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Capacity design in Earthquake Engineering
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Natural Hazards and Risks in Structural Engineering
Lecture: Earthquake Engineering
Capacity Design
Analysis of frame structures considering the interaction with
infill walls
Dr. J. Schwarz and Lars Abrahamczyk
Bauhaus-Universität Weimar, Earthquake Damage Analysis Center
Bauhaus-Universität Weimar
1. Introduction • Motivation • Strategies
2. Strategies • overview • Details to “walls as masses” • Details to “walls as diagonal braces”
3. Simple diagonal braces
4. Example of calculation
5. Damage pictures
6. Conclusions
7. References
Table of contents Bauhaus-Universität Weimar
Introduction Bauhaus-Universität Weimar
Motivation:
Killari 1993 El Asnam 1980
Introduction
as masses
- no stiffness effect
- for damaged and weak infill walls
as diagonal braces
- consideration of stiffness
- possibility to define hinges and damage grades
as slabs
- exact characterization of the behavior
- use of exact material laws
- assignment of damage grades difficult
Strategies:
Bauhaus-Universität Weimar
As masses
Example building SEM:
Bauhaus-Universität Weimar
fundamental calculated
NS EW NS EW
2,50 Hz 2,97 Hz
SLang 2,46 Hz 3,10 Hz
ETABS 2,27 Hz 2,63 Hz 60% Young’s modulus
Created by GermanTaskForce 2002
Diagonal braces
overview • simple brace model
• consideration of stiffness for elastic and plastic behaviour
• failure modes:
• corner crushing (compression)
• diagonal compression mode
• diagonal cracking mode and/or bed joint sliding
• simple brace model with orthogonal bending stiffness
• additional failure mode: out of plane behaviour
• multi brace model
• consideration of effects from the infill to the frame elements
• possibility to describe failure modes on the frame elements
Bauhaus-Universität Weimar
Diagonal braces acc. to FEMA 306 [1]
a) stiffness
4
1
inf
inf1
4
2sin
hE
tE
colfe
me
tinf thickness of infill panel and equivalent strut
Eme expected modulus of elasticity of infill material (2,10e+6)
Efe expected modulus of elasticity of frame material
Icol moment of inertial of column
tan-1(hinf / Linf), radians
hcol
hinf
Linf
Lcol
inf
4,0
1 )(175,0 rha col
rinf
a
material properties for the brace: masonry
Bauhaus-Universität Weimar
Diagonal braces acc. to FEMA 306 [1]
b) strength I sliding-shear failure
hcol
hinf
Linf
Lcol
rinf
a
II compression failure
shear force horizontal component of the diagonal strut capacity
cos'
90inf mec ftaV
2
infinf me
i EtLVslide
f’me90 … expected strength of masonry in the horizontal direction (~50% f’me)
Modified version of the method suggested by Stafford-Smith and Carter (1969)
Based on the Mohr-Coulomb failure criteria
= tan f f … angle of sliding friction
… inter-story drift angle
Bauhaus-Universität Weimar
Diagonal braces acc. to FEMA 306 [1]
b) strength
hcol
hinf
Linf
Lcol
rinf
a
III diagonal tension failure of panel
IV general shear failure of panel
inf
inf
inf
inf
inf22
L
h
h
L
tV cr
cr
'
infinf 2 memi ftLV mimf VV 3,0
Using the recommendation of Saneinejad and Hoobs (1995)
'20 mecr f
Based on the recommendation of FEMA 273 and [2] Vmi … initial shear capacity (during the first half-cyclic loading) Vmf … final shear capacity (as result of cyclic loading effects)
Bauhaus-Universität Weimar
Diagonal braces acc. to FEMA 306 [1]
c) deformation
- no clear experimental results for the behavior modes (b)
- experimental evidence supports the following inter-story drift limit states for different masonry infill panels:
- brick masonry 1,5 %
- grouted concrete block masonry 2,0%
- un-grouted concrete block masonry 2,5 %
Bauhaus-Universität Weimar
Diagonal braces acc. to [2] T. Paulay, M.J.N. Priestley
w = 0,25 dm
w - depends on the relative stiffness of frame and panel, stress-strain curves of the materials and the load level
h
hm
Lm
l
dm
w
Failure modes (compression force):
- compression failure of diagonal struts
- sliding shear failure of the masonry
td
lh
fR m
mS
3,01
03,0 '
sec3
2 '
mftzRC
2sin
4
2 tE
hIEz
m
mgc
Bauhaus-Universität Weimar
Diagonal braces – behaviour
Hysteresis envelope of the brace elements: [5]
Bauhaus-Universität Weimar
infinf
inf
3
inf
,2,1
1
tLG
h
IEC
hK
mememeF
hi
Assumptions: CE = 0; OZ = 0; CR = 0,5;
CF 3 cantilever action of filler-wall
12 filler-wall constrained at both ends
Ime moment of inertia of horizontal cross sectional area
Gme shear modulus of infill material
ftp between 4 and 8% of fc (masonry)
11
1,15,0
2infinf
, I
I
tp
hy CC
ftLF
inf
inf1,12h
LCI
Diagonal braces – behaviour
Definition of nonlinear hinges in brace elements
Bauhaus-Universität Weimar
d
hy
y
FF
cos
,
2
,
cos
hi
i
KK
i
y
yK
Fd 1,1
11 yu FF yu dd
2
ud
FF
4
ue
FF
u
F
udK
ddu
2
2
,
cos
1,0 hi
u
KK
2
4
u
u
K
F
de dd
0
5
10
15
20
25
30
35
40
45
50
0.0E+00 1.0E-03 2.0E-03 3.0E-03 4.0E-03 5.0E-03 6.0E-03
Zarnic 1 Zarnic 2 Sliding-shear
Compression Initial shear capacity Final shear capacity
Diagonal braces – behaviour
Comparison of failure strength:
Bauhaus-Universität Weimar
Diagonal braces – procedure
Modeling - calculation of the diagonal brace dimensions and the failure relationship
- modeling of the brace elements - without masses - pinned on the frame structure
- allocation of the infill masses on the frame structure (loads)
- definition of hinges (axial failure)
Analysis - run “push-over” analysis
- start iteration to determine the different limit states - slight damage - moderate damage - extensive damage
- apply the capacity spectrum method
Bauhaus-Universität Weimar
Diagonal braces – capacity curve
Determination of the capacity curve
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Roof Displacement
Base S
hear
Roof Displacement
Base S
hear
Diagonal braces – example [3]
Example building DUZ-1
Bauhaus-Universität Weimar
Created by GermanTaskForce 2002
Diagonal braces – example [3]
Calculated damage progression (ETABS)
North facade at slight damage state (HAZUS 99)
North facade
at extensive damage state (HAZUS 99)
Bauhaus-Universität Weimar
Diagonal braces – example [3]
First mode shape - transverse direction (DUZ-1).
at slight damage grade (HAZUS 99) at extensive damage grade (HAZUS 99)
Bauhaus-Universität Weimar
Diagonal braces – example [3]
Capacity curves of DUZ-1 (ETABS)
in transverse direction in longitudinal direction
Bauhaus-Universität Weimar
Damage pictures
Compression failure of diagonal strut
Bauhaus-Universität Weimar
GermanTaskForce 2003
Damage pictures Bauhaus-Universität Weimar
GermanTaskForce 2003
Damage pictures Bauhaus-Universität Weimar
GermanTaskForce 2003
Damage pictures
Short column effect
Bauhaus-Universität Weimar
GermanTaskForce 2003 GermanTaskForce 2003
Conclusions
- existence of different possibilities in order to model infill walls
- as masses
- as braces
- as slabs
- tools to model infill´s
- stiffness acc. to FEMA 306
- strength and failure mode acc. to presented equations
- up to now, models of masonry infill walls based on a variety of assumptions
- a large field for researchers …
Bauhaus-Universität Weimar
References
[1] FEMA 306
“Evaluation of earthquake damaged concrete and masonry wall buildings”, basic procedures manual, Washington D.C., USA, 1998.
[2] T. Paulay and M.J.N. Priestley
“Seismic design of reinforced concrete and masonry buildings”, New York : Wiley, 1992.
[3] Abrahamczyk L., Schott C., Schwarz J., Swain T.M.
“Vulnerability of RC frame structures in Turkish earthquake regions (Part 2): modeling and analysis” Proceedings of the 13th World Conference on Earthquake Engineering 2004, Vancouver, Canada; Paper no. 220.
[4] Fajfar P., Dolšek M., Žarnić R., Gostič S.
“Development of numerical methodologies for infilled frames”, Towards European integration in seimic design and upgrading of building structures, Euroquake-project, Final report, February 2001.
Bauhaus-Universität Weimar