Performance-Based Design and
Nonlinear Modeling of Coupled
Shear Walls and Coupling Beams
Danya Mohr, Dawn Lehman and Laura Lowes,
University of Washington
NEESR Project Overview
 Research Objectives:
 Improve understanding of the seismic behavior of reinforced
concrete core walls and develop tools to enable performancebased design of these components.
 Project Scope:
 Experimental investigation of core wall components using the
UIUC MUST-SIM NEES facility.
 Development of numerical models and modeling
recommendations to enable simulation of the seismic response
of buildings with core walls.
 Development of damage-prediction models and performancebased design recommendations.
The Research Team
 University of Washington
 Laura Lowes, Assistant Professor
 Dawn Lehman, Assistant Professor
 Danya Mohr, Claudio Osses, Blake Doepker & Paul Oyën, Graduate
Student Researchers
 University of Illinois
 Dan Kuchma, Assistant Professor
 Chris Hart and Ken Marley, Graduate Student Researcher
 University of California, Los Angeles
 Jian Zhang, Assistant Professor
 Yuchuan Tang, Graduate Research Assistant
 External Advisory Panel
 Ron Klemencic and John Hooper, Magnusson Klemencic Associates
 Andrew Taylor, KPFF Consulting Engineers
 Neil Hawkins, Professor Emeritus, University of Illinois
Experimental Test Program
Bidirectional
Loading
Unidirectional
Loading
Moment – Shear Ratio
Planar (2) Flanged Coupled
Core-Wall System
Long. Reinf.
Distribution
Load
History
Coupling
Beam
Strength
Scope of the Coupled Wall Research Effort and
Presentation Outline
 Design a “typical” coupled wall
specimen for testing at UIUC.
 Compare current code
confinement requirements for
diagonally reinforced coupling
beams to proposed alternative
methods.
 Investigate performance of the
coupled wall system using
existing non-linear finite element
software (VecTor2).
 Identify appropriate parameters
for the experimental investigation.
Washington Mutual Tower
Photo Courtesy of
Magnusson Klemencic Assoc.
Design of the Reference Coupled Wall Specimen:
Building Inventory Review
 Review drawings for ten buildings (7 to 30 stories) designed for
construction on the West Coast using UBC 1991, 1994 and 1997.
 Four buildings were found with coupled shear walls.
 Developed data set of wall properties including: wall configuration,
geometry, aspect ratio, and reinforcement ratios.
 With consultation from Advisory Panel, average values used as a basis
for coupled wall configuration.
Design of the Reference Coupled Wall Specimen:
Review Previous Experimental Research
 Experimental testing of coupled walls
 Numerous planar wall and coupling beam tests.
 Very few coupled wall tests completed.
 Coupled wall specimens were not representative of current design
practices.
 Experimental testing of coupling beams
 Fairly extensive testing of coupling beams has been done.
 7 test programs and 35 coupling beam tests were presented in the
literature with sufficient detail for use in the current study.
 Of these, 22 coupling beams with horizontal or diagonal
reinforcement were reviewed in detail for the current study.
 It should be noted that few data characterizing damage and
damage progression in coupling beams are presented in the
literature.
Design Approach
 Code based elastic design to determine wall flexural strength,
coupling beam strength, and detailing requirements using

IBC 2007, ACI 318-05
 Performance-base plastic design approach to determine pier wall
shear demand

SEAOC Seismic Design Manual Vol. III
(International Code Council - Structural/Seismic Design Manual)
 Fundamental design parameters taken from the building inventory
review





10 Story wall, (120 ft high)
30 ft wide, 4.0 aspect ratio, (Avg. = 29.4, 5.5)
Aspect ratio of coupling beams = 1.5 ,(Avg. = 1.7)
Initial horizontal reinforcement ratio of piers set to code min. 0.25%
Diagonal reinforcement ratio, d = 0.83% (Avg. d = 1.09%)
Code-Based Elastic Design
 ELF procedure using ASCE 7-05 results in triangular lateral load
distribution
 Elastic effective stiffness model to determine force distribution. Effective
stiffness values taken from New Zealand and Canadian Design Code
Recommendations.

0.10EIg for coupling beams.

0.70EIg for wall piers.
 Forces from elastic analysis used to design wall pier and coupling
beam reinforcement according to ACI 318-05.
 Building Code would allow design process to stop here. However,
current practice recommends completing a plastic analysis to,


establish shear demand corresponding to flexural strength, and
identify potential plastic hinge regions.
Plastic Analysis of Flexural Mechanism in Wall
 Determine the probable strength (Mpr) of
the coupling beams and piers assuming
1.25fy and = 1.0
 Assume “preferred” behavior mechanism
with plastic hinges at the base of the wall
piers and the ends of all coupling beams.
 Evaluate the plastic mechanism by
equating internal vs. external work to
determine the plastic shear demand at the
base of the wall.
(SEAOC Seismic Design Manual Vol. III)
 Adjust shear reinforcement of wall piers to
ensure that shear strength exceeds the
flexural capacity.
Plastic
Hinges
Coupled Wall Reinforcement
 Pier Reinforcement Ratios
 1st Floor Pier




h = 0.54%, Horizontal
v = 0.27%, Vertical
b = 3.64%, Boundary
Typical Pier



h = 0.27%, Horizontal
v = 0.27%, Vertical
b = 3.64%, Boundary
 Coupling Beams
 Diagonally Reinforced

d = 0.83%
Coupling Beam Reinforcement
Evaluation of Coupled Wall Performance Using
VecTor2
 VecTor2
 Nonlinear finite element analysis software suite for
reinforced concrete membrane structures.
 Formworks - Model Builder
 VecTor2 - Analysis Software
 Augustus - Post Processor/Data Viewer

Developed at the University of Toronto by Frank
Vecchio and his students over the last two decades.

Based on the Modified Compression Field Theory
(MCFT) (Vecchio and Collins 1986) and the Disturbed
Stress Field Model (DSFM) (Vecchio 1994).
VecTor2 Analysis Software
 Modified Compression Field Theory
 Uniformly distributed reinforcement
 Uniformly distributed cracks and rotating cracks
 Average stress and strain over each element
 Orientation of principle strain and principle stress are
the same
 Perfect bond between reinforcement and concrete
 Independent constitutive models for concrete and
steel
 Disturbed Stress Field Model
 Builds on MCFT
 Crack shear slip modeled explicitly
 Orientations of principle stress and principle strain
are decoupled
 Discrete reinforcement may be layered on top of
Element Subject to
Shear & Normal Stress1
the RC continuum.
1. Vecchio & Wong, (2006),
VecTor2 User Manual
Evaluation of VecTor2

The results of previous research by Paul
Oyen, a UW MS student, as well as numerous
other researchers suggested that VecTor2
could be expected to




Predict well the strength and stiffness of RC
continua
Predict deformation capacity with less accuracy.
Further evaluation of VecTor2 for coupling
beams, in which discrete reinforcement
determines behavior, was required for the
current study..
Simulate 17 experimental coupling beam tests


5 Monotonically Loaded
5 Cyclically Loaded
Diagonally Reinforced



Diagonal
Compression
Conventionally Reinforced


Flexure
2 Monotonically Loaded
5 Cyclically Loaded
Coupling beam tests include multiple behavior
modes





Flexure
Flexure / Shear
Diagonal Compression
Flexure / Compression
Flexure / Diagonal Tension
Flexure
Compression
Flexure
Shear
Galano & Vignoli, (2000), ACI Structural Journal 97 (6)
Nonlinear Continuum Models
 Geometry and Materials
 Dimensions and scale of
specimens used.
 Reported material properties for
concrete and steel used.
 Entire test specimen was
modeled (including loading
blocks)
 Reinforcement modeling
 Primary longitudinal or diagonal
reinforcement modeled as
discrete truss-bar elements.
 All other bars modeled as
smeared reinforcement
Conventionally Reinforced Coupling Beam
Zones of different
Reinf. Ratios &
Reinf. Orientation
Discrete Truss-Bar
Elements
Diagonally Reinforced Coupling Beam
Simulation versus Experimental
VecTor2 Simulation
Experimental Results
Model: Galano P01
Monotonically Loaded
Conventionally Reinforced
Galano & Vignoli, (2000),
ACI Structural Journal 97 (6)
Simulation versus Experimental
VecTor2 Simulation
Model: Galano P05
Monotonically Loaded
Conventionally Reinforced
Experimental Results
Galano & Vignoli, (2000),
ACI Structural Journal 97 (6)
Simulation versus Experimental
VecTor2 Simulation
Model: Galano P07
Cyclically Loaded
Conventionally Reinforced
Experimental Results
Galano & Vignoli, (2000),
ACI Structural Journal 97 (6)
Simulation versus Experimental
VecTor2 Simulation
Model: Tassios CB1A
Cyclically Loaded
Conventionally Reinforced
Experimental Results
Tassios, Maretti and Bezas (1997)
ACI Structural Journal 97 (6)
Results for Complete Coupling Beam
Evaluation Study
Vy/Vye
Vu/Vue
Ky/Kye
Ku/Kue
K1.5/ K1.5e
δy/δye
δu/δue
Average
1.05
0.98
1.34
3.00
1.07
0.89
0.42
Mean
1.06
1.00
1.27
2.50
1.04
0.92
0.45
Std. Dev.
0.17
0.10
0.52
1.70
0.17
0.34
0.21
δu Vu
δue Vue
K1.5
δye
Vδyey
Ku1.5e
VK
y ye
Ky
Kue
Coupling Beam Evaluation Summary
 VecTor2

Provides a good prediction of behavior through yield and up
to ultimate strength.




Under predicts Vy by 5% on average
Over predicts Vu by 2% on average
Under predicts y by 11%
Poor prediction of displacement at ultimate strength


Under predicts u 42% on average
Early loss of strength due to crushing of elements and poor
redistribution of stress
Evaluation of the Coupling Beam Designs for
the Coupled Wall Test Specimen Diagonal
ACI 318-05 Code

Diagonal reinforcement must be used if:



Aspect Ratio, ln/d that is less than two, and
Factored Shear, Vu exceeding 4√f’cbwd
Additionally, confinement required around
diagonal bar groups to meet:


§21.4.4.1(b) - Ash = 0.09s bc f’c/fy
§21.4.4.2 - Spacing less than

1/4 min. member dimension

6 times db long. bar

4 + (14 +hx)/3
ACI 318-05 Code Compliant
Coupling Beam
Alternate Designs

ACI 318H-CH047 Proposal



Reduce spacing of ties on diagonal bars by
eliminating the 1/4 of member dimension rule.
Or, provide confinement of entire beam
Modified ACI 318H-CH047

Further reduce confinement requirements by
reducing the area of steel required, Ash, by half.
ACI 318H Full Confinement
Proposal
Coupling Beam Model Properties
l
v
h
Ad
Specimen
(Ast/dt)
(Av/st)
(Ah/ds)
(in2)
CBR-ACI
0.31%
0.27%
0.10%
0.80
1.63%
CBR-318H
0.31%
0.27%
0.10%
0.80
CBR-318H-F
0.42%
0.74%
0.74%
CBR-318H-M
0.28%
0.56%
0.35%
Concrete
f'c
ft
Ec

5.0
0.50
4030
0.003
Ksi
Ksi
Ksi
Reinforcement
fy
fu
Es
Es h

60
90
29000
170
0.010
Ksi
Ksi
Ksi
Ksi
dv
dt
Diag
sdiag t ies
Ties
(in)
3.27%
2 #2
1
1.09%
2.18%
2 #2
1.5
0.80
-
-
-
-
0.80
-
-
-
-
(Adt/d c st) (Adt/tc st)
Geometry
Scale
Aspect Ratio
Length
Height
Depth
1/3
1.5
24
16
6
in
in
in
Comparisons / Results

All specimens fail due to fracture of
diagonal bars.

CBR-318H provides same
performance as ACI-318

Full Confinement models provide
an increase in displacement
ductility of 50% to 70%
Coupled Wall Models
 Full ten story wall modeled.
 Use same model parameters
and analysis assumptions as
coupling beam simulations.
CW-318H-F
VecTor2 Model
Coupled Wall Models
 Investigate effects of lateral load
distribution.



Inverted Triangular
Uniform over height
0.30 Effective shear height
 Investigate effects of coupling
beam confinement and strength.



CBR-ACI - Reference coupling
beam
CBR-318H-F – Newly proposed
confinement details – full
confinement over beam depth
CBR-318H-FR - Reduced
strength, new detailing
requirements with full
confinement over beam depth
 Nine Coupled Wall Models
Wall Model
Coupling Beam
Load Dist.
CW-ACI-T
CBR-ACI
Inv. Tri.
CW-ACI-U
CBR-ACI
Uniform
CW-ACI-3H
CBR-ACI
0.3H
CW-318HF-T
CBR-318H-F
Inv. Tri.
CW-318HF-U
CBR-318H-F
Uniform
CW-318HF-3H
CBR-318H-F
0.3H
CW-318HFR-T
CBR-318H-FR
Inv. Tri.
CW-318HFR-U
CBR-318H-FR
Uniform
CW-318HFR-3H
CBR-318H-FR
0.3H
Deformed Shape at Max Base Shear
Inv. Triangular Load Distribution
CW-ACI-T
CW-318HF-T
CW-318HFR-T
Deformed Shape at Max Base Shear
Uniform Load Distribution
CW-ACI-U
CW-318HF-U
CW-318HFR-U
Deformed Shape at Max Base Shear
0.3H Eff. Height Load Distribution
CW-ACI-3H
CW-318HF-3H
CW-318HFR-3H
Effect of Coupling Beam Strength



CW-ACI and CW-318HF provide
essentially the same maximum base
shear for all load distributions.
Reduced strength model, CW-318HFR
 10% average reduction in maximum
base shear
 Increase in roof drift
14% - Uniform Load
35% - Inverted Triangular load
59% - 0.3H Load
Base shear is a function of the load
distribution since walls always develop
flexural hinge at the base.
Conclusions
 VecTor2 Modeling
 Can provide a good prediction of yield strength and displacements as well
as ultimate strength
 Under-estimates the drift capacity
 Coupling Beam Confinement
 ACI 318-H CH047 proposals provide the same level of performance as ACI
318-05 requirements. reference beam.
 Coupled Wall Design
 Current Plastic design method may not provide expected behavior.



Strength of coupling beams must be reduced to achieve desired plastic
mechanism


“Desired” plastic mechanism is unlikely to occur in a wall designed to the ICC
recommendations.
Coupling beams are too strong in comparison to the wall piers, yielding of wall
piers occurs before sufficient drift demands in the coupling beams are developed.
A reduction in coupling beam strength of 75% reduced the base shear capacity
by 10% while increasing the roof drift by 35%.
Lateral load distribution has a significant effect on the magnitude of the
base shear, however, for these models it did not change the plastic
mechanism.
Future Research Activities
 Experimental verification of coupled wall behavior
with full and reduced strength coupling beams.
 Development of design recommendations to ensure
preferred plastic mechanism is developed.
Appendix
 Contains slides not intended for presentation
Simulation vs. Experimental Results
VecTor2 Simulation
Experimental Results
Model: Galano P02
Cyclically Loaded
Conventionally Reinforced
 Background  Validation  Design  Analysis  Conclusions
Simulation vs. Experimental Results
VecTor2 Simulation
Experimental Results
Model: Tassios CB2B
Cyclically Loaded
Diagonally Reinforced
 Background  Validation  Design  Analysis  Conclusions
Experimental Test Program
Bidirectional
Loading
Unidirectional
Loading
Moment – Shear Ratio
Planar (2) Flanged Coupled
Core-Wall System
Long. Reinf.
Ratio
Load
History
SSI
Boundary
Conditions
Coupled Wall Test Program
 Research activities to support design of the coupled
wall test program.





Design a coupled wall representative of current design practices.
Obtain data on the performance and damage patterns of coupled
walls over the entire range of deformation.
Obtain data for development and verification of nonlinear
continuum models.
Compare a new coupling beam reinforcement design to the code
specified diagonally reinforced coupling beam.
Determine the effects of foundation stiffness on coupled wall
performance (to be done by UCLA).
Coupling Beam Reinf. Ratio
Diagonal Reinforcement Ratio
Diagonal Reinf. Coupling Beams
2.50%
2.00%
Galano 2000
Kw an 2004
Paulay 1971
Shiu 1978
Tassios 1996
BTT
EH
FS
MFC
1.50%
NEESR Wall
1.00%
0.50%
0.00%
0.00
1.00
2.00
3.00
Aspect Ratio
4.00
5.00
6.00
Kwan & Zhao 2002
Damage at ultimate drift
L/d = 1.17
Du/L = 5.7%
L/d = 1.17
Du/L = 5.4%
L/d = 1.40
L/d = 1.75
Du/L = 4.3%
Du/L = 3.6%
Galano & Vignoli 2000
Damage at ultimate state
L/d = 1.50
Du/L = 4.6%
L/d = 1.50
Du/L = 5.2%
L/d = 1.50
Du/L = 3.9%
L/d = 1.50
Du/L = 4.8%
Coupling Beam Performance
Nonlinear Continuum Model
 Nonlinear Continuum Models in Vector2
 Modeling of 7 experimental coupling beam tests to validate modeling assumptions
and process.
 Modeling approach will be used to predict the behavior of the wall specimens prior to
testing.
 Model Properties
 Disturbed Stress Field Theory (DSFT)



Based on the Modified Compression Field Theory (MCFT)
Allows for slip along crack surfaces
Nonlinear Material Models




Popovics/Mander Concrete model
Kupfer/Richart Confinement model
Vecchio 1992-B Compression Softening Model
Tri-linear Reinforcement hardening model
Correlations of Shear Strength to v
Yield Force vs. Vertical Reinf. Ratio
69.0
Shear at yield and ultimate increases
with vertical reinforcement ratio?
68.0
67.0
Specimen
MCBR-ACI
CBR-ACI
CBR-318H
MCBR-318H
CBR-318H-M
MCBR-318H-M
CBR-318H-F
MCBR-318H-F
Vy (kip)
Vu (kip)
v (%)
62.5
62.9
63.7
63.8
64.3
64.4
68.3
68.4
71.4
71.4
70.6
70.1
74.6
76.5
78.7
81.5
0.27
0.27
0.27
0.27
0.56
0.56
0.74
0.74
Vy (kip)

66.0
65.0
64.0
63.0
62.0
0.20
0.30
0.40
0.50
0.60
v (%)
 Background  Validation  Coupling Beams  Coupled Walls  Conclusions
0.70
0.80
Vector2 Compressive Stresses
Vector2 Crack Patterns
ZHAO MCB4 Specimen
Vector2 Model
Questions to Address
 What is the true failure or plastic mechanism of the coupled
shear wall?
 How should the coupling beams be detailed to minimize the
construction process and to provide adequate ductility?
 What effect does the foundation have on the performance of the
coupled shear wall?
VecTor2 Model Parameters
Constitutive Behavior
Model
Compression Base Curve
Popovics (NSC)
Compression Post-Peak
Popovics / Mander
Compression Softening
Vecchio 1992-B (e1/e0-Form)
Tension Stiffening
Modified Bentz 2003
Tension Softening
Bilinear
Tension Splitting
Not Considered
Confinement Strength
Kupfer / Richart Model
Concrete Dilation
Variable - Kupfer
Cracking Criterion
Mohr-Coulomb (stress)
Crack Slip Check
Vecchio-Collins 1986
Crack Width Check
Agg/5 Max Crack Width
Slip Distortions
Vecchio-Lai
Concrete Hysteresis
Nonlinear w/ Plastic Offsets
Steel Hysteresis
Elastic-Plastic w/ Hardening
Rebar Dowel Action
Tassios (Crack Slip)
Popovics Concrete Model
Vecchio & Wong, (2006),
VecTor2 User Manual
 Background  Model Evaluation  Coupling Beams  Coupled Walls  Conclusions
Suggestions for Future Research

Continue analysis of coupled walls under cyclic loading

Investigate additional wall configurations/designs


Lower degree of coupling in design
Vary coupling beam aspect ratio

Develop design recommendations that can ensure a coupled wall will exhibit the
“preferred” plastic mechanism, with yielding in the wall piers and at the end of all
the coupling beams.

Develop a method to account for over-strength in coupling beams with full
confinement per ACI 318H-CH047
Effect of Lateral Load Distribution

Effect of lateral load distribution is the
same for all coupled wall models.

Maximum base shear is inversely
proportional to effect shear height of
applied load.

Peak roof drift is directly proportional to
effective shear height.
Inter-story Drift
Full Strength coupling beams do not yield
resulting in a concentration of
deformation in the lower levels.

Reduced Strength coupling beams show
well distributed deformation over the
height of the wall.
Inter-story Drift vs. Level
Inter-story Drift,
12
fi (%)
Level
CW318HF-T
CWACI-T
CW318HFR-T
1
0.43
0.42
0.42
2
0.18
0.20
0.59
3
0.13
0.14
0.56
4
0.11
0.11
0.57
5
0.08
0.09
0.56
6
0.05
0.05
0.52
7
0.03
0.03
0.51
8
0.02
0.02
0.49
9
0.02
0.02
0.47
10
0.01
0.01
0.46
10
8
Level

CW-318HF-T
6
CW-ACI-T
CW-318HFR-T
4
2
0
0.00
0.20
0.40
0.60
Inter-story Drift (%)
0.80
Coupling Beam Demands

Full Strength coupling beams have very
little drift demand.
Coupling Beam Drift,

Reduced Strength coupling beams show
drift demand levels of 1 to 2.5%, sufficient
to cause yielding of the diagonal
reinforcement.
cb (%)
Level
CW318HF-T
CWACI-T
CW318HFR-T
1
0.03
0.03
1.11
2
0.09
0.09
2.00
3
0.10
0.16
2.31
4
0.09
0.12
2.46
5
0.08
0.10
2.51
6
0.08
0.10
2.47
7
0.07
0.08
2.42
8
0.05
0.06
2.35
9
0.04
0.04
2.29
10
0.02
0.02
2.11
CW-318HF-T - Full Strength
CW-318HF-T - Reduced Strength