DESIGN OF FRP STRUCTURES IN SEISMIC ZONE - … of FRP structures in seismic zone Manual by Top Glass S.p.A. and IUAV University of Venice 5 1. INTRODUCTION 1.1. Overview Starting from

DESIGN OF FRP STRUCTURES IN SEISMIC ZONE

Giosue' Boscato, Carlo Casalegno, Salvatore Russo

Design of FRP structures in seismic zone

Manual by Top Glass S.p.A. and IUAV University of Venice 1

DESIGN OF FRP STRUCTURES IN SEISMIC ZONE

Giosuè Boscato(**)

Carlo Casalegno(*)

Salvatore Russo(*)

(*) IUAV University of Venice, Department of Design and Planning in Complex Environments,

Dorsoduro 2206, 30123, Venice, Italy, phone +39 041 2571290 fax +39 041 5312988;

[email protected]

(**) IUAV University of Venice, Laboratory of Strength of Materials (LabSCo), Via Torino 153/A -

30173 Mestre, Venice, Italy, phone +39 041 2571481 fax +39 041 5312988; [email protected]

mailto:[email protected]

mailto:[email protected]



Preface

The use of FRP (Fibre Reinforced Polymer) material in the structural engineering field is by now

current practice and supported by theoretical studies as well as many applications and constructions.

FRP material is widely accepted in the strengthening of existing structures (made by reinforced

concrete, steel, wood and masonry) but not yet commonly used for new buildings even if some

recent all-FRP constructions, in particular built with FRP members made by pultrusion process, are

very promising.

The study of the structural behaviour of pultruded FRP members, especially in the case of static

loads, has been widely developed. Instead, for what concerns the dynamic response, very few

experimental and analytical research projects have been proposed. The issue is particularly

interesting because of the mechanical characteristics of pultruded FRP material. The elastic-brittle

constitutive law with anisotropic mechanical behaviour imposes some specific precautions, while

the high durability, the low density of 1700-1900 kg/m3 and the relatively high values of strength

suggest its potential and promising application also in seismic zones.

The dynamic properties of pultruded FRP material are characterized by high periods of vibration,

low frequency and a spontaneous dissipative capacity of the dynamic actions due to its low density.

Currently there are no available guidances for the seismic design for structures with pultruded FRP

members.

The aim of this manual is to address the issues related to the design of pultruded FRP structures

subjected to static and dynamic loading.

After a thorough introduction the manual gives a practical guidance on how to address the structural

design of pultruded FRP structures. The final part – chapter 5 - is dedicated to a new software,

named FRP-Design Software (FRP-DS), with which is possible set up to structural verifications in

supporting the common commercial numerical code.

For the use of this present manual it is considered fundamental that the reader is in possession of the

information already available in the following documents:

CNR-DT205/2007. Guide for the design and constructions of structures made of FRP pultruded

elements, National Research Council of Italy, Advisory Board on Technical Recommendations.

http://www.cnr.it/sitocnr/IlCNR/Attivita/NormazioneeCertificazione/DT205_2007.html.

CEN TC250 WG4L, Ascione, J-F. Caron, P. Godonou, K. van IJselmuijden, J. Knippers, T.

Mottram, M. Oppe, M. Gantriis Sorensen, J. Taby, L. Tromp. Editors: L.Ascione, E. Gutierrez, S.

Dimova, A. Pinto, S. Denton. ‘Prospect for New Guidance in the Design of FRP,’ Support to the

http://www.cnr.it/sitocnr/IlCNR/Attivita/NormazioneeCertificazione/DT205_2007.html



implementation and further development of the Eurocodes, JRC Science and Policy Report

JRC99714, EUR 27666 EN, European Union, Luxembourg, (2016), p 171. ISBN 978-92-79-

54225-1 doi:10.2788/22306

NTC08. Norme Tecniche per le Costruzioni (last update of the Italian Building Code), Decree of

the Ministry of Infrastructures of 14th January 2008. (in Italian).

Eurocode 8 Design of structures for earthquake resistance. Part 1: General rules, seismic actions and

rules for buildings. EN1998-1:2004 (E): Formal Vote Version (Stage 49), 2004.

The development of the manual is the following:

Chapter 1 (pp. 6 - 20), INTRODUCTION, provides a general background on FRP pultruded

profiles, for what concerns the material, the structural behavior, the availability of standards,

guidance documents and manuals; a part is dedicated to notable applications.

In Chapter 2 (pp. 21 - 35), BASIC PRINCIPLES FOR THE SEISMIC ANALYSIS, the synthesis

of the key-aspects related to the seismic design, such as the definition of period of vibration,

damping coefficient, behaviour factor and the dissipation capacity are discussed.

Chapter 3 (pp. 36 - 87), EXAMPLE OF CALCULATION, provides a calculation example of a FRP

spatial truss structure taking into account the different load combinations in static and seismic fields

and the analysis at ultimate and serviceability limit state.

In Chapter 4 (pp. 88 - 94), FINAL EVALUATION FOR DEISGN OF FRP STRUCTURES IN

SEISMIC ZONE, some final considerations for the design of FRP structures in seismic zone are

presented.

Chapter 5 (pp. 95 - 116), FRP DESIGN SOFTWARE (FRP-DS), illustrates the features of the FRP-

Design Software.

Acknowledgements

The authors thank Top Glass SpA (www.topglass.it) for the understanding of the potential capacity

of the pultruded FRP material in civil engineering, architecture and construction fields. This work

was possible thanks to the fundamental support of the Top Glass SpA and OCV Italia Srl - OWENS

CORNING (www.ocvitalia.it) and Polynt (www.polynt.it) as official suppliers of raw materials used

for the manufacturing of profiles used in experimental tests.

The authors thank also Eng. Mauro Calderan, from IUAV University of Venice, Italy, who

collaborated to the build the FRP-DS software.



Index

INTRODUCTION

1.1. Overview

1.2. Materials and manufacturing

1.3. Normative, design guidelines and technical references

1.4. Constructions and applications with pultruded FRP profiles

SYNTHESIS OF BASIC PRINCIPLES FOR THE SEISMIC ANALYSIS

EXAMPLE OF CALCULATION

3.1. Statement of the structural design

3.2. Materials

3.3. Basic assumptions

3.4. Load analysis

3.4.1. Permanent loads

3.4.2. Variable loads

3.4.3. Seismic analysis

3.4.3.1. Modal analysis

3.4.3.2. Spectral analysis

3.4.3.2.1. Elastic response spectrum

3.4.3.2.2. Design spectra for ULS design

3.4.3.2.3. Displacement response spectra

3.4.3.3. Pushover analysis

3.5. ULS analysis

3.5.1. Forces and moments diagrams

3.5.1.1. Axial force

3.5.1.2. Bending moment

3.5.1.3. Shear force

3.5.1.4. Torsional moment

3.5.2. Example of verification of a compressed member

3.6. SLS analysis






3.6.2. Verification of elements

3.6.2.1. Stresses

3.6.2.2. Deformations

3.7. Joint's verification

3.7.1. Net-tension failure of the plate

3.7.2. Shear-out failure of the plate

3.7.3. Bearing failure of the plate

3.7.4. Shear failure of the steel bolt

3.8. References

FINAL EVALUATION FOR DESIGN OF FRP STRUCTURES IN SEISMIC

ZONE

4.1. References

4.2. Symbols

4.3. Verification’s functions

4.4. References

p. 6

p. 20

p. 35

p. 86



1. INTRODUCTION

1.1. Overview

Starting from the 90's there has been a significant increase throughout the world in the use of

pultruded FRP members in primary load-bearing systems for general constructions, as well as for

strengthening and rehabilitation of existing structures. The interest in this material lies in the several

advantages that it offers compared with traditional construction materials, such as the corrosion

resistance, the durability, the high strength to weight ratio, the versatility and the ease of

transportation and erection.

FRP structural profiles are commonly produced through the pultrusion process. General profiles

present the same cross-sectional shapes (I, H, leg-angle, channel, box, etc.) as found in structural

steelwork. They consist of fibre reinforcement with layers of unidirectional roving along Z-direction

covered by continuous mats, in X- and Y-directions, in a resin-based matrix, see Figure 1.1.

Figure 1.1 "I" FRP pultruded open shape

Different fibres, characterized by different mechanical properties, can be adopted. Their percentage

in volume can also be varied, as well as their dimensions, geometry and orientation, defining

different mechanical properties of the final products. Also the resin matrix can have different

characteristics, but the performance of the final product mostly depends on the type and percentage

of reinforcement. Anyway, the matrix plays a significant role in the transverse mechanical behavior,

and in specific performance characteristics as the impact strength and the cyclic behavior. This

production versatility allows the design of the FRP material to be oriented time by time with respect

to specific structural applications.

The mass density of the pultruded FRP material is between 1700-1900 kg/m3, that is about 1/4 of

steel density, while the tensile strength in the longitudinal direction is more than 240 MPa.

Nevertheless, the use of FRP structural profiles in civil engineering presents also some sensitive

aspects, such as the high deformability, the anisotropic and brittle-elastic behavior. The longitudinal

modulus of elasticity lies in the range of 20-30 GPa and both the elastic modulus and the strength

values are significantly lower in the transversal direction, where the influence of the matrix is



dominant due to the pultrusion process. Moreover, the pultruded FRP material presents different

characteristics in tension and compression. In general, the risk of buckling tends to govern the

design.

Due to the brittle-elastic behavior of the material, it is not possible to take advantage of the plastic

deformation and of the related dissipation capacity; this aspect partially influences the seismic

design approach. Nevertheless, some ductile phenomena are observed focusing on structural

systems, particularly on the moment–rotation curves of all-FRP beam-column connections.

Similarly to steel structures, the design of joints represents one of the most important aspects. The

preferred method of connecting the FRP profiles is by means of bolted joints that mimic steel

connections, sometimes used in conjunction with adhesives; the bolts are usually made of steel.

Nevertheless, due to the anisotropy the mechanical behavior of joints is more complex than that

realized with isotropic materials.

1.2. Materials and manufacturing

FRP materials are realized by the combination of fibres and matrix. The fibres generally used for

the realization of structural FRP composite members are carbon, aramid, PVA and glass; the glass

fibre is the most commonly employed, due to the relatively low cost and the good mechanical

properties. In general, pultruded FRP elements are realized with a volume percentage of continuous

filaments of fibres around 40%. The mechanical properties of the fibres are orders of magnitude

greater than those of the polymer resin that they reinforce. The function of the matrix is first of all

to protect the fibres. Moreover, it creates the continuity, through the cohesion, between the

filaments of fibres; it guarantees the transferring of the stresses between the fibres through its shear

stiffness and creates, through also the polymerization process, the desired shape. The matrices most

commonly employed for the realization of the fibre reinforced composites are polyester and

vinylester but they can be also thermoplastic, thermosetting and epoxy type. The mechanical

characteristics of some commonly used fibres and matrices are reported in Tables 1.1 and 1.2. The

tensile behavior of the FRP material is linear elastic up to failure, which is characterized by a brittle

mechanism. The behavior of the FRP material is anisotropic, due to fibres orientation, and - as

already specified - the mechanical performances in the transversal directions is significantly lower

than the one in the longitudinal direction.

The main manufacturing methods used to produce FRP material are the pultrusion process, the hand

lay-up, the filament winding and the molding process. Pultrusion is a continuous process used to

create FRP mono-dimensional elements with constant cross-section. A pultruded member can have



a symmetric or asymmetric open cross-section, a single closed cross-section or a multicellular

cross-section. In the pultrusion process the reinforcing material impregnated with the resin is guided

into a heated die, where it is cured to form the desired part as illustrated in Figure 1.2. The FRP is

cured as the material is pulled through the die by a pulling apparatus. After exiting the die and

extending past the pullers, the part is cut to length. In profiles produced through the pultrusion

process the internal core constituted by continuous longitudinal fibres, called roving, is covered by

an external thin layer of short fibres with random orientation, called mat, whose function is to

increase the transversal stiffness.

Figure 1.2 Pultrusion process (courtesy of TopGlass)

Hand lay-up is a manual method of constructing an FRP composite part by laying up successive

layers of fibres into a mold and impregnating them with a liquid polymer resin, which than cures to

form a solid FRP composite element. Typical products realized through the hand lay-up technique

are boat hulls, tanks and ducts. The filament winding method is used to create tubular and big

hollow products such as stay-in-place column forms, pipes, poles and pressure tanks. The process

consists in wounding continuously a resin-saturated fibre roving around a cylindrical mandrel at a

variety of wind angles. Finally, different variations of open and closed molding can be used to

create panels for FRP bridge deck, sandwich, fender piles, and plates for connections. In this

process, the dry fibres forms are arranged in molds and are saturated with resin and cured.

Indicatively the ranges of physical and mechanical characteristics of pultruded FRP material are

shown in Table 1.3.

Reinforcing fibre Tensile strength (MPa) Elastic modulus (GPa) Ultimate strain (‰)

Carbon 2400-5700 230-400 3-18 Aramid 2400-3150 62-142 15-44 Glass 3300-4500 72-87 48-50 PVA 870-1350 8-28 90-170

Table 1.1. Mechanical properties of fibres

Reinforcing fibre Tensile strength (MPa) Elastic modulus (GPa)

Unsaturated polyester 34-104 2.0-4.4 Epoxy resin 55-130 2.7-4.0

Phenolic resin 50-55 3

Table 1.2. Mechanical properties of resins



Mechanical properties Notations Range values

Tensile strength (L) σZ 200-500 MPa

Tensile strength (T) σX = σY 50-70 MPa

Elastic modulus (L) EZ= EL 20-30 GPa

Elastic modulus (T) EX = EY=ET 8-8.5 GPa

Shear modulus (L) GXY=GL 3.4 GPa

In-plane shear modulus of elasticity (T) GZX=GZY=GT 3 GPa

Poisson’s ratio (L) νZX = νZY= νL 0.23-0.28

Poisson’s ratio (T) νXY= νYX= νT 0.09-0.12

Density γ 1600-2100 kg/m3

Fibres percentage in volume Vf 40%-45%

L=longitudinal, T=transversal

Table 1.3. Range of values of pultruded FRP material

In a conventional manner the FRP pultruded standard profile refers to the coordinate system defined

by the XY plane of cross-section and Z axis orthogonal to it, see again Figure 1.1. Fibres run along

the global Z axis of each element defining the anisotropic behaviour in the Z direction and isotropic

in the X and Y directions. The condition of transversal isotropy is defined by the relationships

EX=EY=ET, νXY= νYX= νT, and GXY=GT. The local co-ordinate system for the wall segments forming

the cross-section and webs and flanges is also defined, with the z-direction in the longitudinal

direction of pultrusion, x in the transverse direction and y for the through-thickness direction.

In detail, for the characterization of pultruded FRP material it must be distinguished between two

different products in function of the layering ways. A greater amount of mat increases the

transversal stiffness classifying the FRP with grade 23 (EN 13706), see Table 1.4; while a minor

percentage of mat (i.e. TopGlass standard profiles) favors the increment of longitudinal stiffness

(Table 1.5).

Properties Notation Value

Longitudinal tensile modulus of elasticity Ez = EL 28.5 (GPa)

Transverse tensile modulus of elasticity Ey = Ex = ET 8.5 (GPa)

Transverse shear modulus of elasticity Gyx= GL 3.5 (GPa)

In-plane shear modulus of elasticity Gxz = Gyz = GT 2.5 (MPa)

Longitudinal Poisson’s ratio νzx = νzy= νL 0.25

Transversal Poisson’s ratio νxy= νyx= νT 0.12

Bulk weight density γ 1850 (kg/m3)

Longitudinal tensile strength σzt = σLt 350 (MPa)

Transverse tensile strength σxt = σyt = σTt 70 (MPa)

Longitudinal compressive strength σzc = σLc 413 (MPa)

Transverse compressive strength σxc = σyc= σTc 80 (MPa)

Shear strength τxy= τxz = τyz 40 (MPa)


Table 1.4. Mechanical properties of pultruded FRP profiles (Grade E23)



Properties Test method Notation Value

Flexural Modulus (L) EN 13706 - 2 (full scale) EL 28 (GPa)

Shear Modulus (L) EN 13706 - 2 (full scale) GL 3 (GPa)

Tensile strength (L) ASTM D638 σtL 400 (MPa)

Tensile strength (T) ASTM D638 σtT 30 (MPa)

Compressive strength (T) ASTM D695 σcL 300 (MPa)

Compressive strength (L) ASTM D695 σcT 70 (MPa)

Flexural strength (L) ASTM D790 σfL 420 (MPa)

Flexural strength (T) ASTM D790 σfT 70 (MPa)

In plane shear strength ASTM D2344 τ 28 (MPa)

Bearing strength (L) ASTM D953 170 (MPa)

Bearing strength (T) ASTM D953 70 (MPa)

Tensile modulus (L) ASTM D638 EtL 29 (GPa)

Tensile modulus (T) ASTM D638 EtT 8 (GPa)

Compressive modulus (L) ASTM D695 EcL 20 (GPa)

Compressive modulus (T) ASTM D695 EcT 7 (GPa)

Poisson's ratio (L) ASTM D638 0.28

Poisson's ratio (T) ASTM D638 0.12

Bulk weight density ASTM D792 γ 1820 (Kg/m3)

Glass content by weight ASTM D2584 60%

Glass content by volume ASTM D2584 42.5%

Thermal conductivity EN 12667/EN 12664 0.3 (W/mK)

Surface resistivity EN 61340 1012

(Ω)


Table 1.5. Mechanical properties of pultruded FRP standard profiles (TopGlass)

1.3. Normative, design guidelines and technical references

The static behavior of the FRP material and of FRP structural systems is nowadays studied quiet in-

depth, as demonstrated by the availability of several manuals, handbooks and scientific

publications. Nevertheless, to date a normative reference for the structural design with FRP

materials is not yet available, unless the recent CEN TC250 WG4 which gives finally a depth and

support in this so strategic design field. For what concerns the seismic response of pultruded FRP

elements/structures the researches are still growing. In the following the main normative references,

concerning the material properties, and the main available guidelines and literature references for

the design of FRP structures are listed.

Normative references:

EN 13706-1:2002 Reinforced plastic composites – Specification for pultruded profiles – Part 1:

Designation


Methods of test and general requirements


Specification requirements

EN 13121-1:2003 GRP tanks and vessels for use above ground – Part 1: Raw materials –

Specification conditions and acceptance conditions



EN 13121-2:2003 GRP tanks and vessels for use above ground – Part 2: Composite materials –

Chemical resistance

EN 13121-3:2008 GRP tanks and vessels for use above ground – Part 3: Design and

workmanship

EN 13121-4:2005 GRP tanks and vessels for use above ground – Part 4: Delivery, installation

and maintenance

EN-ISO 14125:1998 Fibre-reinforced plastic composites. Determination of flexural properties

EN-ISO 14126:1999 Fibre-reinforced plastic composites. Determination of compressive

properties in the in-plane direction

EN-ISO 14129:1997 Fibre-reinforced plastic composites. Determination of the in-plane shear

stress/shear strain response, including the in-plane shear modulus and strength, by the ±45°

tension test method

EN-ISO 14130:1997 Fibre-reinforced plastic composites. Determination of apparent interlaminar

shear strength by short-beam method

EN 16245:2013 Fibre-reinforced plastic composites – Part 1-5: Declaration of raw material

characteristics

ASTM D 790:2010 Standard test method for flexural properties of unreinforced and reinforced

plastics and electrical insulating materials

ASTM D 2344:2006 Standard test method for short beam strength of polymer matrix composite

materials and laminates

ASTM D 3039:2008 Standard test method for tensile properties of polymer matrix composite

materials

ASTM D 3410:2008 Standard test method for compressive properties of polymer matrix

composite materials with unsupported gage section by shear loading

ASTM D 3518:2007 Standard test method for in-plane shear response of polymer matrix

composite materials by tensile test of a ±45° laminate

ASTM D 4255:2007 Standard test method for in-plane shear properties of polymer matrix

composite materials by the rail shear method

Guidelines:


Mottram, M. Oppe, M. Gantriis Sorensen, J. Taby, L. Tromp. Editors: L.Ascione, E. Gutierrez,

S. Dimova, A. Pinto, S. Denton. ‘Prospect for New Guidance in the Design of FRP,’ Support to

the implementation and further development of the Eurocodes, JRC Science and Policy Report


54225-1 doi:10.2788/22306

CUR 96 Fibre reinforced polymers in civil load bearing structures (Dutch recommendation,

1996)



EUROCOMP Structural design of polymer composites (Design code and background document,

1996)

BD90/05 Design of FRP bridges and highway structures (The Highways Agency, Scottish

Executive, Welsh Assembly Government, The Department for Regional Development Northern

Ireland, 2005)

CNR-DT 205/2007 Guide for the design and construction of structures made of pultruded FRP

elements (Italian National Research Council, 2008)

ACMA Pre-standard for load and resistance factor design of pultruded fiber polymer structures

(American Composites Manufacturer Association, 2010)

DIN 13121 Structural polymer components for building and construction (2010)

ASCE, 1984, Structural Plastics Design Manual, 1984, ASCE Manual No. 63, ASCE, VA.

Books:

P. K. Mallick, Fiber-reinforced composites, Marcel Dekker Ltd., New York, 1993

D. Gay et al., Composite materials: design and applications, CRC Press, Boca Raton, 2002

L. C. Bank, Composites for construction – Structural design with FRP materials, John Wiley &

Sons Inc., New Jersey, 2006

B. D. Agarwal et al., Analysis and performance of fiber composites, John Wiley & Sons Inc.,

New Jersey, 2006

Russo, S. Strutture in composito. Sperimentazione, teoria e applicazioni, Hoepli, Milano, 2007.

Boscato G. (2011). Dynamic behaviour of GFRP pultruded elements. Published by University of

Nova Gorica Press, P.O. Box 301, Vipavska 13, SI-5001 Nova Gorica, Slovenia.

Pecce, M. and Cosenza, E., ‘FRP structural profiles and shapes, in Wiley. Encyclopedia of

Composites, 2012 - Wiley Online Library.

Dedicated conference series:

CICE (Composites in Civil Engineering)

ACIC (Advanced Polymer Composites for Structural Applications in Construction)

ICCS (International Conference on Composite Structures)

Main dedicated journals:

Advances in Structural Engineering

Applied Composite Materials

Composite Structures

Composites Part B: Engineering

Composites Science and Technology

International Journal of Adhesion and Adhesives

Journal of Composites for Construction, ASCE

Journal of Reinforced Plastics and Composites

http://cedb.asce.org/cgi/WWWdisplay.cgi?42891

http://www.multi-science.co.uk/advstruc.htm

http://www.springer.com/materials/characterization+%26+evaluation/journal/10443

http://www.elsevier.com/wps/find/journaldescription.cws_home/405928/description#description




http://scitation.aip.org/cco/

http://jrp.sagepub.com/



1.4. Constructions and applications with pultruded FRP profiles

The pultrusion process for producing FRP profiles was developed first in 1950s. Although the first

profiles were realized primarily for industrial applications, the potentials related to their adoption as

substitutes for conventional beams and columns in civil engineering applications were always

envisioned. By the late 1960s and early 1970s, in fact, a number of pultrusion companies were

producing I-shaped and tubular profiles.

The first large FRP structures were single-story frames realized for the electromagnetic and

computer industry. The electromagnetic transparency was the key advantage offered by the FRP

pultruded profiles in this field. In 1985 the Composite Technology Inc. designed and realized an

innovative EMI (electromagnetic interference) composite building for Apple Computer. Similar

structures where realized for IBM and others in the 1980s. Another significant use of FRP profiles

is found in the construction of cooling towers. In the bridge engineering field, pultruded FRP

profiles have been widely used since the mid-1970s. Hundreds of FRP footbridges have been

designed and realized all around the world. In 1992 a FRP footbridge 131 m long has been realized

in Aberfeldy, Scotland. A 127 m long FRP footbridge has been realized in 2012 in Floriadebrug,

Netherlands. The first pedestrian bridge (25 m of span length) in Italy has been realized in 2011 in

Prato. Another FRP pedestrian bridge 148 m long is actually under construction in Salerno. FRP

profiles have not been yet widely employed in multi-story residential and commercial buildings.

Neverthless, a significant prototype of a multi-story frame, called Eyecatcher, has been realized by

Fiberline in Basilea, Switzerland, in 1999. To date, the largest FRP strut and tie spatial structure

ever realized is probably represented by the 1,050 m2 by 30 m high FRP temporary shelter located

inside the church of Santa Maria Paganica in L’Aquila, Italy, in order to protect the monument after

the 2009 earthquake. Among other structural types, in 2014 a FRP grid-shell, made with pultruded

tubes, has been realized in Creteil, France. Also a demonstrative composite house has been built in

2012 in Borne, UK. More generally, a depth and updated overview of the all more significant

pultruded FRP structures realized is reported in CEN TC250 WG4L.



Besides, it is important to outline that the characteristics of pultruded FRP profiles, such as the

reduced density, the durability and the ease of erection make them particularly suitable for the use

in the field of the reinforcing of RC (reinforced concrete) structures or traditional masonry

structures, with particular regards for historical constructions. The structural reinforcement of these

buildings through the use of pultruded FRP profiles represents an efficient solution that allows

realizing non-invasive, reversible and durable interventions for the improving of the structural

performance with a very limited added structural mass.

Examples are the reinforcement of the timber deck of the Collicola Palace in Spoleto, Italy, through

H-shaped pultruded FRP profiles; the reinforcement of roof of the San Domenico Church in Siena,

Italy; the reinforcement of the Paludo bridge in Venice, Italy, which was necessary due to the

serious deterioration of the iron structure induced by the aggressive environment conditions.

Another example of interaction between FRP structural systems and historical construction is the

realization of an auxiliary floor in the Cogollo house in Vicenza (Figure 1.3), Italy, realized in order

to optimize the available space.



Following are illustrated some all-FRP constructions which are new and built in existing sites.

FRP spatial frame, Cogollo house in Vicenza (Italy)

The beams of the spatial frame, illustrated in Figure 1.3, are wide flanges "H" shapes

(200x200x20x10 mm), while the built-up columns are assembled from four off-the-shelf pultruded

leg-angle-shaped sections having same cross-section dimensions (100x100 mm) and wall thickness

of 8 mm. The connection elements (angle) between FRP members, the bolts, and the braces are

made of stainless steel; the circular deck (diameter of 5 m) is made of 5 cm thick multilayer wooden

panels.

Figure 1.3 FRP spatial frame, Cogollo house in Vicenza, Italy, 1999 (measures in meters)



FRP auxiliary floor in Verona (Italy)

The auxiliary floor, shown in Figure 1.4, made of pultruded FRP profile, has been built in Verona

(Italy) and is constituted by:

- a double frame that with four and two vertical “I” (200x100x10 mm) FRP profiles supports,

through the steel cables, the auxiliary deck;

- the deck that is realized by coupled “I” FRP profiles that together with individual “I” profiles form

a structural grid; for all joints steel bolts and flanges have been used and the deck is realized by self

bearing panels with a capacity equal to 250 kg/ m2;

- the backstays that are steel cables of 6 mm of diameter.

Figure 1.4 Auxiliary floor, Verona, Italy, 2006 (measures in metres)



Structural rehabilitation of an historic pedestrian bridge

The pedestrian “Paludo” bridge is a typical venetian bridge built at the end of XIX century, with

arch static scheme – 12.7 meters for the length and 3.25 meters for the width - built entirely with

iron and wood materials.

The flexural stiffness has been increased substituting the existing longitudinal wood beams with

double "I" shape pultruded FRP profiles (120x60x8 mm) assembled by bolted FRP plates (Figure

1.5). The details of Figure 1.5 show the workers operating facility to execute the cut (a), the holes

(b) and the final assemblage (c), the mechanical connection with the bridge abutments through the

galvanic steel gussets (d), the two “I” FRP profiles and the beam-beam joint realized through the

FRP pultruded plates and stainless bolts (e) and the final positioning in the thickness of the deck (f).

Figure 1.5 Rehabilitation of historic pedestrian bridge, Paludo bridge, Venice, Italy (2007).



FRP pedestrian bridge in Prato (Italy)

The pedestrian bridge is fully made with pultruded FRP profiles, except steel bolts. The total length

of the footbridge is equal to 25 meters, with reinforced concrete piers and FRP ramps, see detail of

Figure 1.6; at the edges the access ramps have been designed with a staircase made in FRP and an

elevator. With a load bearing capacity of 5 kN/m² the bridge weighs only 8 tons. With the spatial

truss configuration the top chord is able to resist compression, while the lower chord has to resist

only to tension. The two frame trusses are strongly braced by a lateral system in the plane of its

chord in order to diminish the buckling effective length.

Figure 1.6 Plan, views and details of the spatial strut and tie all-FRP pedestrian bridge, Prato,

Italy (2013)



Spatial all-FRP truss structure

The temporary covering-structure of S.M. Paganica church, in L'Aquila, has been made of

pultruded FRP members (Figure 1.7) produced with grade 23 (EN 13706), see Table 1.4. The

structure is still inside the historic church and mentioned in CEN TC250 WG4L (2016). The truss

members are built-up “C” shape members connected with stainless steel bolts.

As shown in Figures 1.7 and 1.8, Structure 1 covers 607 m2 for the nave, having a maximum height

of 22.5 m; Structure 2 covers 266 m2 for the apse, having a maximum height of 29.4 m; Structure 3

(130 m2) protects cells along one longer side; Structure 4 (76 m

2) is protecting the entrance-façade.

Figure 1.7 Plan and view of the spatial truss all-FRP structure, L’Aquila, Italy, 2010 (measure

in meters)



Figure 1.8 All-FRP sub-structures; L’Aquila (2010)

The frame joints use conventional steel bolts and gusset plates of FRP material made by the bag

molding process, see Figure 1.9. Detail (a) shows the built-up member’s cross-section comprising

four channel (C) profiles having same cross-section dimensions 152x46x9.5mm; while detail (b)

shows the connection between the built-up member’s cross-section of four channel (C) profiles

having same cross-section dimensions 300x100x15mm and bracings.

Figure 1.9 Details of joints of structure 1 (a) and structure 2 (b); L’Aquila (2010)



2. SYNTHESIS OF BASIC PRINCIPLES FOR THE SEISMIC ANALYSIS

To facilitate the reading of this manual, in the following a short introduction in the form of sheets to

some aspects and based concepts of seismic design is presented.

1. Single Degree of Freedom (SDoF)

2. Multiple Degrees of Freedom (MDoF)

3. Natural period of vibration

4. Damping coefficient

5. Response spectra

6. Spectral analysis

7. Pushover analysis

8. Dissipative capacity

It is noted that the insights discussed in these short presentations are specific of the analyzes and

studies carried out in this manual. For more clarification, the specific texts present in the literature

and cited in every sheet are the following:

Chopra AK. Dynamics of structures, 3rd Ed., Pearson Prentice Hall, 2007.

Eurocode 8 Design of structures for earthquake resistance. Part 1: General rules, seismic actions

and rules for buildings. EN1998-1:2004 (E),: Formal Vote Version (Stage 49), 2004.

NTC08. Norme Tecniche per le Costruzioni (last update of the Italian Building Code), Decree of the

Ministry of Infrastructures of 14th January 2008. (in Italian).



1- Single Degree of Freedom (SDoF)

SDoF (Single Degree of Freedom) system is characterized

by mass m and a spring with stiffness k (N/m).

The stiffness k is the external force that keeps the system

in equilibrium when a unit displacements u=1 is applied.

Dynamic equilibrium

0)()()( tumtkutp

)(tum frictions inertia force (product of mass time its

acceleration )(tk elastic stiffness force

)(tu acceleration imposed on mass

)(tp external force

Free vibration

Undamped system

The structure depends by its static equilibrium. The

system vibrates without any applied forces through the

following equation of motion:

0 kuum

Viscously damped system

The linear viscous damper (c) gives a friction in the

structure. The linear viscous damper develops a force

proportional to the velocity (fD)

)(tucfD

The equation of motion is: 0 kuucum

Assuming:

damping coefficient m

c

n

2

damped pulsation 21 nD

Equation of motion of damped system is:

02 2 uuu nn

Coulomb-damped system

The Coulomb-damped free vibration is controlled by

sliding of two dry surfaces through friction.

The friction force is F=Nμ where:

μ=equal coefficients of static and kinetic friction

N=normal force between the sliding surfaces

F=independent to velocity of the motion with direction

opposed to the motion.

The equations of motion from left to right or viceversa

are;

Fkuum

k

FtBtAtu nn )sin()cos()( 2,12,1

The constant A1, B1, A2, B2 depend on the initial

conditions.

SDoF subjected to seismic action

The equation of dynamic equilibrium is:

msv FFF

Where

vF viscoelastic force proportional to relative velocity

sF elastic force proportional to relative displacement

mF inertial force proportional to the absolute

acceleration ug

then:

))()(()()( tutumtkutuc g

and finally

))()()(2)( 2 tutututu g



2a - Multiple Degrees of Freedom (MDoF)

MDoF (Multi Degrees of Freedom) is characterized by

following equation )(tpukucum

with

[m] mass matrix; [c] damping matrix; [k] stiffness matrix

Mass and stiffness matrices depend on the structure's

discretisation and on the choice of the degrees of freedom

that are involved. The damping cannot be calculated by

discretisation.

For the analysis of multiple-degrees-of-freedom (MDoF)

elastic systems, the development of the code-based

equivalent lateral force (ELF) procedure (scheme a) and

modal superposition analysis must be carried out.

In the analysis of MDoF the basic assumptions are: the

vertical and rotational masses are not required; horizontal

mass be lumped into the floors; floors are axially rigid; for

each joint (12, scheme b) three d.o.f. (degree of freedom)

must be computed (see joint 12, scheme b); motion is

predominantly lateral (see joint 4, scheme b).

The 36 static degrees of freedom may be reduced to only 3

lateral degrees of freedom for the dynamic analysis. The

three dynamic d.o.f. are u1, u2 and u3 (see scheme c).

The relative displacements not include the ground

displacements.

The flexibility matrix is simply a column-wise collection of

displaced shapes. The lateral deflection under any loading

may be represented as a linear combination of the columns

in the flexibility matrix (see schemes d, e and f).

K may be determined by imposing a unit

displacement at each DOF while restraining

the remaining DOF. The forces required to

hold the structure in the deformed position

are the columns of the stiffness matrix.

The mass matrix is obtained by imposing a

unit acceleration at each DOF while

restraining the other DOF. The columns of

the mass matrix are the (inertial) forces

required to impose the unit acceleration.

There are no inertial forces at the restrained

DOF because they do not move. Load F(t)

and displacement U(t) vary with time.



2b - Multiple Degrees of Freedom (MDoF)

For three-story frame MDOF the coupled equations of

motion for undamped forced vibration is:

)()()( tftKUtUM and then:

)(

)(

)(

)(

)(

)(

0

0

)(

)(

)(

00

00

00

3

2

1

3

2

1

323

2211

11

3

2

1

3

2

1

tf

tf

tf

tu

tu

tu

kkk

kkkk

kk

tu

tu

tu

m

m

m

The equations are solved transforming the coordinates from

normal coordinates (displacements at each of the three

original DOF) to modal coordinates (amplitudes of the

natural mode shapes).

Through the orthogonality property of the natural mode

shapes the equations of motion can be solved by

simplifying in SDOF equations.

For system in undamped free vibration field the modal shapes and frequencies are expressed by: 0)()( tKUtUM

Where ttU sin)( and ttU sin)( 2

Then 02 MK has three solutions



2c - Multiple Degree of Freedom (MDoF)

Idealized mode shapes for a 3-story building

The modal shapes depend by boundary conditions;

noteworthy is the relationship between modal

shapes and nodes. The displaced shapes are obtained

by the following linear combination: YU

3

2

1

3,32,31,3

3,22,21,2

3,12,11,1

y

y

y

U

3

3,3

3,2

3,1

2

2,3

2,2

2,1

1

1,3

1,2

1,1

yyyU

Where ji, modal shape; while 1y modal

coordinate, amplitude of modal shape

The orthogonality condition 321 allows the

full uncoupling of the equations of motion: MDoF equation )(tFKUUCUM

With YU

Then )(tFYKYCYM

And )(tFYKYCYM TTTT

Obtaining the following uncoupled equations of motions

)(

)(

)(

*

3

*

2

*

1

3

2

1

*

3

*

2

*

1

3

2

1

*

3

*

2

*

1

3

2

1

*

3

*

2

*

1

tf

tf

tf

y

y

y

k

k

k

y

y

y

c

c

c

y

y

y

m

m

m

Generalized mass

*

3

*

2

*

1

m

m

m

MT

Generalized stiffness

*

3

*

2

*

1

k

k

k

KT

Generalized damping

*

3

*

2

*

1

c

c

c

CT

Generalized force

)(

)(

)(

*

3

*

2

*

1

tf

tf

tf

FT

Expliciting, with y=amplitude and *=generalized quantities

we have:

mode 1 )(*

11

*

11

*

11

*

1 tfykycym

mode 2 )(*

22

*

22

*

22

*

2 tfykycym

mode 3 )(*

33

*

33

*

33

*

3 tfykycym

Dividing by mass m* and defining

ii

ii

m

c

*

*

2

mode 1*

1

*

11

2

11111

)(2

m

tfyyy

mode 2*

2

*

22

2

22222

)(2

m

tfyyy

mode 3*

3

*

33

2

33333

)(2

m

tfyyy

MDoF system subjected to earthquake force

The inertial force = sum of two vectors through the

influence coefficient vector R; R=1 for each mass that

produces an inertial force triggered by horizontal

acceleration.

For each floor the inertial force iF is equal to mass times

M the total acceleration (ground acceleration (gu scalar)

and relative acceleration (iru ,

vector)).

)()(

)()(

)()(

)(

3,

2,

1,

tutu

tutu

tutu

MtF

rg

rg

rg

i



2d - Multiple Degree of Freedom (MDoF)

Definition of modal participation factor

For earthquakes

)()(*

2 tuMRtf g

T

i

Than the typical modal equation is

)()(

2**

*2 tu

m

MR

m

tfyyy g

i

T

i

i

iiiiiii

With

i

T

i

T

i

i

T

ii

M

MR

m

MRp

*

Modal partecipation factor p with 3 first mode shape normalized, x=1

Effective modal mass for each mode i is

iii mpm 2

Where: -the sum of effective modal mass

is equal to the structural mass; -the value

of effective mass not depend by mode

shape scaling; - are needed a number of

modes to reach the activation of modal

mass at least of the 90% of the total

structural mass (as defined by standard

codes).

The effective modal mass not depend on

modal scaling as, instead, the modal

participation factor.

The modal shape is normalized, x=1



3 - Natural period of vibration

The natural period of a structure T is the time needed by the structure to perform a whole oscillation, triggered by an

initial perturbation. The natural period of vibration depends by mass (m) and stiffness (k) of structure.

0

0

2

2

0

0

2

1

2

1

u

u

kk

kk

u

u

m

m

A pendulum (SDoF) with a short period of vibration (i.e. stiffer or less mass) tends to move with the support (i.e. soil)

and then not records any earthquake, a pendulum with a greater period of vibration tends to remain stationary while the

support varies.

The natural period of vibration depends by mass (m) and

stiffness (k) of structure.

The natural period of vibration T affects the response of

structure to seismic action both for the acceleration and

displacement. Buildings with different T subjected to same

seismic action record different acceleration values.

Resonance phenomenon:

the soil is also characterized by a natural period of vibration. When the natural period of vibration of the ground is very

close to that of the building, the stress of building increases.

m

k (rad/sec)

Natural circular frequency

2

1

Tf (Hz)

Natural frequency

For every structure the natural modes of vibration correspond to the number of degree of freedom and represent the free

periodic oscillations of undamped elastic system.

When the system oscillates according to one of the natural modes, all the masses oscillate with the same pulse

(corresponding to the mode) and the same phase, by keeping unchanged the relationships between the amplitudes.

For each oscillation the masses reach the point of maximum displacement in the same instant.

Adapted from Chopra (2007)



Damping coefficient

The equivalent viscous damping coefficient ζ is the most used approach to analyze the dissipative capacity of structures

in dynamic field. ζ depends by effects induced by hysteretic behavior, internal friction of the material, geometrical

characteristics and typology of ground taking into account the structural response in the variation of time.

Free vibration with 10% damping coefficient ζ

Free vibration with 3% damping coefficient ζ

Logarithmic decrement method

The logarithmic decrement is an experimental approach

that takes into account a linear viscoelastic damping ζ.

To evaluate the reduction in the amplitude values that the

sinusoidal oscillatory behaviour exhibits in the time

domain, the method used is that of the logarithmic

decrement obtained from the ratio between two consecutive

maximum amplitudes in the time range of a damped period

of one or more cycles, as in:

nx

x

cn

0ln1

where δ=logarithmic decrement; cn=cycles number;

x0=initial amplitude; xn=final amplitude.

The damping coefficient (ζ) is determined through: 5.0

2

241

Equation can be simplified for small values of ζ i.e., when

(1- ζ2)

0.5 is close to 1, becoming

2

Band-width method

The Half Power Bandwidth (HPB) method in the frequency

range is employed to analyze experimentally the capacity

of the specimens to dissipate the accumulated energy from

the dynamic excitation. The bandwidth (BW) is the

frequency within a range of 3 dB, corresponding to the

measured dominant (first natural) frequency, f1, from the

action of the piling machine. This quantifies, indirectly, the

velocity from the accelerometer response from initial

frequency fi to final frequency fi+1; where fi and fi+1 are the

two frequency limits for calculating BW. Damping

coefficient ζ is given in terms of f1 and BW = (fi+1 - fi,) by

2222221 1122111221 NNfBW

where N = U/U* and U = U* - 3 dB, and U* is the peak

amplitude at f1. The relationship in Equation between ζ and

BW/f1 holds only for ζ 0.353, and by letting N=21/2

the

expression for the damping coefficient is simplified to

12 f

BW

The representation of the seismic action components is the elastic response spectrum for a conventional damping

coefficient ζ of 5%. It provides the maximum acceleration response of the generic dynamic system with natural period

of T≤4s and is expressed as the product between the spectral shape and the maximum acceleration of the ground.

On the right the deformation response factor and phase angle for a damped system.

For NTC08 and Eurocode8 the equivalent viscous damping

coefficient ζ is taken into account through the damping

correction factor η=√(10/(5+ζ))≥0.55;

This equation vales for ULS (Ultimate Limit State); then

assuming ζ=5% (reinforced concrete RC structure) we have

η=1 (unchanged spectrum); with ζ=2-3% (steel structure)

η=1.2-1.12 (amplified spectrum); while with ζ=0% η=1.41

(amplified spectrum).

In brief passing from RC to steel structure increase the

horizontal components of the design response spectrum which

tend to maximize for ζ=0, that is for a elastic structure and,

therefore, extremely rigid with respect to a dissipative structure.



5a - Response spectra

SDoF Systems

SDoF system is subjected to ground motion ug(t); u(t)is

the calculated displacement response.

EQUIVALENT STATIC FORCE

fs(t)is the static force which must be applied to create the

displacement u(t)

RESPONSE SPECTRA

A response spectrum is a plot of a

maximum response, in

displacement or velocity or

acceleration form, of a SDoF

system with respect to a given

ground acceleration against

systems parameters (Tn (natural

period of vibration) and ζ

(damping coefficient)).

A response spectrum is calculated

numerically (through Duhamel

integral or time integration

methods) for (Tn and ζ). Adapted from Chopra (2007)

DETERMINATION OF RESPONSE SPECTRA

Starting from the seismic action for specific soil

characterized by )(tug :

-I apply )(tug to SDoF system with Tn and fixed

damping coefficient ζ;

-I solve the problem calculating u(t) and plotting the

graph ω2u(t)in time domain;

-I calculate the maximum value of

spectral displacements SDe={u(t)}max

spectral pseudo-velocity SVe=ω{u(t)}max

spectral pseudo-acceleration SVe=ω2{u(t)}

max

Following the relationship:

AeDe StuS2

max 1

For a given seismic action the D-V-A

(Displacement, pseudo-Velocity, pseudo-

Acceleration) elastic response spectra summarizes

the behavior in term of maximum D-V-A of all

elastic SDoF system with 0<Tn< and fixed

damping coefficient.

In detail pseudo-velocity is related to energy while

pseudo-acceleration is proportional to static load.

Combined D-V-A response spectrum for El-Centro ground motion

with ζ=0, 2, 5, 10 and 20%, (Chopra 2007).



5b - Response spectra

The elastic response spectrum is obtained by many seismic events, and it isn't refered to the real earthquake.

The spectrum which characterizes the site is obtained as the envelope of the most response spectra.

The development of response spectra for a specific site requires a study of geological and seismological characteristics

of the site. It is known that the characteristics of seismic action are affected by the source that triggers the earthquake,

from the wave's directions up to the site and by local conditions.

For the equivalent static force Fsmax

The seismic analysis becomes the equivalent static

analysis.

Response spectrum (ζ =0, 2, 5 and 10%) and peak values

of ground acceleration (A), ground velocity (V) and

ground displacements (D) for i.e. El Centro ground

motion, (Chopra 2007).

For a SDOF:

The elastic design spectrum is defined through the

accelerograms recorded during past earthquakes with

similar seismic characteristics.

Construction of elastic design spectrum (Chopra 2007)

Response to El Centro earthquake (i.e.) of different

buildings changing T0 and ζ fixed:

-with higher T0 (→∞) the maximum pseudo-acceleration

→0;

-with lower T0 (→0) the maximum pseudo-acceleration

→maximum ground acceleration.

Response to El Centro earthquake (i.e.) of different

buildings changing T0 and ζ:

-the maximum displacements tend to grow with increasing

the natural period (T0)

-the maximum displacements decrease with increasing

damping coefficient (ζ)



6a- Spectral analysis

The seismic loading for structural design is described by response spectra (Eurocode 8, 2004; NTC08, 2008). Design

that is in accordance with the requirements of Eurocode 8 has only ULS spectra. Working to the Italian Building Code

(NTC08 2008] requires there to be both SLS and ULS spectra.

Structures in seismic regions shall be designed and constructed taking into account the reference seismic action

associate with a reference probability of exceedance or a reference return period.

For NTC08 the seismic action depends by VR=CUxVN (where VN=service life while CU=structural class).

The period return TR= VR/(ln(1-PVr) where PVr=probability of exceedance that changes in function of the different

damage levels (SLO=operational; SLD=immediate occupancy; SLV=life safety; SLC=collapse prevention).

For EC08 the recommended values for the no-collapse requirement are PNCR=10% (probability of excedeence) and

TNCR=475 years (return period) while for the damage limitation requirement are PDLR=10% (probability of excedeence)

and TDLR=95 years (return period).

Eurocode 8, 2004 and NTC08, 2008 shall be take into account for basic informations about ground conditions, seismic

actions and general parameters.

Elastic Response Spectra

The reference action model to describe the seismic motion at floor (ground) level is the elastic response spectra for

horizontal and vertical components. In this sheet the notation, the design process and equations are, where applicable,

in accordance with the requirements of Part 1 of Eurocode 8 (2004). Euroocde 8 sesimic loading is more severe than

the Italian seismic loading the approach is for a conservative and pragmatic design.

The two elastic response spectra for horizontal and vertical components were established from the normalised spectrum

in Eurocode 8 with reference to an assumed viscous damping coefficient (ζ) of 0.05, which is independent of the

seismicity level. EN 1998-1-1:2004 states that these elastic response spectra may be applied to structures having a

vibration period < 4 s. This criterion is acceptable for FRP structure.

Equations in the right are used to present the four stages of

the elastic response spectrum for the horizontal

component.

The parameters in Eqs. (a) to (d) are: Se(T) for the elastic

horizontal ground acceleration response spectrum (also

called "elastic response spectrum”) with units of

acceleration (g); T for the vibration period of a linear

oscillator, namely Single Degree of Freedom (SDoF),

defined by its natural period and by its damping factor; S

for the soil factor; η for a damping correction factor, which

is calculated from 550100510 ./ ; TB, TC and

TD are for time periods, depending on type of ground, to

define the different stages in the spectrum; Fo (NTC08

2008) is for the horizontal amplification factor. Note that

Fo is the notation taken from publication NTC08, an

alternative notation in Eurocode 8 is Fh, where the

subscript ‘h’ is for horizontal component.

At T = 0 s, the spectral acceleration given by Se(T) equals

the design ground acceleration on type A ground multiplied

by the soil factor S.

Elastic response spectrum for the horizontal component

Se(T) used in Eurocode 8 (2004) and NTC08 (2008).



6b- Spectral analysis

The elastic response spectrum for the vertical ground

acceleration (Sve(T)) is defined by the four expressions in

the right Table. In Equs. (a) to (d) the new parameters

respect to horizontal component are: avg for the design

ground acceleration in the vertical direction that is given by

0.9 ag and Fv for the vertical amplification factor that is

given by 1.35Fh(avg/g)0.5

.

Elastic response spectrum for the vertical component Sve(T)

used in Eurocode 8 (2004) and NTC08 (2008).

The horizontal component of acceleration is always higher than in the vertical direction. It can be seen that the elastic

response spectra from Eurocode 8 are significantly higher, and have different time differentials, than those obtained on

using NCT08.

Design spectra for ULS design

For the purpose of seismic design the dissipation capacity of any structure can be taken into consideration by

introducing a reduction factor to the elastic spectral accelerations. This is accomplished in Eurocode 8 (2004) and in

Italian Building Code (NCT08, 2008) by introducing q.

To ensure the structural design for the structure could be conservative, and when the material plasticity is minimal, the

factor q was set to be 1.0. In other words there was no reduction in the spectrum’s accelerations for the structural

analysis to establish the seismic performance.

Displacement response spectra

To gain an insight into how much horizontal displacement the structure is to experience due to ground movement the

displacement response spectrum, SDe(T), is obtained from the acceleration response spectrum (Se(T)), by using the

relationship:2

eDe2

)()(

TTSTS



7 - Pushover analysis

In performance-based engineering it is necessary to obtain realistic estimates of inelastic deformations in structures so

that these deformations may be checked against deformation limits as established in the appropriate performance

criteria. Two basic methods are available for determining these inelastic deformations: Nonlinear static “pushover”

analysis and Nonlinear Dynamic Response History analysis.

In the non linear static analysis method a structure is subjected to gravity loading and a displacement-controlled

lateral load pattern which continuously increases through elastic and inelastic behavior until an ultimate condition is

reached. Lateral load may represent the range of base shear induced by earthquake loading.

Different types of non linear behaviour exist: mechanical (connected to the non linearity of the material), geometrical

(connected to the fact that the application point of the loads changes increasing the actions) and of beam-column

joints (connected to the interaction of structural elements).

The pushover analysis is based on: 1-Definition of capacity curve of MDoF system; 2-Definition of equivalent SDoF

system; 3-Calculation of capacity displacement (umax); 4-Calculation of displacement demand (dmax); 5-Comparison

between umax and dmax; 6-Validation when umax >dmax (see figure below).

The capacity curve= relationship between the horizontal displacement and horizontal force.

The demand curve is basically an elastic response spectrum that has been modified for expected performance and

equivalent viscous damping. The demand curve is used in concert with the capacity curve to predict the target

displacement.

The expected displacement is determined locating on the capacity curve the displacement compatible with the seismic

action of the site. The identification of this displacement is pursued by operating in Acceleration Displacement

Response Spectrum (ADRS), and then describing the capacity curve and the response spectrum in terms of spectral

acceleration and spectral displacement. In the space ADRS the response spectrum and capacity curve should

respectively take the name of the Demand spectrum and Capacity spectrum capacity. The different forms of horizontal actions are:

a)Uniform load proportional to the mass distribution

b)Triangular load proportional to the mass distribution

c)Horizontal load proportional to the lateral force distribution of the mode with the highest mass participation

‘‘Modal’’.

The P-Δ effect must be taken into account. The P-Δ effect is a destabilizing moment equal to the force of gravity

multiplied by the horizontal displacement a structure undergoes when loaded laterally.



8a – Dissipative capacity

For the seismic design the dissipation capacity of any structure can be taken into consideration by introducing a

reduction factor to the elastic spectral accelerations. This is accomplished in standard codes by the behaviour factor q.

The design seismic action Sd(T) is given by the elastic response spectra with the elastic accelerations (forces) adjusted

downward by dividing by q. The determination of the q depends on the: materials; structural form; hyperstaticity degree

of structure; structural response (e.g. its ductility); soil-structure interaction. To ensure the structural design for the

structure could be conservative the factor q =1.0. In other words there was no reduction in the spectrum’s accelerations

in the elastic response spectrum for the structural analysis to establish the seismic performance.

The q factor is determined through kinematic or energetic equivalence conditions.

Kinematic equivalence for structure with higher period of

vibration

qu

u

F

Fq

yy

e max

Energetic equivalence for structure with short period of

vibration

221 max yy

e

y

e

u

u

u

u

F

F

12212 qq

Hence, considering the previous criteria

sifTq

sTsifq

sifTq

1.01

5.01.012

5.0

Generalizing the SDoF, the q of MDoF could be evaluated through the relationship between the different peek ground

acceleration (PGA) of collapse and yielding state:

y

u

PGA

PGAq

or through the pushover analysis considering the static forces equivalent to seismic actions:

y

uq

Elastic response spectra in SLS for horizontal and vertical

components based on Eurocode 8 (2004) and NTC08 (2008).

Design response spectrum for ULS structural analysis

based on using Eurocode 8 (2004) and NTC08 (2008).



8b - Dissipative capacity

The displacement response spectrum, SDe(T), is obtained

from the acceleration response spectrum (Se(T)).

This is valid for a vibration period T< 4.5s (4.5 s is time

parameter TE for a type A ground). The acceleration

response spectra and the displacement response spectra

have three time zones that are proportional to the imposed

ground acceleration. Between times TB and TC there is a

zone of constant spectral acceleration. This is followed to

time TD by the zone of constant spectral velocity and for

higher times to TE there is the zone of constant

displacement response too. Horizontal displacement response spectra based on

Eurocode 8 and NTC08 for SLS and ULS design.

The dashed lines show the displacements calculated with NTC08 and EC8 considering q=1. In the same the elastic

displacement response spectra is calculated considering q=1.5. Figure shows that the structure responds to design

seismic action resisting to a maximum displacement of 116mm for EC8 and 124mm for NTC8. The effect of the

behaviour factor is shown through the reduction of the displacements induced by design seismic action.

For the seismic spectral analysis the response-spectrum analysis (RSA) has been carried out. It is a linear-dynamic

statistical analysis method which measures the contribution from each natural mode of vibration to indicate the likely

maximum seismic response of an essentially elastic structure. Response-spectrum analysis provides insight into

dynamic behavior by measuring pseudo-spectral acceleration, velocity, or displacement as a function of structural

period for a given time history and level of damping. It is practical to envelope response spectra such that a smooth

curve represents the peak response for each realization of structural period. Response-spectrum analysis is useful for

design decision-making because it relates structural type-selection to dynamic performance. Structures of shorter period

experience greater acceleration, whereas those of longer period experience greater displacement.



3. EXAMPLE OF CALCULATION

A numerical example relative to the design and verification of a pultruded frame subjected to static

and seismic actions is illustrated (see Figure 3.1). The procedure will be the same also in presence

of different structures as simple frame, multistory frame or irregular structure all made by beam-

column connections or, again, for local reinforcement using pultruded FRP systems.

Figure 3.1 View of structure (dimensions in meters).

In this first part of the chapter, the characteristics of the structure are described and general

indications are given about the seismic behavior and design of pultruded frames.

In the second part of the chapter, Load analysis (p. 42), the static and seismic loads acting on the

structure are evaluated. The seismic response of the building is evaluated first through a spectral

response analysis and then through a pushover analysis.

The third part of the chapter, from page 55, describes some structural verifications of the single

members at the ultimate (ULS) and serviceability limit state (SLS). In addition, a verification of a

bolted joint is carried out, considering the different failure mechanisms.



In particular, for what concerns the ULS and SLS, the following verifications are considered (Table

3.1):

Ultimate Limit State, ULS Serviceability Limit State, SLS

Example of verification of a

compressed member

p. 59 Stresses p. 76

Deformations p. 77

Table 3.1 Chapters of ULS and SLS verifications

For what concerns the verifications of joints the following verifications are considered (Table 3.2):

Joint's verification

Net-tension failure of the plate p. 82

Shear-out failure of the plate p. 82

Bearing failure of the plate p. 83

Shear failure of the steel bolt p. 85

Table 3.2 Chapters of joint verifications

On the base of the verifications results some considerations about the structural performance of

pultruded members are then provided. Finally, the possible strategies are described for enhancing

the seismic stability of the structures.

3.1. Statement of the structural design

The structure of Figure 3.1 has been designed in accordance with the Italian building code (NTC08)

and Eurocode. Individual components (frames, members, connections and bolted joints) and the

whole structure have been analyzed with respect to Ultimate Limit States (ULS) and Serviceability

Limit States (SLS). The adopted design method takes into account the load combinations of wind,

snow and earthquake. Seismic loading was based on seismic zoning in accordance with the Italian

Building Code NTC08 (2008).

The structure has been designed for a design working life VN≥50 years (see also Eurocode1

category C and NTC08 type 2 class III).

The referred life’s period VR is so assumed equal to 75 years by the product between VN and CU

(class of use) =1.5.

The parameters to identify the structures are the fundamental period of vibration T1 and the beam-

column stiffness ratio ρ, equation 3.1(Chopra 2007):

http://en.wikipedia.org/w/index.php?title=Ultimate_limit&action=edit&redlink=1

http://en.wikipedia.org/wiki/Serviceability_limit

http://en.wikipedia.org/wiki/Serviceability_limit



c

ccolumns

b

bbeams

L

EJ

L

EJ

(3.1)

with the flexural stiffness of beam (EJb) and column (EJc) compared to Lb (lengths of beam) and Lc

(lengths of column) indicated in Figure 3.2.

The different ρ value affects the fundamental period and the modal shapes. The relative closeness or

separation between the natural periods and the corresponding participation mass evidences the

global or local structural response.

The deflected shapes in function of ρ values are indicated in Figure 3.2:

ρ=0 0<ρ<∞ ρ=∞

Figure 3.2 Deflected shapes with different ρ; (Chopra 2007)

With ρ=0 the frame is not restrained on joint rotations, then the behaviour of the frame is affected

by the flexural response of the beams. When 0<ρ<∞ (semi-rigid joints) beams and columns are

subjected to bending deformation with joint rotations. With ρ=∞ (rigid joints) the joint rotation is

completely restrained.

In general, the connections between pultruded structural members can be realized through bolted or

bonded joints or a combination of the two.

All-FRP structures should be designed also evaluating local and global buckling and their designing

in function of the lower value.

As reported in EN 1998-1, §6.7.1, the concentric braced frames should be designed so that the

strength hierarchy criteria are activated.



The structure should exhibit similar global load-deflection characteristics at each story in opposite

senses of the same braced direction under load reversals. For this reason the diagonal elements of

bracings should be placed as shown in Figure 3.3 (see Figure 6.12 of EN 1998-1).

Figure 3.3 Figure 6.12 of EN 1998-1.

To this end, the equation 3.2 should be met at every story in order to concentrate the axial load in

the bracings unloading the much as possible columns and beams.

05.0

AA

AA (3.2)

where A+ is the area of the horizontal projection of the cross-section of tension diagonals with

positive seismic action; A- is the area of the horizontal projection of the cross-section of tension

diagonals with negative seismic action.

The effects of connections deformations on global drift must be taken into account using pushover

global analysis or non-linear time history analysis, see Sheet 8 and Priestley et al. (2007).

As suggested by EN 1998-1:2004 the dissipative semi-rigid and/or partial strength connections are

permitted if: 1-the connections have a rotation capacity consistent with the global deformations; 2-

members framing into the connections are demonstrated to be stable at ULS; 3-the effect of

connection deformation on global drift is taken into account using non-linear global analysis or non-

linear time history analysis.



3.2. Materials

Table 3.3 shows the mechanical properties for the pultruded profiles with vinylester based matrix

reinforced by E-glass fibre.

Mechanical properties Symbol Mean value

Longitudinal tensile strength σZ = σLt 400 MPa

Longitudinal compressive strength σZc = σLc 220 MPa

Transversal tensile strength σXt = σYt = σTt 70 MPa

Shear strength τXY= τXZ = τYZ 40 MPa

Longitudinal elastic modulus EZ= EL 23 GPa

Transversal elastic modulus EX = EY=ET 7 GPa

Shear modulus GXY=GL 4.5 GPa

Shear modulus GZX =GZY=GT 4.5 GPa

Poisson’s ratio νZX = νZY= νL 0.3

Poisson’s ratio νXY= νT 0.3

Bulk weight density of FRP γ 1850 kg/m3

Volume fraction of E-glass fibre Vf 48%

Table 3.3 Mechanical and physical characteristics of pultruded FRP material, mean

value

To assemble the whole FRP structure the use of stainless steel bolts will be suggested. For the

frame joints the bolting is M14 class 8.8, UNI5737.

The bolt clearance hole should be constant at 1.0 mm. The M14 bolts should be tightened to a

torque where the effects will be less than the transversal tensile strength. From the torque moment

M it is possible to detect the axial load N through the Equation 3.3.

d

MN

(3.3)

where d is equal to the diameter of the bolt while ς is a coefficient friction (ς = 0.14 to 0.22,

Mottram et al. 2004). Bolts should be partially threaded (at least for half length of bolt) to minimise

any local damage from thread embedment into the FRP materials.



3.3. Basic assumptions

The structure has been designed taking into account the following basic assumptions:

- full fixed restraint at column-base

- rigid diaphragm as horizontal partition

- for the material of bracing the constitutive law of Figure 3.4a has been considered that takes into

account the partial cross section area due to presence of holes for bolted connection. The

normalized constitutive law and the idealized curve for FEM analysis are reported in Figure 3.4b.

(a) (b)

Figure 3.4 Experimental and normalized constitutive law for the bracing elements

- for the beam-column joints the constitutive law of Figure 3.5 has been assumed. The moment-

rotation relationship (Figure 3.5a) has been extracted by experimental tests carried out in the

Laboratory of Strenght of Materials of IUAV Univesity of Venice, Italy (Feroldi and Russo 2016).

The normalized constitutive law and the idealized curve for FEM analysis are reported in Figure

3.5b; other constitutive laws can be deduced by Turvey and Cooper (2004).

(a) (b)

Figure 3.5 Experimental and normalized Moment-Rotation relationship



3.4. Load analysis

For the ultimate and serviceability limit states, ULS and SLS respectively, the combinations of

actions are listed in Table 3.4

fundamental combination in ULS ...30332022112211 kQkQkQGG QQQGG

characteristic combination in SLS ...303202121 kkk QQQGG

frequent combination in SLS ...32322211121 kkk QQQGG

quasi-permanent combination in

SLS ...32322212121 kkk QQQGG

seismic combination in ULS ...22212121 kk QQGGE

Table 3.4 Combination of actions

where G1 and G2 are the dead loads of the structural and non structural elements respectively, Q is

the accidental load and E is the seismic action.

The recommended values of ψ factors for buildings (Table 3.5) are extracted by Table A1.1 for

Eurocode 1 and Table 2.5.1 for NTC08.

Action/Category Ψ0j Ψ1j Ψ2j

Category C: congregation areas 0.7 0.7 0.6

Snow load on building for sites located at altitude H≤1000 m a.s.l. 0.5 0.2 0

Wind loads on buildings 0.6 0.2 0

Table 3.5 Recommended values for ψ coefficients

For the ULS the design values of actions are shown in Table 3.6, see Tables A1.2(B) and A1.2(C)

for Eurocode 1 and Table 2.6.1 for NTC08

Loads/Actions γF

Permanent γG1 1.3, 1.5

Permanent γG2 1.5

Variable γG2 1.5

Table 3.6 Unfavourable condition of design values of actions

3.4.1. Permanent loads

The total self-weight of structural and non-structural members should be taken into account in the

combinations of actions as a single action.

The scheme of the structure is indicated in Figure 3.6. Along X and Y-direction the frames 1-2-3-4

and A-B are shown, respectively. The horizontal bracing in the plan scheme of Figure 3.6 is

repeated for every floor. The details of cross sections of pultruded members of the structure (Figure

3.1) are shown in Figures 3.6 and 3.7, while Table 3.7 lists the main geometric characteristics.



Figure 3.6 Details of members for every floor and frame (meters)

Figure 3.7 Geometric characteristics of cross section members (millimetres)

Section name Area

Second

moment of

inertia Imax

Second

moment of

inertia Imin

Torsional second

moment of

inertia

Shear area

for Imax

Shear area

for Imin

mm2 mm

4 mm

4 mm

4 mm

2 mm

2 2U-152x43x9.3 4080.84 11834397 1975906 108225.2 2827.2 1599.6 2U-200x60x10 6000 31400000 4687500 187400 4000 2400 2U-300x100x15 14100 1.71E+08 26811875 993712.5 9000 6000 4U-152x43x9.3 8162 31829200 13809900 232400 7112 3196

L-75x6.5 932.75 503065.6 503065.6 12698.89 487.5 487.5 P-75x9.5 712.52 334004.9 5359.02 16303.56 712.5 180.52

Table 3.7 Characteristics of pultruded FRP members



A composite cross section constituted by pultruded panels and concrete slab has been considered in

addition to G1 for every floor and the roof. In detail, the pultruded panels have a self-weight of

0.5kN/m2 with a thickness of 80mm, while the concrete slab is 100 mm thick, see Figure 3.8.

Figure 3.8 Detail of deck (millimetres)

The permanent load G1 weighing on beams with maximum span for every floor and on the beam of

the roof is shown in Figure 3.9, for the references about the frames see Figure 3.6.

Figure 3.9 Permanent load G1 (N/mm)

G2 is characterized by non-structural permanent load as infill vertical panels, internal partitions and

layer of pavement, see Figure 3.10; for the references of the frames see Figure 3.6.

In detail, the load of non-structural layer of pavement and internal partitions is equal to 3.8 kN/m2

while the load of perimetral infill vertical panel is 0.5 kN/m2.



Figure 3.10 Non-structural permanent load G2 (N/mm)

3.4.2. Variable loads

The variable action Q on building floor is 4 kN/m2, weighing on beams with maximum span (see

Figure 3.1) as shown in Figure 3.11; for the references about the frames see Figure 3.6.

Figure 3.11 Variable actions Q load (N/mm)

The wind action has been evaluated considering the characteristics of the Zone 3 in NTC08 (Table

3.3.I of §3.3). The fundamental value of the basic wind velocity, vb,0, is obtained by the following

relationship:

)( 00, aakvv sabb for a0<as<1500m

sec66.32)500783(02.027

mvb

where vb,0, a0, ka, are parameters listed in Table 3.3.I of §3.3 of NTC08 while as is the altitude

above the sea level. The velocity pressure p is given by:



dpeb cccqp

with ce=exposure factor, cp=shape parameter, cd=dynamic coefficient=1, while the basic velocity

pressure qb is calculated through

2

2

1bb vq

where ρ is the air density equal to 1.25kg/m3, then

2

2 67.666)66.32(25.12

1

m

Nqb

for the exposure factor ce the following relationship must be applied

00

2 ln7ln)(z

zC

z

zCkzC ttre

where for the category III kr, z0 and z are listed in Table 3.3.II of NTC08 while Ct is equal to

topographic coefficient =1 , hence:

42.21.0

4.15ln17

1.0

4.15ln12.0)(

2

zCe

For the shape parameter, cp, the net pressure is the difference between the pressures on the opposite

surfaces that in this specific case is cp = 1.2. Finally, the velocity pressure p is detailed in Figure

3.12.



Figure 3.12 Wind actions in X and Y-direction, force in N

The snow load, as defined by NTC08 and EC1, is shown in the following relationship.

tEsks CCqq 1

Where qs (S, for EC1) = snow load, µi = shape coefficient, CE = exposure coefficient, Ct =

thermal coefficient and qsk (Sk = permanent and SAd = variable, for EC1) = characteristic value. The

different parameters are listed in Table 3.8. Figure 3.13 shows the snow load applied to structure;

for the references of the frames see Figure 3.6.

µi CE Ct qsk (Sk=permanent, for EC1) qsk (SAd=variable, for EC1)

EC1 0.8 1.1 1

2

2

2

15.3452

7831)209.0498.0(

4521)209.0498.0(

m

kN

ASk

2296.6148.32

m

kNSCS keslAd

NTC08 0.8 1.2 1 2

2

86.1481

151.0m

kNaq s

sk

(with as=783)

Table 3.8 Coefficients for snow load

Figure 3.13 Snow load (N/mm)



3.4.3. Seismic analysis

A dynamic analysis has been carried in the following taking into account the modal analysis,

spectral analysis and non linear static analysis.

3.4.3.1. Modal analysis

The modal analysis, associated with the design response spectrum, can be performed on three-

dimensional structures in order to obtain a reliable structural response.

This is a linear dynamic-response procedure which evaluates and superimposes free-vibration mode

shapes to characterize displacement patterns. Mode shapes describe the configurations into which a

structure will naturally displace in the dynamic field.

Typically, lateral displacement patterns are of primary concern. The analysis can be considered

reliable as it reaches the mass participant >85% (§7.3.3.1 of NTC08), see Table 3.9. In detail in

Table 3.9 the letter U sets the direction along the respective axis while R indicates the rotation about

the correspondent axis. Sum for every direction and rotation is the progressive sum of the

participating mass (PM). Figure 3.14 shows the modal shapes and related dynamic parameters.

StepNum Period (secs) UX UY UZ SumUX SumUY SumUZ RX RY RZ SumRX SumRY SumRZ

1 0.67 0% 88% 0% 0% 88% 0% 99% 0% 8% 99% 0% 8%

2 0.60 89% 0% 0% 89% 88% 0% 0% 100% 80% 99% 100% 88%

3 0.19 0% 11% 0% 89% 98% 0% 0% 0% 1% 99% 100% 89%

4 0.17 10% 0% 0% 99% 98% 0% 0% 0% 9% 99% 100% 98%

5 0.12 0% 1% 0% 99% 100% 0% 0% 0% 0% 99% 100% 98%

6 0.11 1% 0% 0% 100% 100% 0% 0% 0% 1% 99% 100% 99%

7 0.09 0% 0% 0% 100% 100% 0% 0% 0% 0% 99% 100% 99%

8 0.08 0% 0% 0% 100% 100% 0% 0% 0% 0% 99% 100% 99%

9 0.07 0% 0% 0% 100% 100% 0% 0% 0% 1% 99% 100% 100%

10 0.05 0% 0% 0% 100% 100% 0% 0% 0% 0% 99% 100% 100%

11 0.05 0% 0% 0% 100% 100% 0% 0% 0% 0% 99% 100% 100%

12 0.05 0% 0% 0% 100% 100% 0% 0% 0% 0% 99% 100% 100%

13 0.03 0% 0% 86% 100% 100% 86% 1% 0% 0% 100% 100% 100%

14 0.02 0% 0% 0% 100% 100% 86% 0% 0% 0% 100% 100% 100%

15 0.02 0% 0% 0% 100% 100% 86% 0% 0% 0% 100% 100% 100%

16 0.02 0% 0% 0% 100% 100% 86% 0% 0% 0% 100% 100% 100%

17 0.02 0% 0% 0% 100% 100% 86% 0% 0% 0% 100% 100% 100%

18 0.02 0% 0% 1% 100% 100% 87% 0% 0% 0% 100% 100% 100%

19 0.02 0% 0% 0% 100% 100% 87% 0% 0% 0% 100% 100% 100%

20 0.02 0% 0% 0% 100% 100% 87% 0% 0% 0% 100% 100% 100%

Table 3.9 Period of vibration (secs) and participation mass respect to X, Y and Z axes.



Figure 3.14 Modal analysis, deformed shapes in black color and undeformed shapes in

gray color

3.4.3.2. Spectral analysis

The seismic loading for structural design is realized through response spectra, see Sheet 5,

Eurocode 8, 2004 and NTC08, 2008. Design that is in accordance with the requirements of

Eurocode 8 has only ULS spectra. Working to the Italian Building Code (NTC08 2008) requires

there to be both SLS and ULS spectra.



Based on a 10% probability of exceedance over a reference period of 50 years in the Italian seismic

zone 1 (NTC05 2005), and in accordance with Eurocode 8 (2004), the design ground acceleration

on type A ground, ag, can be taken to be 0.35g. Note that by applying the specific seismic zoning

requirements in NTC08 (2008) the designer will have different ground accelerations for the SLS

and ULS design response spectra, which are defined to account for the different reference periods of

50 and 712 years. Type A ground is a stiff soil (Eurocode 8, 2004; NTC08, 2008) characterized by

rock or other rock-like geological formation, including at most 3 m from using NTC08 (2008) or 5

m from using Eurocode 8 (2004), of weaker material below the surface possessing a shear wave

velocity (vs) in excess of > 800 m/s.

3.4.3.2.1. Elastic response spectrum

The Eurocode 8 spectra are compared with the spectra obtained using the specific design parameters

for considered zone, which are taken from the Italian Building Code (NTC08 2008).

For the structure in exam the parameter values listed in Table 3.10 are used to specify this

horizontal spectrum (for type A ground conditions) with the damping coefficient ζ set to 0.05. The

parameters from using Eurocode 8 are presented in column (2) and the SLS and ULS parameters

from using NTC08 (2008) are given in columns (4) and (5), respectively. Comparing the rows in

columns (2) and (5) shows the differences in the parameters for Eqs. (a) to (d) of Sheets 6 and 7

between the two standards. Euroocde 8 seismic loading is more severe than the Italian seismic

loading. Parameters for the vertical spectrum are listed in column (3) of Table 3.10 for Eurocode 8

(2004) and in columns (6) and (7) for NTC08 (2008).

Parameters

Eurocode 8 NTC08

Components

Horizontal Vertical Horizontal Vertical

SLS ULS SLS ULS

(1) (2) (3) (4) (5) (6) (7)

ag (g) 0.35 - 0.125 0.3 - -

avg (g) - 0.9 ag - - 0.06 0.222

Fh 2.5 - 2.316 2.384 - -

Fv - 3 - - 1.105 1.762

S 1 1 1 1 1

η 1 1 1 1 1

TB (s) 0.15 0.05 0.097 0.119 0.05

TC (s) 0.4 0.15 0.29 0.356 0.15

TD (s) 2 1 2.1 2.799 1

Note: - is for not applicable.

Table 3.10 Spectra parameters (Eurocode 8, 2004, NTC08, 2008)



Plotted in Figure 3.15a are the two elastic spectra at SLS for the horizontal Se(T) and vertical Sve(T)

acceleration components for NCT08 and Eurocode 8. Three distinct stages in the seismic response

are established by the time parameters TB, TC, and TD with Eqs. (a) to (d) in Sheets 6 and 7.

3.4.3.2.2. Design spectra for ULS design

The design seismic action Sd(T) is given by the elastic response spectra with the elastic

accelerations (forces) adjusted downward by dividing by q, Sheet 8.

One outcome on making this is that, because η = 1/q, the parameter η becomes 0.67 (i.e.

damping coefficient is assumed to be 0.05). With the modelling assumption that q = 1.5, the

Eurocode 8 spectra for the horizontal and vertical components remain defined by the four

expressions in Sheet 6, respectively, with parameters Fo and Fv reduced by q = 1.5.

Figure 3.15b presents the design spectra for ULS design from Eurocode 8 (2004) and NTC08

(2008), using the same plot construction as in Figure 3.15a and the parameters given in Table 3.10

(see Sheets 6, 7 and 8). It is observed that there has been no change in the Eurocode 8 spectra

between Figures 3.15a and 3.15b, while the NCT08 spectra curves of NTC08-horizontal and

NTC08-vertical in Figure 3.15b have much higher values than in Figure 3.15a.

(a) (b)

Figure 3.15 Elastic response spectra in SLS (a) and design response spectra for ULS (b)

3.4.3.2.3. Displacement response spectra

The displacement response spectra SDe through equation of Sheet 6 for the horizontal component

(defined by Eqs. (a) to (d) in Sheet 6) gives a direct transformation that is valid for a vibration

period T, that is not > 4.5 s (4.5 s is time parameter TE for a type A ground). Plotted in Figure 3.16

is SDe using Eq. in Sheet 6 for the Eurocode 8 (EC8-horizontal) and for the NCT08 (NTC08-

horizontal).



The elastic displacement response spectrum of horizontal components of seismic actions is

extracted by acceleration response of Figure 3.15b. The dashed lines of Figure 3.16 show the

displacements calculated with NTC08 and EC8 considering q=1. In the same figure the elastic

displacement response spectra have been calculated considering q=1.5. Figure 3.16 shows that the

structure responds to the design seismic action resisting to a maximum displacement of 116mm for

EC8 and 124mm for NTC8. Also the effect of the behaviour factor is shown through the reduction

of the displacements (see Sheet 8).

Figure 3.16 Horizontal displacement response spectra

In the seismic combination at ultimate limit state the horizontal (X and Y) and vertical components

(Z) that have been considered are NTC08-horizontal_q=1.5 and NTC08-vertical_q=1.5

respectively, of Figure 3.15, through the combinations shown in Table 3.11 (NTC08, §7.3.5 and EN

1998-1-1:2004); the Z combination can be ignored if not necessary.

X direction Y direction Z direction

zyx EEE 3.03.01 zyx EEE 3.013.0 zyx EEE 13.03.0

Table 3.11 Combination of the horizontal (X and Y) and vertical components (Z)

In the spectral analysis all the vibration modes with a participating mass bigger than 5% should be

considered summing up a number of modes so that the total participating mass is larger than 85%

(§7.3.3.1 of NTC08). In order to calculate stresses and displacements in the structure, the complete

quadratic combination CQC rule may be used.

Through the spectral analysis the maximum displacements in x and y direction, taking into account

the previous combinations, are shown in Figure 3.17 where deformed shapes are in red and

undeformed in gray. The assumed limitation of inter-story drift is < 0.01h with h=height of inter-



story (§4.4.3.2 in EC8). For both seismic directions the analysis is satisfied, 42.2 mm < 46 mm (x

direction) and 15.9 mm < 46 mm (y direction).

Seismic action in x direction, maximum inter-story drift = 42.2 mm

Seismic action in y direction, maximum inter-story drift = 15.9 mm

Figure 3.17 Maximum displacements (Spectral analysis)

3.4.3.3. Pushover analysis

Two different horizontal actions have been studied as suggested in the chapter §4.3.3.4.2.2 of

Eurocode 8:

i) horizontal load proportional to the mass distribution (denoted as ‘‘Mass’’),



ii) horizontal load proportional to the lateral force distribution of the mode with the highest mass

participation (denoted as ‘‘Modal’’).

The seismic design codes (EC8 and NTC08) have suggested the use of both configurations. For

both analyses the P-Δ effect must be taken into account, see Sheet 8.

As specified by Eurocode 8 (§4.3.3.4.2.3.) the maximum lateral displacement could be between

zero and the value corresponding to 150% of the target displacement (defined in §4.3.3.4.2.6. of

EC8).

The target displacement has been determined from the elastic response spectrum, see Sheet 7,

following the annex B of Eurocode 8 (EN 1998-1:2004).

For the case in exam the modal and mass pushover methods have been addressed as required by

specific standards.

Figure 3.18 compares the capacity curves of different methods (a) mass, (b) modal and (c) the

Acceleration Displacement Response Spectrum (ADRS) extracted by the modal curve (Figure

3.18b).

(a) mass (b) modal

(c) ADRS of modal curve of (b)



Figure 3.18 Capacity curves: (a) mass, (b) modal and (c) ADRS of modal curve of (b)

The maximum displacements of capacity curves (Figure 3.18a and b), equal to 224 mm and 179

mm for mass and modal methods respectively, show that the displacement capacity of the structure

in exam is greater than the required displacement capacity determined for that site (116 mm), see

curve EC8_q=1.5 of Figure 3.16. For this reason the seismic analysis of the structure is satisfied.

The demand curve (detailed in Sheet 7) is used in agreement with the capacity curve to predict the

target displacement point T*, see Figure 3.18c.

Considering the case in exam, umax = 0.179m and dmax = 0.1375 m, see Figure 3.18c, the seismic

analysis is verified.

3.5. ULS analysis

In the following the diagrams of the forces and moments in four frames are reported for the

different ultimate limit state load combinations, and an example of structural verification of a

compressed member is carried out. The diagrams relative to the seismic load combinations present

two values of the internal actions in the frame elements, since the oscillations due to the earthquake

produce internal actions with opposite signs. Only the diagrams in the x-z plane are considered, for

which the highest values of forces and moments are obtained. The structural verification is based on

the formulations given in (CNR-DT205/2007). Anyway, since in the document mentioned above

only double-T sections are considered, indications are given also for the verification of other kinds

of profiles, on the base of formulations available in the literature (Bank 2006, Kollar 2003, Tarjan et

al 2010a-b).




In the following every figure shows the forces and moment diagrams of the structure subjected to

the different load combinations in x- and y-direction, see Table 3.4. In every scheme the most

stressed member is evidenced by a black circle and the related value of the internal action is

indicated for the specific frame detailed in Figure 3.1.


Frame 1 = -387kN

Frame 1 = -387kN

Frame 2 = -467kN Frame 2 = -467kN



Wind in x-direction Wind in y-direction

Figure 3.19 Fundamental load combination, axial force diagrams

Frame 1 118kN

-517kN

Frame 1 162kN

-560kN

Frame 2 49kN

-510kN Frame 2

-114kN

-348kN

Frame 3 49kN

-510kN Frame 3

-114kN

-348kN

Frame 4 118kN

-517kN Frame 4

162kN

-560kN

Earthquake in x-direction Earthquake in y-direction

Figure 3.20 Seismic load combination, axial force diagrams


Frame 1 71922

kNmm

Frame 1 71922

kNmm

Frame 2 134739

kNmm Frame 2

134739

kNmm

Frame 3 134739

kNmm Frame 3

134739

kNmm



Frame 4 71922

kNmm Frame 4

71922

kNmm


Figure 3.21 Fundamental load combination, bending moment diagrams

Frame 1 40382kNmm

44234kNmm

Frame 1 41666kNmm

42951kNmm

Frame 2 76312kNmm

80221kNmm Frame 2

77615kNmm

78918kNmm

Frame 3 76312kNmm

80221kNmm Frame 3

76312kNmm

80221kNmm

Frame 4 40384kNmm

44236kNmm Frame 4

41667kNmm

42952kNmm


Figure 3.22 Seismic load combination, bending moment diagrams


Frame 1 = 79kN

Frame 1 = 79kN

Frame 2 = 149kN Frame 2 = 149kN




Figure 3.23 Fundamental load combination, shear force diagrams

Frame 1 46kN

47kN

Frame 1 46kN

47kN

Frame 2 86kN

87kN Frame 2

87kN

87kN

Frame 3 86kN

87kN Frame 3

87kN

87kN

Frame 4 46kN

47kN Frame 4

46kN

47kN


Figure 3.24 Seismic load combination, shear force diagrams




Frame 1 = 0.5kNmm

Frame 1 = 0.5kNmm

Frame 2 =

0.02kNmm

Frame 2 =

0.02kNmm

Frame 3 =

0.03kNmm

Frame 3 =

0.03kNmm

Frame 4 = 0.5kNmm Frame 4 = 0.5kNmm


Figure 3.25 Fundamental load combination, torsional moment diagrams

Frame 1 0.6kNmm

0.4kNmm

Frame 1 1.5kNmm

1.4kNmm

Frame 2 0.5kNmm

0.4kNmm Frame 2

1.5kNmm

1.4kNmm

Frame 3 0.5kNmm

0.4kNmm Frame 3

1.5kNmm

1.4kNmm

Frame 4 0.6kNmm

0.4kNmm Frame 4

0.6kNmm

0.4kNmm


Figure 3.26 Seismic load combination, torsional moment diagrams

3.5.2. Example of verification of a compressed member

The next verifications – in detail till page 84 – will be proposed., as anticipated in the introduction,

strictly following the CNR-DT205/2007 and the more recent CEN TC250 WG4L (2016). As an

example, a buckling verification is carried out for the member in compression evidenced in Figure

3.27. The stability verification of a compressed member requires the following relation to be

satisfied:

2,, RdcSdc NN (3.4)

where Nc,Rd2 is the design value of force that causes buckling of the member.



Frame 4 -516706 N

Earthquake in x-direction

Figure 3.27 Seismic load combination, axial force diagram

In order to carry out the stability verification, the built-up cross-section of the member (2 U

300x100x15 mm) is considered as being a 300x200 double-T section, with the thickness of the web

equal to 30 mm and the thickness of the flanges equal to 15 mm.

For the case of double-T profiles the value of Nc,Rd2 is computed as:

RdlocRdc NkN ,2, (3.5)

where the design value of the compression force that causes the local instability of the profile,

Nloc,Rd, can be deduced from the relation:

axial

dlocRdloc fAN ,, (3.6)

where axial

dlocf , is the design value of the local critical stress, and can be computed as:

w

axialklocf

axialkloc

f

axialdloc fff ,,, ,min

1

(3.7)

where f

axial

klocf , and w

axial

klocf , represent, respectively, the critical stress of the flanges and of the web.

For the ultimate limit states, the partial coefficient of the material, γf, can be obtained by the

expression:

21 fff (3.8)

where factor γf1 takes into account the uncertainty level in the determination of the material

properties with a coefficient of variation Vx (Table 3.12); factor γf2 takes into account the brittle

behaviour of the material and for it a value of 1.30 is suggested by CNR-DT205/2007.



Vx ≤ 0.10 0.10 < Vx ≤ 0.20

1.10 1.15

Table 3.12 Values of the coefficient of variation Vx

The value of the coefficient of variation Vx related to the characteristic strength or deformation

property of the material must be determined through an appropriate series of experimental tests.

For the serviceability limit states the unit value is suggested for the material partial coefficient.

Adopting the symbols of Figure 3.28, the value of f

axial

klocf , can be conservatively assumed equal

to:

2

, 4

f

f

Lf

axialkloc

b

tGf (3.9)

where GL is the shear modulus. The use of equation (3.9) corresponds to considering the flanges as

simply supported in correspondence of the web. In order to consider the restraint degree offered by

the web it is suggested to adopt the formulations reported in Appendix A of (CNR-DT205/2007).

Figure 3.28 Double-T section: symbols adopted for the geometrical properties (CNR-

DT205/2007)

Similarly, the value of the critical stress in the compressed web, w

axial

klocf , , can conservatively be

assumed equal to (CNR-DT205/2007):

2

22

,112 wTL

wLccw

axialkloc

b

tEkf

(3.10)



where ELc is the longitudinal compressive elastic modulus, νL is the longitudinal Poisson ratio and

νT is the transverse Poisson ratio.

Coefficient kc is given by:

Lc

TcL

Lc

TcL

LcLc

Tcc

E

E

E

E

E

G

E

Ek

2142 2 (3.11)

where ETc is the transverse compressive elastic modulus, ELc is the longitudinal compressive elastic

modulus, GL is the shear modulus, νL is the longitudinal Poisson.

Coefficient k of equation (3.5) represents a reduction factor that takes into account the interaction

between local and global buckling of the member. This coefficient assumes a unit value if the

slenderness of the member tends to zero or in presence of restraints that prevent global buckling.

The value of the coefficient can be computed as (CNR-DT205/2007):

22

2

1

c

ck (3.12)

where symbol c denotes a numerical coefficient that, in absence of more accurate experimental

evaluations, can be assumed equal to 0.65, and:

2

1 2 (3.13)

The slenderness λ is equal to:

Eul

Rdloc

N

N , (3.14)

with:

20

min2

1

L

IEN

eff

f

Eul

(3.15)



In equation (3.15) Eeff is the effective modulus of elasticity, Imin is the minimum moment of inertia

of the cross-section and L0 is the effective length of the member.

In Figure 3.29a the trend of k for varying λ is represented.

(a) (b)

Figure 3.29 Local and global buckling modes for columns: (a) CNR-DT205/2007 and (b)

Barbero, 1999.

The effective length of the member, L0, to be introduced in equation (3.15), can be evaluated

through the formulations reported in Eurocode 3. For a column in a non-sway mode, as for the case

in exam, the buckling length ratio l/L can be obtained from the diagram of Figure 3.30.

For a continuous column, as the one in exam, and with reference to Figure 3.31, coefficients η1 and

η2 can be obtained from relations (Eurocode 3):

12111

11

KKKK

KK

c

c

(3.16)

22212

22

KKKK

KK

c

c

(3.17)

where Kc is the stiffness coefficient of the column I/L (I = second moment of inertia while L =

length of column), K1 and K2 are the stiffness coefficients for the adjacent lengths of columns and

Kij is the effective beam stiffness coefficient.

If the beams are not subjected to axial forces, as in the case in exam, their effective stiffness

coefficients can be determined from Table 3.13.



Conditions of rotational restraint at far end of beam Effective beam stiffness coefficient K

Fixed at far end 1.0 I/L

Pinned at far end 0.75 I/L

Rotation as at near end (double curvature) 1.5 I/L

Rotation equal and opposite to that at near end (single

curvature) 0.5 I/L

General case. Rotation θa at near end and θb at far end (1 + 0.5θb/θa) I/L

Table 3.13 Effective beam stiffness coefficient (Eurocode 3)

Figure 3.30 Buckling length ratio l/L for a column in a non-sway mode (EC3)

Figure 3.31 Distribution factors for the case in exam (a); distribution factors for

continuous columns, EC3 (b)



For the case in exam we have (Figure 3.31a):

4600/268118751KKc 5829 mm3

5400/46875000.111K 868 mm3 (fixed at far end, Table 3.13)

02 mm3 (the base of the column is fixed)

From equation (3.16) we have:

86858295829

582958291 0.93

From Figure 3.30, considering η1=0.93 and η2=0 (see red point in Figure 3.30), a buckling length

l/L between 0.675 and 0.7 is obtained. We conservatively adopt the value 0.7. Thus, the effective

length of the member, to be introduced in equation (3.15), results:

7.046000L 3220 mm

From equation (3.15) the Euler buckling load results:

2

2

3220

2681187523000

3.115.1

1 EulN 392249 N

From equation (3.11) the value of coefficient kc results:

23000

70003.02

23000

70003.01

23000

45004

23000

70002 2

ck 2.05

From equation (3.10) the value of the critical stress in the compressed web results:

2

22

,2853.03.0112

302300005.2

w

axialklocf 472 MPa

From equation (3.9) the value of the critical stress of the flanges results:

2

,200

1545004

f

axialklocf 101 MPa

The design value of the local critical stress, computed through equation (3.7), results:



472,101min

3.115.1

1,

axialdlocf 68 MPa

From equation (3.6) the design value of the compression force that causes the local instability

results:

6814100,RdlocN 958800 N

From equation (3.14) the slenderness results:

958800

392249 1.56


2

56.11 2

1.72

From equation (3.12) coefficient k results:

22

256.165.072.172.1

56.165.0

1k 0.35

From equation (3.5) the value of 2,RdcN results:

, 2 0.35 958800c RdN 335580 N

Since 516706 N > 335580 N the verification is not satisfied. It would be necessary to adopt a stiffer

profile for the member. For example, adopting a 400x400x20 mm wide flange profile the critical

load would result about 590 kN (using the same value of the effective length) and the verification

would result verified.

The reported formulas are valid for the case of a double-T profile. For general cross-section types,

the value of 2,RdcN can be assumed.

locRdc

f

globRdcRdc NNN ,2,,2,2,

1,min

(3.18)



where globRdcN ,2, is the design value of the global buckling strength and locRdcN ,2, is the design value

of the local buckling strength.

The design value of the global buckling strength, globRdcN ,2, , can be computed as following (Bank

2006):

VL

Eul

EulglobRdc

AG

N

NN

1

,2,

where EulN is the Euler buckling load, defined in equation (3.15), LG is the design value of the

shear modulus and VA is the shear area of the cross-section.

For box-section profiles, if the webs and the flanges are considered as simply supported, their

buckling loads for unit length is (Kollar 2003, Tarjan et al 2010a-b):

ffff

f

SS

fcrx DDDDb

N 661222112

2

, 222

(3.19)

wwww

w

SS

wcrx DDDDb

N 661222112

2

, 222

(3.20)

In previous equations (3.19) and (3.20) subscripts f and w refer to the flange and to the web,

respectively, b is the width (see Figure 3.32) and 11D , 22D , 12D and 66D are elements of the

bending stiffness matrix D of a plate. For a plate consisting of a single orthotropic layer they are

given by R

hED

12

31

11 , R

hED

12

32

22 , 221212 DD , 12

312

66

hGD

where 12

2

12 /1 EER , h is the thickness of the plate, 12 is the Poisson’s ratio, 1E and 2E are

the Young’s moduli and 12G is the shear modulus.

The flange buckles first when (Kollar 2003, Tarjan et al 2010a-b):

w

SS

wcrxf

SS

fcrx NN 11,11, (3.21)



where 11 is the tensile compliance of plate. For a plate consisting of a single orthotropic layer:

hE 111 /1 (3.22)

In this case the webs elastically restrain the rotation of the flange as springs with constant given

from (Kollar 2003, Tarjan et al 2010a-b):

w

SS

wcrx

f

SS

fcrx

w

w

N

N

b

Dck

11,

11,221

(3.23)

with 2c .

The buckling load for unit length of the flange is then calculated with this spring constant using the

following expression:

26612

22211

2, /262.02139.412 yfcrx LDDDDN (3.24)

where yL is the width of the flange, 101/1 and yLkD /22 .

The web buckles first when:

w

SS

wcrxf

SS

fcrx NN 11,11, (3.25)

In this case the flanges restrain the rotation of the web, and the spring constant is (Kollar 2003,

Tarjan et al 2010a-b):

f

SS

fcrx

w

SS

wcrx

f

f

N

N

b

Dck

11,

11,221

(3.26)

with 2c .

The buckling load of the web is calculated with this spring constant by expression (3.27).

For C and Z-section profiles the local buckling loads of the flange, SS

fcrxN ,, and of the web,

SS

wcrxN , considered as simply supported, are computed as (Kollar 2003, Tarjan et al 2010a-b):



2

66

,

12

f

fSS

fcrxb

DN

(3.27)

wwww

w

SS

wcrx DDDDb

N 661222112

2

, 222

(3.28)

The flange buckles first when:

w

SS

wcrxf

SS

fcrx NN 11,11, (3.29)

In this case the web restrains the rotation of the flange (see Figure 3.32), and the spring constant is

given from equation (3.26), with 2c .

The buckling load of the flanges is calculated with this spring constant by the following

expressions:

2

2211, /12.41/17

16111.15yfcrx L

K

KDDN

when 1K (3.30)

22211, /1611.15 yfcrx LKDDN when 1K (3.31)

Where 22111266 /2 DDDDK , 55.322.71/1 and 126612 2/ DDD .


w

SS

wcrxf

SS

fcrx NN 11,11, (3.32)

In this case the flanges restrain the rotation of the edges of the web and the restraining torsional

stiffness is given as indicated in equation 3.33 (see Figure 3.32):

f

SS

fcrx

w

SS

wcrx

fftLN

NbDJG

11,

11,

66 14

(3.33)

The buckling load is then calculated by expression (3.27).



For L-section profiles the local buckling loads of the flange, SS

fcrxN ,, and of the web, SS

wcrxN ,,

considered as simply supported, are computed as (Kollar 2003, Tarjan et al 2010a-b):

2

66

,

12

f

fSS

fcrxb

DN

(3.34)

2

66

,

12

w

wSS

wcrxb

DN

(3.35)

The flange buckles first when:

w

SS

wcrxf

SS

fcrx NN 11,11, (3.36)

In this case the web restrains the rotation of the flanges (see Figure 3.32), and the restraining

torsional stiffness is given from:

w

SS

wcrx

f

SS

fcrx

wwtLN

NbDJG

11,

11,

66 14

(3.37)

The buckling load of the flange is calculated with this torsional stiffness by the following

expression:

26622, /12'/3 yfcrx LDDN when 1/'17.1 2211 DD (3.38)

26622112211, /12/'12.47 yfcrx LDDDDDN when 1/'17.1 2211 DD (3.39)

Where ty JGLD /' 22 .


w

SS

wcrxf

SS

fcrx NN 11,11, (3.40)

The buckling load is then calculated by expression (3.27).



Figure 3.32 Cross-sections of thin-walled members (Kollar 2003, Tarjan et al. 2010)

The buckling loads of the web and flange considered as simply supported (equations. 3.19, 3.20,

3.27, 3.28, 3.34, 3.35) can also be conservatively adopted. This approximation can result in a

critical load about 5% to 60% lower (Kollar 2003, Tarjan et al 2010a-b).

Instead of using the previously reported formulations, the critical load can be determined by

numerical-analytical procedures, imposing an initial imperfection, i.e. a displacement field

proportioned to the first critical mode.

In consideration of the viscoelastic behaviour of the pultruded FRP material, in buckling

verifications of members subjected to long-term loading it might be appropriate to adopt reduced

values of the elastic constants (see section 3.6.2.2).

3.6. SLS analysis

In the following the diagrams of the forces and moments in the four frames are reported, for the

different serviceability limit state load combinations, and the structural verifications are carried out

for some members. In particular, a verification of the stresses and a verification of the maximum

deflection are conducted. Only the diagrams in the x-z plane are considered. The structural

verifications are based on the indications given in (CNR-DT205/2007).


In the following every figure shows the forces and moment diagrams of the structure subjected to

the different load combination in x- and y-direction, see Table 3.4. In every scheme the most

stressed member is evidenced by a black circle and the related value of the internal action is

indicated for the specific frame detailed in Figure 3.1.




Frame 1 = -269kN

Frame 1 = -289kN





Figure 3.33 Rare load combination, axial force diagrams

Frame 1 = -244kN

Frame 1 = -261kN





Figure 3.34 Frequent load combination, axial force diagrams

Frame 1 = -236kN

Frame 1 = -253kN





Figure 3.35 Quasi-permanent load combination, axial force diagrams




Frame 1 =

49477kNmm

Frame 1 =

49479kNmm

Frame 2 =

92610kNmm

Frame 2 =

92611kNmm

Frame 3 =

92611kNmm

Frame 3 =

92610kNmm

Frame 4 =

49479kNmm

Frame 4 =

49477kNmm


Figure 3.36 Rare load combination, bending moment diagrams

Frame 1 =

44101kNmm

Frame 1 =

44102kNmm

Frame 2 =

81853kNmm

Frame 2 =

81853kNmm

Frame 3 =

81853kNmm

Frame 3 =

81853kNmm

Frame 4 =

44103kNmm

Frame 4 =

44101kNmm


Figure 3.37 Frequent load combination, bending moment diagrams

Frame 1 =

42309kNmm

Frame 1 =

42310kNmm

Frame 2 =

78267kNmm

Frame 2 =

78267kNmm

Frame 3 =

78267kNmm

Frame 3 =

78267kNmm

Frame 4 =

42310kNmm

Frame 4 =

42309kNmm


Figure 3.38 Quasi-permanent load combination, bending moment diagrams




Frame 1 = 54kN

Frame 1 = 54kN





Figure 3.39 Rare load combination, shear force diagrams

Frame 1 = 48kN

Frame 1 = 48kN





Figure 3.40 Frequent load combination, shear force diagrams

Frame 1 = 46kN

Frame 1 = 46kN





Figure 3.41 Quasi-permanent load combination, shear force diagrams




Frame 1 =

0.3kNmm

Frame 1 =

0.4kNmm

Frame 2 =

0.01kNmm

Frame 2 =

0.03kNmm

Frame 3 =

0.02kNmm

Frame 3 =

0.005kNmm

Frame 4 =

0.3kNmm

Frame 4 =

0.3kNmm


Figure 3.42 Rare load combination, torsional moment diagrams

Frame 1 =

0.3kNmm

Frame 1 =

0.3kNmm

Frame 2 =

0.02kNmm

Frame 2 =

0.03kNmm

Frame 3 =

0.02kNmm

Frame 3 =

0.009kNmm

Frame 4 =

0.3kNmm

Frame 4 =

0.3kNmm


Figure 3.43 Frequent load combination, torsional moment diagrams

Frame 1 =

0.3kNmm

Frame 1 =

0.3kNmm

Frame 2 =

0.02kNmm

Frame 2 =

0.03kNmm

Frame 3 =

0.02kNmm

Frame 3 =

0.01kNmm

Frame 4 =

0.3kNmm

Frame 4 =

0.4kNmm


Figure 3.44 Quasi-permanent load combination, torsional moment diagrams



3.6.2. Verification of elements

3.6.2.1. Stresses

A verification of the compressive stress induced by the axial force and the bending moment is

carried out for the column evidenced in Figure 3.45.

Frame 3

-182,513

N

Frame 3

57,139,508

Nmm

axial force diagram bending moment diagram

Wind in x-direction

Figure 3.45 Quasi-permanent load combination; axial force and bending moment diagrams

It must be verified that the design value of the stress, Sdf , is lower than the limit value, Rdf ,

defined as follows (CNR-DT205/2007):

f

RkRd

ff

(3.41)

where is the conversion factor, Rkf is the characteristic value of the corresponding strength

component and f is the partial coefficient of the material.

The conversion factor η is the product of the environmental factor ηe and of the one related to the

long-term effects, ηl.

The mechanical properties of FRP profiles can be degraded in presence of certain environmental

conditions: alkaline environment, humidity, extreme temperatures, thermal cycles, ultraviolet

radiations. In aggressive environments the value of the environmental factor ηe can be assumed

equal to 1 if appropriate protective coatings are used. Otherwise the value of ηe must be

conveniently reduced, also in relation to the design life.

The mechanical properties of FRP profiles can also be degraded due to rheological phenomena

(creep, relaxation, fatigue). Values of the conversion factor ηl for long-term actions and for cyclic



loading (fatigue) are reported in Table 3.14. In presence of both long-term and cycling loading the

overall conversion factor is obtained by the product of the two related conversion factors.

Type of loading (SLS) (ULS)

Quasi-permanent loading 0.3 1.0

Cyclic loading (fatigue) 0.5 1.0

Table 3.14 Values of the conversion factor for long-term effects

The compressive stress induced by the axial force is:

14100

182513,

A

Nf Sd

axialSd 13 MPa

The compressive stress induced by the bending moment is:

1141050

57139508,

W

Mf Sd

bendingSd 50 MPa

The total compressive stress in the column results:

5013,, bendingSdaxialSdSd fff 63 MPa


1

2203.01Rdf 66 MPa

Since Rdf is higher than Sdf the verification is satisfied.

3.6.2.2. Deformations

For the beam evidenced in Figure 3.46 a verification of the deflection is carried out.

Figure 3.46 The beam for which the deflection analysis is carried out



The deflection of members must be evaluated taking into account the contributions due to flexural

and shear deformability.

Deflection limits are reported in Table 3.15. In order to take into account the creep behaviour of the

material, the evaluation of the displacements for the quasi-permanent load condition must be

conducted adopting reduced values of the elastic constants, with respect to a time equal to the

design working life of the structure (CNR-DT205/2007).

Values of the elastic and shear moduli at time t, for a load applied at t=0, can be computed as:

t

EtE

E

LL

1 (3.42)

t

GtG

G

LL

1 (3.43)

In serviceability limit state, SLS, the action load can be calculated in relationship with the values for

the transversal deflection η assumed as limitation in design, Tables 3.16 and 3.17.

The values of the creep coefficient for the longitudinal strains, tE , and for the shear strains,

tG , are reported in Table 3.15.

t (time from the application of the load) tE tG

1 year 0.26 0.57

5 years 0.42 0.98

10 years 0.50 1.23

30 years 0.60 1.76

50 years 0.66 2.09

Table 3.15 Creep coefficient for longitudinal and shear strains (CNR-DT205/2007)

Quasi-permanent load combination δmax Floors in presence of plasters, non-flexible partition walls or other brittle finishing

materials L/500

Floors without previous limitations L/250 Rare load combination δmax Footbridges or other structures with an high ratio between accidental and permanent loads L/100

Table 3.16 Recommended deflection limits (CNR-DT205/2007)

In Table 3.17 (Clarke 1996) η is presented as ηmax and η1. ηmax is the maximum deflection while η1

is the variation of deflection due to the variable loading increased by time dependent deformations

due the permanent load.



Typical conditions Limiting values for the vertical deflection

ηmax η1

Walkways for occasional non-public access Length/150 Length/175

General non-specific applications Length/175 Length/200

General public access flooring Length/250 Length/300

Floors and roofs supporting plaster or other brittle

finish or non-flexible partitions Length/250 Length/350

Floors supporting columns (unless the deflection

has been included in the global analysis for the

ultimate limit state)

Length/400 Length/450

Where δmax can impair the appearance of the

structure Length/250 -

Table 3.17 Recommended limiting values for deflection in SLS (Clarke 1996)

In Table 3.18 the formulas for the computation of the maximum deflection η of beams taking into

account the shear deformability are reported for some common support and loading conditions.

a

VLL AG

Lq

IE

Lq

28

24

max e

VLL AG

Lq

IE

Lq

6384

24

max

b

VLL AG

LF

IE

LF

3

3

max f

VLL AG

LF

IE

LF

4192

3

max

c

VLL AG

Lq

IE

Lq

8384

5 24

max

g

VLL AG

aFaL

IE

aF

68

22

max

d

VLL AG

LF

IE

LF

448

3

max

Table 3.18 Maximum deflection η of beams with the shear effects.

The considered beam is subjected to a total distributed load q of 31 N/mm in the quasi-permanent

load combination.

Assuming a design working life of 50 years we have, from equations (3.42) and (3.43) and from

Table 3.18:

66.01

23000tEL 13855 MPa



09.21

4500tGL 1456 MPa

Assuming for the considered beam the static scheme e) of Table 3.18 we have:

400014566

540031

3140000013855384

540031 24

maxd 184 mm

The computed deflection results significantly larger than the limit of L/250 (22 mm). Adopting, for

example, a 500x250x20 mm I-profile the maximum deflection would result 17 mm and the

verification would be satisfied.

3.7. Joint's verification

The verification of the joint represented in Figure 3.47 is carried out in the following. In particular,

the verification is carried out for the truss evidenced in the figure, subjected to axial tension. The

joint is realized using 14 mm diameter steel bolts that connect the pultruded FRP truss to a

laminated FRP plate. The member has a built-up cross-section realized by 2 U 200x60x10 mm. The

verification is carried out on base of the indications reported in CNR-DT205/2007.

Figure 3.47 Detail of joint (dimensions in millimetres), L’Aquila 2010 (p. 20)

In the case of bolted connections the forces acting on every single bolt can’t be evaluated though

simple equilibrium criteria, as it is usual in the case of ductile materials.



In general, the bolted connections should meet the following requirements: 1) the barycentric axes

of the structural elements should be converge in the same point; 2) with shear action, all bolts must

have the same diameter and at least two of them must be arranged in the direction of the load; 3)

stiffer washers should be placed under the bolt head and the nut; 4) the bolt torque should be such

as to ensure an adequate diffusion of the stresses around the hole; 5) the tightening of the bolts

should be take into account the compressive strength of the profile in the direction orthogonal to

fibres. The fastening torque must be appropriate to the diameter and class of the bolts; the

manufacturers recommend 20-25 Nm.

The geometrical limitations for the bolted connections are summarized in Table 3.19.

Bolts diameter tmin ≤ db ≤ 1.5 ∙ tmin

Holes diameter d ≤ db + 1 mm

Washers diameter dr ≥ 2 ∙ db

Distance between holes wx ≥ 4 ∙ db; wy ≥ 4 ∙ db (Figure 3.48-A)

Distance from the end of the plate e/db ≥ 4; s/db ≥ 0.5 ∙ (wy/db) (Figure 3.48-A)

Table 3.19 Geometrical limitations in bolted connections (CNR-DT205/2007)

Where: db = diameter of the bolts; tmin = thickness of the thinnest joined element; d = diameter of

hole; dr = external diameter; wx and wy = distances between the centre of the holes (Figure 3.48-A);

e = distance of the bolt from the end of the plate in the direction of the force; s = distance of the bolt

from the edge in the direction orthogonal to the force.

In the case in which the resultant of the applied external forces passes through the centroid of the

bolting (Figure 3.48-B), it is possible to assign to the bolts forces that are proportional to the

coefficients reported in Table 3.20 (CNR-DT205/2007).

Number of rows row 1 row 2 row 3 row 4

1 FRP/FRP 120 %

FRP/metal 120 %

2 FRP/FRP 60 % 60 %

FRP/metal 70 % 50 %

3 FRP/FRP 60 % 25 % 60 %

FRP/metal 60 % 30 % 30 %

4 FRP/FRP 40 % 30 % 30 % 40 %

FRP/metal 50 % 35 % 25 % 15 %

> 4 Not recommended

Table 3.20 Shear force distribution coefficients in every bolts row in a bolted connection (CNR-

DT205/2007)



3.7.1. Net-tension failure of the plate

The verification, with respect to normal stresses, of the resisting cross section of the plate weakened

due to the presence of the holes results satisfied if the following limitations are respected (CNR-

DT205/2007):

- tensile stress parallel to the fibres direction (Figure 3.48-Ca):

tdnwfV RdLt

Rd

Sd ,

1

(3.44)

- tensile stress orthogonal to the fibres direction (Figure 3.48-Cb):

tdnwfV RdTt

Rd

Sd ,

1

(3.45)

where Rd is the partial coefficient of the model, assumed equal to 1.11 for cross-sections with

holes, SdV is the force transmitted from the bolts to the plate, RdLtf , and RdTtf , are, respectively, the

design value of the tensile strength of the material in the direction parallel to fibres and in the

direction orthogonal to the fibres, t is the thickness of the element and n is the number of holes.

For the case in exam, since we have two bolt rows, the shear force in every row results, from Table

3.20, 6.0136961SdV 82177 N

From equation (3.44) we obtain:

2014220026811.1

1 830559 N > 82177 N

so the verification is satisfied.



3.7.2. Shear-out failure of the plate

The verification with respect to the shear-out failure mode (Figure 3.48-D) results satisfied if the

following limitation is respected (CNR-DT205/2007):

tdefV RdVSd 2, (3.46)

where RdVf , is the design value of the shear strength of the FRP element.

For the case in exam we have, from equation (3.46):

201490227 89640 N > 82177 N


3.7.3. Bearing failure of the plate

In the verification with respect to the bearing failure of the plate, the mean value of the pressure

exerted by the bolt shank on the walls of the hole must satisfy the following limitations (CNR-

DT205/2007):

- stress parallel to the fibres direction (Figure 3.48-Ea):

tdfV bRdLrSd , (3.47)

- stress orthogonal to the fibres direction (Figure 3.48-Eb):

tdfV bRdTrSd , (3.48)

where RdLrf , and RdTrf , are, respectively, the design value of the bearing strength of the material in

the directions parallel and orthogonal to the fibres.

For the case in exam we have, from equation (3.47):

20214147 82320 N > 82177 N




(A) Bolted connection (CNR-DT205/2007)

(B) Arrangement of the bolts rows in a bolted connection between two FRP plates or between a

FRP plate and a metal one. The resultant of the external forces passes through the centroid of the

bolting (CNR-DT205/2007)

(C) Net-tension failure mode (CNR-DT205/2007)

(D) Shear-out failure mode (CNR-DT205/2007)

(E)_Bearing failure mode (CNR-DT205/2007)

Figure 3.48 Verification of the joints; schemes reported in CNR-DT205/2007

Figure 3.49



3.7.4. Shear failure of the steel bolt

The verification with respect to the shear failure of the steel bolt results satisfied if the following

limitation is respected (CNR-DT205/2007):

bRdVbSd AfV , (3.49)

where RdVbf , represents the design value of the shear strength of the bolt, as defined in current

standards, and Ab is the resistance area of the cross-section of the bolt.

For the case in exam we have:

25.1

8006.06.0

2

,

M

ubRdVb

ff

384 MPa

In previous equation ubf is the tensile strength of the bolt and 2M is the partial safety factor.

Since the shear force acting on every bolt is 2/82177SdV 41089 N, we have, from equation

(3.49):

115384 44160 N > 41089 N


3.8. References

Ascione, L., Giordano, A. and Spadea, S., Lateral buckling of pultruded FRP beams, Composites

Part B: Engineering, 42 4, 2011, 819-824.

Ascione, L., Berardi, V.P., Giordano, A. and Spadea, S., Buckling failure modes of FRP thin-

walled beams, Composites Pt B: Engineering, 47, 2013, 357-364. DOI:

10.1016/j.compositesb.2012.11.006

Ascione, L. Berardi, V.P., Giordano, A. and Spadea, S., Local buckling behavior of FRP thin-

walled beams: A mechanical model, Composite Structures, 98, 2013, 111–120.

Ascione, L., Berardi, V.P. and Spadea, S., Macro-scale analysis of local and global buckling

behavior of T and C composite sections, Mechanics Research Communications (Special Issue), 58,

2014, 105-111. http://www.sciencedirect.com/science/article/pii/S0093641313001614

Ascione, L., Berardi, V.P., Giordano, A. and Spadea, S., Pre-buckling imperfection sensitivity of

pultruded FRP profiles, Composites Part B – Engineering, 72, 2015, 206-212.

Bank LC. Composites for construction-structural design with FRP materials, John Wiley & Sons,

NJ, 2006.



Bartbero, E.J., De Vivo, L., Beam-Column Design Equation for Wide-Flange Pultruded Structural

Shapes, Journal of Composite for Construction, Vol. 3, n. 4 (1999), pp. 185-191.

Boscato, G., and Russo, S. Dissipative capacity on FRP spatial pultruded structure, Composite

Structures, 2014; Volume 113(7), p.339–353.


Clarke JL. (Ed.). EUROCOMP design code and handbook: Structural design of polymer

composites, E & FN Spon, London, 1996.

CNR-DT205/2007 Guide for the design and constructions of structures made of FRP pultruded

elements, National Research Council of Italy, Advisory Board on Techincal Recommendations.


Creative pultrusions design guide,’ Creative Pultrusions, Inc., Alum Bank, Pa, 1988.

Engesser, F. (1889). “Ueber die Knickfestigkeit gerader Stabe”, Zeitschrift für Architekter und

Ingenieurwsen, 35(4), 455-462 (in German).

Eurocode 1: Basis of structural design. EN 1990:2002 (E)

Eurocode 3: Design of steel structures - Part 1-1: General rules. ENV 1993-1-1: 1992. Incorporating

Corrigenda February 2006 and March 2009.


rules for buildings. EN1998-1:2004 (E),: Formal Vote Version (Stage 49), 2004.

Feroldi, F. and Russo, S. (2016). Structural Behavior of All-FRP Beam-Column Plate-Bolted

Joints. J. Compos. Constr. ,10.1061/(ASCE)CC.1943-5614.0000667, 04016004.

Girão Coelho, A.M. and Mottram, J.T., ‘A review of the behaviour and analysis of mechanically

fastened joints in pultruded fibre reinforced polymers,’ Materials & Design, 74, (2015), 86-107.

ISSN: 0261-3069

Girão Coelho, A.M., Mottram J.T. and Harries, K.A., Bolted connections of pultruded GFRP:

Implications of geometric characteristics on net section failure, Composite Structures, 131, (2015),

878-884. http://dx.doi.org/10.1016/j.compstruct.2015.06.048

Mottram, J.T., Lateral-torsional buckling of thin-walled composite I-beams by the finite difference

method, Composites Engrg., 2 2, 1992, 91-104.

Mottram, J.T., Lutz, C., and Dunscombe, G.C., Aspects on the behaviour of bolted joints for

pultruded fibre reinforced polymer profiles, International Conference on Advanced Polymer

Composites for Structural Applications in Construction (ACIC04), Woodhead Publishing,

Cambridge, 348-391.



Pecce, M. and Cosenza, E., Local buckling curves for the design of FRP profiles, Thin-Walled

Structures, 37 3, 2000, 207-222.

Pecce, M. and Cosenza, E., FRP structural profiles and shapes, in Wiley. Encyclopedia of

Composites, 2012 - Wiley Online Library.

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Poursha M, Khoshnoudiana F, Moghadam A.S. A consecutive modal pushover procedure for

estimating the seismic demands of tall buildings. Engineering Structures 31 (2009) 591_599.

Poursha M, Khoshnoudiana F, Moghadam A.S. A consecutive modal pushover procedure for

nonlinear static analysis of one-way unsymmetric-plan tall building structures. Engineering

Structures 33 (2011) 2417–2434.

Priestley M.J.N., Calvi, M.C., and Kowalsky, M.J. (2007) Displacement-Based Seismic Design of

Structures IUSS Press, Pavia, 670 pp.

Russo, S., Experimental and finite element analysis of a very large pultruded FRP structure

subjected to free vibration, Compos. Struct., 2012; 94(3): 1097–1105.

SAP2000 Advanced v. 10.1.2. Structural Analysis Program, Computers and Structures, Inc., 1995

University Ave, Berkeley, CA.

Kollar L.P., Local Buckling of Fiber Reinforced Plastic Composite Structural Members with Open

and Closed Cross Section. Journal of Structural Engineering, ASCE, 2003. 129: 1503-1513.

Tarjan, G., Sapkas, A. and Kollar, L.P. Local Web Buckling of Composite (FRP) Beams. Journal of

Reinforced Plastics and Composites, Vol. 29, No. 10/ 2010.

Tarjan, G., Sapkas, A. and Kollar, L.P. Stability Analysis of Long Composite Plates with

Restrained Edges Subjected to Shear and Linearly Varying Loads, J. of Reinf. Plastics and Comp.,

Vol. 29, No. 9/ 2010.

Turvey GJ, Cooper C. Review of tests on bolted joints between pultruded GRP profiles.

Proceedings of the Institution of Civil Engineers Structures & Buildings 157, June 2004 Issue SB3.

p. 211–233.

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http://www.sciencedirect.com/science/journal/02638223

http://www.sciencedirect.com/science/journal/02638223/94/3



4. FINAL EVALUATION FOR DESIGN OF FRP STRUCTURES IN SEISMIC ZONE

Overview

The absence of specific calculation codes for the seismic design of FRP structures implies that the

most restrictive parameters must be taken. The behaviour factor q is calibrated with the real material

characteristics and structural types (therefore with q = 1 and damping coefficient ζ=5%, as

suggested by Eurocode 8 (2004) and NTC08 (2008)); this leads to a conservative calculation

approach.

The low density of the FRP material (1700-1900 kg/m³) is a fundamental point in seismic design,

since it brings a spontaneous reduction of the seismic actions and a limited participating mass and

acceleration.

This feature must be opportunely managed in the design phase by adopting appropriate boundary

conditions at the base and/or stabilizing loads at different heights, to withstand the horizontal

displacements.

On the basis of some researches (Boscato and Russo 2014) the low frequencies of the vibration

modes and the limited dissipation capacity of FRP structures (1.5<ζ<2) must be accounted for, with

reference to the seismic characteristics of the soil.

The increment of flexural deformability with the height of FRP structures tends to increase the

period of vibration T0.



Figure 4.1. Fundamental period of RC, Steel and FRP structures (detail A)

The fundamental periods T0 (Sheet 3) of different FRP structures have been compared with

traditional materials, such as RC (Reinforced Concrete) and Steel, in Figure 4.1.

As regards the FRP structures two T0-height relationships are experimental values (labeled EXP),

while the others have been calculated by numerical model. The best linear relation concerns the RC

structures having the R2 (coefficient of determination) value closest to 1, while for FRP and steel

the R2

value is less than 0.5 highlighting the scattering of results due to the high variability of the

mechanical-physical-geometrical characteristics. The linear regressions of FRP and steel structures

show the tendency to high period of vibration due to the greater deformability of these structures

with respect to RC buildings.

When an earthquake’s PGA (Peek Ground Acceleration) happens along a period shorter than 0.5 s,

FRP structures - that are characterized by a long vibration period - keep on moving in free

vibrations that slowly damp and avoid resonance between the time-delayed response of the structure

and the fast one of stiff types of soil (i.e. A and B types).

Since that the high deformability could be faced with an over dimensioning of the FRP elements

and so over passing the above prudential approach a detailed preliminarily Design by Testing phase

is judged necessary, to assess the parameters and coefficients that identify the dynamic structural

response of FRP structures.



The results of the first study conducted on the damping value of the mono-dimensional elements

(Boscato 2011, Boscato and Russo 2009) and of the FRP structures (Boscato and Russo 2014) are

particularly interesting when compared with the values recorded in the following table defined by

Chopra (1995) and Newmark and Hall (1982) which refers to traditional materials, Tables 4.1 and

4.2.

Structure typologies and boundary conditions ζ

Structures with elements below of 50% than elastic limit

RC Structures with first cracks

RC Prestressed Structures

Welded steel structures

2-3%

RC Structures cracked 3-5%

Bolted or nailed steel structures

Bolted or nailed wood structures 5-7%

Structures with elements near to elastic limit

RC Prestressed Structures without pretension loss

Welded steel strutures 5-7%

RC Prestressed Structures

RC Structures 7-10%

Bolted or nailed steel structures

Bolted wood structures 10-15%

Nailed wood structures 15-20%

Masonry structures

Normal masonry structures 3%

Reinforced masonry structures 7%

Table 4.1. Damping coefficients ζ; Chopra (1995) and Newmark and Hall (1982)

Structure typologies and boundary conditions ζ

Members

Columns with fixed boundary conditions 2.5%

Beams with supported boundary conditions 2.5-3.5%

Structures

Structures with bolted beam-column connections 1.3%

Table 4.2. Damping coefficients ζ for pultruded FRP elements and structures

Nevertheless, in the design phase, the structure’s maximum displacements must be evaluated with

reference to the design earthquake and thus to the soil characteristics. For such highly deformable

structures, the absolute displacement of the whole mass is null under the inertial force, while the

relative displacement referred to the soil is maximum and opposite.

General recommendations

This document contains general rules for earthquake-resistant design of FRP buildings and should

be used in conjunction with CNR-DT205/2007, CEN TC250 WG4L and Sections 2 to 4 of EN

1998-1 and, finally, Chapter 7 of NTC08.

For the performance requirements and compliance criteria of structures, Section 2 of EN 1998-1

and NTC08 should be applied.



For the ground conditions and seismic action, Section 3 of EN 1998-1 and Chapter 3.2 of NTC08

must be applied.

For the general rules of design of structures, Section 4 of EN 1998-1 and Chapter 7 of NTC08

should be taken into account.

Design concepts

Earthquake resistant pultruded FRP structures should be designed in accordance with one of the

following design concepts (Table 4.3):

a) Low-dissipative structural behaviour for conservative approach

b) Dissipative structural behaviour

Design concept Structural Ductility Class a) Low dissipative structural

behaviour DCL (Low)

b) Dissipative structural behaviour DCM (Medium)

DCH (High)

Table 4.3. Structural ductility classes (EC8, EN 1998-1:2004)

In design concept a) the action effects may be calculated on the basis of an elastic global analysis

without taking into account the dissipative behaviour of pultruded FRP structure offered by bolted

joints. In the case of irregularity in elevation the behaviour factor q should be corrected as indicated

in §2.2.5.3 but it needs to be taken smaller than minimum value. The resistance of the members and

of the connections should be assessed in accordance with CNR-DT205/2007 and NTC08. The

capability of parts of the structure to resist earthquake actions out of their elastic range is taken into

account. A structure belonging to a given ductility class should meet specific requirements in one or

more of the following two aspects: structural type and rotational capacity of connections.

In design concept b) the capability of parts of the structure to resist and dissipate the earthquake

actions through the strength hierarchy criteria is taken into account. Structures designed in

accordance with design concept b) should belong to structural ductility classes DCM or DCH.

These classes correspond to increased ability of the structure to dissipate energy through

mechanisms that involve the global structure. Depending on the ductility class, specific

requirements in one or more of the following aspects should be met: global geometry, strength

hierarchy criteria and rotational capacity of joints and connections.

Structural types

All-FRP buildings should be assigned to one of the structural types outlined in EN 1998-1, Section

6.3 according to the behaviour of their primary resisting structure under seismic actions:



a) Moment resisting frame (see EN 1998-1, Section 6.3);

b) Frames with concentric bracings (see EN 1998-1, Section 6.3);

d) Moment resisting frames combined with concentric bracings (see EN 1998-1, Section 6.3);

e) Structures with stiff cores or walls (see EN 1998-1, Section 6.3).

Behaviour factor

For regular pultruded FRP structures the behaviour factor q is listed in Table 4.4.

Structural Ductility Class Behaviour factor q DCL (Low) 1

DCM (Medium) 1-1.5 DCH (High) >1.5

Table 4.4. Behaviour factors

For non-regular structures in elevation (see EN 1998-1, Section 4.2.3.3) the q-values listed in Table

5.2 should be reduced by 20%, but don’t need to be taken lower than q=1.

For structures having different and independent properties in the two horizontal directions, the q

factors to be used for the calculation of the seismic action effects in each main direction should

correspond to the properties of the structural system in the analyzed direction and then can be

different.

A conservative design approach is adopted in the manual with the consequence upon the choice of

the force reduction factor and of the damping coefficients required to define the response spectra.

Advices and precautions

In absence of ductile behaviour for brittle failure of pultruded FRP material, the ratio between the

residual strength after degradation and the initial one should be taken into account. The global

dissipative response of aforementioned design concept b is assumed to be due to the progressive

response of different parts involved by consecutive failure mechanisms through the strength

hierarchy criteria. Moment resisting frames combined with concentric bracings are recommended in

FRP structures to withstand horizontal actions. Dissipative zones should be located in joints and

connections, whereas the pultruded FRP members themselves should be regarded as behaving

elastically. The damage propagation in FRP pultruded bolted joints could be taken into account

through a design by testing at the preliminary phase.



With soil classes of low stiffness (C, D or E classes, see Eurocode 8 and NTC08), the constant

acceleration branch of the spectrum (from Tb to Tc) - and thus also the soil’s fundamental period of

resonance - increases. Taking into account the high vibration periods of FRP structures (about

>0.65 s), the design in presence of soils with a large frequency band of the acceleration plateau

must address the increase in eigenfrequencies (with a stiffness increase by inserting bracings) or the

increase in participating mass to avoid resonance in the soil-to-structure interaction.

The seismic design must account above all for second order phenomena that regard particularly

FRP members. Besides, dynamic actions induce member stress inversion that must be carefully

evaluated with reference to the high deformability of the material and to the higher vulnerability

(weakness) of FRP profiles in compression than in tension.

Even if not yet defined from clear rules and recommendations, the high deformability of FRP

structures suggests to limit the framed building to 2-3 floors with an interstory height of circa

3meters; this is due in order to exalt a conservative approach while waiting for more studies

especially on full size FRP structures.

The results of the verifications put in evidence some of the critical aspects of the structural

behaviour of pultruded FRP profiles. In particular, deformation and buckling limit states, rather than

material strength limits, frequently govern the design of FRP structural shapes because of their low

moduli and anisotropic behaviour. Moreover, the high shear deformability of the pultruded material

can also have a significant influence on the buckling behaviour. In fact, for the examined case, the

compression buckling check didn’t result satisfied, as well as the deflection check at the

serviceability limit state. Another critical aspect can regard the verification of the shear stress. In

fact, the shear response of pultruded FRP profiles is governed by the resin’s characteristics,

resulting in relatively low shear strength of the composite material. On the contrary, the material

performance in the longitudinal direction mostly depends on the fibre's characteristics, thus showing

very high values of the compressive and, especially, tensile strength.

Design strategies for enhanced seismic performance

For design purposes in order to achieve a dissipative response the following basic conditions must

be satisfied:

- base column connections, beam-to-column joints and bracing details must be designed in order to

sustain the anticipated cyclic deformation demand, without strength degradation or local failure, so

that the lateral strength and dissipative capacity is maintained during the seismic action;



- a specific over-strength of structural elements and strength hierarchy must be taken into account in

order to preserve the structural integrity under seismic action;

- only the concentrically braced configuration assures a better dynamic response of the frame. The

moment resisting frame must be solved with an over-strength design of structural elements and

joints. The combination of aforementioned configurations - moment resisting frame and concentric

bracings - guarantees a better seismic behavior both in term of resistance and dissipative capacity

through the interactive response;

- failure mechanisms triggered by local buckling and net section fracture preclude the global ductile

behavior. Mitigation of all potentially undesirable failure modes through appropriate detailing is

required to achieve good seismic performance;

- with regard to the FRP structure, characterized by elastic-brittle material, it is important to design

the collapse mechanism at the desired locations prior to the occurrence of other failure modes;

- the global second order effects (P-Δ) must be taken into account in the design phase to avoid the

amplification of drift. Considering the low self-weight these structures must possess sufficient

lateral stiffness and strength to control the deformation demand from earthquake;

- phases of progressive damage under repeated loading can be taken into account in design stage to

provide a global ductile response;

- several structural configurations can be adopted to reduce the seismic loads: moment resisting

frame MRF with dissipative point in beam-to-column joint, combination with shear walls,

concentrically braced frames CBF, buckling-restrained frames, eccentrically braced frames;

- frames with concentric V-bracings should be avoided. This configuration makes the beams work

in shear, then in the weakest direction.



4.1. References

Bernal D, Kojidi SM, Kwan K, Döhler M, 2010. Damping identification in buildings from

earthquake records. SMIP12 SEMINAR PROCEEDINGS.

G. Boscato, S. Russo (2009). Free Vibrations of Pultruded FRP Elements: Mechanical

Characterization, Analysis, and Applications. ASCE Journal of Composite for Construction, 13 (6),

pp. 565-574.

Boscato G. (2011). Dynamic behaviour of GFRP pultruded elements. Published by University of

Nova Gorica Press, P.O. Box 301, Vipavska 13, SI-5001 Nova Gorica, Slovenia. ISBN 978-961-

3611-68-7.

Boscato, G., and Russo, S. Dissipative capacity on FRP spatial pultruded structure, Composite

Structures, 2014; Volume 113(7), p.339–353.






54225-1 doi:10.2788/22306






rules for buildings. EN1998-1:2004 (E),: Formal Vote Version (Stage 49), 2004.

Gallipoli M.R., Mucciarelli M., Šket-Motnikar B., Zupanćić P., Gosar A., Prevolnik S., Herak M.,

Stipčević J., Herak D., Milutinović Z., Olumćeva T., (2012). Empirical estimates of dynamic

parameters on a large set of European buildings, Bulletin of Earthquake Engineering, 8, pages: 593

– 607.

Newmark, N.M., Hall, W.J., Earthquake spectra and design, Earthquake Engineering Research

Institute, Berkeley, California, 1982.



http://scholar.google.it/citations?user=uFgVU_oAAAAJ&hl=it&oi=sra

http://scholar.google.it/citations?user=yHc1izoAAAAJ&hl=it&oi=sra

http://conservation.ca.gov/cgs/smip/docs/seminar/SMIP12/Documents/P3_Paper_Bernal_Others.pdf

http://conservation.ca.gov/cgs/smip/docs/seminar/SMIP12/Documents/P3_Paper_Bernal_Others.pdf

http://www.sciencedirect.com/science/journal/02638223/113/supp/C




4.2. Symbols

Station = output station

COMB = load combination

SdN = design value of the acting normal force

SdV ,2 = design value of the acting shear force in direction 2

SdV ,3 = design value of the acting shear force in direction 3

SdT = design value of the acting torsional moment

SdM ,2 = design value of the acting bending moment around axis 2

SdM ,3 = design value of the acting bending moment around axis 3

Shape = cross-section shape

t3 = height of the cross-section

t2 = width of the cross-section

tf = thickness of the flange

tw = thickness of the web

A = area of the cross-section

tI = torsional constant

33I = moment of inertia with respect to axis 3

22I = moment of inertia with respect to axis 2

2SA = shear area in direction 2

3SA = shear area in direction 3

33W = section modulus with respect to axis 3

22W = section modulus with respect to axis 2

1E = longitudinal elastic modulus in direction 1

2E = transverse elastic modulus in direction 2

3E = transverse elastic modulus in direction 3



12G = shear modulus in direction 1-2



12 = Poisson ratio in direction 1-2



e = environmental factor (default = 1)

ULSl , = factor related to the long-term effects for ultimate limit states (default = 1) (see Table

5.1)

SLSl , = factor related to the long-term effects for serviceability limit states (default = 0.3) Table

5.1)

Type of loading SLSl , ULSl ,

Quasi-permanent loading 0.3 1.0

Cyclic loading (fatigue) 0.5 1.0

Table 5.1 Values of the conversion factor for long-term effects

ULSf ,1 = partial coefficient of the material related to the uncertainty level in the determination

of the material properties for ultimate limit states (default = 1.15) (see Table 5.2)

SLSf ,1 = partial coefficient of the material related to the uncertainty level in the determination of

the material properties for serviceability limit states (default = 1) (see Table 5.2)

ULSf ,2 = partial coefficient of the material related to the brittle behavior for ultimate limit

states (default = 1.3) (see Table 5.2)

SLSf ,2 = partial coefficient of the material related to the brittle behavior for serviceability limit

states (default = 1) (see Table 5.2)

Value of the coefficient of

variation for the material

properties Vx ULSf ,1 SLSf ,1 ULSf ,2 SLSf ,2

Vx ≤ 0.10 1.10 1.0 1.3 1.0

0.10 < Vx ≤ 0.20 1.15 1.0 1.3 1.0

Table 5.2 Values of the partial coefficient of the material

Rd = partial coefficient that takes into account the uncertainties related to the mechanical

model (default = 1.11)

t = target time for long-term deformations verifications (default = 0) (see Table 5.3)



Structural type t (years)

Temporary structures 10

Ordinary structures 50

Table 5.3 Target time for deformation verifications of different structural types

ktf , = characteristic value of the longitudinal tensile strength of the material (default = 250)

kcf , = characteristic value of the longitudinal compressive strength of the material (default =

250)

kVf , = characteristic value of the shear strength of the material (default = 35)

LcE = longitudinal elastic modulus in compression (default = 1E )

TcE = transversal elastic modulus in compression (default = 2E )

c = coefficient used for the stability verifications of double-T profiles (default = 0.65)

effE = effective longitudinal elastic modulus (default = 1E )

effG = effective shear modulus (default = 12G )

n = number of holes (default = 0)

d = diameter of holes (default = 0)

t = thickness of the profile (default = 0)

cK = multiplicative coefficient of the length of the member, for stability verifications in

compression (default = 1) (see Table 5.4)

1st extremity support

condition

2nd

extremity

support condition cK

Fixed Free 2

Hinged Hinged 1

Fixed Hinged 0.8

Fixed Fixed 0.7

Table 5.4 Values of coefficient cK for single structural members. For members of a frame the

value of cK should be evaluated as indicated in Eurocode 3

qz = coordinate of the point of application of the load with respect to the center of gravity of

the cross-section (default = t3/2)

fK = multiplicative coefficient of the length of the member, for stability verifications in flexure

(unbraced length of the member = LK f ) (default = 1)

1C = coefficient used for the flexural stability verifications of double-T profiles (default = 1.13)



2C = coefficient used for the flexural stability verifications of double-T profiles (default = 0.45)

3C = coefficient used for the flexural stability verifications of double-T profiles (default = 1)

2fk = coefficient used for the flexural stability verifications of box and pipe profiles (default =

1)

Static scheme = static scheme for the computation of the deflection (default = c)

F = value of the applied force for the computation of the deflection (default = 0)

q = value of the applied distributed load for the computation of the deflection (default = 0)

a = distance between the points of application of the load and the extremities of the beam, for

the computation of the deflection (default = 0)

ULS = conversion factor for ultimate limit states

SLS = conversion factor for serviceability limit states

ULSf , = partial coefficient of the material for ultimate limit states

SLSf , = partial coefficient of the material for serviceability limit states

ULSdtf ,, = design value of the longitudinal tensile strength, for ultimate limit states

SLSdtf ,, = design value of the longitudinal tensile strength, for serviceability limit states

netA = net area of the cross-section with holes

ULSRdtN ,, = design value of the tensile strength of the profile

ULSdcf ,, = design value of the compressive strength of the material

ULSRdcN ,, = design value of the compressive strength of the profile

ULSRdM ,,2 = design value of the flexural strength of the profile for flexure around axis 2

ULSRdM ,,3 = design value of the flexural strength of the profile for flexure around axis 3

RdVf , = design value of the shear strength of the material

ULSRdV ,,2 = design value of the shear strength of the profile in direction 2

ULSRdV ,,3 = design value of the shear strength of the profile in direction 3

L = length of the member

0M = value of the banding moment at the beginning of the member



AM = value of the banding moment at 1/4 of the length of the member

BM = value of the banding moment at 1/2 of the length of the member

CM = value of the banding moment at 3/4 of the length of the member

1M = value of the banding moment at the end of the member

f

axial

klocf , = critical stress of the flanges, for stability verifications of compressed double-T

profiles

ck = coefficient used for the stability verifications of compressed double-T profiles

w

axial

klocf , = critical stress of the web, for stability verifications of compressed double-T profiles

axial

dlocf , = local critical stress, for stability verifications of compressed double-T profiles

RdlocN , = design value of the compressive force that causes local instability of a double-T profile

EulN = Euler buckling load

= slenderness, used for the stability verifications of compressed double-T profiles

= coefficient used for the stability verifications of compressed double-T profiles

k = coefficient used for the stability verifications of compressed double-T profiles

2,RdcN = design value of the force that causes buckling of a compressed double-T profile

globRdcN ,2, = buckling load taking into account shear deformability

R = coefficient used in the elements of the bending stiffness matrix of a plate

fD ,11 = element of the bending stiffness matrix of a plate

wD ,11 = element of the bending stiffness matrix of a plate









SS

boxfcrxN,,

= local buckling load of the flange of a box-section profile

SS

boxwcrxN,, = local buckling load of the web of a box-section profile

SS

CfcrxN,,

= local buckling load of the flange of a C-section profile

SS

CwcrxN,, = local buckling load of the web of a C-section profile

SS

LfcrxN,,

= local buckling load of the flange of a L-section profile

SS

LwcrxN,, = local buckling load of the web of a L-section profile

locRdcN ,2, = design value of the local buckling strength

fk = coefficient used for the stability verifications of double-T profiles subjected to bending

w

flex

klocf , = value of the critical stress of the web of double-T profiles subjected to bending

flex

dlocf , = design value of the stress that causes local buckling of a double-T profile subjected to

bending

RdlocM , = design value of the bending moment that causes local instability of a double-T profile

subjected to bending

J = warping constant of a double-T profile

FTM = critical bending moment for flexural-torsional buckling of double-T profile

FT = coefficient used in flexural-torsional buckling verifications of double-T profiles



2RdM = design value of the critical bending moment for double-T profiles

maxM = maximum value of the bending moment in a member

mM = mean value of the bending moment in a member

eqM = equivalent bending moment

bC = coefficient used in flexural stability verifications

bL = unbraced length of a member subjected to bending



globRdM ,2 = design value of the global buckling strength of a member subjected to bending

SS

boxfcrxN,,

= buckling load of the flange of a box-section profile subjected to bending

SS

boxwcrxN,, = buckling load of the web of a box-section profile subjected to bending

SS

CfcrxN,,

= buckling load of the flange of a C-section profile subjected to bending

SS

CwcrxN,, = buckling load of the web of a C-section profile subjected to bending

locRdM ,2 = design value of the local buckling strength of a member subjected to bending

K = coefficient used for the stability verifications of members subjected to shear

klocVf ,, = characteristic value of the tangential stress that causes local buckling in the web panel

2RdV = design value of the shear force that causes local buckling of the member

= coefficient used for the computation of the warping constant of C-section profiles

CJ , = warping constant of C-section profiles

CglobRdM ,,2 = design value of the bending moment that causes global buckling of C-section

profiles

compRdcN ,2, = design value of the buckling strength, for compression and flexure stability

verifications

compRdM ,2 = design value of the buckling strength, for compression and flexure and shear and

flexure stability verifications

2,EulN = Euler buckling load, for stability verifications of member subjected to axial force and

bending moment

tE = creep coefficient for axial strains

tG = creep coefficient for shear strains

tEL = long-term value of the longitudinal elastic modulus

tG = long-term value of the shear modulus

SLSdcf ,, = design value of the compressive strength, for serviceability limit states

SLSRdVf ,, = design value of the shear strength, for serviceability limit states



To facilitate the reader and the designer much of the symbology adopted is equal to that of CNR-

DT205/2007.

4.3. Verification’s functions

V1= tensile stress (ULS)

V2= compressive stress (ULS)

V3= flexural stress 22 (ULS)

V4= flexural stress 33 (ULS)

V5= flexure 22 - compression stress (ULS)

V6= flexure 22 - tension stress (ULS)

V7= flexure 33 - compression stress (ULS)

V8= flexure 22 - tension stress (ULS)

V9= shear 2 stress (ULS)

V10= shear 3 stress (ULS)

V11= flexure 33 - shear 2 stress (ULS)

V12= flexure 22 - shear 3 stress (ULS)

V13= torsional stress (ULS)

V14= global buckling - compression (ULS)

V15= local buckling - compression (ULS)

V16= global buckling - flexure (ULS)

V17= local buckling - flexure (ULS)

V18= shear buckling (ULS)

V19= buckling - compression and flexure (ULS)

V20= buckling - shear and flexure (ULS)

V21= tensile stress (SLS)

V22= compressive stress (SLS)

V23= shear 2 stress (SLS)

V24= shear 3 stress (SLS)

V25= flexural stress 22 (SLS)

V26= flexural stress 33 (SLS)



V27= torsional stress (SLS)

V28= axial force and flexure 22 stress (SLS)

V29= axial force and flexure 33 stress (SLS)

V30 = maximum deflection (SLS)

4.4. References

Bank LC. Composites for construction-structural design with FRP materials, John Wiley & Sons,

NJ, 2006.






54225-1 doi:10.2788/22306




Kollar L.P., Local Buckling of Fiber Reinforced Plastic Composite Structural Members with Open

and Closed Cross Section. Journal of Structural Engineering, ASCE, 2003. 129: 1503-1513.

Eurocode 3: Design of steel structures - Part 1-1: General rules. ENV 1993-1-1: 1992. Incorporating

Corrigenda February 2006 and March 2009.

SAP2000 Advanced v. 10.1.2. Structural Analysis Program, Computers and Structures, Inc., 1995

University Ave, Berkeley, CA.

Tarjan, G., Sapkas, A. and Kollar, L.P. Local Web Buckling of Composite (FRP) Beams. Journal of

Reinforced Plastics and Composites, Vol. 29, No. 10/ 2010.

Tarjan, G., Sapkas, A. and Kollar, L.P. Stability Analysis of Long Composite Plates with

Restrained Edges Subjected to Shear and Linearly Varying Loads, J. of Reinf. Plastics and Comp.,

Vol. 29, No. 9/ 2010.


The use of FRP (Fibre Reinforced Polymer) material in the structural engineering field is by now current practice and supported by theoretical studies as well as many applications and constructions. FRP material is widely accepted in the strengthening of existing structures (made by reinforced concrete, steel, wood and masonry) but not yet commonly used for new buildings even if some recent all-FRP constructions, in particular built with FRP members made by pultrusion process, are very promising. The study of the structural behaviour of pultruded FRP members, especially in the case of static loads, has been widely developed. Instead, for what concerns the dynamic response, very few experimental and analytical research projects have been proposed.

The issue is particularly interesting because of the mechanical characteristics of pultruded FRP material. The elastic-brittle constitutive law with anisotropic mechanical behaviour imposes some specific precautions, while the high durability, the low density of 1700-1900 kg/m3 and the relatively high values of strength suggest its potential and promising application also in seismic zones.

The dynamic properties of pultruded FRP material are characterized by high periods of vibration, low frequency and a spontaneous dissipative capacity of the dynamic actions due to its low density.

THE AIM OF THIS MANUAL IS TO ADDRESS THE ISSUES RELATED TO THE DESIGN OF PULTRUDED FRP STRUCTURES SUBJECTED TO STATIC AND DYNAMIC LOADING.