Masonry Structures, lesson 10a slide 1 Seismic Design and Assessment of Masonry Structures Lesson 10a: Response and Analysis of Out-of-Plane URM Walls, Part 2 Notes Prepared by: Daniel P. Abrams Willett Professor of Civil Engineering University of Illinois at Urbana-Champaign October 26, 2004 Masonry Structures, lesson 10a slide 2 Influence of Diaphragm Flexibility on the Out-of-Plane Dynamic Response of Unreinforced Masonry Walls PhD Dissertation by Can C. Simsir September 17, 2004 Department of Civil & Environmental Engineering University of Illinois at Urbana-Champaign
Transcript
Masonry Structures, lesson 10a slide 1
Seismic Design and Assessment ofMasonry Structures
Seismic Design and Assessment ofMasonry Structures
Lesson 10a: Response and Analysis of Out-of-Plane URM Walls, Part 2
Notes Prepared by:Daniel P. Abrams
Willett Professor of Civil EngineeringUniversity of Illinois at Urbana-Champaign
October 26, 2004
Masonry Structures, lesson 10a slide 2
Influence of Diaphragm Flexibility on the Out-of-Plane Dynamic Response of
Unreinforced Masonry Walls
PhD Dissertationby
Can C. Simsir
September 17, 2004
Department of Civil & Environmental EngineeringUniversity of Illinois at Urbana-Champaign
Masonry Structures, lesson 10a slide 3
Motivation
1886 Charleston 1994 Northridge
2001 Nisqually
Out-of-plane failure, rather than in-plane failure, of URM wallsis considered the main cause of personal injury and loss of life.
1976 Tangshan
Masonry Structures, lesson 10a slide 4
Motivation
• Attenuation rates are low• URM buildings are common• Seismic loads were not considered in design
Consequences can be catastrophic
Essential facilities inventory by S. French & R. Olshansky
Central and Eastern US
Western US• Earthquakes are frequent• Large numbers of pre-1933 URM buildings remain• Historic URM buildings are preserved
Masonry Structures, lesson 10a slide 5
Objectives
• Examine stability of URM bearing walls connected to flexible floor diaphragm and subjected to seismic input.
• Develop dynamic stability analysis tools to compute response of URM out-of-plane walls.
• Establish the factors and their effect on out-of-plane response of URM walls.
• Develop recommendations for treating URM wall stability.
Masonry Structures, lesson 10a slide 6
Research Scope
• Perform shake table tests on URM out-of-plane walls as part of an idealized building.
• Develop analytical tools (linear and nonlinear dynamic stability models):
• RSA• SDOF• MDOF• 2DOF
• Perform parametric studies.
• Evaluate seismic guidelines, confirm or develop recommendations.
Masonry Structures, lesson 10a slide 7
Test Specimen
Masonry Structures, lesson 10a slide 8
Connection Details
Masonry Structures, lesson 10a slide 9
Material Tests
• Unit block compression tests• Mortar (Type O) compression tests• Masonry prism tests• Masonry flexural tension and bond wrench tests
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Period (s) scaled in time
1.4% damping
STIFF
RUN 1 12
Spa (g)
Sd (in)
1992 Big Bear Ground Acceleration History
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 4 8 12 16 20Time (sec)
Gro
und
Acc
eler
atio
n (g
)
1992 Big Bear Response Spectrum
0
1
2
3
4
5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Period (s)
1.4% damping
STIFF FLEXIBLE
RUN 13 201716
Sd (in)
Spa (g)
Shake table tests + frequency sweep and free vibration tests
Masonry Structures, lesson 10a slide 12
• 20th run: – Out-of-plane rocking about the cracked bedjointat the base– Flexible diaphragm (steel beam) yielded– No mid-height cracks– No collapse– Peak drift ratio=3.4%
• 7th run: – Bedjoint cracking at the base of the out-of-plane wall.
Measured (West Wall Top) Good correlation verified that the response of the out-of-plane walls was associated with the change in the period of vibration of the flexible diaphragm.
Discrepancy between computed and measured results may be attributed to the use of:• smaller than true viscous damping ratios.• elastic response spectra as opposed to inelastic spectra.
Masonry Structures, lesson 10a slide 20
Wall is assumed strong and rigid as it freely rotates about its base.
2. Single-degree-of-freedom (SDOF) Model
h
kT
)(tug&&
dw
dwT kk
kkk
+=
22
Masonry Structures, lesson 10a slide 21
Bilinear model was based on measured values of mass, damping, and stiffness.
2. Single-degree-of-freedom (SDOF) Model
( ) ( ) )()()()(32 tummtu
hgm
hgm
ktuctumm gwdwd
Twd &&&&& +−=⎟⎠
⎞⎜⎝
⎛−−++⎟
⎠⎞
⎜⎝⎛ +
Generalized SDOF response:
Masonry Structures, lesson 10a slide 22
Displacement and acceleration responses were computed with reasonable accuracy using the nonlinear SDOF system subjected to the measured table excitations.
Modified SDOF (similar to RSA): kT was calculated based on measured T.
SDOF model was more accurate than the RSA and the modified SDOF models.
Masonry Structures, lesson 10a slide 23
3. Multi-degree-of-freedom (MDOF) Model
MDOF model computes out-of-plane wall response and considers bedjoint cracks developing along the wall under combined bending moments and axial forces.
Location (or eccentricity) of the two fibers was determined by considering the stiffness and strength of the whole cross-section of the wall under combined bending moments and axial forces.
Masonry Structures, lesson 10a slide 24
3. Multi-degree-of-freedom (MDOF) Model
kw and kd:Bilinear springs with inelastic unloading.
Blocks:Linear elastic beam-column elements that ignore shear deformations and are rigid at the interface with the mortar bedjoint.
Fiber element:Mortar and block-mortar interface lumped into one element (simplified micro-modeling).Bilinear tensile behavior (per the Fictitious Crack Model) with inelastic unloading and no stiffness degradation.
Strain
Stress, f (psi)
fc=704
½fc
1.00.01
ft=17
1.25E-3 2.5E-4
1.7
Unloading
∆ (in)
F (kips)
kd/2=15.1 k/in
Fd/2=16.0
-16.0
STIFF
∆ (in)
F (kips)
kd/2=1.83 k/in
Fd/2=3.54
-3.54
FLEXIBLE
0.694k/in
Masonry Structures, lesson 10a slide 25
3. Multi-Degree-of-Freedom (MDOF) Model
MDOF model response compared very well with the measured out-of-plane wall response.
Static pushover analyses of the out-of-plane wall with the MDOF model were used in the development of the 2DOF model.
Simulations with the MDOF model were also used in the parametric studies.
Masonry Structures, lesson 10a slide 26
4. Two-degree-of-freedom (2DOF) Model
Hinge location is based on experimental and analytical results.
Model considers a known failure mechanism.
Two rigid wall segments are connected by bilinear rotational springs.
q1 and q2 are the two DOF.
k1
k3
k2
Wd
Ww/3
2Ww/32h/3
h/3
h/3
h/3
h/6
h/6
q1
q2
Masonry Structures, lesson 10a slide 27
4. Two-degree-of-freedom (2DOF) Model
Wd
h/3
t
F
F
Wd+Ww
Ww/3
2Ww/3
Wd+Ww/3
2h/3
FFMmax
qmaxqmax/9q
M
Wd
h/3
t
F
F
Wd+Ww
Ww/3
2Ww/3
Wd+Ww/3
2h/3
FFMmax
qmaxqmax/9q
M
)231(
32
max Ψ+= tWM w
htq
23
max1 =
)31(23
max Ψ+= tWM w
⎥⎦⎤
⎢⎣⎡
Ψ+Ψ+
=61313
max2 htq
Ψ=Wd/Ww
0
0.02
0.04
0.06
0.08
0.1
0.12
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Displacement (in)
Forc
e (k
ips)
k1 and k2 are determined from post-cracked static moment-rotation relationships of the two semi-rigid wall segments.
from MDOF model
Masonry Structures, lesson 10a slide 28
4. Two-Degree-of-Freedom (2DOF) Model
Compared to MDOF model, 2DOF:• is a less complicated nonlinear dynamic model with fewer DOF.• has a shorter computing time.
Measured response was simulated well, especially during the post-cracked stage.
Run 22
2DOF model successfully integrates URM wall behavior with flexible diaphragm with the semi-rigid-body dynamics while considering the failure mechanism.
Masonry Structures, lesson 10a slide 29
Parametric Studies
720 simulations were performed with the MDOF model.
Out-of-plane wall in the simulations was composed of full-scale normal-weight masonry units.
h/t Unitweight
n(stories)
P/A(psi)
e/t L/b aV Ground motionrecords
10.515.721.026.231.5
Concretehollow
block orclay solid
brick
12345
1020304050
00.250.50
2.02.53.0
NoYes
Nahanni (intra-plate)Big Bear (SD)
Valparaiso (LD)Loma Prieta (FD)
Parameters:
Not considered in the ABK tests
Determined not to have a significant effect on URM wall stability
Masonry Structures, lesson 10a slide 30
In ABK tests:• e/t, aV were not considered.• Diaphragm flexibility was not considered by a nonlinear element.
• Given h/t ratios are somewhat conservative.• Presence of cross walls may not necessarily increase stability of walls.• Other parameters are influential too.• SDOF, MDOF, 2DOF are introduced for stability check.
The allowable h/t ratios in FEMA 310 (1998)
Regions of High SeismicitySx1 > 0.3g or Sxs > 0.75g
Regions of ModerateSeismicity
0.1g < Sx1< 0.3g or0.25g < Sxs< 0.75g
with crosswalls without crosswalls
Walls of one story buildings 16 16 13First story walls of
multistory buildings18 16 15
Walls in top story ofmultistory buildings
14 14 9
All other walls 16 16 13Parapet walls 2.5 1.5 1.5
h/t ratios 1980sABKJoint
Venture
ug(t)
αug(t)
Basis for h/t values in FEMA 356
Masonry Structures, lesson 10a slide 31
Story Drift Levels
Slight damage observed would correspond to an IO performance level, when such large story drifts would imply LS or CP demand levels.
Tests: Except for cracking at the base, walls were undamaged at 3.4% drift.Parametric studies: Walls were stable at 3.8% drift.
Masonry Structures, lesson 10a slide 32
FEMA 356 coefficient χ for calculation of out-of-plane wall forces
Structural Performance Level Flexible Diaphragms Other DiaphragmsCollapse Prevention 0.9 0.3
Life Safety 1.2 0.4Immediate Occupancy 1.8 0.6
Floor Anchorage
• Proper anchorage of URM wall to floor diaphragm should be the first step in retrofitting the wall to mitigate out-of-plane failure.
• Diaphragm-wall connections with pockets in the wall for diaphragm joist seating are encouraged to minimize e/t of axial compressive force on the wall.
• Force demands on walls with stiffer flexible diaphragms will be greater than on those with more flexible diaphragms; a distinction not made in the current seismic guidelines.
Masonry Structures, lesson 10a slide 33
• Unlike shear walls, nonlinear response of a URM out-of-plane wall is governed by rocking, not by f’m. Geometry and boundary conditions of the wall are important rather than type and strength of masonry.
• Nonlinear rocking provides a reserve of capacity over that calculated using conventional methods.
• Proper anchorage of wall to diaphragm is the first step in retrofitting a URM out-of-plane wall to prevent sliding or pullout.
Conclusions
• A moderate increase in axial compressive stress in a URM building is beneficial to the stability of out-of-plane walls.
Masonry Structures, lesson 10a slide 34
• Eccentricity of floor diaphragm should be kept at a minimum for dynamic stability of out-of-plane walls. Pockets may be introduced in the wall to minimize eccentricity of diaphragm joist seating.
• Flexible diaphragms reduce in-plane forces on shear walls at the cost of driving out-of-plane displacement response higher.
• A diaphragm stiffened for seismic rehabilitation can induce instability in a previously stable out-of-plane wall; dynamic stability of the wall should be re-evaluated.
Conclusions
• Out-of-plane walls with flexible diaphragms can have large displacement demands but they remain stable if proper anchorage is provided. Stiffer diaphragms induce larger force demands on the walls, which are then likely to lose their stability.
Masonry Structures, lesson 10a slide 35
Conclusions
• Results of the parametric studies as well as the analytical models that were developed can be used as tools for dynamic stability analysis of URM out-of-plane walls.
• General trends discussed so far remain the same for different earthquakes: A wall with a smaller h/t ratio, larger concentric axial stress and larger diaphragm aspect ratio is more likely to maintain its stability for a given ground motion.
• The effect of vertical accelerations can be significant on stability of URM walls under large axial stresses.
• Allowable h/t ratios can be increased from 16 or 20 to as much as 31 for low intensity ground accelerations. Influence of other parameters on wall stability needs to be addressed in the guidelines.
