Title: Performance-Based Design and Nonlinear Modeling of Coupled Shear Walls and Coupling Beams
1Performance-Based Design and Nonlinear Modeling
of CoupledShear Walls and Coupling Beams
- Danya Mohr, Dawn Lehman and Laura Lowes,
- University of Washington
2NEESR Project Overview
- Research Objectives
- Improve understanding of the seismic behavior of
reinforced concrete core walls and develop tools
to enable performance-based 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
performance-based design recommendations.
3The 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
4Experimental Test Program
Coupling Beam Strength
Long. Reinf. Distribution
Load History
Moment Shear Ratio
Unidirectional Loading
Flanged
Planar (2)
Coupled
Bidirectional Loading
Core-Wall System
5Scope 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.
6Design of the Reference Coupled Wall
SpecimenBuilding 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.
7Design of the Reference Coupled Wall
SpecimenReview 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.
8Design 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)
9Code-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.
10Plastic 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.
11Coupled Wall Reinforcement
- Pier Reinforcement Ratios
- 1st Floor Pier
- ?h 0.54, Horizontal
- ?v 0.27, Vertical
- rb 3.64, Boundary
- Typical Pier
- ?h 0.27, Horizontal
- ?v 0.27, Vertical
- rb 3.64, Boundary
-
- Coupling Beams
- Diagonally Reinforced
- rd 0.83
12Coupling Beam Reinforcement
13Evaluation 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).
14VecTor2 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
the RC continuum.
Element Subject to Shear Normal Stress1
1. Vecchio Wong, (2006), VecTor2 User
Manual
15Evaluation 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
- Conventionally Reinforced
- 5 Monotonically Loaded
- 5 Cyclically Loaded
- Diagonally Reinforced
- 2 Monotonically Loaded
- 5 Cyclically Loaded
- Coupling beam tests include multiple behavior
modes - Flexure
- Flexure / Shear
- Diagonal Compression
- Flexure / Compression
- Flexure / Diagonal Tension
Flexure
Diagonal Compression
Flexure Shear
Flexure Compression
Galano Vignoli, (2000), ACI Structural Journal
97 (6)
16Nonlinear 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
Diagonally Reinforced Coupling Beam
17Simulation versus Experimental
VecTor2 Simulation
Experimental Results
Model Galano P01 Monotonically
Loaded Conventionally Reinforced
Galano Vignoli, (2000), ACI Structural
Journal 97 (6)
18Simulation versus Experimental
VecTor2 Simulation
Experimental Results
Model Galano P05 Monotonically
Loaded Conventionally Reinforced
Galano Vignoli, (2000), ACI Structural
Journal 97 (6)
19Simulation versus Experimental
VecTor2 Simulation
Experimental Results
Model Galano P07 Cyclically Loaded Conventionally
Reinforced
Galano Vignoli, (2000), ACI Structural
Journal 97 (6)
20Simulation versus Experimental
VecTor2 Simulation
Experimental Results
Model Tassios CB1A Cyclically Loaded Conventional
ly Reinforced
Tassios, Maretti and Bezas (1997) ACI Structural
Journal 97 (6)
21Results for Complete Coupling Beam Evaluation
Study
Vy/Vye Vu/Vue Ky/Kye Ku/Kue K1.5/ K1.5e dy/dye du/due
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
22Coupling 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
23Evaluation 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 4vfcbwd
- Additionally, confinement required around
diagonal bar groups to meet - 21.4.4.1(b) - Ash 0.09s bc fc/fy
- 21.4.4.2 - Spacing less than
- 1/4 min. member dimension
- 6 times db long. bar
- 4 (14 hx)/3
- 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 318-05 Code Compliant Coupling Beam
ACI 318H Full Confinement Proposal
24Coupling Beam Model Properties
25Comparisons / 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
26Coupled Wall Models
- Full ten story wall modeled.
- Use same model parameters and analysis
assumptions as coupling beam simulations.
CW-318H-F VecTor2 Model
27Coupled 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
28Deformed Shape at Max Base Shear Inv. Triangular
Load Distribution
CW-ACI-T
CW-318HF-T
CW-318HFR-T
29Deformed Shape at Max Base ShearUniform Load
Distribution
CW-ACI-U
CW-318HF-U
CW-318HFR-U
30Deformed Shape at Max Base Shear0.3H Eff. Height
Load Distribution
CW-ACI-3H
CW-318HF-3H
CW-318HFR-3H
31Effect 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.
32Conclusions
- 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. - 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. - Strength of coupling beams must be reduced to
achieve desired plastic mechanism - 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.
33Future 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.
34Appendix
- Contains slides not intended for presentation
35Simulation vs. Experimental Results
VecTor2 Simulation
Experimental Results
Model Galano P02 Cyclically Loaded Conventionally
Reinforced
? Background ? Validation ? Design ? Analysis ?
Conclusions
36Simulation vs. Experimental Results
VecTor2 Simulation
Experimental Results
Model Tassios CB2B Cyclically Loaded Diagonally
Reinforced
? Background ? Validation ? Design ? Analysis ?
Conclusions
37Experimental Test Program
SSI Boundary Conditions
Long. Reinf. Ratio
Load History
Moment Shear Ratio
Unidirectional Loading
Flanged
Planar (2)
Coupled
Bidirectional Loading
Core-Wall System
38Coupled 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).
39Coupling Beam Reinf. Ratio
40Kwan Zhao 2002Damage at ultimate drift
L/d 1.17 Du/L 5.4
L/d 1.17 Du/L 5.7
L/d 1.40 Du/L 4.3
L/d 1.75 Du/L 3.6
41Galano Vignoli 2000Damage at ultimate state
L/d 1.50 Du/L 4.6
L/d 1.50 Du/L 3.9
L/d 1.50 Du/L 5.2
L/d 1.50 Du/L 4.8
42Coupling Beam Performance
43Nonlinear 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
44Correlations of Shear Strength to ?v
- Shear at yield and ultimate increases with
vertical reinforcement ratio?
? Background ? Validation ? Coupling Beams ?
Coupled Walls ? Conclusions
45Vector2 Compressive Stresses
46Vector2 Crack Patterns
ZHAO MCB4 Specimen
Vector2 Model
47Questions 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?
48VecTor2 Model Parameters
Popovics Concrete Model
Vecchio Wong, (2006), VecTor2 User Manual
49Suggestions 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
50Effect 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.
51Inter-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.
52Coupling Beam Demands
- Full Strength coupling beams have very little
drift demand.
- Reduced Strength coupling beams show drift demand
levels of 1 to 2.5, sufficient to cause yielding
of the diagonal reinforcement.
CW-318HF-T - Full Strength
CW-318HF-T - Reduced Strength