Performance-Based Design and Nonlinear Modeling of Coupled Shear Walls and Coupling Beams
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Transcript of Performance-Based Design and Nonlinear Modeling of Coupled Shear Walls and Coupling Beams
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 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.
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
Moment – Shear RatioCoupling
Beam Strength
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Planar (2) Flanged Coupled
Core-Wall System
LoadHistory
Long. Reinf.Distribution
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 TowerPhoto 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.
PlasticHinges
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
the RC continuum.
1. Vecchio & Wong, (2006), VecTor2 User Manual
Element Subject to Shear & Normal Stress1
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 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 Compression
FlexureShear
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
Diagonally Reinforced Coupling Beam
Discrete Truss-Bar Elements
Zones of different Reinf. Ratios & Reinf. Orientation
Simulation versus Experimental
VecTor2 Simulation Experimental Results
Model: Galano P01Monotonically Loaded
Conventionally Reinforced
Galano & Vignoli, (2000), ACI Structural Journal 97 (6)
Simulation versus Experimental
VecTor2 Simulation Experimental Results
Model: Galano P05Monotonically Loaded
Conventionally Reinforced
Galano & Vignoli, (2000), ACI Structural Journal 97 (6)
Simulation versus Experimental
VecTor2 Simulation Experimental Results
Galano & Vignoli, (2000), ACI Structural Journal 97 (6)
Model: Galano P07Cyclically Loaded
Conventionally Reinforced
Simulation versus Experimental
VecTor2 Simulation Experimental Results
Model: Tassios CB1ACyclically Loaded
Conventionally Reinforced Tassios, Maretti and Bezas (1997)
ACI Structural Journal 97 (6)
δueδu
Vye
Vy
K1.5e
K1.5
Kue
Ku
Vue
Vu
Kye
Ky
δye
δy
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
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
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 CompliantCoupling Beam
ACI 318H Full ConfinementProposal
Coupling Beam Model Properties
f'c 5.0 Ksi fy 60 Ksi Scale 1/3
ft 0.50 Ksi fu 90 Ksi Aspect Ratio 1.5
Ec 4030 Ksi Es 29000 Ksi Length 24 in
0.003 Esh 170 Ksi Height 16 in
0.010 Depth 6 in
Concrete Reinforcement Geometry
l v h Ad dv dt Diag sdiag ties
Specimen (Ast/d t) (Av/s t) (Ah/d s) (in2) (Adt/d c st) (Adt/t c st) Ties (in)
CBR-ACI 0.31% 0.27% 0.10% 0.80 1.63% 3.27% 2 #2 1
CBR-318H 0.31% 0.27% 0.10% 0.80 1.09% 2.18% 2 #2 1.5
CBR-318H-F 0.42% 0.74% 0.74% 0.80 - - - -
CBR-318H-M 0.28% 0.56% 0.35% 0.80 - - - -
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-FVecTor2 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 ShearUniform Load Distribution
CW-ACI-U CW-318HF-U CW-318HFR-U
Deformed Shape at Max Base Shear0.3H 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 Load35% - Inverted Triangular load59% - 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.
“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.
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
Background Validation Design Analysis Conclusions
Model: Galano P02Cyclically Loaded
Conventionally Reinforced
VecTor2 Simulation Experimental Results
Simulation vs. Experimental Results
Background Validation Design Analysis Conclusions
Model: Tassios CB2BCyclically Loaded
Diagonally Reinforced
VecTor2 Simulation Experimental Results
Experimental Test Program
Moment – Shear RatioSSI
BoundaryConditions
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Planar (2) Flanged Coupled
Core-Wall System
LoadHistory
Long. Reinf.Ratio
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 Reinf. Coupling Beams
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
0.00 1.00 2.00 3.00 4.00 5.00 6.00
Aspect Ratio
Dia
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Rat
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Galano 2000
Kwan 2004
Paulay 1971
Shiu 1978
Tassios 1996
BTT
EH
FS
MFC
NEESR Wall
Kwan & Zhao 2002Damage at ultimate drift
L/d = 1.17Du/L = 5.7%
L/d = 1.75
Du/L = 3.6%
L/d = 1.17
Du/L = 5.4%
L/d = 1.40
Du/L = 4.3%
Galano & Vignoli 2000Damage at ultimate state
L/d = 1.50Du/L = 4.6%
L/d = 1.50Du/L = 5.2%
L/d = 1.50Du/L = 3.9%
L/d = 1.50Du/L = 4.8%
Coupling Beam Performance
Coupling BeamsDisplacement Ductility vs. Shear Stress Demand
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0
Ultimate Ductility
Conventional
Diagonal
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
62.0
63.0
64.0
65.0
66.0
67.0
68.0
69.0
0.20 0.30 0.40 0.50 0.60 0.70 0.80
v (%)
Vy
(kip
)
Specimen Vy (kip) Vu (kip) v (%)
MCBR-ACI 62.5 71.4 0.27CBR-ACI 62.9 71.4 0.27CBR-318H 63.7 70.6 0.27MCBR-318H 63.8 70.1 0.27CBR-318H-M 64.3 74.6 0.56MCBR-318H-M 64.4 76.5 0.56CBR-318H-F 68.3 78.7 0.74MCBR-318H-F 68.4 81.5 0.74
Shear at yield and ultimate increases with vertical reinforcement ratio?
Background Validation Coupling Beams Coupled Walls Conclusions
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
Popovics Concrete Model
Vecchio & Wong, (2006), VecTor2 User Manual
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)
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.
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
Inter-story Drift, fi (%)
Inter-story Drift vs. Level
0
2
4
6
8
10
12
0.00 0.20 0.40 0.60 0.80
Inter-story Drift (%)
Level
CW-318HF-T
CW-ACI-T
CW-318HFR-T
Reduced Strength coupling beams show well distributed deformation over the height of the wall.
Coupling Beam Demands
Full Strength coupling beams have very little drift demand.
Level CW318HF-T CWACI-T CW318HFR-T
1 0.03 0.03 1.112 0.09 0.09 2.003 0.10 0.16 2.314 0.09 0.12 2.465 0.08 0.10 2.516 0.08 0.10 2.477 0.07 0.08 2.428 0.05 0.06 2.359 0.04 0.04 2.29
10 0.02 0.02 2.11
Coupling Beam Drift, cb (%)
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