ecm) and the Poisson’s ratio (νc).

Table 3.5-4 Properties of concrete. Average

fck [MPa] 38,2

Ecm [GPa] 34,6

fctm [MPa] 3,4

νc 0,2

3.5.4. Element Model

The behaviour of elements was analysed using push-out tests and device models. From tests were obtain load – relative displacement relationships concerning devices with rubber and devices with rough steel surface.

Figure 3.5-3 depicts the curves for specimens with rubber. Several tests were performed, varying in type and time of loading. It was observed that with load higher than 40 kN the device starts slipping. Consequently, this is the curve that must be used, as shown in Figure 3.5-4.

Table 3.5-5 Characteristics of specimens.

name description surface load bolts water Fu [KN]

type of test

PO-R-M5 load with 20KN, wait 10 minutes after stable and unload R L N N - LW-20

PO-R-M6.2 load with 60KN, wait 10 minutes after stable and unload R R N N - LW-60

219

PO-R-M7 load with 30KN, wait 10 minutes after stable and unload R L N N - LW-30

PO-R-M8 load with 40KN, wait 10 minutes after stable and unload R R N N - LW-40

PO-R-M9 load with 50KN, wait 10 minutes after stable and unload R L N N - LW-50

PO-R-M3.2 load till slip and unload R R N N 143 LS

Figure 3.5-3 Load vs. relative displacement (average of transducers TR5 and TR6).

Figure 3.5-4 Load vs. relative displacement (average of transducers TR5 and TR6).

Figure 3.5-5 depicts the curves for specimens with rough steel surface. Similar to devices with rubber, several tests were performed, varying in type and time of loading. It was observed that with load higher than 100 kN the device starts slipping. Figure 3.5-6 shows the curve that must be used.

Table 3.5-6 Characteristics of specimens.

name description surface load bolts water Fu [KN] type of test

PO-S-M6.1 load with 75KN, wait 10 minutes after stable and unload S L N N - LW-75

PO-S-M6.2 load with 25KN, wait 10 minutes after stable and unload S R N N - LW-25

PO-S-M6.3 load with 50KN, wait 10 minutes after stable and unload S R N N - LW-50

220

PO-S-M6.4 load with 100KN, wait 10 minutes after stable and unload S R N N - LW-100

PO-S-M6.5 load till slip and unload S R N N 119 LS

Figure 3.5-5 Load vs. relative displacement (average of transducers TR1 and TR4).

Figure 3.5-6 Load vs. relative displacement (average of transducers TR1 and TR4)

These force-displacement curves can be used to determine stiffness and strength of elements. For the Serviceability Limit States (SLS) the force should be limited to 40% of ultimate force obtained in tests. Concerning the Ultimate Limit States (ULS) this value should be 60 to 70%. The stiffness of devices may be determined using these values, as shown in Figure 3.5-9 and Table 3.5-7. As can be observed in Figure 3.5-4 and Figure 3.5-6 with these levels of force it is acceptable to consider an elastic behaviour for the element.

δ

0,4Fu

Fu

F

0,7Fu

kULS

kSLS

Figure 3.5-7 Determination of stiffness of devices

221

Table 3.5-7 - Determination of stiffness of devices.

Device Surface Test Fmax

[kN] 0,4Fmax [kN]

δ [mm]

kSLS [kN/m]

0,7Fmax [kN]

δ [mm]

kULS [kN/m]

R PO-R-M8 40 16 0,29 5,52E+04 28 0,70 4,00E+04

S PO-S-M6.4 100 40 0,10 4,00E+05 70 0,2 3,50E+05

3.5.5. Connections

Connections between existing structure and new devices is achieved using rubber strips in the contact surface timber beam – steel devices or producing a rough steel surface in the inner part of devices, as previously described.

In addition, connection between walls and floors is extremely important since a stiff concrete slab is added to the existing structure. This connection may be improved using special devices which add stiffness to the structure and allow energy dissipation, as shown in Figure 3.5-8. Nevertheless, other type of connections, as shown in Figure 3.5-9, may need to be added since the walls will be subjected to high tension, compression and shear stresses.

Figure 3.5-8 Connection using special devices (Cóias e Silva, 2001)

Figure 3.5-9 – Connection using reinforced concrete (Cóias e Silva, 2001)

3.5.6. System Model

The system can be modelled using composite timber – concrete beam sections. Since timber is a brittle material and experimental results show that concrete exhibited approximately elastic behaviour during

222

tests, an elastic model can be used. As a consequence of slipping of devices, the model should consider partial interaction between both materials.

Analytical Method Considering Slip

The analytical calculation model to design composite sections with partial interaction can be based on equilibrium equations. This theory considers that beam comprises elements in equilibrium joined together by displacement compatibility equations. It is based in the following assumptions:

- joints between elements are continuous and uniform all over the beam (connectors have uniform spacing);

- relative displacement of interface surface is proportional to shear force applied to the connection (each connector presents a linear behaviour);

- deflections are small and equal in both elements;

- Bernoulli hypothesis is valid (distribution of deformation throughout the height of elements is linear);

- material behaviour follows Law of Hooke;

shear deformation is neglected.

Each connector is subjected to longitudinal shear leading to displacements.

sFv s= Cuv =

sKC = ( 3.5-1)

Where:

ν - longitudinal shear

Fs - shear force in the connector

s - spacing between connectors

C - stiffness of the connection

u - slippage in the connection

K - slip modulus

Figure 3.5-10 Composite beam and equilibrium configuration of an elemental segment with length

dx (Kreuzinger, 1995)

Relative displacement between parts can be obtained considering shear deformation neglectable and simple bending.

223

Figure 3.5-11 Deformations (Kreuzinger, 1995)

awuu2

h2hwuuu '

1221'

12 +−=⎟⎠

⎞⎜⎝

⎛ ++−= ( 3.5-2)

Where:

u - relative displacement or slippage between the parts of connection

u1 and u2 - longitudinal displacement of axis 1 and 2 of cross section

w - vertical displacement

w’ – rotation

Adding the elasticity principles, the following expressions are obtained: '1111 uAEN =

'2222 uAEN = (3.5-3)

''111 wIEM −=

''222 wIEM −= (3.5-4)

'''111 wIEV −=

'''222 wIEV −= (3.5-5)

( )awuuCCuv '12 +−== (3.5-6)

Where:

N1 and N2 - axial force in part 1 and 2

M1 and M2 - bending moment in part 1 and 2

V1 and V2 - shear force in part 1 and 2

E1 and E2 - modulus of elasticity in part 1 and 2

A1 and A2 - area of part 1 and 2

I1 and I2 - inertia of part 1 and 2

Using the equilibrium principles in each part in both longitudinal and vertical directions and bearing in mind that load px=0 and (N1+N2)’=0:

0vN'1 =+ (3.5-7)

0vN'2 =+ (3.5-8)

2hvVM 1

1'1 −= (3.5-9)

2hvVM 2

2'2 −= (3.5-10)

224

''2

'1 VpVV =−=+ (3.5-11)

Where:

p – load

Adding bending moments and differentiating with respect to x:

0pavMM '''2

''1 =+++ (3.5-12)

From equations (3.4-2), (3.4-7), (3.4-8) and (3.4-12):

( ) 0awuuCuAE '12

''111 =+−+ (3.5-13)

( ) 0awuuCuAE '12

''222 =+−− (3.5-14)

( ) ( ) pawuuCawIEIE '''1

'2

IV2211 =+−−+ (3.5-15)

For the resolution of these equations an approximate method (Kreuzinger, 1995) can be adopted. Hence a sinusoidal distribution of loading is assumed. Consequently, displacements in longitudinal and vertical directions have also cosinusoidal and sinusoidal shapes, respectively.

⎟⎠⎞

⎜⎝⎛ π= xL

senpp 0 (3.5-16)

⎟⎠⎞

⎜⎝⎛ π= xL

cosuu 101 ⎟⎠⎞

⎜⎝⎛ π= xL

cosuu 202 ⎟⎠⎞

⎜⎝⎛ π= xL

senww 0 (3.5-17)

Where:

L - beam span

p0 – maximum load

u10 and u20 – maximal longitudinal displacements at the beam end)

w0 – maximum vertical displacement (at mid-span)

Replacing these equations in (3.4-13), (3.4-14) and (3.4-15) the following expressions are obtained:

[ ] 0aL

CwCuCAEL

u 020112

2

10 =⎥⎦⎤

⎢⎣⎡ π+−⎥

⎦

⎤⎢⎣

⎡−π− (3.5-18)

[ ] 0aL

CwCAEL

uCu 0112

2

2010 =⎥⎦⎤

⎢⎣⎡ π−+⎥

⎦

⎤⎢⎣

⎡−π−+ (3.5-19)

( ) 02

2

2

22114

4

02010 paL

CIEIEL

waL

CuaL

Cu =⎥⎦

⎤⎢⎣

⎡ π++π+⎥⎦⎤

⎢⎣⎡ π+⎥⎦

⎤⎢⎣⎡ π− (3.5-20)

The solution of the system is given by:

( )eff4

4

00 EI1Lpw

π= (3.5-21)

22111

221010 AEAE

AEaL

wu+γ

γπ= 22111

111020 AEAE

AEaL

wu+γ

γπ−= (3.5-22)

( ) 2222

211112211

22

111

2111

2211eff aAEaAEIEIE

AEAE1

aAEIEIEEI +γ++=γ+

γ++=

225

1

211

2

1 KLsAE1

−

⎥⎦

⎤⎢⎣

⎡ π+=γ

2hha 21 +=

22111

1112 AEAE

aAEa+γ

γ= 21 aaa −= (3.5-23)

The stresses at both elements can be obtained relating principles of elasticity to these deformations:

LuE

2LxuE 101

'111

π−=⎟⎠⎞

⎜⎝⎛ ==σ

LuE

2LxuE 202

'222

π−=⎟⎠⎞

⎜⎝⎛ ==σ (3.5-24)

Where:

σ1 and σ2 - stress in elements 1 and 2 of the cross section

Figure 3.5-12 shows the distribution of stresses in the model considering slip.

Figure 3.5-12 Cross section and distribution of stresses

Bearing in mind equations (3.4-25) and (3.4-26), stresses in the cross section can be obtained.

sup

01, W

Mm =σ

inf

02, W

Mm =σ (3.5-25)

2

2

00 πLpM = (3.5-26)

( ) 1110

1 aEEIM

eff

γσ = ( ) 220

2 aEEIM

eff

=σ (3.5-27)

( )effm EI

MhE 0111,

5,0=σ ( )effm EI

MhE 0222,

5,0=σ (3.5-28)

Where:

σm,1 and σm,2 - stress in elements 1 and 2 due to bending

M0 – maximum bending moment

Wsup and Winf – section modulus referred to upper and lower fibres, respectively

226

Slip Moduli

The values for slip modulus between timber and concrete when beams undergo bending can be based on the equations above described and the beam tests performed. The slip modulus is calibrated in order to obtain the same result as in beam tests for a determined level of load, as shown in Figure 3.5-13. Effective bending stiffness and tension limits allow sketching lines for Serviceability Limit States (SLS) and Ultimate Limit States (ULS), according to equations (3.4-38). To allow this comparison, it is assumed that there is total interaction and the beam stiffness is the effective bending stiffness. Also, material properties used to limit tension are the ones obtained in experimental tests (mean values for timber bending strength and elasticity modulus, characteristic value for concrete compressive strength and mean values for concrete tensile strength and modulus of elasticity).

aM2

F maxmax = ⎟⎟

⎠

⎞⎜⎜⎝

⎛−=δ 2

2

eff

maxmax a

4L3

)EI(6M2 (3.5-29)

Where:

Fmax - maximum force in mid-span cross section

Mmax - maximum bending moment in mid-span cross section (obtained limiting tension)

(EI)eff - effective bending stiffness

L - span

a - distance between support and place of application of load

For SLS, the slip modulus can be obtained using the secant to the curve when force is 40% of ultimate beam force. In this level of force it is acceptable to consider elastic behaviour for the connection. Concerning ULS, the slip modulus can be obtained using the secant to the curve when force is 60 to 70% of ultimate beam force. Alternatively, it can be considered 2/3 of SLS slip modulus.

Figure 3.5-13 – Slip moduli

Table 3.5-8 shows the values of slip modulus for maximum load obtained for each beam test. It is possible to observe that specimens with rough steel surface present a higher slip modulus for SLS. However, for ULS the slip modulus decreases and the beam that presents a higher value is the one with bolts connecting timber and concrete. Moduli do not vary significantly between identical tests. Figure 3.5-14 shows the lines sketched for a beam test with rubber and uniform spacing.

Table 3.5-8 Determination of slip modulus and effective bending stiffness SLS ULS

Name 40% Fu [kN] KSLS [GPa] (EI)eff,SLS [kNm2] 70% Fu [kN] KULS [GPa] (EI)eff,ULS

[kNm2]

Test 1 (B-RU) 19,66 0,030 2,97E+03 34,40 0,012 2,28E+03

227

Test 2 (B-RV) 35,23 0,055 3,62E+03 61,65 0,042 3,31E+03

Test 3 (B-SU, with bolts) 32,82 0,150 4,84E+03 57,43 0,070 3,92E+03

Test 4 (B-RU) 21,82 0,035 3,12E+03 38,18 0,013 2,32E+03

Test 5 (B-RV) 17,21 0,040 3,26E+03 30,12 0,017 2,49E+03

Test 6 (B-SV) 27,02 0,300 5,54E+03 47,28 0,027 2,87E+03

Figure 3.5-14 Determination of slip modulus for beam Test 1

Table 3.5-9 – Comparison of results of experimental tests and design model in terms of maximum force and displacement. Tests Serviceability Limit States Ultimate Limit States

Name Fu [kN] δu [mm] Fmax [kN] δmax [mm] Fmax [kN] δmax [mm]

Test 1 B-RU 49,15 68,11 68,86 66,07 59,26 73,98

Test 2 B-RV 88,07 93,00 76,32 59,92 72,99 62,66

Test 3 B-SU 82,04 72,99 86,99 51,13 79,20 57,55

Test 4 B-RU 54,54 93,10 70,74 64,52 59,95 73,41

Test 5 B-RV 43,03 51,70 72,39 63,16 62,51 71,30

Test 6 B-SV 67,54 76,81 91,78 47,18 67,61 67,10

Figure 3.5-14 and Table 3.5-9 show that this method is adequate for describing the behaviour of the solution and design composite sections. Nevertheless, the maximum load can be underestimated due to variability of timber properties.

3.5.7. Analysis Types

In the global analysis of the structure including the composite system should be used an elastic analysis. Since this system is used to strengthen the floor to vertical loads, this is the most adequate approach. Concerning seismic strengthening, the effect of the system is to produce a rigid diaphragm effect. This effect can be obtained by simply modeling the concrete slab with elastic properties.

3.5.8. Performance Criteria

To design the strengthened building using the composite timber-concrete system, the partial factor method can be used, in accordance with Eurocodes. The composite sections must be verified using an elastic model with partial interaction and different slip moduli for SLS and ULS.

228

Effective Bending Stiffness

Slip moduli for SLS and ULS were determined using beam tests. Using these values it is defined the inertia reducing factor:

1

211

2

1 KLsAE1

−

⎥⎦

⎤⎢⎣

⎡ π+=γ (3.5-30)

Spacing between connectors may be uniform or vary according to shear force between smin and smax, with smax≤4smin. In this case, an effective spacing may be used:

maxmineff s25,0s75,0s += (3.5-31)

The theory of linear elasticity considers a simply supported beam with a span L. For continuous beams expressions may be used with L equal to 0,8 of relevant span and for cantilevered beams with L equal to twice the cantilever length.

The distance between centres of gravity of each part of the section and neutral axis is:

Error! Objects cannot be created from editing field codes. Error! Objects cannot be created from editing field codes. (3.5-32)

As a result, it is possible to determine the effective bending stiffness of the beam:

( ) 2222

211112211eff aAEaAEIEIEEI +γ++= (3.5-33)

Normal Stresses

Normal stresses can be obtained using:

Error! Objects cannot be created from editing field codes. Error! Objects cannot be created from editing field codes. (3.5-34)

Error! Objects cannot be created from editing field codes. Error! Objects cannot be created from editing field codes. (3.5-35)

As can be observed in the stress distribution in the cross section, stresses should be limited using the following equations:

c1,m1 f≤σ+σ ct1 f≤σ t2,m2 f≤σ+σ (3.5-36)

Where:

fc – concrete compressive strength

fct – concrete tensile strength

ft – timber bending strength

As mentioned, the partial factor method can be used to design beams, in accordance with Eurocode 0 (CEN, 2001). In Eurocode 2 (CEN, 2003) and Eurocode 5 (CEN, 2004) is possible to obtain the properties of materials, as shown in the following equations:

c

ckcdc

fff

γ==

c

ctkctdct

fff

γ==

t

tkmodtdt

fkff

γ==

(3.5-37)

cE

cmcd1

EEE

γ==

t

tmtd2

EEE

γ== (3.5-38)

Where:

fcd - design value of concrete compressive strength

229

fck - characteristic compressive cylinder strength of concrete at 28 days

fctd - design value of concrete tensile strength

fctk - characteristic axial tensile strength of concrete

γc - partial factor for concrete (Eurocode 2 suggests 1,50)

ftd - design value of timber bending strength

ftk - characteristic compressive strength of timber bending strength

γt - partial factor for timber (Eurocode 5 suggests 1,30)

kmod - modification factor for timber, depending on the effect of time of load and moisture content

Ecd - design value of modulus of elasticity of concrete

Ecm - secant modulus of elasticity of concrete

γc - partial factor for concrete for the elasticity modulus (Eurocode 2 suggests 1,20)

Etd - design value of modulus of elasticity of timber

Etm - mean value of modulus of elasticity of timber

3.5.9. References

CEN European Committee for Standardization (2004) EN 1995-1-1 - Eurocode 5: Design of Timber Structures – Part 1.1: General – Common Rules and Rules for Buildings. Bruxels, Belgium.

CEN European Committee for Standardization (2003) prEN 1992-1-1 - Eurocode 2: Design of Concrete Structures – Part 1.1: General Rules and Rules for Buildings. Bruxels, Belgium.

CEN European Committee for Standardization (1993) prEN 1993-1-1 - Eurocode 3: Design of Steel Structures – Part 1.1: General Rules and Rules for Buildings. Bruxels, Belgium.

CEN European Committee for Standardization (2001) prEN 1990 - Eurocode: Basis of Structural Design. Bruxels, Belgium.

Cóias e Silva, V. (2001) Viabilidade Técnica de Execução do Programa Nacional de Reduçãoda Vulnerabilidade Sísmica do Edificado. Encontro Sobre Redução da Vulnerabilidade Sísmica do Edificado, Ordem dos Engenheiros, Portugal (in portuguese).

Esposito, V. (2006) Analisi Numerico-Sperimentali di un Sistema di Connessione in Acciaio per Solai Composti Legno-Acciaio-Calcestruzzo. Tesi di Laurea. Università degli Studi di Napoli “Federico II”, Italia. (in italian)

Farinha, J., Farinha, M., Farinha, J., Reis, A. (2003) Tabelas Técnicas. Edições Técnicas ETL,Lda. Lisboa, Portugal. (in Portuguese)

Kreuzinger, H. (1995) Mechanically Jointed Beams and Columns. Timber Engineering - Step1. Almere: Centrum Hout.

3.6. Development of design rules for the iron columns reinforced by FRP

This section was prepared in accordance with data-sheet no. 9-3 “Development of design rules for cast iron columns reinforced by FRP” provided by Ly L., Demonceau J.F. and Jaspart J.P., from University of Liège, Belgium. The report presents a design methodology for strengthening iron columns with FRP techniques. The analytical model presented below was validated through comparisons with numerical

230

results and was experimentally verified. The proposed numerical model was able to provide a safe prediction of the buckling resistance of iron members with or without FRP.

3.6.1. Description of the device/technique

In the available literature, some techniques of reinforcement are proposed: reinforcement with the use of cables, replacement of damage elements, creation of a composite action by connecting the damage elements to a concrete slab, etc; but few of them are applicable to the Umberto 1 gallery. The one that seems to be applicable is the FRP (Fibre Reinforcement Polymer) technique. The behaviour of composite elements composed of FRP and steel members under tension seems to be known, but little information is available as far as the behaviour of such elements in compression.

Following the "Iron meeting" held in Naples on June 8th, 2006, tests on stocky elements with and without FRP are planned to be performed in tension and in compression to identify the effect of FRP on such elements. In addition, tests on slender columns will be performed with and without FRP to investigate the influence of the latter on the buckling resistance. All the tests will be accompanied by coupon tests to identify the mechanical properties of the constitutive material of the tested specimens (Liège contribution to WP7).

Based on the test campaign, analytical design rules founded on an elastic approach have been developed for the computation of the resistance of iron columns reinforced by FRP; these rules are detailed in the present section.

3.6.2. Material model

FRP material

The applicability and the effectiveness of strengthening with FRP depend largely on the material and the nature of the member to be strengthened. When applied as reinforcement, the strengthening material should have a similar or higher stiffness compared to the member to be strengthened. Figure 3.6-1 shows stress-strain behaviour laws for different commercial FRPs compared to the steel one.

The strengthening of steel or iron members with FRP may be both mechanically and economically satisfactory in retrofitting due to ease of installation and the potential of eliminating welded and bolted repairs. In particular, for historical buildings, the overall aim is to preserve the appearance of all structural elements to be reinforced, what is possible with the FRP technique.

Figure 3.6-1: Stress-strain behaviour curves for different FRPs compared to the steel one 0

As shown in Figure 3.6-1, FRP material is characterized by an elastic behaviour with an elastic modulus Ef, a tensile strength σf,u and a Poisson coefficient νf (Figure 3.6-2). As no information is available concerning the behaviour of this material subjected to compression, it will be assumed here below that this behaviour is the same than the one observed when this material is subjected to tensile stresses.

231

Figure 3.6-2 Elastic mechanical law of mono-axial FRP material

3.6.3. Element model

State of the art

For elastic designs, some rules are available in the literature (CNR-DT 202/2005) to predict the resistance of steel elements reinforced by FRP subjected to tension loads or to bending moments, but no rules have yet been addressed to predict the buckling resistance of these elements under bending and/or axial compression. Three main buckling problems may occur when members are subjected to such loadings: compressive buckling associated to members under axial compression, lateral torsional buckling associated to members under bending, and compressive flexural buckling associated to members under bending and axial compression.

For the simplicity’s sake, it is possible to solve all these problems through the solution found for the compressive buckling associated to members under axial compression:

a) Members under bending (Lateral Torsional Buckling – LTB)

No information relative to the resistance of iron elements affected by lateral torsional buckling seems available. As an alternative to the study of the actual LTB effects, it is possible to refer, for I-shape elements, to a traditional approach which consists in considering LTB as the transverse flexural buckling of the compression flange.

b) Members under bending and axial compression

An iron member in bending and axial compression is affected, at the same time, by compressive buckling and by LTB. Accordingly, it is possible to refer to an elastic interaction criteria to combine these two phenomena.

That is why the priority of this research is first to focus on the computation of the buckling resistance of iron columns reinforced by FRP under axial compression.

In parallel with analytical activities, experimental and numerical investigations have also been performed in order to validate the proposed design rules. Hollow cast iron columns (Figure 3.6-3) have been selected to investigate the behaviour, and particularly when they are reinforced by FRP sheets.

Figure 3.6-3: Hollow cast iron columns selected for buckling tests

Through the performed numerical works which are not detailed in the present section, the problems of local transfer of shear stresses between FRP and iron elements, especially at the extremities of the FRP sheets has been carefully studied. Both cases where compression and tension forces are respectively applied have been investigated. At some distance from the extremities, no relative displacement between

232

FRP and iron is reported and so, in these zones, a full composite interaction between both components may be assumed. Besides that, when compression is applied, a debonding of the FRP sheets may be observed which leads to a sort of buckling of the FRP reinforcement and so to a local reduction of section resistance. For sure this last aspect can not be disregarded.

As a result, for FRP material, compressive strains should be limited to prevent such a complex failure mode involving localized debonding associated with local buckling and crushing (Shaat and Fam, 2007) According to the latter, the limit strain value is equal to 0.13% for steel columns strengthened by high modulus composite materials. That significantly restricts the enhancement of the stiffness and resistance properties of iron columns with FRP whatever the quality of the latter. Therefore, transversal FRP sheets should be also applied in addition with longitudinal ones so as to improve the limit compressive strains.

Cross-sectional resistance in compression

During their life span, iron elements may be affected by corrosion. The main consequence of the latter is to make the iron section thinner; procedures (Guerrieri, Di Lorenzo and Landolfo) are available to estimate this effect. Once the reduction of thickness of structural element sections is known, a re-evaluation of slenderness of the constitutive elements of the cross-section (“b/t”) should be done to ensure that there is not any risk of local buckling for these elements.

Experimental tests on stocky elements show that within the elastic domain (ε ≤ 0.2%), FRP and iron member behave as different parts of a monolithic cross-section (Ly, Demonceau, Jaspart, 2008). Then the elastic resistance of a composite cross-section in compression can be calculated with the entire transversal area as follows:

, ,0.2,e Rd i c eqN Aσ= ( 3.6-1)

Aeq is the equivalent cross-sectional area, see formula 3.6-2.

EC3’s criteria to classify steel transversal sections can be used for cast iron columns. FRP reinforcement can be designed to reinforce the resistance of iron elements and to increase the stiffness of the member. In particular, the FRP reinforcement should be designed such as the so-obtained composite cross-section can be assumed as class 1, 2 or 3 and accordingly, its elastic resistance can be estimated through formula (3.6-1) .

Members under axial compression

An analytical formulation is proposed by Rondal and Rasmussen (2003) to predict the buckling resistance of iron columns subjected to axial compression. Its extension to FRP reinforced iron is here contemplated. As iron is quite resistant in compression, but relatively weak in tension, two possible failure modes have to be successively considered (Figure 3.6-4):

Figure 3.6-4: Strain and stress distribution for FRP-iron composite section

- failure by excess of compression on the thin side;

233

- failure by excess of tension on the thick side.

The location where failure occurs in the section (thin or thick side) results from the eccentricity geq between the centroid and the load introduction axis.

a) Mechanical characteristics of a composite cross-section

The strain and stress distribution within a composite section is described in Figure 3.6-4. The equivalent area of the composite cross-section can be calculated with the following formula:

eq i eq fA A n A= + ( 3.6-3)

where

- the equivalent coefficient neq is given by

feq

i

En

E= ( 3.6-4)

- the areas of FRP Af (assuming that the thickness of FRP sheets tf is much smaller than the outer diameter of iron member de) and iron section Ai are given by

e22f

f f

tA t rπ ⎛ ⎞

= +⎜ ⎟⎝ ⎠

( 3.6-5)

and

( )2 2i e iA r rπ= − ( 3.6-6)

The equivalent second moment of inertia for the composite cross-section can be estimated by the following formula:

eq i eq fI I n I= + ( 3.6-7)

where

- the second moment of inertia for the iron member section Ii is given by

( )24 2 4 2

4 4i e e eq i i eqI r r g r r g jπ ππ π⎡ ⎤= + − + +⎢ ⎥⎣ ⎦ ( 3.6-8)

with the position of the gravity centre geq, according to the centre of the outer perimeter of the iron member, estimated through formula

2

ieq

eq f i

jrgn A A

π=+

( 3.6-9)

- the second moment of inertia for the FRP area If is estimated by 3

2

2f

f f e f eq

tI t r A gπ ⎛ ⎞

= + +⎜ ⎟⎝ ⎠

( 3.6-10)

The distances veq and veq’ between the gravity centre geq and the extreme fibres of the iron member, as illustrated in Figure 3.6-4, are equal to

eq e eqv r g= + ( 3.6-11)

'eq e eqv r g= − ( 3.6-12)

b) Compression failure

234

Working with the equivalent iron cross-section, the nominal buckling compressive stress σb,c (Nu/Aeq), when the column reaches the buckling resistance (Nu), can be derived through the following formula:

, ,0.2,b c c i cσ χ σ= ( 3.6-13)

where σi,0.2,c is the 0.2% proof stress of iron in compression and χc, the slenderness reduction factor calculated when the most stressed iron or FRP fibre (the farthest fibre) reaches its elastic strength (σi,0.2,c or σf,u,c). In other words, the farthest fibre of the equivalent cross-section reaches a stress σi,c corresponding to a strain εi,c, the latter being defined as the minimum of the two values εi,0.2,c and εf,u,c corresponding to the ultimate strain for the iron material and the FRP respectively (Figure 3.6-4). If fc designates the ratio σi,c /σi,0.2,c, χc can be calculated as follows:

22

cc

c c c

f

fχ

ϕ ϕ λ=

+ − ( 3.6-14)

with 21 (1 )

2c c cfϕ η λ= + + ( 3.6-15)

where

e

λλλ

= ( 3.6-16)

eq

Lr

λ = ( 3.6-17)

eqeq

eq

Ir

A= ( 3.6-18)

and

,0.2,

ie

i c

Eλ πσ

= ( 3.6-19)

The imperfection parameter ηc is given by

( )1 0eq

c c eq eqeq

vg A

Iβη α λ λ λ⎡ ⎤= − − +⎣ ⎦ ( 3.6-20)

(α, β, λ0, λ1), accounting for the column imperfection, depend on the material parameters n and ,0.2, /i c ie Eσ= (parameters which can be defined from the Ramberg-Osgood law. The link between these

material parameters and (α, β, λ0, λ1) is given in Rasmussen and Rondal (2000):

0.550.0048 0.61.40.6

1.5 0.002( , )( 0.03)( 13)e

n ee

e nα

+= +

+ + ( 3.6-21)

6

0.45 1.4

0.36exp( ) 6 10( , ) tanh 0.040.007 180

n nn ee e

β−⎛ ⎞− ×= + + +⎜ ⎟+ ⎝ ⎠

( 3.6-22)

0 ( , ) 0.82 0.01 0.20.0004en e n

eλ ⎛ ⎞= − ≥⎜ ⎟+⎝ ⎠

( 3.6-23)

235

0.62

155( , ) 0.8 1 6 0.00540.00180.0015

e nn e ee ne

λ

⎧ ⎫⎡ ⎤⎛ ⎞⎪ ⎪⎢ ⎥⎜ ⎟−⎪ ⎪⎢ ⎥= −⎨ ⎬⎜ ⎟−+ ⎢ ⎥⎪ ⎪⎜ ⎟+⎢ ⎥+⎝ ⎠⎪ ⎪⎣ ⎦⎩ ⎭

( 3.6-24)

The term /eq eq eq eqg A v I in formula (3.6-20) accounts for the cross-section imperfections.

c) Tension failure

Cast iron is relatively weak and brittle in tension; a column failure by excess of tension may be observed, as a result of the development of significant second-order bending moment in slender columns. The verification of the tension failure mode can be achieved through the following resistance formula:

, ,0.2,b t t i cσ χ σ= ( 3.6-25)

As in the previous paragraphs, χt should be calculated when the farthest iron or FRP fibre reaches its elastic strength in tension (σi,u,t or σf,u,t). But in practice the FRP strength σf,u,t is much higher than the iron one; so the tension failure takes place in the iron material. If ft designates σi,u,t /σi,0.2,c, the slenderness reduction factor χt can be calculated through the following formula:

22

tt

t t t

f

fχ

ϕ ϕ λ=

+ + ( 3.6-26)

where 21 ( 1 )

2t t tfϕ η λ= − + + ( 3.6-27)

( )1 0

'eqt c eq eq

eq

vg A

Iβη α λ λ λ⎡ ⎤= − − +⎣ ⎦ ( 3.6-28)

The term ' /eq eq eq eqg A Iυ in formula (3.6-28) accounts for the cross-section imperfections in case of tension failure mode.

Validation of the model with numerical simulations

To validate the analytical model developed in the previous sections, the prediction with the so-defined analytical model are compared to numerical results obtained through full non-linear analyses performed with the homemade finite element software FINELG (see Ly 2008).

In order to compare easily results obtained for iron columns respectively with and without FRP, all the buckling curves will be presented in a "NB - Lambda Bi" format, "NB" (= N ) being the non-dimensional resistance defined by formula (3.6-29)

,0.2,

u

i c i

NNAσ

= ( 3.6-29)

and "Lambda Bi" (= iλ ), the non-dimensional slenderness of the corresponding columns without FRP defined by formula (3.6-29)

1i

ei

i

LIA

λλ

= ( 3.6-30)

In these formulas, Ai and Ii are the area and the second moment of inertia of the iron column sections and Nu is the buckling resistance of the column (with or without FRP).

236

In the present study, Nu has been predict numerically through the FEM software FINELG and analytically through the procedure described in the previous sections (= min(σb,t; σb,c).Aeq).

The columns which are investigated herein are the columns tested at the University of Liège. As the present study was performed during the pre-experimental analyses on cast iron columns reinforced by FRP, the mechanical and the geometrical properties for the investigated columns have been defined according to information available in the literature (Shaat and Fam 2006,2007; Rondal and Rasmussen 2002, 2003, 2005).

Also, in order to facilitate the comparison between the numerical and the analytical investigations, some assumptions have been done, in particular concerning the imperfections.

Accordingly, the properties which have been used within this study are the following:

- Iron material behaviour when subjected to compression is approximated through a Ramberg-Osgood law with the following parameters: Ei = 88000 N/mm², n = 6 and σi,0.2,c = 375 N/mm² in compression; and when subjected to tension, through a linear elastic law with the following parameters: σi,u,t = 75 N/mm² and Ei = 88000 N/mm².

- The FRP sheets used to reinforced the iron columns is CFRP 530. It is a brittle elastic material with an elastic modulus (Ef) equal to 640 GPa, a tensile strength (σf,u,t) equal to 2650 MPa and a Poisson's coefficient equal to 0.28; the compressive strength (σf,u,c) is assumed to be equal to the tensile strength, as no information is available concerning this property.

- For the iron columns reinforced by FRP, it is assumed that three longitudinal FRP sheets (3x0.19 mm) are set up around their outer perimeter. In addition, one transversal FRP is placed to prevent the out-of-plan buckling of the longitudinal FRP sheets.

- Member imperfection: an initial crookedness equal to 1/1000 of the column length is used.

- Geometry of the cross section: the latter has been defined with the help of a segment extracted from a tested column: de = 126.5 mm, di = 94 mm, tmin = 14.5 mm, tmax = 18 mm, j = 1.75 mm and gi = 2.16 mm (see chapter 1 – Iron elements). These values have been assumed, for the simplicity’s sake, to be constant along the length of the columns.

a) Iron columns without FRP

Axial compression buckling curves for iron columns without FRP obtained through numerical and analytical models are reported in Figure 3.6-5. The dashed curve represents analytical buckling resistances in the tension failure mode on the thick side; the continuous curve, the compression failure on the thin side; whereas the dots represent numerical results. It has to be noted that the risk of having a tension failure mode increases with the increase of the column slenderness.

The good agreement between the numerical and the analytical results, whatever the failure modes, means that the analytical model permits a good prediction of the buckling resistance of iron columns.

237

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00

Lambda Bi

NB

Compression failure in thin side

Traction failure in thick side

Numerical model without FRP

Figure 3.6-5 Axial compression buckling curves for iron columns without FRP

b) Iron columns reinforced by longitudinal FRP sheets only

For the studied iron material, the compressive strain at the 0.2% compressive proof stress εi,0.2,c is equal to 0.626% and the tensile one εi,u,t, 0.085%. As mentioned previously, the strain εf,u,c of the longitudinal FRP sheets in compression must be limited at a certain value because of the local buckling phenomenon associated to debonding effects.

If the limit value 0.13%, much lower than εi,0.2,c of iron, is used for the FRP sheets in compression within the numerical simulations, results are those plotted in Figure 3.6-6: the two dashed curves represent the analytical buckling resistances of iron columns without FRP, whereas the dots are numerical buckling resistances of iron columns with longitudinal FRP sheets only.

It may be seen that longitudinal FRP sheets, with a limited compressive strain associated to out-of-plane buckling effects, do not improve significantly the buckling resistance of iron columns. That is why transverse FRP sheets should be applied in addition to longitudinal ones so as to prevent these out-of-plane buckling effects.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00

Lambda Bi

NB

without FRP, compression failure in thin side

without FRP, traction failure in thick side

Numerical model

Figure 3.6-6 Axial compression buckling curves for iron columns with only longitudinal FRP

c) Iron columns reinforced by longitudinal and transversal FRP sheets

Now, with the use of transversal FRP sheets, the longitudinal FRP sheets can reach the maximum strain εf,u,c (= Ef/σf,u,c) equal to 0.414%. By introducing this value in the numerical and analytical models, results shown in Figure 3.6-7 are obtained: the two dashed curves represent analytical buckling

238

resistances of iron columns without FRP, while the two continuous curves correspond to analytical buckling resistances of FRP reinforced columns; again, the dots indicate numerical buckling resistances of iron columns with FRP.

The obtained numerical and analytical results are in good agreement for stocky or very slender columns, but not very optimal for the range of medium slenderness in which buckling resistance significantly depends on every imperfection factors. As the imperfection parameters (α, β, λ0, λ1) have been proposed for iron material, but not for the composite one composed of iron and FRP, new imperfection levels should be found so as to improve the proposed analytical formulation. Anyway, the actual analytical formulation gives safe results.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00

Lambda Bi

NB

without FRP, compression failure in thin side

without FRP, traction failure in thick side

with FRP, compression failure in thin side

with FRP, traction failure in thick side

Numerical model

Figure 3.6-7: Axial compression buckling curves for iron columns with FRP not experiencing local

buckling

3.6.4. Conclusions

Within the present section, an analytical model able to predict the buckling resistance of iron columns reinforced or not with FRP sheets has been developed and validated. The presented design method is based on the modern buckling curve approach, as for steel columns, and is able to predict the resistance of iron columns, taking into account of the asymmetric behaviour of the iron material when subjected to tension or compression.

The analytical model was validated through comparisons with numerical results. This work was performed during the pre-experimental analyses on cast iron columns reinforced by FRP. Then, all parameters regarding the database of columns as the material properties of iron and FRP, the imperfections and the geometry of columns had to be adopted from the literature (Shaat and Fam 2006,2007; Rondal and Rasmussen 2002, 2003, 2005) and some simplified assumptions had to be adopted in order to perform comparative investigations between the proposed analytical model predictions and numerical results.

In another study (Ly, 2008) comparing the numerical predictions and the experimental results obtained at the University of Liège (Ly, 2008), it is illustrated that the proposed numerical model is able to provide a safe prediction of the buckling resistance of iron members with or without FRP. Accordingly, as it was demonstrated herein that the analytical model produces safe results if compared to the numerical ones, it can be concluded that the proposed analytical model permits to predict a safe value of the buckling resistance of iron columns with or without FRP if compared to its actual resistance.

239

Through the performed investigations, it was demonstrated that transverse FRP sheets should be also used to prevent any out-of-plane buckling effects of the longitudinal sheets, what permits to increase the efficiency of the reinforcement.

It was also demonstrated that the accuracy of the model could be improved by defining appropriate imperfection parameters (α, β, λ0, λ1) for FRP-iron composite columns. To achieve that, further developments are requested, what constitutes a perspective to the presented study.

Notations

Af Cross-section area of FRP

Ai Cross-section area of iron

de Outer diameter

di Inter diameter

neq Equivalent coefficient of FRP modulus compared with the iron one

Aeq Equivalent cross-section area

Ieq Equivalent second moment of a composite cross-section

Ii Second moment of iron cross-section

If Second moment of FRP cross-section

geq Gravity centre of composite cross-section

gf Gravity centre of FRP cross-section

veq Distance of the extreme compressive fibres of iron to geq

v'eq Distance of the extreme tensile fibres of iron to geq

re Outer rayon

ri Inner rayon

Eb Elastic modulus of bond

Ef Elastic modulus of FRP

Ei Elastic modulus of iron

gi (g) See chapter 1 – Iron elements

j See chapter 1 – Iron elements

L Length

Nu Buckling resistance in compression

r Gyration rayon

tmax Thickness of the thick side of iron cross-section

tmin Thickness of the thin side of iron cross-section

σb,u Strength of bond

εb,u Ultimate strain of bond

σf,u,c Compressive strength of FRP

εf,u,c Ultimate compressive strain of FRP

240

σf,u,t Tensile strength of FRP

εf,u,t Ultimate tensile strain of FRP

σi,0.2,c 0.2% proof stress of iron in compression

εi,0.2,c Strain at 0.2% proof stress of iron in compression

σi,u,c Compressive strength of iron

εi,u,c Ultimate compressive strain of iron

σi,u,t Tensile strength of iron

εi,u,t Ultimate tensile strain of iron

3.6.5. References

Eurocode 3: Design of Steel Structures, Part 1.1: General Rules and Rules for Building, prEN-1993, European Committee for Standardisation, Brussels.

Studi Preliminari finalizzati alla redazione di Istruzioni per Interventi di Consolidamento Statico di Structture Metalliche mediante l'utilizzo di Compositi Fibrorinforzatti, Commissione incaricata di formulare pareri in material di normativa tecnica relative alle costruzoni, CNR-DT 202/2005.

Historical development of iron and steel in buildings, ESDEP lecture 1B.4.3.

A. A. El Damatty, M. Abushagur, "Testing and modelling of shear and peel behaviour for bonded steel/FRP connection", Thin-Walled Structures 41 (2003) 987-1003.

A. Morin (1862), “Résistance des matériaux – Tome 1”, Librairie de L. Hachette et Cie.

A. Morin (1862), “Résistance des matériaux – Tome 2”, Librairie de L. Hachette et Cie.

Ali A. Mortazavi, Kypros Pilakoutas, Ki Sang Son, "RC column strengthened by lateral pre-tensioning of FRP", Construction and Building Materials 17 (2003) 491-497.

Amr Shaat and Aimr Fam, "Finite element analysis of slender HSS columns strengthened with high modulus composites", Steel and Composite Structures, Vol 7, No 1 (2007) 19-34.

Amr Shaat, Amir Fam (2006), "Axial loading tests on short and long hollow structural steel columns retrofitted using carbon fibre reinforced polymers", J. Civ. Eng. 33: 458-470.

Amr Shaat, Amir Fam (2007), "Fiber-Element model for slender HSS columns retrofitted with bonded high-modulus composites", J. Struc. Eng. ASCE.

BASF, “MBrace fibre, Rinforzo fibroso a base di tessuti unidirezionali in fibra di carbonio, aramide e vetro del sistema MBrace FRP (Fiber Reinforced Polymer)”, The Chemical Company, Italia.

David Schnerch, Mina Dawood, Emmett A. Summer and Sami Rizkalla, "Behaviour of steel-concrete composite beams strengthened with unstressed and prestressed high-modulus CFRP strips", North Carolina State University, USA.

E.H. Salmon (1921), “Columns – a treatise on the strength and design of compression members”, Oxford Technical Publications.

J. Blanchard, M. Bussell, A. Marsden and D. Lewis (1997), “Appraisal of existing ferrous metal structures”, Stahlbau 6.

J. Rondal and K.J.R Rasmussen (2003), “On the strength of cast iron columns”, Research report N°R829.

241

J. Rondal and K.J.R. Rasmussen (2002) “Old industrial buildings: the cast-iron column problem”, International Colloquium on Stability and Ductility of Steel Structures, Akademiai Hiado, Budapest.

J. Rondal and K.J.R. Rasmussen (2005), “Design of cast iron columns with explicit calculation of tension fracture capacity”, Eurosteel 2005 - 4th European conference on steel and composite structures, Maastricht, the Netherlands.

K.J.R. Rasmussen and J. Rondal (2000), "Strength curves for aluminium alloy columns", Engineering Structures 23 (2000) 1505-1517.

M. A. Youssel, "Analytical prediction of the linear and nonlinear behaviour of steel beams rehabilitated using FRP sheets", Engineering structures 28 (2006) 903-911.

M. Bussell (1997), “Appraisal of existing iron and steel structures”, SCI publication 138, ISBN 1 85942 009 5.

M.N. Bussell and M.J. Robinson (1998), “Investigation, appraisal and reuse of a cast-iron structural frame”, Ordinary Meeting, The Structural Engineer.

M.N.S. Hadi, "Behaviour of FRP strengthened concrete columns under eccentric compression loading", Composite structures 77 (2007) 92-96.

M.R. Guerrieri, G. Di Lorenzo and R. Landolfo, “Influence of atmospheric corrosion on the XIX century iron structures: assessment of damage for Umberto I Gallery in Naples”.

Michael V. Seica, Jeffrey A. Packer, "FRP materials for the rehabilitation of tubular steel structures for underwater application", Composite Structures 80 (2007) 440-450.

Oral Buyukozturk et all, "Progress on understanding debonding problems in reinforced concrete and steel members strengthened using FRP composites", Construction and Building Materials 18 (2004) 9-19.

R. Käpplein (1991), “Assessment of the load bearing capacity of old cast iron columns”, Fourth International Colloquium on Structural Stability, Istanbul.

R. Käpplein (1997),“Untersuchung und Beurteilung alter Gubkonstruktionen”, Stahlbau 6.

R. Landolfo, O. Mammana and F. Portioli, “Assessment of the seismic performance of the iron roofing structure of the Umberto I Gallery in Naples”.

S. Cescotto, S. Gilson, A. Plumier and J. Rondal (1983), “Etude du flambement plan de poutres colonnes en acier à section non symétrique”, Publication du CRIF.

S. Fawzia et all, "Bond characteristics between CFRP and steel plates in double strap joints", Department of Civil Engineering Monash University, Clayton, Victoria 3800, Australia.

S. Fawzia et all, "Strengthening of circular hollow steel tubular sections using high modulus CFRP sheets", Construction and Building Materials 21 (2007) 839-845.

Sabrina Fawzia et all, "Experimental and finite element analysis of a double strap joint between steel plates and normal modulus CFRP", Composite Structure 75 (2006) 156-162.

T. Swailes and J. Marsh (1998), “Structural appraisal of iron-framed textile mills”, ICE design and practice guide.

W. Bates (1991), “Historical structural steelwork handbook”, The British constructional steelwork association, ISBN 0 85073 015 5, 4th impression.

Xiao-Ling Zhao, Lei Zhang, "State-of-the-art review on FRP strengthened steel structures", Engineering Structures 29 (2007) 1808-1823.

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L. Ly, J.F. Demonceau, J.P. Jaspart (2008), WP7 “Tests on iron materials”, Prohitech project ref. 02.07.01.02.

L. Ly, J.F. Demonceau, J.P. Jaspart (2008), WP7 “Tests on iron columns reinforced by FRP”, Prohitech project ref. 02.07.02.02.

L. Ly, J.F. Demonceau, J.P. Jaspart (2008), WP8, Materials and elements, "Iron and FRP materials ", Prohitech project ref. 02.08.01.02.

L. Ly, J.F. Demonceau, J.P. Jaspart (2008), WP8, Sub-systems, "Iron columns reinforced by FRP under axial compression", Prohitech project ref. 02.08.02.02.

3.7. Reinforced Concrete frames retrofited with eccentric braces

3.7.1. Introduction

This section was prepared in accordance with data-sheet no. 9-13 “Design methods for eccentric braces”, provided by M. D’Aniello, G. Della Corte and F. M. Mazzolani, from University of Naples “Federico II”, Italy. The report presents some aspects regarding the use of eccentric braces, as connection types and performance of these devices.

3.7.2. Connections

An important aspect in the design of steel bracing for RC structures is the correct design of brace-to-RC structure connections. Maheri and Sahebi (1997) have studied and tested different types of such connections. In case of existing RC structures the best solution seems to adopt gusset plates bolted to RC beam-to-column joints by means of bolts passing through holes drilled in the RC members, as shown in Figure 3.7-1.

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Figure 3.7-1 Diagonal brace-to-RC connections

Analogously, link-to-RC beam connections can be made by bolting end plates to the RC structure by means of bolts passing through holes drilled in the RC beams, as shown in Figure 3.7-2. This type of connection should be designed to be rigid in order to have sufficient rotational stiffness to justify analysis based on full continuity. Moreover, this connection must be designed to have a flexural resistance larger than the one of the link that it connects.

a)

b)

Figure 3.7-2 Link-to-RC beam connections

Figure 3.7-2b shows the brace-to-link connection. This joint is usually characterized by a low flexural rigidity; hence it should be schematized as a pinned connection. However, this connection has to be calculated in order to have a shear resistance larger than the shear link capacity. Modern building codes suggest to amplify with an over-strength factor of 1.5 the forces transmitted by the link to the outer parts of the structure, that are connected to it. Several recent experimental investigations demonstrate that steel link built with European hot-rolled steel profiles can manifest larger value of shear overstrength, in the order of 3 up to 5 times the nominal plastic shear link capacity (Della Corte et al., 2006).

244

3.7.3. Performance criteria

The seismic performance of a structure equipped with EBs is significantly influenced by the link response. In fact, the maximum interstory drift depends on the link rotation. Referring to a Y-inverted configuration, the ratio between the maximum link deformation angle γ and the story drift angle θ can be approximated as follows:

eH /=θγ ( 3.7-1)

This relationship can be simply derived by assuming the frame outside the link as rigid (because the elastic deformation in the frame outside the link is small if compared with the link plastic deformation), as shown in Figure 3.7-3, assuming the inextensibility and rigid plastic behaviour of members.

Figure 3.7-3 Kinematic of plastic mechanism of Y-inverted EB configuration

Ghobarah & Elfath (2001) performed several numerical analyses on RC structures equipped with EBs. They noted that the difference between the γ/θ ratio calculated from Eq. (20) and the values obtained from the dynamic analysis is very small and it is due to the axial deformations of the brace members and the RC frame members that are neglected in the derivation of Eq. (20). Their analyses indicated that the link deformation angle is the most important parameter. In order to limit the link deformation angle below the allowable level γall, the story drift angle θ (story displacement/story height) of the rehabilitated building should not exceed γall×(link length/story height). This represents a limitation on the deformation of the existing building when eccentric steel bracing is used in its seismic rehabilitation. In fact, RC frames can usually sustain story drift deformations of 2.5% under the design earthquake intensity, while the presence of EBs reduces this value. In order to keep the link deformations in its allowable range, RC structures with EBs are characterised by inter-story drift lesser than 1.5%.

In detail, FEMA356 suggests the values of link shear deformation angle referring to the generalized load-deformation curve (Figure 3.7-4), adopted to schematize the link response. The parameters a, b, c, are defined in Table 1.

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Figure 3.7-4 Link force-deformation relationship according to FEMA356.

Table 3.7-1 Parameters of Link force-deformation (FEMA356)

Modeling parameters Acceptance Criteria

Plastic Rotation Angle (rad) Residual Strength ratio

Plastic Rotation Angle (rad)

a b c IO LS CP

0.15 0.17 0.8 0.005 0.11 0.14

3.7.4. References

Bruneau M., Uang C.M., Whittaker A., (1998). “Ductile design of SteelStructures“, McGraw- Hill

Della Corte G., D’Aniello M., Barecchia E., Mazzolani F.M. (2006) “Experimentaltests and analysis of short links for eccentric bracing of RC buildings”.Engineering Structures (Submitted for publication).

Engelhardt M.D, Popov E.P,, (1989). On Design of Eccentrically Braced Frames. Earthquake Spectra, vol.5, No.3, 495-511.

Engelhardt M.D, Popov E.P,, (1992). Experimental performance of long links in eccentrically braced frames. Journal of Structural Engineering, Vol.188, No.11:3067-3088.

Ghobarah A., Elfath A.H., (2001). Rehabilitation of a reinforced concrete frame using eccentric steel bracing. Engineering Structures, vol. 23, 745–755

Hjelmstad K.D., Popov E.P., (1983). Cyclic Behavior and Design of Link Beams. Journal of Structural Engineering, vol.109, No. 10, 2387-2403,.

Itani A, Douglas B.M. & ElFass S., (1998). Cyclic behavior of shear links in retrofitted Richmond-SanRafael Bridge towers. Proceedings of the First World Congress on Structural Engineering – San Francisco, Paper No. T155-3, Elsevier Science Ltd.

Kasai K., Popov E.P,. (1986a). General Behavior of WF Steel Shear Link Beams. Journal of Structural Engineering, vol.112, No. 2, 362-382, 1986

Kasai K., Popov E.P., (1986b). Cyclic Web Buckling Control for Shear Link Beams. Journal of Structural Engineering, vol.112, No. 3, 505-523.

Malley J.O., Popov E.P., (1984). Shear Links in Eccentrically Braced Frames. Journal of Structural Engineering, vol.110, No. 9, 2275-2295.

Mazzolani, F.M., “Seismic upgrading of RC buildings by advanced techniques. The ILVA-IDEM research project”. POLIMETRICA Publisher, Italy 2006.

Mc Daniel, C. C., Uang, C. & Seible, F., (2003). Cyclic Testing of Built-Up Steel Shear Links for the new Bay Bridge. Journal of Structural Engineering, vol. 129, No 6.

Nader M., Lopez-Jara J. & Mibelli, C., (2002). Seismic Design Strategy of the New San Francisco-Oakland Bay Bridge Self-Anchored Suspension Span, Proceedings of the Third National Seismic Conference & Workshop on Bridges & Highways, MCEER Publications, State University of New York, Buffalo, NY.

Popov E.P., Engelhardt M.D., (1988). Seismic Eccentrically Braced Frames. Journal of Construction and Steel Research, (10) 321-354.

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Popov E.P., Malley J.O., (1983) Design of links and beam-to-column connections for eccentrically braced steel frames. Report No. EERC 83-03.

Berkeley (CA): Earthquake Engineering Research Center, University of California. Ramadan T, Ghobarah A., (1995). Analytical model for shear–link behavior. J Struct Engng, ASCE, 121(11):1574–80.

3.8. Reinforced Concrete structures retrofitted with Metal shear panel

3.8.1. Introduction

This section was prepared in accordance with data-sheet no. 9-14 “Metal Shear Panels for Seismic Upgrading of Existing RC Buildings”, provided by G. De Matteis, A. Formisano, S. Panico and F. M. Mazzolani, from University of Chieti/Pescara “G. d’Annunzio” and University of Naples “Federico II”, Italy. The report presents some aspects regarding the use of metal shear panels to retrofit RC structures and a case study for validation of the proposed design model.

3.8.2. Retrofitting design method

The general approach

A preliminary design method for structures retrofitted with slender panels, which increase the structural stiffness and strength, can be performed according to the provisions given by ATC-40 American guidelines (1996) in the framework of the performance based design methodology. Such a design approach can be explained through the example of Figure 3.8-1 (De Matteis and Mistakidis, 2003).

Line of minumum required acceleration capacity

IO limit

Line of minimum required stiffness

0.02

0.05

0.010

0

Spe

ctra

l acc

eler

atio

n (g

)

0.15

0.2

0.25

0.3

0.35

0.1

0.45

0.5

0.4

Spectral displacement (m)LS limit

0.03 0.040.037

SS limit

0.05 0.06 0.080.07

Performance point ofthe initial structure

Line of target displacement

Desired performance point

at desired performance

=5%

=10%

=20%

=30%

Figure 3.8-1 Preliminary retrofitting design of a RC structure endowed with shear panels

The curve with the solid line is the capacity spectrum for the original structure, while the one having dashed line is the capacity spectrum for the structure retrofitted with LYS panels.

The purpose of the retrofitting design is to decide what target spectral displacement is desired for the retrofitted structure, and then to determine the characteristics of the LYS panels which will be able to pursue such a target.

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For this example structure, the spectral displacements that correspond to the Immediate Occupancy (IO), Life Safety (LS) and Structural Stability (SS) performance levels, are indicated. Since the examined structure fails to fulfil even the Structural Stability performance level, the retrofitting design has to be developed by assuming as a target displacement the Life Safety one.

The next step is to determine an appropriate initial stiffness for the retrofitted structure. At this aim, based on the “equal displacements” simplifying assumption, an estimate of the initial period required for the retrofitted structure can be obtained by extending the vertical line corresponding to the desired target (LS) displacement until it intersects with the elastic response spectrum (demand spectrum for 5% viscous damping). A radial line drawn from the origin of the demand/capacity spectrum plot through this intersection defines the minimum initial stiffness for the retrofitted structure Tret. This period can be calculated from the equation

ae

d

SSπ2=retT (3.8-1)

where Sd is the target displacement and Sae is the spectral acceleration corresponding to the intersection of the target displacement line with the elastic response spectrum. The target stiffness for the retrofitted structure can be calculated from the relationship

2

ret

ini

TT

⎟⎟⎠

⎞⎜⎜⎝

⎛= iniret KK ( 3.8-2)

where Kini and Tini are respectively the initial stiffness and period of the original structure and Kret is the stiffness required for the retrofitted one. Once that the required stiffness has been determined, the stiffness Kp of the LYS panels can be determined from the equation

Kret = Kini + Kp ( 3.8-3)

Then, in order to determine the strength of the retrofitted structure, it is necessary to make a simplified assumption about its damping properties, considering that it will be able to provide at least the same level of damping of the initial structure one. Therefore, the approximate solution for the performance point of the retrofitted structure is obtained as the intersection of the vertical line at the desired target spectral displacement with the demand spectrum that corresponds to the damping level of the initial structure. This point is annotated in the figure as the “desired performance point”. A horizontal line extending from the desired performance point to the y axis indicates the minimum spectral acceleration capacity required for the retrofitted structure. Once this information is known, the required ultimate base shear capacity for the retrofitted structure can be obtained from the equation

Vret= iniinia

reta VS

S ( 3.8-4)

where Vini is the ultimate base shear capacity of the initial structure, Vret is the required ultimate shear capacity of the retrofitted structure,

iniaS and retaS are the ultimate spectral acceleration for the

unretrofitted and retrofitted structures, respectively. Finally, the shear strength Vp of the LYS panels can be determined from the equation

Vret = Vini + Vp ( 3.8-5)

Once the required stiffness and strength of the slender panels have been determined, it is possible to develop preliminary sizes of panels that provide these properties. However, it should be emphasized, that

248

while the presented approach is suitably accurate to lead to a preliminary design solution, it is extremely important that the actual demand and capacity spectra for the retrofitted structure be formally computed as part of the final design process.

3.8.3. The study case

In the framework of the ILVA-IDEM research project (Mazzolani, 2006), the attention is herein focused on the RC module nr.5 (Figure 3.8-2a), where steel and aluminium shear panels, connected with bolts to an external reaction steel frame, will be longitudinally placed. The bare module has been preliminarily tested, without reaching the collapse of the system, by means of a pushover test, employing two hydraulic jacks able to apply a total force of 300 kN. The test results, reported in terms of force-displacement curve in Figure 3.8-2b relatively to the first floor displacements, provide useful information on the ultimate strength and the exact lateral stiffness levels offered by the bare structure for performing the seismic retrofitting design.

MODULO N. 5 0

10

20

30

40

0 10 20 30First floor displacement [mm]

Shea

r for

ce [k

N]

Figure 3.8-2 The module under study (a) and its response under lateral actions applied in

longitudinal direction (b)

In fact, in the case under study, a second category seismic zone, characterized by a peak ground acceleration equal to 0.25 g, and a soil type B have been considered. The target design displacement of the first level of the RC structure, under collapse conditions, corresponding to the attainment of its maximum lateral strength, has been fixed equal to 2.5 cm. On the other hand the viscous damping coefficient of the reinforced structure has been assumed equal to 20%. As a consequence, the shear panel design parameters Vp and Kp have been determined, and finally, on the basis of the proposed design methodology, the capacity curve of the reinforced structure has been defined in the spectral acceleration – spectral displacement (ADRS) plane (Figure 3.8-3).

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14

Sd [m]

Sa [g]Soil type BSoil type B (10%)Soil type B (15%)Soil type B (20%)Bare RC structureRetrofitted structure (design)

Performance Point

Figure 3.8-3 Capacity curve of the RC structure reinforced with metal shear panels

3.8.4. Application methodology

Based on the theoretical PFI method and according to the mentioned retrofitting design methodology, the panel dimensions have been reached as b = 600 mm and h = 2400 mm, with a thickness of 1.15 and 5

MODULE

a) b)

249

mm for steel and aluminium panels, respectively. Subsequently, in order to check the reliability of the above theoretical formulations, both simple (SAP2000 - CSI, 2003) and refined (ABAQUS - Hibbitt et al., 2004) finite element models of the considered shear panels have been implemented (Figure 3.8-4). The materials used for panel are DX56D steel and pure aluminium, whose properties, together with the detailed description of the above FEM models, have been defined in (De Matteis et al., 2006)

For the sake of example, the results of the numerical study have been herein reported with reference to steel panels only. The comparison among results is illustrated in Figure 3.8-5, where it is apparent as the theoretical and numerical methods give the same shear wall response both in terms of strength and stiffness.

Figure 3.8-4 Finite element modelling of the shear panel by means of Sap 2000 (a) and ABAQUS

(b)

0

20

40

60

80

100

120

0 20 40 60 80 100Displacement [mm]

Theoretical behaviour

ABAQUS model

Sap model

Shea

r for

ce [k

N]

Figure 3.8-5 Comparison between theoretical and numerical steel shear panel responses

3.8.5. The behavior of the retrofitted structures

The combination of the shear panels numerical response with the bare structure experimental one allows to achieve the capacity curve of the retrofitted structure. With reference to the ABAQUS model, the obtained result is very similar to the one obtained by means of the simplified design procedure, like is shown in Figure 3.8-6 for the structure upgraded with steel panels. In particular, the same spectral

250

acceleration is obtained, while the curve stiffness (fundamental period) is slightly greater than the theoretical one. This is due to some slip phenomena between the steel and the RC structure, which could occur during the test but have not been considered in the adopted design procedure.

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14

Sd [m]

Sa [g]Soil type BSoil type B (10%)Soil type B (15%)Soil type B (20%)Bare RC structureRetrofitted structure (design)Retrofitted structure (ABAQUS)

Performance Point

Figure 3.8-6 Comparison between theoretical and numerical (ABAQUS) curves for the RC

structure retrofitted with steel shear panels

In order to confirm the validity of the proposed design solution and for evaluating the possible relative interaction problems between the RC structure, whose material characteristics are given in (Formisano et al., 2006), and the added devices, global analyses of the retrofitted structures have been performed by using SAP2000 v.8.23 non linear code.

The so obtained capacity curves are provided in Figure 3.8-7 and Figure 3.8-8, where the good agreement with the theoretical curve corresponding to the seismic retrofitting design and the result of the ABAQUS model can be observed for the structure reinforced with steel and aluminium panels, respectively.

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14

Sd [m]

Sa [g] Soil type BSoil type B (10%)Soil type B (15%)Soil type B (20%)Bare RC structureRetrofitted structure (design)Retrofitted structure (ABAQUS)Retrofitted structure (SAP2000)

Figure 3.8-7 Comparison among numerical curves for the RC structure retrofitted with steel shear

panels

251

0

50

100

150

200

250

300

350

400

0 20 40 60 80 100 120 140 160 180

s [mm]

F [KN]

ABAQUS model

SAP 2000 model

Figure 3.8-8 Comparison among numerical results for the RC structure endowed with aluminium

panels

3.8.6. References

Astaneh-Asl, A. (2001). “Seismic Behavior and Design of Steel Shear Walls”. Steel TIPS Report, Structural Steel Educational Council, Moraga, CA.

Astaneh-Asl, A., Zhao, Q., (2002). “Cyclic behaviour of traditional and an innovative composite shear wall”. Report No. UCB-Steel-01/2002, Department of Civil and Env. Engineering, University of California, Berkeley.

Computer and Structures, Inc., (2003). “SAP 2000 Non linear Version 8.23”. Berkeley, California, USA.

De Matteis, G., Mistakidis, E.S., (2003). “Seismic retrofitting of moment resisting frames using low yield steel panels as shear walls”. Proceedings of the 4th International Conference on Behaviour of Steel Structures in Seismic Areas (STESSA 2003), Naples, pp. 677-682.

De Matteis, G., Landolfo, R., Mazzolani, F. M. (2003a). “Seismic response of MR steel frames with low-yield steel shear panels”. Journal of Structural Engineering, 25.

De Matteis, G., Mazzolani, F. M., Panico, S. (2003b). “Steel bracings and shear panels as hysteretic dissipative systems for passive control of MR steel frame”. Costruzioni Metalliche, 6.

De Matteis, G., Formisano, A., Panico, S., Calderoni, B., Mazzolani, F. M., (2006). “Metal shear panels”. Seismic upgrading of RC buildings by advanced techniques – The ILVA-IDEM Research Project, Mazzolani, F. M. co-ordinator & editor, Polimetrica International Scientific Publisher, Monza, pp. 361-449.

Formisano, A., De Matteis, G., Panico, S., Calderoni, B., Mazzolani, F.M., (2006). “Full-scale experimental study on the seismic upgrading of an existing RC frame by means of slender steel shear panels”. Proceedings of the International Conference on Metal Structures (ICMS ‘06), Poiana Brasov, September 16-18, pp. 609-617.

Hibbitt, Karlsson, Sorensen, Inc., (2004). “ABAQUS/Standard, v. 6.4”, Patwtucket, USA.

Mazzolani, F.M., co-ordinator & editor, (2006). “Seismic upgrading of RC buildings by advanced techniques – The ILVA-IDEM Research Project”. Polimetrica International Scientific Publisher, Monza.

Sabouri-Ghomi, S., Roberts, T. M. (1991). “Nonlinear Dynamic Analysis of Thin Steel Plate Shear Walls”. Computers & Structures, Vol. 39., No. 1/2, pp. 121-127.

Thorburn, L. J., Kulak, G. L., Montgomery, C. J. (1983). “Analysis of Steel Plate Shear Walls”. Struct. Eng. Rep No. 107, Dept. of Civ. Engrg., University of Alberta, Edmonton, Alta., Canada.

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Timler, P. A. (2000). “Design Evolution and State-of-the-Art Development of Steel Plate Shear Wall Construction in North America”. Proc. of the 69th Annual SEAOC Convention, Vancouver, British Columbia, Canada, pp. 197-208.

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D11 – Development of simplified models for the global seismic analysis of historical constructions

4. Models for global analysis

4.1. Analysis methods

Introduction

The most important effect of earthquakes on building structures is the inertia forces produced in the building due to ground shaking. Being a rare event, structures are usually designed to resist earthquake action in the inelastic range of response. Most of the existing structures were not designed for seismic action at all, and are therefore expected to respond beyond the elastic limit under a major earthquake. The dynamic nature of earthquake action, which has components along the two horizontal directions as well as the vertical one, and the possible inelastic structural response, implies a nonlinear dynamic analysis procedure on a three-dimensional model of the building structure. Though this type of analysis provides the most "exact" modelling of structural response under earthquake action, it requires a high degree of expertise, and can be very time-consuming. In many cases it is possible to adopt more simple analysis procedures. The simplifications may involve the model of the structure (two plane models instead of a three-dimensional one), time-history response (static analysis instead of dynamic one), and inelastic structural response (linear elastic analysis instead of nonlinear analysis).

There are five generally adopted analysis procedures used for seismic analysis of structures (FEMA 356 [18]; Eurocode 8 [15]) presented bellow in a hierarchical order:

• lateral force method (linear static procedure);

• response spectrum analysis;

• linear time-history analysis;

• nonlinear static procedure (pushover analysis);

• nonlinear time-history analysis.

The linear procedures maintain the traditional use of a linear stress-strain relationship, but incorporate adjustments to overall building deformations and material acceptance criteria to permit better consideration of the probable nonlinear characteristics of seismic response. The Nonlinear Static Procedure, often called “pushover analysis,” uses simplified nonlinear techniques to estimate seismic structural deformations. The Nonlinear Dynamic Procedure, commonly known as nonlinear time history analysis, requires considerable judgment and experience to perform [45].

The acceptance criteria for the various performance objectives are prescribed for each of the analytical procedures and numerical values of the acceptance criteria for various structural and nonstructural systems are provided in PBE codes.

Guidance on the global model of the structure and criteria for selection of analysis procedure are available in seismic design codes ([18]; [15]; [16]). A summary of their requirements is presented hereafter.

4.1.1. Global analysis and modeling requirements

General considerations

Due to the dynamic nature of seismic action, the structural model should adequately represent not only the distribution of stiffness, but also the distribution of mass within the structure. When nonlinear

254

analysis methods are used, in addition to stiffness and mass, the global structural model should include the distribution of strength within the structure. [45].

Horizontal torsion

It is not needed to be considered in structures with flexible floor diaphragms. An accidental eccentricity is introduced to account for uncertainties in the distribution of stiffness and mass, as well as for the rotational components of the ground motion.

A three-dimensional model of the structure accounts directly for torsion due to eccentricity between the centres of mass and stiffness, and need an explicit consideration of accidental eccentricity only.

Diaphragms

It is generally preferred that floor diaphragms be rigid in their plane. Rigid diaphragms provide a connection between lateral force resisting systems and the gravity load resisting systems within a building, and enable for the different lateral load resisting systems in the building to contribute to the global lateral resistance of the structure [45].

When diaphragms cannot be considered rigid, structural models should account explicitly for the in-plane stiffness of the floor diaphragms.

Second-order effects

When a structure is very flexible under lateral loads, a first-order analysis may underestimate substantially forces and deformation. A second-order analysis is necessary in this case. When a non-linear analysis is used, second-order effects should be considered directly in the formulation of force-deformation relationships for all elements subjected to axial forces.

Displacement analysis

If the structure responds mainly in the elastic range under the design seismic action, lateral displacements can be estimated reliably based on a linear analysis (static or dynamic). However, if the structure is expected to experience significant yielding under the design seismic action, lateral deformations can be significantly larger than the ones estimated based on a linear analysis. The effects that can contribute to inelastic deformations larger than the elastic ones are: (1) frequency content of the ground motion, in relation to the fundamental period of vibration of the building, (2) duration of the ground motion, (3) hysteretic load deformation characteristics of structural elements, including strength and stiffness degradation [45].

Soil-structure interaction

The most important effect of soil-structure interaction is the elongation of period of vibration of the structure due to flexibility of the foundation-soil interface. It needs to be considered when the increased period of vibration of the building amplifies spectral accelerations [45].

Modeling Parameters and Acceptance Criteria

The acceptability of force and deformation actions shall be evaluated for each component of building. Prior to selecting component acceptance criteria, each component shall be classified as primary or secondary and each action shall be classified as deformation-controlled (ductile) or force-controlled (nonductile). Component strengths, material properties, and component capacities shall be determined. Component acceptance criteria not presented in standards shall be determined by qualification testing [18].

All primary and secondary components shall be capable of resisting force and deformation actions within the applicable acceptance criteria of the selected performance level [18].

255

All actions shall be classified as either deformation-controlled or force-controlled using the component force versus deformation curves shown in Figure 4.1-1

Figure 4.1-1 Component Force versus Deformation Curves (FEMA 356 356) [18]

The Type 1 curve depicted in Figure 4.1-1 is representative of ductile behaviour where there is an elastic range (point 0 to point 1 on the curve) followed by a plastic range (points 1 to 3) with non-negligible residual strength and ability to support gravity loads at point 3. The plastic range includes a strain hardening or softening range (points 1 to 2) and a strength-degraded range (points 2 to 3). Primary component actions exhibiting this behaviour shall be classified as deformation-controlled if the strain-hardening or strain softening range is such that e > 2g; otherwise, they shall be classified as force-controlled. Secondary component actions exhibiting Type 1 behaviour shall be classified as deformation-controlled for any e/g ratio [18].

The Type 2 curve depicted in Figure 4.1-1 is representative of ductile behaviour where there is an elastic range (point 0 to point 1 on the curve) and a plastic range (points 1 to 2) followed by loss of strength and loss of ability to support gravity loads beyond point 2. Primary and secondary component actions exhibiting this type of behaviour shall be classified as deformation-controlled if the plastic range is such that e > 2g; otherwise, they shall be classified as force controlled [18].

The Type 3 curve depicted in Figure 4.1-1 is representative of a brittle or nonductile behaviour where there is an elastic range (point 0 to point 1 on the curve) followed by loss of strength and loss of ability to support gravity loads beyond point 1. Primary and secondary component actions displaying Type 3 behaviour shall be classified as force – controlled [18].

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Figure 4.1-2 Generalized Component Force-Deformation Relations for Depicting Modeling and

Acceptance Criteria [18]

For some components it is convenient to prescribe acceptance criteria in terms of deformation (e.g., θ or ∆), while for others it is more convenient to give criteria in terms of deformation ratios. To accommodate this, two types of idealized force vs. deformation curves are used in Figure 4.1-2 (a) and (b) [18].

Figure 4.1-2 (a) shows normalized force (Q/QCE) versus deformation (θ or ∆) and the parameters a, b, and c. Figure 4.1-2 (b) shows normalized force (Q/QCE) versus deformation ratio (θ/θy, ∆/∆y, or ∆/h) and the parameters d, e, and c [18].

Elastic stiffness and values for the parameters a, b, c, d, and e that can be used for modeling components are given. Acceptance criteria for deformation or deformation ratios for primary members (P) and secondary members (S) corresponding to the target Building Performance Levels of Collapse Prevention (CP), Life Safety (LS), and Immediate Occupancy (IO) as shown in Figure 4.1-2 (c) are given in specific chapters of standards [18].

Structural typologies

P-BSA of building it is treated separately regarding to the structural typologies. FEMA 356 [18] provides in the general chapter qualitative definition and in the dedicated chapters provides quantitative acceptance criteria for ensuring that a specific level of performance is achieved.

Detailed criteria for calculation of individual component force and deformation capacities shall comply with the requirements in individual materials chapters as follows [18]:

1. Foundations;

2. Elements and components composed of steel or cast iron:

a. Steel Moment Frame;

b. Steel Braced Frame;

c. Steel Plate Shear Walls;

d. Steel Frame with Infills;

e. Diaphragm.

3. Elements and components composed of reinforced concrete:

a. Concrete Moment Frames;

b. Precast Concrete Frames;

c. Concrete Frames with Infills;

d. Concrete Shear Walls;

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e. Concrete Braced Frames;

f. Cast-in-place Concrete Diaphragms;

g. Precast Concrete Diaphragms.

4. Elements and components composed of reinforced or unreinforced masonry:

a. Masonry Walls;

b. Masonry Infills.

5. Elements and components composed of timber, light metal studs, gypsum, or plaster products:

a. Wood and Light Frame Shear Walls;

b. Wood Diaphragms.

6. Seismic isolation systems and energy dissipation systems;

7. Nonstructural (architectural, mechanical, and electrical) components;

8. Elements and components comprising combinations of materials are covered in the Chapters associated with each material.

For exemplification Generalized Component Force-Deformation Relations for Reinforced Concrete Beams and Masonry Walls Modeling and Acceptance Criteria are presented in Figure 4.1-3

Figure 4.1-3 Modeling Parameters and Acceptance Criteria [18]

Linear – Elastic Analysis

Lateral force method

In the case of assessment of existing structure ([18], [16]), the lateral forces are determined based on the elastic response spectrum, and not on the design one (reduced by the behaviour factor q). This procedure intends to estimate the design lateral displacements of the structure rather than the design forces in structural elements, because displacements are better indicator of damage to the structure in the inelastic range than forces [45].

Modal response spectrum and linear time-history

Response spectrum procedure is a generalization of the lateral force method, accounting for more than one mode of vibration in determining seismic response of the structure.

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Response spectrum analysis provides an envelope of displacements and internal forces. When the time-history response is of interest, linear time-history analysis is employed. [45].

When used for assessment of existing structures, both procedures are intended to provide an estimate of design displacements rather than design forces (FEMA 356, [18]; Eurocode 8-3, [16]).

Acceptance criteria for linear analysis

If linear procedures are used, capacities for deformation-controlled actions shall be defined as the product of m-factors (modification factor used in the acceptance criteria of deformation-controlled components or elements, indicating the available ductility of a component action) or q-factor, and expected strengths, QCE. Capacities for force-controlled actions shall be defined as lower-bound strengths, QCL [18].

Deformation-controlled design actions shall be calculated in accordance with [18]:

UD G EQ Q Q= ± (4.1-1)

Where QE = action due to design earthquake loads calculated using elastic analysis methods; QG = Action due to design gravity loads [18].

Deformation-controlled actions in primary and secondary components and elements shall satisfy following equation [18]:

CE UDm Q Qκ⋅ ⋅ > (4.1-2)

Where m = component or element demand modifier (factor) to account for expected ductility associated with this action at the selected Structural Performance Level. M-factors are specified in dedicated chapters; QCE = expected strength of the component or element at the deformation level under consideration for deformation-controlled actions; κ = knowledge factor taken according to knowledge level [18].

Force-controlled actions in primary and secondary components and elements shall satisfy the following equation [18]:

CL UFQ Qκ ⋅ > (4.1-3)

QCL = lower-bound strength of a component or element at the deformation level under consideration for force-controlled actions.

Force-controlled design actions QUF shall be taken as the maximum action that can be developed in a component based on a limit-state analysis considering the expected strength of the components delivering load to the component under consideration, or the maximum action developed in the component as limited by the nonlinear response of the building. Alternatively QUF can be determined as [18]:

1 2 3

EUF G

QQ QC C C J

= ± (4.1-4)

Displacement amplifiers, C1, C2, and C3 are divided out when seeking an estimate of the force level present in a component when the building is responding inelastically. J = a coefficient used in linear procedures to estimate the actual forces delivered to force-controlled components by other (yielding) components [18].

Non-linear Analysis

Static – Pushover

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Nonlinear static analysis is usually used together with different procedures (e.g. coefficient method, capacity spectrum method - FEMA 356 [18]; or the N2 method - Eurocode 8-1, [15]) in order to estimate the target displacement under the design seismic action.

Considering that target displacement is intended to represent the maximum displacement experienced during seismic action, and that element inelastic response is modelled directly, nonlinear static procedure will provide reasonable estimates of both displacements and internal forces [45].

Dynamic – Time-history

Nonlinear time-history analysis represents the most advanced method of analysis for evaluation of seismic response of structures. Nonlinear time-history analysis provides reasonable estimates of both displacements and internal forces in structural elements [45].

Acceptance criteria for nonlinear analysis

If nonlinear procedures are used, component capacities for deformation-controlled actions shall be taken as permissible inelastic deformation limits, and component capacities for force-controlled actions shall be taken as lower-bound strengths, QCL [18].

4.1.2. Choice of analysis procedure

Knowledge factor

Data on the as-built condition of the structure, components, site, and adjacent buildings shall be collected in sufficient detail to perform the selected analysis procedure. The extent of data collected (material properties, initial project drawings, condition assessment and addition information obtained by testing) shall be consistent with minimum, usual, or comprehensive levels of knowledge. Depending of the level of knowledge shall be determined the selected Rehabilitation Objective and analysis procedure in accordance with Table 2 [18].

Table 2 Data Collection Requirements [18]

Level of knowledge

Minimum Usual Comprehensive

Rehabilitation Objective BSO or Lower BSO or Enhanced Enhanced

Analysis Procedures LSP, LDP All All

LSP – linear static procedure

LDP – linear dynamic procedure

Requirements for analysis procedure selection

Lateral force method

In the elastic range, dynamic response is governed by the fundamental mode of vibration if the structure is regular in elevation and it is not very flexible. The second requirement is expressed in Eurocode 8-1 (2003) by limitation of the fundamental period of vibration of structures that can be analyzed using the lateral force method to the lesser of 4TC and 2 seconds (where TC is the limit between the constant acceleration and constant velocity region of the spectrum) [45].

Response spectrum and linear time-history analysis

Response spectrum and linear time-history analyses suffer from the drawbacks of linear (elastic) analysis, when applied to highly inelastic structural response. Therefore, these analysis procedures are still not adequate when inelastic demands are non-uniform within the structure and when the structural response is expected to be highly inelastic [45].

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Nonlinear static procedure

It is subjected to several limitations, due to the fact that it relies on the assumption that structural response is governed by the fundamental mode shape, and that this shape does not change when the structure yields under increasing lateral loading. Pushover analysis is mainly applicable to estimating seismic demands on low-rise and medium rise structures in which inelastic demands are uniformly distributed along the height of the structure [11]. Eurocode 8-1 [15] requires at least two lateral force distributions ("modal" and uniform).

Several improved procedures based on pushover analysis were proposed by different researchers, in order to account for influence of higher modes of vibration and change in distribution of lateral forces as a result of change in dynamic properties of the structure as a result of yielding.

Nonlinear time-history analysis

Nonlinear dynamic analysis offers the most "correct" evaluation of seismic response of a structure, and can be applied in all cases. However, it requires the greatest degree of expertise of the engineer and the most comprehensive degree of knowledge on the properties of materials and elements.

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4.1.3. Choice of the intervention technique

General criteria

Every rehabilitation program of buildings aims at

1. The removal of the causes of the continuing deterioration;

2. The better conservation of the building after the work is completed;

3. The improvement of the value.

Alternative solutions shall be finally validated in terms of four group criteria of different nature [48].

• Cultural and/or social values; • Technical aspects

o Reversibility of intervention, Compatibility, Durability, Corrosion, UV resistance, Aging, Creep, Local conditions, Availability of material/device, Technical capability, Quality control

• Structural aspects o Structural performance (Strength, Stiffness, Ductility, Fatigue), Response to fire,

Sensitivity to changes of actions/resistances e.g. seismic action, temperature, fire, soil conditions, Accompanying measures, Technical support (Codification, Recommendations, Technical rules), Installation/Erection e.g. availability/necessity for lifting equipment

• Economical and sustainability aspects o Costs, Design, Material/Fabrication, Transportation, Erection / Installation / Maintenance,

Preparatory works Technical aspects refer to decisions covering the overall design and the selection of materials and techniques [48].

Structural performance based validation

Choice of one or an other strengthening technique is a multi-criteria problem, as previously shown. The designer has always several solutions at his disposal. Finally one has to select one which matches better with assembly of validation criteria. In fact, the solution will represent always a rational compromise among different criteria, because the one criterion based optimisation leads, in general, to an unacceptable choice.

Moreover, hereby we will show as an example, the analysis of possible strengthening solutions considering the structural performance only.

The example of a R.C. frame which is required to be retrofitted in order to enhance both strength and stiffness to resist seismic actions (see Figure 4.1-4) On this purpose six different strengthening techniques are examined. In order to decide which of the six is the appropriate one, we need first to fix the target of intervention in terms of strength, stiffness and ductility.

Starting from the idea that current strengthening interventions, of the type shown in Figure 4.1-4, increase both the stiffness and lateral load capacity of the RC frame, the judgement can be based on the analysis of capacity curve. The capacity curve of the strengthened structure, Cs, generally has a higher slope and peak compared to the capacity curve before strengthening, Cu. In Figure 4.1-5 a theoretical situation is considered. Due to the increased stiffness, which translates into a decreased fundamental period, the seismic demand on the structure is also increased, as shown by the demand curve for the strengthened structure, Ds, compared to that for the unstrengthened structure, Du. Although the capacity increase is partly alleviated by the increase in seismic demand, the overall performance of the structure

262

is improved as shown by the locations of the performance points on the spectral displacement axis for before and after strengthening [7].

Figure 4.1-4 Strengthening solutions for a RC Frame (CEB – Fastenings for seismic retrofitting

[8]; Sugano 1989)

a) Effect of structural strengthening b) Effect of deformation enhancement

c) Effect of enhanced energy dissipation

Figure 4.1-5 Analysis of the concept of strengthening solutions [4][35]

Such type of analysis has to be developed for all six solutions in the Figure 4.1-4. After, depending by the hierarchy the demand in strength, stiffness and ductility, and also considered the other complementary criteria of previous section (e.g. 0), the final decision can be taken.

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4.1.4. PBE Methodologies and examples

Review of the main evaluation methods

The structural engineering community has developed a new generation of design and seismic evaluation procedures that incorporates performance-based engineering concepts. In a short term, the most appropriate approach seems to be a combination of the nonlinear static (pushover) analysis and the response spectrum approach [49].

Examples of such an approach are:

• Capacity spectrum method (CSM), applied in o ATC 40 (Seismic Evaluation and Retrofit of Concrete Buildings, 1996) o U.S. Army Corps of Engineers, Technical Manuals (Seismic Design for Buildings and

Seismic Design Guidelines for Upgrading Existing Buildings, 1998) o Japanese Building Standard Law (BSL 2000)

• Nonlinear static procedure, applied in o FEMA 356 (Prestandard and Commentary for the Seismic Rehabilitation of Buildings,

2000), o N2 method developed at the University of Ljubljana [17] and implemented in the draft

Eurocode 8 (Design of structures for earthquake resistance, 2001), o Modal Pushover Analysis [10]

All methods combine the pushover analysis of a multi-degree-of-freedom (MDOF) model with the response spectrum analysis of an equivalent single-degree-of-freedom (SDOF) system. Inelastic spectra or elastic spectra with equivalent damping and period are applied. As an alternative representation of inelastic spectrum the Yield Point Spectrum has been proposed [3]. Some other simplified procedures based on deformation-controlled design have been developed, e.g. the approaches developed by Priestley [40] and by Panagiotakos and Fardis [37].

The essential difference is related to the determination of the displacement demand (target displacement). If an equivalent elastic spectrum is used, displacement demand is determined based on equivalent stiffness and equivalent damping, that depend on the target displacement and, consequently, iteration is needed. The quantitative values of equivalent damping, suggested by different authors, differ considerably. On the other side, for the methods using inelastic spectra, bilinear idealization of the pushover curve is required. If the bilinear idealization depends on the displacement demand, then the computational procedure becomes iterative, also. The procedures differ also in the assumed lateral load pattern, used in pushover analysis, and in the displacement shape, used for the transformation from the MDOF to the SDOF system (and vice versa). Only if the two vectors are related, i.e. if the lateral load pattern is determined from the assumed displacement shape, the transformation from the MDOF to the SDOF system is based on a mathematical derivation [49].

Related to the organization of evaluation procedure or design for retrofitting a given structure the following general items are emphasized [20]:

o Role of the displacement in the design process o Deformation – calculation based (DCB) o Iterative deformation – specification based (IDSB) o Direct deformation – specification based (DDSB)

o Type of analysis used in the design process o Response spectra – initial stiffness based o Response spectra – secant stiffness based o Time history analysis based

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o Structural type limitations o Limit-state or performance objectives limitations

The matrix in Table 3 summarizes the various design procedures, which can apply:

Table 3 Matrix of design procedures [20]

Deformation – calculation based (DCB)

Iterative deformation – specification based (IDSB)

Direct deformation – specification based (DDSB)

Response spectra – initial stiffness

Moehle [34]

FEMA 356 [18]

UBC [47]

Panagiotakos & Fardis [37]

Albanesi [1]

Fajfar [17]

Browning [6]

SEAOC [42]

Aschheim & Black [3]

Chopra & Goel [10]

Response spectra – secant stiffness

Freeman [22]

ATC [5]

Paret [39]

Chopra & Goel [9]

Gulkan & Sozen [23]

Kowalsky [32]

SEAOC [42]

Priestley & Kowalsky [40]

Time history analysis Kappos & Manafpour [31] N/A N/A

Approximate analysis requires basic structural information in addition to visual screening methodology such as the dimensions of columns, beams and shear walls, which can be determined from building drawings or measurements, usually on the ground floor. Where building drawings are not available, minimum reinforcement is assumed in the structural elements. Concrete strength is usually assumed a conservative value, however, on site (e.g. Windsor probe) or laboratory measurement of concrete strength is more appropriate for buildings in areas known for variability in material properties. The lateral seismic design loads on the building are calculated using the static equivalent load method and distributed to the floors according to seismic codes [35]. The calculated load demand is compared with the lateral load capacity of the floor determined either individually for each member, or as a whole by simplifying the building system to one of the forms shown in Figure 4.1-6.

Figure 4.1-6 Simplified equivalent building systems for the approximate analysis [35]

The former requires distribution of the floor load to members according to their rigidities. Evaluation of the building is performed by means of a seismic index, Is, determined by a ratio between the total allowable lateral load and the probable lateral seismic load demand, given by

265

alls

VIV

= (4.1-5)

This evaluation is generally performed for ground floor only for savings in time and labour. In case it is performed for each floor, the most critical index is assigned for the building. A significant advantage of approximate structural evaluation methodologies, other than considerable time savings compared to detailed analysis methods, is the ability to perform a first level prioritization, based on the level of lateral load resistance, for a detailed analysis or retrofit application [35].

Detailed evaluation through linear analysis methods is the most commonly used approach since most seismic codes (e.g. [46], [29]) require use of these methods. Based on detailed structural information, member forces under design loads are determined and compared with their ultimate strength. With this methodology, it is possible to accurately determine the overstressed members under design loads; however, it is difficult to assess the seismic risk of the building at the system level. Thus, although this method is useful in prioritizing deficient structures, it may not yield sufficient information needed for determining the optimum retrofit strategies. The current trend is to use the nonlinear analysis techniques, which require approximately the same amount of data, but more engineering effort and expertise compared to the approaches based on linear analysis techniques.

Detailed evaluation using nonlinear analysis provides the most accurate and reliable risk assessment, loss estimation, and retrofit optimization practices at the expense of detailed site, structural, and material information, longer computation times, and a higher level of technical expertise. The linear analysis methodology described above is an integral part of this methodology. By considering the nonlinear inelastic behaviour of structural members under increasing loads, this methodology can predict the nonlinear behaviour of the structural system much more realistically compared to linear analysis techniques [35].

Determining the nonlinear structural behaviour allows for performance-based design, which results in significant savings in seismic retrofit applications ([4], [18]). Figure 4.1-7(a) shows the typical top displacement vs. base shear curve obtained from nonlinear pushover analysis of buildings. Using this curve alone, one can perform a preliminary evaluation of the structure’s seismic safety by comparing its capacity with the seismic demand determined using the equivalent static load method described in seismic codes. A better performance evaluation can be performed by converting both the capacity curve and the seismic demand spectrum to the acceleration-displacement response spectrum (ADRS) format formed as a relationship of spectral displacement vs. spectral acceleration as shown in Figure 4.1-7(b). A further improved evaluation can be achieved by obtaining a reduced inelastic response spectrum for the seismic demand to consider the increased damping due to inelastic deformations in the building [4].

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Figure 4.1-7 Seismic safety evaluation of buildings using nonlinear analysis [35] [4]

The intersection of the capacity and demand curves shown in Figure 4.1-7 (b) is called the performance point of the building. Based on the location of this performance point, performance level of the building is determined. The intervals of spectral displacement that correspond to different Performance Levels are in principle shown in Figure 4.1-7(b) and the limits of the performance levels, that are expressed in terms of interstory drift values, are recommended in Error! Reference source not found..

If the performance point is located in the initial portion of the capacity curve where the inelastic deformations are not significant the performance level of the building is Immediate Occupancy, which is self explanatory.

For interstory drift values, corresponding to the range of Immediate Occupancy and Life Safety levels, respectively, the performance level of the building is Life Safety (or Damage Control). In this region, inelastic deformations are expected in the building that poses no significant threat to the stability of the building and the safety of its occupants. Between the Life Safety and Collapse Prevention (or Structural Stability) Levels, the building performance level is described as Collapse Prevention (Limited Safety). Large inelastic deformations are expected which may result in excessive cracking and failure of some structural members, which may pose threat to occupants or result in local failures. Beyond the Collapse Prevention (or Structural Stability) level, the collapse of the building is imminent.

From this discussion, it is apparent that nonlinear analysis is a very convenient methodology for development of realistic fragility curves [35].

4.1.5. Vulnerability Analysis

Vulnerability can simply be defined as the sensitivity of the exposure to seismic hazard(s). The vulnerability of an element is usually expressed as a percentage loss (or as a value between zero and one) for a given hazard severity level [12]. In a large number of elements, like building stocks, vulnerability may be defined in terms of the damage potential to a class of similar structures subjected to a given seismic hazard. Vulnerability analysis reveals the damageability of the structure(s) under varying intensity or magnitudes of ground motion. Multiple damage states are typically considered in the analysis [35].

267

Figure 4.1-8 Structural vulnerability and damage states for various level of seismic demand [35]

Figure 4.1-8(a) shows the damage states of a building based on the applied base shear, which can be determined as a function of the seismic demand. The roof displacement – base shear curve, also called the capacity curve, shown in this figure represents the nonlinear behaviour of a building under increasing load or displacement demand. The damage state of the building varies between none to collapse under increasing levels of demand, which is graphically illustrated in Figure 4.1-8(a). A relatively more convenient representation of the damage states is provided in Figure 4.1-8(b) by overlaying both building capacity and seismic demand curves on a different set of axes showing spectral displacement vs. spectral acceleration. Two different capacity and seismic demand curves are shown in the Figure 4.1-8. Intersection of the capacity and demand curves represents the damage state likely to be experienced by the structure. As can be seen from the figure, the strong structure is likely to suffer from light to moderate damage due to the low seismic demand, and moderate to extensive damage due to the high seismic demand. On the other hand, the weak structure is expected to suffer from moderate to extensive damage due to low seismic demand, and collapse during the high seismic demand due to insufficient seismic resistance [35].

Methods of vulnerability analysis vary based on the exposure information and the complexity of the approach. Vulnerability of structures to ground motion effects is often expressed in terms of fragility curves or damage functions that take into account the uncertainties in the seismic demand and capacity. Fragility functions can be developed for buildings or its components depending on how detailed the risk analysis is performed. Early forms of fragility curves were developed as a function of qualitative ground motion intensities largely based on expert opinion. Recent developments in nonlinear structural analysis have enabled development of fragility curves as a function of spectral parameters quantitatively related to the magnitude of ground motion. Figure 4.1-9(a) shows the typical seismic demand and structural capacity curves together with their uncertainties expressed in terms of probabilistic distributions. Based on these curves and the associated uncertainties, the fragility curves shown in Figure 4.1-9(b) can be constructed for various damage states. Since each damage level is associated with a repair/replacement cost, the probabilistic estimates of the total cost can be estimated using these curves once the hazard is known. This can be achieved by use of predefined representative fragility curves developed for structures in the same class, or custom damage curves developed through nonlinear analysis of individual structures [35].

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Figure 4.1-9 Uncertainties in seismic performance and use of fragility curves [35]

Construction of the fragility or damage curves is the key element in estimating the probability of various damage states in buildings or building components as a function of the magnitude of a seismic event. Thus, development of realistic fragility curves for the building stock and lifelines in a seismic region constitutes an essential part of a meaningful seismic risk analysis [35].

One of the most known methodologies for assessing fragility function is HAZUS. This software it is based on a methodology for estimating potential earthquake losses on a regional basis, developed under coordination of the National Institute of Building Science (NIBS) under a cooperative agreement with the Federal Emergency Management Agency (FEMA).

(1) Selection of scenario earthquakes and PESH inputs

(2) Selection of appropriate methods (modules) to meet different user needs

(3) Collection of required inventory data, i.e., how to obtain necessary information

(4) Costs associated with inventory collection and methodology implementation

(5) Presentation of results including appropriate terminology, etc.

(6) Interpretation of results including consideration of model/data uncertainty.

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Figure 4.1-10 Steps evaluation of building safety [24]

4.1.6. Reference

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[2] Arzhang Alimoradi, Performance Performance-Based Seismic Design Application of New Developments, West Tennessee Structural Engineers Meeting, May 27, 2004

[3] Aschheim M.A., Black E.F. – Yield point spectra for seismic design and rehabilitation, Earthquake Spectra, vol.16, no.2, 2000

[4] ATC 40 – Seismic evaluation and retrofit of concrete buildings – volume 1, November 1996 [5] ATC, Development of Performance-based Earthquake Design Guidelines, ATC-58, Redwood

City, 2002. [6] Browning J.P. – Proportioning of Earthquake-Resistant RC Building Structures, Journal of the

structural division AISC, vol. 127, no.2, 2001 [7] Buyukozturk O., Gunes O., Karaca E. – Advances in Earthquake Risk Assessment and Hazard

Reduction for Large Inventory of Structures with High Characteristic Variability, MIT - IST – Infrastructure Science and Technology Group – Department of Civil and Environmental Engineering

[8] CEB Fastenings for Seismic Retrofitting - State-of-the-art Report (Bulletin 226 part 2, Telford, London, 1996)

[9] Chopra A.K., Goel R.K. – Capacity Demand Diagram Methods based on Inelastic design spectrum, Earthquake Spectra 15(4), 1999

[10] Chopra A.K., Goel R.K. – Direct-displacement based design: Use of inelastic vs. elastic design spectra, Earthquake Spectra, vol.17 no.1, 2001

[11] Chopra, A.K. "Estimating seismic demands for performance-based engineering of buildings". 13th World Conf. on Earthquake Engineering, Vancouver, B.C., Canada. Paper no. 5007, 2004

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[12] Coburn A.W., Spence R.J.S. and Pomonis A. – Vulnerability Risk Assessment, DMTP of UNDP, Cambridge 1994

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[14] Earthquake Engineering Research Centre, Performance-based Seismic Design of Buildings: An Action Plan, U.C., Berkeley, 1995.

[15] Eurocode 8-1/2003 "Eurocode 8: Design of structures for earthquake resistance. Part 1: General rules, seismic actions and rules for buildings". CEN - European Committee for Standardization.

[16] Eurocode 8-3/2003. "Eurocode 8: Design of structures for earthquake resistance. Part 3: Strengthening and repair of buildings". CEN - European Committee for Standardization.

[17] Fajfar P. – A nonlinear analysis method for performance-based seismic design, Earthquake Spectra, vol. 16, no. 3, 2000

[18] FEMA 356, Guidelines for Seismic Rehabilitation of Buildings, Vol. 1: Guidelines, FEMA 356, Washington DC, 2002 (formerly FEMA 273).

[19] FEMA 356/EERI, Action Plan for Performance-Based Seismic Design, FEMA 349, Washington DC, 2000.

[20] FIB (CEB-FIP) Displacement-based seismic design of reinforced concrete buildings – state-of-art report – bulletin 25

[21] FIB (CEB-FIP) Seismic assessment and retrofit of reinforced concrete buildings – state-of-art report – bulletin 24

[22] Freeman S.A. – The capacity spectrum method as a tool for seismic design, Proceedings of the 11th European Conference on Earthquake Engineering, Sep. 6-11, Paris, 1998

[23] Gulkan P., Sozen M. – Inelastic Response of Reinforced Concrete Structures to Earthquake Motions, ACI Journal 71(12)

[24] Guragain R. Pandey B.H., Shrestha S.N. – Guidelines for seismic vulnerability assessment of hospitals, NSET, 2004

[25] Hamburger R. - Performance-Based Seismic Engineering: The Next Generation of Structural Engineering Practice (http://www.propertyrisk.com/refcentr/revf96-1.htm)

[26] Hamburger R.O, A Framework for Performance-Based Earthquake Resistive Design - EERC-CURE Symposium in Honour of Vitelmo V. Bertero, January 31 - February 1, 1997, Berkeley, California, 1997

[27] Hamburger, R.O., Performance-Based Analysis and Design Procedure for Moment Resisting Steel Frames, Background Document, SAC Steel Project, Sept. 1998.

[28] Howe R.W., Performance-based design seen as future wave in building codes, Memphis Business Journal, Friday, August 11, 2000

[29] IBC, Int. Code Council, Falls Church (VA, 2000) [30] Kalkan, S.M. and Kunnath, S.K. "Adaptive modal combination procedure for nonlinear static

analysis of building structure". Journal of Structural Engineering, Vol. 132, No. 11, pages 1721-1731, 2006

[31] Kappos A.J., Manafpour A. – Seismic Design of R/C buildings with the aid of advanced analytical techniques, Engineering Structure, vol.23, 2001

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[33] Krawinkler H., Challenges and progress in performance-based earthquake engineering, International Seminar on Seismic Engineering for Tomorrow – In Honour of Professor Hiroshi Akiyama, Tokyo, Japan, November 26, 1999

[34] Moehle JP – Displacement-Based Design of RC Structure Subject to Earthquakes, Earthquake Spectra 8(3), 1992

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[35] O. Buyukozturk and O. Gunes – Advances in earthquake risk assessment and hazard reduction for large inventory of structures with high characteristic variability – ARI volume 53, number 2

[36] P100 part 3 volume 1 - COD DE EVALUARE SI PROIECTARE A LUCRĂRILOR DE CONSOLIDARE LA CLĂDIRI EXISTENTE, VULNERABILE SEISMIC – (Standard for evaluation and retrofitting of existing building), 2003

[37] Panagiotakis T.B., Fardis M.N. – Deformation-Controlled Earthquake-Resistant Design of RC Building, Journal of Earthquake Engineering vol. 3 no. 4, 1999

[38] Pang W., Rosowsky D., Direct Displacement Procedure for Performance-Based Seismic Design of Multistory Wood frame Structures

[39] Paret T.F et all – Approximate inelastic procedures to identify failure mechanisms from higher mode effects, 11th World Conference on Earthquake Engineering, Acapulco, Mexico, 1996

[40] Priestley M.J.N., Kowalsky M.J. – Direct displacement-based design of concrete buildings, Bulletin of the New Zealand National Society for Earthquake Engineering 33(4), 2000

[41] Recommended Seismic Design Criteria for New Steel Moment- Frame Buildings, FEMA 356 350, Federal Emergency Management Agency, Washington DC, July 2000

[42] SEAOC – Recommended Lateral Forces Requirements and Commentary, 1999 [43] SEAOC, Vision 2000: Performance Based Seismic Engineering of Buildings, San Francisco,

April 1995. [44] Stratan A., Bordea S., Dogariu A., D. Dubina - Seismic upgrade of non-seismic reinforced

concrete frames using steel dissipative braces – COST Workshop Prague 2007 [45] Stratan A., Dubina D. – Models and analysis procedure for global analysis – FP6 PROHITECH,

WP9 Calculation Models, 2006 [46] TC-BIB , Specification for Structures to be built in disaster area (Ministry of Public Works and

Settlement, Ankara, Turkey, 1998) [47] Uniform Building Code – International Conference of Building Officials, vol2 [48] Vayas Y, Report on WP10 Validation, FP6 PROHITECH, 2007 [49] Zamfirescu D., Masayoshi Nakashima - Comparison of simplified procedures for performance-

based seismic evaluation of Structures

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4.2. Overview of collapse modes and evaluation of bearing capacity

4.2.1. Introduction

This section was prepared in accordance with data-sheets no. 9-20 “Collapse mechanisms for historical masonry buildings”, no. 9-21 “Ultimate limit state of historical masonry buildings”, no. 9-22 “Collapse mechanisms for masonry buildings” and no. 9 -23 “Collapse mechanisms for churches”, provided by Victor Gioncu and Marius Mosoarca, from Politehnica” University of Timisoara, Romania. The report presents aspects regarding the collapse mechanisms for masonry elements and structures, more detailed for different structures for churches.

4.2.2. Generalities

Most of the historical buildings are, at least in the Mediterranean area, made of masonry, using stone, brick blocks or adobe. These unreinforced masonry structures cannot be considered a continuum, but rather an assemblage of compact elements (stone or brick) linked by means of mortar joist. Seismic events have often caused massive damage or the destruction of such structures with great cultural significance. In the recent events, earthquakes caused great damage and destruction of monumental buildings and churches (see the Umbria-Marche earthquake of September-October 1997), (Figure 4.2-1, Croci, 2006). Unlike today’s structures, where the seismic vulnerability can be inferred by means of existing codes and analysis methodologies, the assessment of seismic behaviour of historical buildings lacks scientific background. The evaluation of seismic vulnerability of such buildings depends on reliable numerical simulation of their seismic response.

Numerical modeling of the seismic behaviour of masonry structures represents a very complex problem due to the constitutive characteristics of the structural material and its highly physical and geometrical non-linear behaviour when subjected to strong ground motions. The main problem is the importance of discontinuities between the masonry units and the joining material such as mortar, so the masonry exhibits as a heterogeneous structure and discontinuous systems.

The ultimate limit state, governed by the blocky nature and the collapse mechanisms of masonry structures behaviour, can remove these difficult problems.

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Figure 4.2-1 Collapse of St. Francis Basilica of Assisi

4.2.3. Calculation models of masonry buildings for seismic design

Strategies for masonry building modeling

The modeling of masonry structures can be divided in two types: local and global modeling. Local models are expressed in terms of continuum mechanics quantities (stress and strain), whereas global models involve generalized quantities, forces and displacements.

Despite that the masonry is an ancient building material, effective methods for modeling its structural local behaviour remains a very active issue, without important practical rules for design. The particularly difficult aspect is given by its constituent materials (mortar and bricks) and geometry (dimensions of bricks, thickness of mortar joints).

The global modeling introduces empirical laws for representing the behavior of structural components (walls, columns, floors, etc). Therefore, the difficulties in defined the material characteristics are eliminate and the global models are often used for the simulation of the historical masonry buildings behaviour, especially for the seismic actions.

Performance-based design of masonry buildings

A current trend in seismic design is the incorporation of performance-based design methodology. In this methodology, every building is designed to have the desired levels of seismic performances corresponding to different specific levels of earthquake ground motion. To achieve this goal, elastic analysis is insufficient, because this cannot realistically predict the forces and deformations during earthquakes. Inelastic analytical procedures become necessary to identify the mode of failure. Inelastic time-history is the most realistic approach for evaluating the performance of a building. However, the inelastic time-history analysis is usually too complex and time-consuming in the design of most

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buildings. As a compromise, a simplified procedure commonly accepted is the pushover analysis, where a sequence of inelastic static analysis is performed for a set of monotonically increasing lateral loads.

For the historical masonry buildings, the pushover methodology is complicated by the definition of the mechanical properties of the materials, the definition of constitutive laws for decayed materials and structure rigidity degradation due to the cracks formation. The behaviour of a masonry triumphal arch of a church is presented in Figure 4.2-2. In the first stage, the arch works as a compact element until occur the first fissures. In this field the masonry element works as an elastic medium with heterogeneous properties. These fissures produce a reducing of arch rigidity, but the elastic behaviour is not modified very much. At the superior level of load, the fissures are turned in a system of cracks, which affects very much the element behaviour. The increase of load produces of a local failure (local collapse), where the first very important damage of arch occurs. In the ultimate limit, a collapse mechanism (global collapse) is formed, which generates the arch failure.

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Figure 4.2-2 Behaviour of a masonry triumphal arch of a church

The same effects of damage in behaviour of a wall are presented in Figure 4.2-3 (Rojahn C., 1998).There can see that, after the formation of first cracks, the nonlinear behaviour, due to the reduction of lateral rigidity, increases very fast and the elastic behaviour cannot be considered.

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Figure 4.2-3 Effects of damage in behaviour of a wall

In the frame of performance-based design philosophy, until the formation of crack system, the structure works without very important damage and the safe occupancy and operational usage can be considered. In this domain the damage control is the main task of design. The field until the local damage is the precursory phase of the structure failure, while the formation of a collapse global mechanism represents the ultimate limit state. In many cases, between the local failure and global collapse, due to the formation of collapse mechanism, there are not very important differences.

Considering the limit states considered in EUROCODE 8, the masonry structure behaviour until the formation of first local failure can be considered as the field of damage limitation stage, while the behaviour until the formation of collapse mechanism, the ultimate limit state. It is very clearly that the methodologies for the two limit states differ very much. While for damage limitation limit state on can use the elastic analysis, where the heterogeneity of material properties and the local effects fissures must be considered, for the ultimate limit state, the methodology must be very different and the collapse mechanisms can be very useful.

Computations on masonry structures

Numerical modelling of a masonry structure is a very difficult task, since masonry does not respect any hypothesis (isotropy, elastic behaviour, homogeneity) assumed for other materials. In the past decades several attempts have been done to assume models used for other materials, but the results were very poor. Elastic models, considering a homogenized continuum, can give an indication on the mechanical behaviour in the undamaged range and can only detect the weak part of the structure and the positions of to come cracks. For ultimate state, nonlinear models, using complex finite elements, based on plasticity theory and considering the joint and interface elements to model the planes of weaknesses, can be used only for simple masonry elements, being inadequate to model a full structure. Therefore, the development of a simple model, able to determine the ultimate limit state for complex masonry structures is a very expected by the designers.

Direct observations of crack patterns recorded in post-earthquake damaged masonry structures yield to the conclusion that often the failures occur by formation of a collapse mechanism, involving all the

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buildings, or only some parts of them. In this case computational models use some rigid body macro-elements, and the discontinuities are concentrating only along the borders of these elements.

This computation method can be validated by the numerical studies performed in (Mele E., 1999) for some church structural elements, the triumphal arch and the longitudinal nave arcade.

The main steps of triumphal arch nonlinear analysis are presented in Figure 4.2-4a. The nonlinear analysis is performed using the ABAQUS computer code for the discretization presented in Figure 4.2-4b, considering a brittle material, namely the “concrete like” model, originally intended to stimulate plain concrete. Cracking occurs when the stresses reach a failure surface. The possible pattern of collapse mechanism is presented in Figure 4.2-4c, involving four hinges in different positions. Varying the position of these hinges in all possible configurations, a class of the kinematics multipliers of horizontal actions is defined, and the minimum value represents the ultimate collapse multiplier. In Figure 4.2-5 the results of pushover, using a concrete model for masonry behaviour, are provided in terms of horizontal force normalized to the vertical load, with different values of compressive and tensile strength. In the same Figure the results obtained using the kinematic theorem for the collapse mechanisms are plotted. One can observe a very good correspondence between the ultimate load obtained a very complex analysis and the more simple analysis using the collapse mechanisms methodology.

a)

b)

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global mechanism semi-global mechanism

c)

Figure 4.2-4 Main steps of a triumphal arch nonlinear analysis

Figure 4.2-5 Results of pushover, using a concrete model for masonry behaviour

The same conclusion results from the analysis of longitudinal arch (Figure 4.2-6a) composed by two parts, the major arch and the arcade. The deformed configuration, using the FEM analysis, is presented in Figure 4.2-6b. The relation between the analytical computation using pushover methodology and the collapse mechanism methodology is presented in Figure 4.2-7.

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Figure 4.2-6 Analysis of a longitudinal arch

Figure 4.2-7 Relation between the analytical computation using pushover methodology and the

collapse mechanism methodology

In conclusion, the numerical results, performed in (Mele E., 1999), have provided indications on the reliability of the collapse mechanisms methodology in the determination of the ultimate limit state capacity of masonry buildings. Therefore, this methodology will be used in the determining the ultimate limit state of masonry buildings.

Modeling masonry building by rigid blocks

The use of theory of rigid blocks to determine the limit state of masonry buildings has the potential to become a powerful tool for small and medium size historical buildings in engineering practice. In particular, this approach avoids the use of sophistical and time-consuming nonlinear finite element techniques. The applicability of this theory to masonry structures modelled as assemblages of rigid blocks interacting through joints depends on some basic hypothesis, confirmed by is-site observations and experimental results:

- limit loads occurs at small displacements, so the linear theory can be used;

- masonry has no tensile strength;

- the compression and shear failures at the joints are perfectly plastic;

- hinging failure at joint does not consider the effects of local crushing.

The method is based on the observations about the in-site formation of rigid blocks or considering the all type of collapse mechanism and the determining the minimum collapse load for these mechanisms. An exemplification of this methodology is presented in Figure 4.2-8. During an experimental test, the formation of the cracks is shows in Figure 4.2-8a and the corresponding collapse mechanism in Figure 4.2-8b. Internal forces are presented in Figure 4.2-8c. The collapse load corresponding to the ultimate

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load is determined using a cinematic method (Tianyi Y., 2006). In this method the following steps must be crossed:

- establishment of the horizontal and vertical loads applied to the structure;

- establishment the possible collapse mechanisms for the structural system;

- determining for each element of the mechanism the vertical forces and the position of these forces;

- imposing to the collapse mechanism of a horizontal virtual displacement;

- determining the compatible virtual displacement for each element of the mechanism;

- using the principle of the minimum of total potential energy (composed by internal and external parts) the amplification factors for horizontal forces, corresponding to the all established collapse mechanisms, are determined;

- the collapse mechanism for the ultimate limit state is determined corresponding to the minimum value of the determined amplification factors.

This methodology allows to model typical strengthening solutions, as the inclusion of steel tie bars or fiber reinforced polymers strips or bars.

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Figure 4.2-8 Modeling masonry building by rigid blocks

4.2.4. Ultimate limit states for masonry elements

In the study of historic masonry buildings subjected to earthquakes there are two main objectives: (i) the understand the way the structure behaves implied the study of possible responses; (ii) to understand the origin and significance of the cracks, local or global collapse (Huerta, 2001).

Unreinforced masonry historical buildings are the most vulnerable during an earthquake. Normally they are conceived for vertical loads and since masonry has adequately compressive strength, therefore the masonry structures behave well as long as the loads are vertical. When such a masonry structure is subjected to horizontal loads during an earthquake, the walls develop shear and flexural stresses. Under these conditions the strength of masonry depends on the bond between brick and mortar, which is quite poor. A masonry wall can undergo in-plane shear stresses, forming diagonal cracks. Catastrophic collapses take place when the wall experience out-of -plane flexure.

Therefore, there is an acute need for programs to better understanding the seismic structural behaviour of historic buildings. This program starts with the determining the ultimate limit state of masonry elements, by replacing the very complex FE methodology by more simple Collapse Mechanism methodology. The main considered masonry elements are walls and floors.

Individual masonry buildings, as well as whole historic centers of cities composed by an ensemble of buildings, are now recognized as vital elements of architectural heritage. They also represent the most vulnerable class of buildings as far as seismic risk is concerned, even for moderate earthquakes.

Traditional historical masonry buildings can be described as a three-dimensional network of orthogonal wall creating cells that resist seismic load through a box behaviour. The floors traditionally are made of timber beams spanning the shortest distance between walls, so that only one of the two orthogonal walls is load bearing while the other set’s role is mainly to provide out-of-plane restraint of the bearing walls. The roof structure is usually similar to the floor structure. In this situation, the restrained effects of floors are much reduced, and, in many cases these effects can be neglected. Only if the floors are made by barrel vaults, the restrained effects can be considered.

Masonry walls

In order to carry out a seismic analysis of a masonry building, it is possible to schematize the structure as an assemblage of the composing walls. The behaviour of whole building is function of the behaviour of each wall, which can be defined in-plane or out-of-plane behavoiur.

(i) For in-plane behaviour, horizontal and vertical masonry strips and openings (doors or windows) define a wall (Figure 4.2-9). The vertical strips located between two alignments of opening are defined as “pier strips”, while the horizontal strips placed between two levels of openings are defined as “storey

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strips”. In the aim of a structural analysis, the masonry walls can be modeled trough macro-panels (Figure 4.2-9): “piers panels“ (horizontally included between two openings), “storey panels” (vertically included between two consecutive openings).

Figure 4.2-9 Component panels of a wall

Figure 4.2-10 The failure modes of a panel. a) Sliding; b) Shear; c) Overturning

The failure mode for a panel is function of the geometrical dimensions and the characteristics of its masonry texture (single or multiple leaf walls, connection between these walls, physical and mechanical characteristics of bricks and mortar).

The different collapse mechanism types for a wall with two doors at the firs level and two windows at the second level are presented in Figure 4.2-11:

- collapse mechanism composed only by overturning failure mode of storey strips and pier strips (Error! Reference source not found.a);

- collapse mechanism composed by overturning failure more for first story strip and sliding failure mode for the second storey strip (Figure 4.2-11b);

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- collapse mechanism composed by shear failure mode of storey panels of the two levels (Figure 4.2-11c);

- collapse mechanism composed by shear failure mode for first level of storey panels and overturning failure mode the pier panels at the last level (Figure 4.2-11d);

- collapse mechanism composed by shear failure mode of pier panels of both levels (Figure 4.2-11e).

Figure 4.2-11 In-plane collapse mechanism types

By determining the collapse mode for all these mechanism types one can determine the ultimate limit state for the minimum amplification factor.

A seismic response of a historic building from Catania, dates back to nineteenth Century, is presented in Figure 4.2-12 (Brencich et al, 2000, Liberatore et al, 2000). Three walls from this building are studied using FEM and the corresponding collapse mechanisms are determined.

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a)

b)

Figure 4.2-12 Collapse mechanisms for historical buildings:

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a) Horizontal plan; b) Computed and proposed collapse mechanisms

Some wall’s in-plane collapse mechanisms occurred during earthquakes are presented in Figure 4.2-13 (Bruneau, 1994).

The case of irregular walls, when the openings are not aligned or have not the same dimensions in horizontal or in vertical, is studied by Augenti (2006) and presented in Figure 4.2-14.

Figure 4.2-13 Regular walls damaged in-plane during 1994 Loma Prieta earthquake

Figure 4.2-14 Irregular walls damaged in-plane

(ii) The case of out-of-plane is the most unfavorable that can occur during an earthquake, due to small lateral stiffness. Traditional masonry buildings can be described as a three-dimensional network of orthogonal-walls creating cells that resist lateral load through a box behaviour. Timber beams at superior levels and masonry vaults traditionally make the horizontal structures over basement and first floor, respectively. In both cases, only one of the walls is load bearing, while for the other the role is mainly to provide out-of-plane restraint to the bearing walls (D’Ayala and Speranza, 2003).

The out-of-plane failure of a façade wall of the Martinho da Arcada-Lisbon historical building (Laurenco, 2001)(Figure 4.2-15) is a very good example of the lack of horizontal rigid diaphragms.

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Figure 4.2-15 Out-of-plane failure of façade wall

So, there are two major elements influencing the wall behaviour, the position of transversal walls and the floors type, assuring or not the support of wall’s top. Considering these effects, different cases must be considered (Martini,1997a,b):

- One-way behaviour, (Figure 4.2-16a) when the distance between transversal walls are large and have no influence on wall behaviour. If the floor cannot assure the support of wall’s top, the wall is completely free for the overturning. In case of existence of rigid floor, the wall is fixed at the top. The collapse mechanisms are very different for the two cases.

- Two-way behaviour (Figure 4.2-16b) occurs when wall panel is supported on the bottom and sides and unsupported or suopported on the top. In this case the collapse mechanism is different for the case when the wall is without or with window.

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Figure 4.2-16 Out-of-plane collapse mechanism types: a) One-way; b) Two-way

Figure 4.2-17 Some out-of-plane collapse mechanisms during 1994 Loma Prieta earthquak

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Figure 4.2-18 Out-of-plane collapse mechanism types:a) One-way; b) Two-way

Figure 4.2-19 Some out-of-plane collapse mechanisms during 1994 Loma Prieta earthquake

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4.2.5. Collapse mechanisms for masonry floors, arches, vaults and domes

In the historical buildings, normally the floors over basements and first level are carried out using masonry barrel, cross and cloister vaults, supported by masonry arches. Therefore, the analysis of these components of floors must be performed.

The structural behaviour of the masonry arches has been studied at length since the end of 17th century. It was the first masonry element for which the collapse approach, using the collapse mechanism, was applied (Heyman, 1969). The correspondence between the limit analysis and non-linear FM analysis is presented in Figure 4.2-20 (Lourenco, 2001) for a vertical loaded arch. However, no conclusive results have been achieved, especially for the arch behavoiur during an earthquake. Generally, the arches with ties behave very well during an earthquake. But there are many problems when its horizontal thrusts are transmitted to the spreading supports, as leaned buttresses. So, during an earthquake, the arch supports have different vertical or horizontal displacements, producing the failure of arch. The collapse mechanism is more complex when the arch is supported by leaned buttresses (Figure 4.2-21), the fracture at the base of one buttress by shear of by overturning having great influence on arch failure mechanism.

Figure 4.2-20 Load-displacements diagrams for different analysis

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Figure 4.2-21 Arches supported by leaned buttresses

Cylindrical ribbed and unrobed barrel vaults work as arches, that the results obtained for arches can be applied for this vaults.

In many masonry structures a cross-vault system is used for floors or roofs (Figure 4.2-22a). The collapse mechanism for this vault is presented in Figure 4.2-22b (Belli et al, 1995,Huerta, 2001, Block, 2005). The influence of boundary conditions is presented in Figure 4.2-23.

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a)

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Figure 4.2-22 Collapse mechanism for cross-vault system

Figure 4.2-23 Influence of boundary conditions on collapse mechanisms of cross-vault systems

A dome can be imagined as composed by a series of arches obtained slicing the dome by meridian planes. The meridian collapse mechanism for symmetrical loads is presented in Figure 4.2-24a. A non-symmetrical load, as resulting from a seismic action, can produce patterns similar to that shown in Figure 4.2-24b.

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Figure 4.2-24 Collapse mechanisms for domes

4.2.6. Ultimate limit state for masonry structures

Collapse mechanisms for buildings

Individual masonry buildings, as well as whole historic centers of cities composed by an ensemble of buildings, are now recognized as vital elements of architectural heritage. They also represent the most vulnerable class of buildings as far as seismic risk is concerned, even for moderate earthquakes.

Traditional historical masonry buildings can be described as a three-dimensional network of orthogonal wall creating cells that resist seismic load through a box behaviour. The floors traditionally are made of timber beams spanning the shortest distance between walls, so that only one of the two orthogonal walls is load bearing while the other set’s role is mainly to provide out-of-plane restraint of the bearing walls. The roof structure is usually similar to the floor structure. In this situation, the restrained effects of floors are much reduced, and, in many cases these effects can be neglected. Only if the floors are made by barrel vaults, the restrained effects can be considered.

Examining the failure of many masonry buildings results that the internal walls were damaged but, only in some very few cases, they collapsed. In exchange, the external walls of a building are typically subjected to out-of-plane collapse mechanisms. The way in which these are developed depends on the quality and strength of the connections with the other elements of masonry buildings, internal partitions, floors and roof elements. If the structure has not strengthened by ties, it is assumed that the only means of restrain to overturning is exerted by the other connected walls by the friction of the contact surfaces.

4.2.7. Collapse mechanisms for individual buildings

Generally, due to lack of adequate connections, the only means of restrain to overturning is exerted by the friction of the contact surfaces of wood beams or orthogonal walls. In many cases these connections are not sufficient to assure the walls against overturning. Therefore, the out-of-plane collapse mechanisms are the most frequently case of building collapse during an earthquake.

The collapse mechanism types differ in function of numer of levels.

For one level buildings the floor is made of wood with no special details to connect the beams from walls. In this case there are the possible collapse types presented in Figure 4.2-25: without connections with orthogonal walls, with good connections and tympanon collapse. Other cases of possible collapse mechanisms for the case of proper connections are presented in Figure 4.2-26 (Beolchini et al 2006).

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Figure 4.2-25 Collapse mechanism types for one-level buildings

Figure 4.2-26 Collapse mechanism types for rigid connections with orthogonal walls

For low multi-level buildings, the mechanisms began to be more complex, due to the presence of different floor types. The importance of the connected elements and the presence of rigid floors result from the Figure 4.2-27, where the overturning of an external wall, for a building with four levels, is analyzed (AEDES 2006), using a specialized computer program. For case that there not exists horizontal rigid floor, the overturning occurs for a spectral acceleration of 0.156g, affecting all the wall. In case of a rigid first floor, overturning does not affect the first level, but the collapse acceleration is only 0.121g, due to the reduced effects of connected walls. In case of two rigid floors, the overturning affects only the last two levels for a spectral acceleration of 0.132g. If all the floors are rigid (with the exception of roof one), only the last level is involved in overturning, for a spectral acceleration of 0.277g.

All the possible collapse mechanisms for low multi-level buildings are presented in Figure 4.2-28 (Cifani et al, 2006)

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Figure 4.2-27 Influence of floor type on collapse mechanisms

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Figure 4.2-28 All possible collapse mechanisms for low-multi-level buildings

4.2.8. Collapse mechanisms for complex buildings

After an earthquake, one can see that the occurred collapse mechanisms are very different for complex buildings in comparison with the isolated buildings, due to the presence of adjacent buildings (Figure 4.2-29).

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The typologies of possible collapse mode can classified as failure of row walls, failure of building corners and failure of upper levels, over the adjacent buildings (Figure 4.2-30). Some very significant collapse mechanisms collapse mechanisms are presented in Figure 4.2-31 (Beolchini et al, 2006).

Figure 4.2-29 Collapse mechanisms for complex buildings

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Figure 4.2-30 Some characteristic collapse mechanisms

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Figure 4.2-31 Occurred collapse mechanisms

A synthesis of these collapse mechanisms and the corresponding load factors for overturning failure, also the possible modes for the case of two-way collapse mechanism, are presented by D’Ayala and Speranza (2004).

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Collapse mechanisms for churches

The level of vulnerability shown by churches with respect to seismic actions has been recognized as different and usually higher than the one associated to ordinary buildings due to open plan, greater height to width ration and often the presence of thrusting horizontal elements as big arches, vaults and domes (D’Ayala, 2000). At these special characteristics it is need to add the conservation of artistic values contained in churches: frescoes, canvases, altars, etc. During the development of structural systems of churches, it can emphasize some different typologies.

Romanesque churches

The Romanesque architecture is developed during the 8th to 12th Centuries in Medieval Europe, using forms and materials characteristic of Roman Architecture: arches, semi-circular barrel and groin vaults. The main concept for churches was the stone vaulting, requiring stronger walls for support. Because of the weight of the ceiling a very important thrust occurs. Therefore it was necessary to built strong, thick walls with narrow openings. Figure 4.2-32 presents the Basilica of San Zeno Maggiore, Verona, considered one of the great achievements of Romanesque architecture.

Figure 4.2-32 San Zeno Basilica Verona

Gothic churches

The gothic architecture flourished in Europe during the high and late medieval period. Beginning in twelfth Century France, the main characteristic features include the ogival or pointed arch, the ribbed

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vaults and flying buttress. The gothic style emphasizes verticality and features almost skeletal stone structures with great expanses of glass windows that allow lighter to enter than was possible with the previous Romanesque style. To achieve this lightness, flying buttresses were used between windows as a means to support to enable higher ceilings and slender columns. Many of these features can be finding in the Amiens Cathedral (Figure 4.2-33).

Figure 4.2-33 Amiens Cathedral

Renaissance churches

Renaissance architecture is the architecture of the period beginning the early 15th and 17th Centuries in different regions of Europe, especially in Italy, where there was a conscious revival and development of certain elements of Classical Greek and Roman thought and material culture. The Renaissance style places emphasis on symmetry, proportion, geometry and regularity of parts as they are demonstrated in the architecture of Classical Antiquity, and in particular, the architecture of ancient Rome. The use of semicircular arches, hemispherical domes replaced the more complex proportional systems and irregular profiles of medieval buildings. Developed first in Florence, the Santa Maria del Fiore of Brunelleschi (Figure 4.2-34) is the most representative example of this architecture, where the dome is the dominant element. One can see that the church’s dome is the dominant structural element. Domes had been used only rarely in the Middle Ages, but after the success of the dome in Brunelleschi’s design ifor the Basilica di Santa Maria del Fiore in Florence and its use by Michelangelo for St. Peter’s Basilica in Rome, the dome became an indispensable element in renaissance church architecture.

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Figure 4.2-34 Basilica di Santa Maria del Fiore, Florence

Byzantine churches

Byzantine architecture is the architecture of the Byzantine Empire. Early Byzantine architecture is essentially a continuation of Roman architecture. Gradually, a style emerged which imbued certain influences from Arabian architecture. The main structural element is the masonry dome supported by pendentives. A dome can site directly on a circular base, however, this is not possible if the base is square. The concave triangular or trapezoidal sections of vaulting that provide the transition between a dome and the square base on which it is set and transfer the weight of dome are called pendentives. The Romans made the first attempts of pendentives, but full achievement of the form was reached only in Hagia Sophia at Constantinople (Figure 4.2-35).

Figure 4.2-35 Pendentive in the Hagia Sophia

But the most important development of this architecture type is for the churches in orthodox area. Figure 5 shows an very significant example: the Neamt Monastery (Figure 4.2-36) from the northern of Romania.

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Figure 4.2-36 Neamt Monastery

In the followings, the studies of ultimate loads for these churches types, using the collapse mechanisms will be presented.

4.2.9. Romanesque churches

It is important that the first assessment of understand the vulnerability of a church is the establishing the possible mechanisms. It is based by the identification of the macro-elements (Figure 4.2-37), which consists in the subdivision of the church into architectonic elements characterized by a proper seismic behaviour, almost independently from the rest of the structure (Lagomarsino, 1998). For each macro-element, considering its typology and connection to the rest of church, it is possible to identify the damage mode and collapse mechanism (Binda and Saisi, 2007). Therefore, the macro-elements of a church are: façade, triumphal arch, lateral walls, abse, lateral chapel and bell tower. The main macro-element types are presented in Figure 4.2-38 (De Luca et al, 2004a,b). Some damaged macro-elements, as result of earthquake effects, are presented in Figure 4.2-39 (Lagomarsino, 1998, D’Ayala, 2000, Lagomarsino and Podesta, 2004, Lagomarsino et al, 2004, Lagomarsino and Resemini, 2005).

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Figure 4.2-37 Church macro-elements

Figure 4.2-38 Some macro-element types in Italian churches

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Figure 4.2-39 Damage of some macro-elements

A synthesis of collapse mechanisms is presented in Figure 4.2-40

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(continuing)

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Figure 4.2-40 Main macro-element collapse mechanism types

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4.2.10. Gothic churches

Gothic structures, based on arches and vaults, among the historic typologies, are with no doubts the most challenging masonry structure, from many different point of views, but in particular from the point of view of the engineering assessment of their structural safe (Ronca and Franchi, 2000). As it is known, the construction technology of gothic vaults is based on the idea of the diagonal ribs with webs resting on them (Figure 4.2-41). The curvature of the vault follows the curvature of the transverse ogive arches, assuring a safe geometrical shape for the static vertical loads. This is due to the fact that the gothic cathedrals were built in Countries with weak seismic activity and the presence of horizontal actions were due to the static forces at the vault impost with pillars. More complex behaviour and structural requirements are need for the gothic churches in seismic areas.

The analysis of gothic Barcelona Cathedral is presented in Error! Reference source not found. (Roca, 2001, Lagomarsino, 2002). The analysis is based on using the FEM and collapse mechanism methodology for determining the limit state for seismic actions.

Figure 4.2-41 Main elements of a gothic church

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Figure 4.2-42 Limit analysis of Barcelona Cathedral

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4.2.11. Renaissance churches

The Renaissance architecture, developed mainly in Italy (Italy had never fully adopted the Gothic style of architecture), takes again the structural elements of Ancient Rome: the arches are semi-circular, the vaults on the square plan (unlike gothic vaults which are rectangular) and do not have ribs, the domes are used frequently, both as a very large structural feature that is visible from the exterior, and also as a means of roofing large spaces where are only visible internally. Unfortunately, there are not studies concerning the behaviour of Renaissance churches during earthquakes, because they were dot damaged during these earthquakes. There are only some results for vertical loads (D’Ayala and Casapulla, 2001).

Figure 4.2-43 presents the case of S. Maria Maddalena-Morano Calabro church (Lucchesi et al, 2007). The distribution of the observed cracks corresponds very well with the FEM results.

Figure 4.2-43 Dome of S. Maria Maddalena- Morano Calabro

4.2.12. Byzantine churches

The Byzantine architecture developed in Balkans is characterized by using of combination of masonry domes supported on pendentives and the presence of many window openings in walls. The main damage occurred in these church type are presented in Figure 4.2-44 (Crisan, 1997). The in-site observations on the damaged churches during the 1977 Vrancea earthquake show that exists the tendency to separate the church’s walls in some separate blocks (Figure 4.2-45).

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Figure 4.2-44 Main damage of Byzantine churches

Figure 4.2-45 Formation of blocks

4.2.13. Retrofitting of masonry buildings using the collapse mechanisms

Traditional and new techniques

As it is shown, the failure of masonry buildings is brittle, produced by formation of some collapse mechanism type. Therefore, in order to increase the bearing capacity, it is necessary to first identity the

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anticipated collapse mechanism, based on the failure modes presented in previous sections. Presently, many methods are successfully used for reinforcement in masonry retrofitting, which can be classified in traditional one, as using ties, or new one, as Fiber Reinforced Polymers (FRPs).

Retrofitting using steel tie bars

Very often the horizontal resistance an historical masonry building is incremented by using steel ties bars passing in the walls at the floor level. There are two procedures two use the tie bars, for retrofitting the in-plane or out-of-plane resistances.

For in-plane retrofitting the presence of steel ties change the collapse mechanism type, in some cases with a remarkable increment of the collapse multiplier (Figure 4.2-46) (Decanini I.D, 2004).

Figure 4.2-46 Increment of the collapse multiplier

In order to prevent the occurrence of out-of-plane overturning of external walls, steel ties were traditionally used to anchor the façade to either the party walls or the floors and roof structures. In this case the collapse mechanism is changed, the arch effect being dominant.

Retrofitting using FRP

Nowadays, FRP sheets represent a new opportunity in restoring field of historical masonry buildings. For a church frontal wall, some possibilities to use the FRP sheets, in order to prevent the formation of collapse mechanisms are shown in Figure 4.2-47. The FRP sheets can be used also for the retrofitting the masonry arches (Fig. 34)

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Figure 4.2-47 Possibilities of use the FRP sheets for a church frontal wall

Figure 4.2-48 Possibilities of use the FRP sheets for retrofitting masonry arches

4.2.14. Conclusions

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The aim of this report was to collect from the references the main results obtained in this field. Only some of these references are presented in the report. The intentions for the final report is to deliver also some practical methodologies for design and to analyze the possibilities give by the determining the most probable collapse mechanism, in order to protect the historical buildings against earthquakes. In the same time, the intention is to study the effects of new proposed technologies in the formation of the collapse mechanisms and evaluation of ultimate limit state.

4.2.15. References

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Abruzzese, D., Lanni, G. (1998): On the lateral strength of historical reinforced masonry buildings with crossed vaulted floors. 11th European Conference on Earthquake Engineering, Paris, 6-11 September 1998

Augenti, N. (2006): Seismic behaviour of irregular masonry walls. 1st European Conference on Earthquake Engineering and Seismology, Geneva, 3-8 September 2006, Paper number 86

AEDES (2006):Software per Ingeneria Civile. Sistema di Analisi Strutturale per Edifici Esistenti

D’Ayala, D. (2000): Establishing correlation between vulnerability and damage survey for churches. 12th World Conference on Earthquake Engineering, Auckland, 30 January - 4 February 2000

D’Ayala, D., Casapulla, C. (2001): Limit state analysis of hemispherical domes with finite friction. Historical Constructions (eds. P.B. Lourenco and P. Roca), Guimares, 7-9 November 2001, 617-626

D’Ayala, D., Speranza, E. (2003): Definition of collapse mechanisms and seismic vulnerability of historic masonry buildings. Earthquake Spectra, Vol. 19, No. 3, 479-509

D’Ayala D., Speranza E.: Definition of collapse mechanisms and seismic vulnerability of historic masonry buildings. Earthquake Spectra, 2004

Binda, L., Saisi, A. (2007): State of the art of research on historic structures in Italy. http:// www.arcchip.cz/w11/w11_binda.pdf

Belli, P., Monaco, L.M., Sineone, A.(1995): On structural behaviour of the masonry cross vault for staircases. Spatial structure: Heritage, Present and Future (ed. G.C. Giuliani) IASS Symposion, Milano 5-9 June 1995, 1143-1150

Beolchini, G.C., Milano, L., Antonacci, E. (2006): Definizioni di modelli per l’analisi structurale degli edifice in muratura. Protocollo di progettazione per gli Interventi di riconstruzioni post-sisma, Vol. II, Parte 1, 1-88

Binda, L., Saisi, A. (2002): State of the art of research on historic structures in Italy. http://www.arcchip.cz/w11_binda.pdf

Block, Ph. (2005): Equilibrium systems. Studies in masonry structure. Massachusetts Institute of Technology Report

Block P. et al: Real-time limit analysis of vaulted masonry buildings. Computers &Structureas 2006

Brencich, a., Gambarotta, L., Lagomarsino, S. (2000): Analisi di alcune pereti in un edificio storico Universitadi Genova. Progetto Catania:Indagine sulla Riposta Sismica di due Edifici in Murature (ed. D. Liberatore), CNR- Grupo Nazionale per la Difensa dei Terremoti

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Bruneau,M. (1994):State-of-the-art report on seismic performance of unreinforced mansonry buildings Journal of Structural Engineering, Vol.120,No. 1, 230-251

Calderoni, B., Marone, P., Pagano, M. (1987): Modelli per verifica degli edifice in muratura in zona sismica. Ingeneria Sismica, Anno 4, N.3, 19-27

Crisan, M. (1997): Restoration of orthodox churches (in Romanian) Ph Thesis, Architecture Institute ,, Ion Mincu’’,Bucurecti.

Decanini I.D., Tocci C.: Sull comportamento sismico di pareti murarie sollicitate nel piano; riflessioni sui criteri di intervento. XI Congresso nationale, Genova, 2004

De Luca, A., Mele, E., Romano, A., Patierno, C., Giordano, A. (2004a): valutazione approssimata della capacita portante di elementi murari tipici di chiese a pianta basilicale. XI Congresso Nazionale L’Ingegneria Sismica in Italia, Genova, 25-29 Gennaio, 2004

De Luca, A., Mele, E., Romano, A., Giordano, A. (2004b): Capacita sotto azioni orizzontali di 4 edifici a piñata basilicale. XI Congresso nazionale L’Ingeneria Sismica in Italia, Genova, 25-29 Gennaio, 2004

Foraboschi P.: Strengthening of masonry arches with fiber-reinforced polymer strips. J. of Composites for constructions, 2004

Giordano, A., Mele, E., De Luca, A. (2001): Assessment of the capacity of triumphal arches. Historical Constructions (eds. P.B. Lourenco and P. Roca), Guimares, 7-9 November 2001, 983 –992

Huerta, S. (2001): mechanisms of masonry vaults: The equilibrium approach. Historical Constructions (eds. PB. Lourenco and P. Roca), Guimares, 7-9 November 2001, 47-69

Heyman, J. (1969): The safety of masonry arches. International Journal of Mechanics Science, Vol.11, 363-372

Lagomarsino, S. (1998): A new methodology for the post-earthquake investigation of ancient churches. 11th European Conference on Earthquake Engineering, Paris, 6-11 September 1998

Lagomarsino, S. (2002): Vulnerability of churches: Diagnosis and forecast of collapse mechanisms. 12th European Conference of Earthquake Engineering, Special session, RISK-UE Project, London, 9-13 September 2002

Lagomarsino, S., Podesta, S. (2004): Seismic vulnaribility of ancient churches: I. Damage assessment and emergency planning; II. Statistical analysis of surveyed data and methods for risk analysis. Earthquake Spectra, Vol. 20, No. 2, 377-394, 395-412

Lagomarsino, S., Podesta, S., Resemeni, S. (2002): Seismic response of historical churches. 12th European Conference on Earthquake Engineering, London, 9-13 September 2002, Paper No. 471k

Lagomarsino, S., Resemini, S. (2005): L’analisi limite delle costruzioni murarie: Uno strumento per il progetto di interventi in zona sismica. Teoria e Practica del Construire: Saperi, Strumenti, Modelli, Ravenna, 27-29 Ottobre 2005, 166-174

Lagomarsino, S., Podesta, S. Cifani, G., Lemme, A. (2004): The 31st October 2002 earthquake in Molise (Italy): A new methodology for the damage and seismic vulnerability survey of churches. 13th World Conference on Earthquake Engineering, Vancouver, 1-6 August 2004, paper No. 1366

Liberatore D., Beolchini, G.C., Binda, L., Gambarotta, L. Magenes, G. (2000): Valutazione della riposte sismica del costruito in muratura del Comune di Catania.

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Lourenco, P.B. (2001): Analysis of historical constructions: From thrust-lines to advanced simulations. Historical Constructions (eds. P.B. Lourenco, P. Roca), Guimares, 7-9 November 2001, 91-116

Lucchesi, M., Padovani, C., Pasquinelli, G., Zani, N. (2007): Static analysis of masonry vaults, constitutive model and numerical analysis. Journal of Mechanics of materials and Structures, Vol.2, No. 2, 221-

Mele, E., De Luca, A. (1999): Behaviour and modeling of masonry church buildings in seismic regions. Earthquake Resistant Engineering Structures,II, Catania, June 1999, 543 – 552

Martini, K. (1997a): Research in the out-of-plane behaviour of unreinforced masonry.

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Martini, K. (1997b): Finite element studies in the to-way out-of-plane failure of unreinforced masonry.

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Mele, E., Gatto, D., De Luca, A. (2001): Structural analysis of basilica churches: A case study. Historical Constructions (eds. P.B. Lourenco, P. Roca), Guimares, 7-9 November 2001, 729-738

Mele E., Giordano A., De Luca A.: Nonlinear analysis of some typical elements of a basilica plan church. In Earthquake Resistant Engineering Structures, Catania, 1999

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CONCLUDING REMARKS

The heterogeneous character of different up-grading techniques and structural systems, which constituted the subjects of experimental and numerical research in PROHITECH Project made quite impossible to assembling coherently, in all the cases, the calculation models and procedures, following the chain Material- Structural Element and/or Device – Structural System, as shown in the Integrated Summary Table.

The application of some techniques involves inherently the design assisted by testing and/or numerical simulation.

In fact, application of simplified calculation procedures is based mostly on classical models. Since the level of approximation could be really significant, such procedures are recommended in the pre-design phase to evaluate the technical and economical feasibility of the initial and upgraded structure in order to decide the intervention technique.

For final design and performance based evaluation of seismically upgraded structure, an advanced numerical simulation, in some specific cases assisted by testing, is recommended.

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Annexes

List of contributors and data sheets:

9-1 A. Dogariu, T. Nagy-Gyorgy, C. Daescu, D. Daniel, V. Stoian and D. Dubina, “Politehnica” University of Timisoara (ROPUT) - “Simplified and Advanced Models for Calculation and Analysis of Masonry Shear Walls”

9-2 L. Pavlovčič and D. Beg , University of Ljubljana, Faculty of Civil and Geodetic Engineering (SL) - “Stone – Unito Limestone”

9-3 Ly Lam, Demonceau Jean-François, Jaspart Jean-Pierre, University of Liege (B) - “Development of design rules for cast iron columns reinforced by FRP”

9-4 Gülay Altay and Ali Bozer, Bogazici University of Istambul (TR) - “Models for materials and elements: timber”

9-5 M. D’Aniello, L. Fiorino, F. Portioli, R. Landolfo, University of Naples “Federico II”, Department of Construction and Mathematical Methods in Architecture, Naples, Italy (NA-ARC) - “Riveted connection”

9-6 L. Pavlovčič and D. Beg, University of Ljubljana, Faculty of Civil and Geodetic Engineering (SL) - “Architrave connection”,

9-7 Ioannis Vayas, Aikaterini Marinelli, Stavros Kourkoulis, Stefanos-Aldo Papanicolopulos, National Technical University of Athens, Greece (GR) - “Anchors in marble”,

9-8 Dan Lungu, Cristian Arion, Technical University of Civil Engineering Bucharest, Romania (RO-TUB) - “Reinforced concrete”

9-9 G. De Matteis, S. Panico, G. Brando, A. Formisano, F.M. Mazzolani, Faculty of Architecture, University of Chieti / Pescara “G. D'Annunzio”, Italy (UNICH) and Engineering Faculty, Department of Structural Analysis and Design, University of Naples “Federico II”, Italy (UNINA) - “Calculation models for pure aluminium shear panels”

9-10 A. Mandara, F. Ramundo, G. Spina, Second University of Naples, Italy (SUN) - “Analytical and numerical models for magnetorheological device”

9-11 A. Stratan, S. Bordea, D. Dubina , Politehnica University of Timisoara, Romania (ROPUT) - “Analytical and numerical models for steeel buckling restrained braces”

9-12 M. D’Aniello, G. Della Corte and F. M. Mazzolani, University of Naples “Federico II” (UNINA) - “Design methods for buckling restrained braces”

9-13 M. D’Aniello, G. Della Corte and F. M. Mazzolani, University of Naples “Federico II” (UNINA) - “Design methods for eccentric braces”

9-14 G. De Matteis, A. Formisano, S. Panico, F. M. Mazzolani, University of Chieti/Pescara “G. d’Annunzio” (UNICH) and University of Naples “Federico II”, Italy (UNINA) - “Metal shear panels for seismic upgrading of existing buildings”

9-15 E. Barecchia, G. Della Corte, F. M. Mazzolani, University of Naples “Federico II”, Italy (UNINA) - “Design methods for fiber reinforced polymers material”

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9-16 I. Vayas, P. Thanopoulos, National Technical University of Athens (GR) - “PIN INERD connections for braced frames”

9-17 Mazzolani F., University of Naples “Federico II”, Italy (UNINA) - “Models for global analysis”

9-18 Nagy-Gyorgy T, Daescu C, Florut C., Stoian V., Politehnica University of Timisoara, Romania (ROPUT) - “Review of design recommendations for the evaluation of in-plane shear capacity of masonry walls strengthened with FRP composites”

9-19 L. Calado, J. Proença and A. Panão, Instituto Superior Técnico, Portugal (P) - “Composite timber-concrete-steel system”

9-20 Victor Gioncu and Marius Mosoarca, Politehnica” University of Timisoara, Romania (ROPUT) “- “Collapse mechanisms for historical masonry buildings”

9-21 Victor Gioncu and Marius Mosoarca, Politehnica” University of Timisoara, Romania (ROPUT) - “Ultimate limit state of historical masonry buildings”

9-22 Victor Gioncu and Marius Mosoarca, Politehnica” University of Timisoara, Romania (ROPUT) - “Collapse mechanisms for masonry buildings

9-23 Victor Gioncu and Marius Mosoarca, Politehnica” University of Timisoara, Romania (ROPUT) - “Collapse mechanisms for churches”

9-24 Stratan A and Dubina D, Politehnica” University of Timisoara, Romania (ROPUT) – “Models for global analysis

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