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Seismic Design and Assessment of
Seismic Design and Assessment of
Masonry Structures
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 1

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


Motivation
Out-of-plane failure, rather than in-plane failure, of URM walls
is considered the main cause of personal injury and loss of life.
1886 Charleston 1994 Northridge

1976 Tangshan 2001 Nisqually


Motivation
Central and Eastern US
• Attenuation rates are low Consequences
• URM buildings are common can be catastrophic
• Seismic loads were not considered in design

Essential facilities inventory by S. French & R. Olshansky
Western US
• Earthquakes are frequent
• Large numbers of pre-1933 URM buildings remain
• Historic URM buildings are preserved Structures, lesson 10a slide 4
Masonry

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.


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.


Test Specimen


Connection Details


Material Tests
Out-of-plane walls:
• Unit block compression tests
• Mortar (Type O) compression tests
• Masonry prism tests
• Masonry flexural tension and bond wrench tests

In-plane walls:
• Mortar (Type S) compression tests
• Masonry prism tests
• Grout compression tests
• Steel reinforcement tension tests


Shake Table Tests

Run Record PGA Diaphragm Peak Drift Ratio of
Number Name (g) Type the out-of-plane wall
1 0.06 0.05%
.
.
.
Nahanni Stiff
12 1.17 0.74%
13 0.39 0.28%
.
.
.
Big Bear Stiff
16 1.20 0.96%
17 0.13 0.62%
.
.
.
Big Bear Flexible
20 1.08 3.38%
21* 0.13 0.72%
Big Bear Flexible
22* 0.37 collapse
* reduced gravity load, increased wall mass

Shake table tests + frequency sweep and free vibration tests
1985 Nahanni Ground Acceleration History 1985 Nahanni Response Spectrum
1.2 RUN 1 12 1.4% damping
5

0.8
4 Sd (in)
Ground Acceleration (g)

0.4
3
0

2
-0.4

1
-0.8 Spa (g)

0
-1.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 4 8 12 16 20
Time (sec) STIFF Period (s) scaled in time

1992 Big Bear Ground Acceleration History 1992 Big Bear Response Spectrum
RUN 13 16 17 20 1.4% damping
0.6 5

0.4
4
Ground Acceleration (g)

0.2
3

0
Sd (in)
2
-0.2

1
-0.4 Spa (g)

-0.6
0
0 4 8 12 16 20 Masonry Structures, lesson 10a slide0.8 Period (s) 1
11 0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Time (sec) STIFF FLEXIBLE

Test Observations
• 7th run:
– Bedjoint cracking at the base of the out-of-plane wall.
• 15th run:
– In-plane walls yielded, sustained diagonal shear cracks.
• 20th run: 20th run: 2.0 × PGABig Bear= 1.08g
– Out-of-plane rocking
about the cracked bedjoint
at the base
– Flexible diaphragm (steel
beam) yielded
– No mid-height cracks
– No collapse
– Peak drift ratio=3.4%

Test Results
Displacement Response History of Out-of-Plane Wall
During Run 20
Mid-height displacements
80
top of wall
mid-height of wall
are in phase with the
60

40
displacements at the top.
Displacement (mm)

20

0

-20
Comparison of Displacements During the 20th Run
-40
40
-60

Displacement (mm) at Mid-height
30
-80
2 7 12 17 22
20
Time (s)

of the Wall
10

0

-10

-20
Mid-height displacements are -30

~½ of the displacements at -40
-80 -60 -40 -20 0 20 40 60 80

the top: Rigid-body rocking Displacement (mm) at the Top of the Wall


Test Observations

22nd run: 0.67 × PGABig Bear= 0.37g
Gravity load on walls reduced by 46%


Test Observations


Test Results


Test Results

• Peak accelerations were similar at the top and mid-height
of the out-of-plane walls, and up to 4.5 times the peak base
accelerations.
• Diaphragm flexibility significantly increased (up to 5
times) the out-of-plane displacement response, but not the
acceleration response.
• Diaphragm flexibility significantly increased displacement
(~7 times) and acceleration (~2 times) amplifications of
diaphragm mid-span w.r.t. in-plane wall tops.


Models for Dynamic Stability Analysis
1. Response Spectrum Analysis (RSA)
Linear elastic response spectra
were computed from recorded
table acceleration histories.
5

4.5

4
Pseudo Spectral Acceleration (g)

3.5

3

2.5
2.36 g
2

1.5

Floor diaphragm period was the
1

0.5

dominant period of vibration
0.41 s
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(SDOF assumption). Period (s)


1. Response Spectrum Analysis (RSA)
4
Computed Sd

Good correlation verified
Measured (West Wall Top)
3.5

3
that the response of the
2.5
out-of-plane walls was
Displacement (in)

associated with the change
2

in the period of vibration
1.5

1

0.5
of the flexible diaphragm.
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Dynamic Test Run

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.

2. Single-degree-of-freedom (SDOF) Model

2k w k d
kT =
2k w + k d

kT

Wall is assumed strong
and rigid as it freely
h

rotates about its base.
u g (t )
&&


Generalized SDOF response:
⎛ 2 ⎞ ⎛ md g mw g ⎞
⎜ m d + m w ⎟ u (t ) + (c ) u (t ) + ⎜ k T −
&& & − ⎟ u (t ) = −(m d + m w ) u g (t )
&&
⎝ 3 ⎠ ⎝ h h ⎠

Bilinear model was based on measured values of
mass, damping, and stiffness.

4
Computed (SDOF)
Computed (modified SDOF)
3.5
Computed Sd (RSA) SDOF model was more
Measured (out-of-plane wall top)
3
accurate than the RSA
2.5
and the modified SDOF
Displacement (in)

2 models.
1.5

1
Modified SDOF (similar to
0.5 RSA): kT was calculated
0
based on measured T.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Dynamic Test Run

Displacement and acceleration responses were computed
with reasonable accuracy using the nonlinear SDOF
system subjected to the measured table excitations.

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.

3. Multi-degree-of-freedom (MDOF) Model
F (kips)

kw and kd: Fd/2=16.0

STIFF
Bilinear springs with inelastic unloading. kd/2=15.1 k/in
∆ (in)

Blocks: -16.0

Linear elastic beam-column elements that F (kips)

ignore shear deformations and are rigid at Fd/2=3.54 0.694
k/in
FLEXIBLE
the interface with the mortar bedjoint. kd/2=1.83 k/in
∆ (in)

Fiber element: -3.54

Mortar and block-mortar interface
lumped into one element (simplified Stress, f (psi)

micro-modeling). fc=704

Bilinear tensile behavior (per the ½fc

Fictitious Crack Model) with inelastic
Unloading

1.25E-3 2.5E-4
Strain

unloading and no stiffness degradation.
1.7 0.01 1.0

ft=17


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.


4. Two-degree-of-freedom (2DOF) Model
Two rigid wall segments are connected by bilinear rotational springs.
Wd k3
q1 and q2 are the two DOF.
h/6
h/3 Ww/3
h/6 q2
Model considers a known
k2
failure mechanism.
h/3
Hinge location is based on
2h/3 2Ww/3 experimental and analytical
results.
h/3 q1

k1


4. Two-degree-of-freedom (2DOF) Model

k1 and k2 are determined from 0.12

post-cracked static moment- 0.1
from MDOF model
rotation relationships of the two 0.08

Force (kips)
semi-rigid wall segments. 0.06

0.04
Wd
F 0.02

M
Ww /3 0
h/3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Displacement (in)

Mmax F
F 3
M max = Ww t (1 + 3Ψ )
W d +W w/3 2
2h/3 3t ⎡1 + 3Ψ ⎤
2W w/3 q 2 max =
h ⎢1 + 6Ψ ⎥
⎣ ⎦
q 2 3
qmax/9 qmax M max = Wwt (1 + Ψ )
t 3 2
F
3t
Ψ=Wd/Ww q max =
Masonry Structures, 1lesson 10a slide 27
W d+W w 2h

4. Two-Degree-of-Freedom (2DOF) Model

Run 22

Measured response was
simulated well, especially
during the post-cracked stage.

Compared to MDOF model, 2DOF:
• is a less complicated nonlinear dynamic model with fewer DOF.
• has a shorter computing time.
2DOF model successfully integrates URM wall behavior
with flexible diaphragm with the semi-rigid-body dynamics
while considering the failure mechanism.

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.

Parameters:
h/t Unit n P/A e/t L/b aV Ground motion
weight (stories) (psi) records
10.5 Concrete 1 10 0 2.0 No Nahanni (intra-plate)
15.7 hollow 2 20 0.25 2.5 Yes Big Bear (SD)
21.0 block or 3 30 0.50 3.0 Valparaiso (LD)
26.2 clay solid 4 40 Loma Prieta (FD)
31.5 brick 5 50

Determined not to have Not considered
a significant effect on in the ABK tests
URM wall stability

1980s
h/t ratios αug(t)
ABK
In ABK tests: Joint
Venture
• e/t, aV were not considered. Basis for
• Diaphragm flexibility was not ug(t) h/t values in
considered by a nonlinear element. FEMA 356
The allowable h/t ratios in FEMA 310 (1998)
Regions of Moderate Regions of High Seismicity
Seismicity Sx1 > 0.3g or Sxs > 0.75g
0.1g < Sx1< 0.3g or with crosswalls without crosswalls
0.25g < Sxs< 0.75g
Walls of one story buildings 16 16 13
First story walls of 18 16 15
multistory buildings
Walls in top story of 14 14 9
multistory buildings
All other walls 16 16 13
Parapet walls 2.5 1.5 1.5

• 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.

Story Drift Levels

Tests: Except for cracking
at the base, walls were
undamaged at 3.4% drift.
Parametric studies: Walls
were stable at 3.8% drift.

Slight damage observed would correspond to an
IO performance level, when such large story
drifts would imply LS or CP demand levels.


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.
FEMA 356 coefficient χ for calculation of out-of-plane wall forces
Structural Performance Level Flexible Diaphragms Other Diaphragms
Collapse Prevention 0.9 0.3
Life Safety 1.2 0.4
Immediate Occupancy 1.8 0.6


Conclusions
• 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.

• A moderate increase in axial compressive stress in a URM building
is beneficial to the stability of out-of-plane walls.


Conclusions
• 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.
• 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.
• 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
• 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.
• The effect of vertical accelerations can be significant on stability of
URM walls under large axial stresses.

• 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.

• 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.

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