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Title: Performance-Based Design and Nonlinear Modeling of Coupled Shear Walls and Coupling Beams


1
Performance-Based Design and Nonlinear Modeling
of CoupledShear Walls and Coupling Beams
  • Danya Mohr, Dawn Lehman and Laura Lowes,
  • University of Washington

2
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.

3
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

4
Experimental Test Program
Coupling Beam Strength
Long. Reinf. Distribution
Load History
Moment Shear Ratio
Unidirectional Loading
Flanged
Planar (2)
Coupled
Bidirectional Loading
Core-Wall System
5
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.
6
Design 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.

7
Design 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.

8
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)

9
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.

10
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.

11
Coupled 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

12
Coupling Beam Reinforcement
13
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).

14
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.

Element Subject to Shear Normal Stress1
1. Vecchio Wong, (2006), VecTor2 User
Manual
15
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 Shear
Flexure Compression
Galano Vignoli, (2000), ACI Structural Journal
97 (6)
16
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
17
Simulation versus Experimental
VecTor2 Simulation
Experimental Results
Model Galano P01 Monotonically
Loaded Conventionally Reinforced
Galano Vignoli, (2000), ACI Structural
Journal 97 (6)
18
Simulation versus Experimental
VecTor2 Simulation
Experimental Results
Model Galano P05 Monotonically
Loaded Conventionally Reinforced
Galano Vignoli, (2000), ACI Structural
Journal 97 (6)
19
Simulation versus Experimental
VecTor2 Simulation
Experimental Results
Model Galano P07 Cyclically Loaded Conventionally
Reinforced
Galano Vignoli, (2000), ACI Structural
Journal 97 (6)
20
Simulation versus Experimental
VecTor2 Simulation
Experimental Results
Model Tassios CB1A Cyclically Loaded Conventional
ly Reinforced
Tassios, Maretti and Bezas (1997) ACI Structural
Journal 97 (6)
21
Results 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
22
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

23
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 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
24
Coupling Beam Model Properties
25
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

26
Coupled Wall Models
  • Full ten story wall modeled.
  • Use same model parameters and analysis
    assumptions as coupling beam simulations.

CW-318H-F VecTor2 Model
27
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

28
Deformed Shape at Max Base Shear Inv. Triangular
Load Distribution
CW-ACI-T
CW-318HF-T
CW-318HFR-T
29
Deformed Shape at Max Base ShearUniform Load
Distribution
CW-ACI-U
CW-318HF-U
CW-318HFR-U
30
Deformed Shape at Max Base Shear0.3H Eff. Height
Load Distribution
CW-ACI-3H
CW-318HF-3H
CW-318HFR-3H
31
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.

32
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.

33
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.

34
Appendix
  • Contains slides not intended for presentation

35
Simulation vs. Experimental Results
VecTor2 Simulation
Experimental Results
Model Galano P02 Cyclically Loaded Conventionally
Reinforced
? Background ? Validation ? Design ? Analysis ?
Conclusions
36
Simulation vs. Experimental Results
VecTor2 Simulation
Experimental Results
Model Tassios CB2B Cyclically Loaded Diagonally
Reinforced
? Background ? Validation ? Design ? Analysis ?
Conclusions
37
Experimental Test Program
SSI Boundary Conditions
Long. Reinf. Ratio
Load History
Moment Shear Ratio
Unidirectional Loading
Flanged
Planar (2)
Coupled
Bidirectional Loading
Core-Wall System
38
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).

39
Coupling Beam Reinf. Ratio
40
Kwan 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
41
Galano 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
42
Coupling Beam Performance
43
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

44
Correlations of Shear Strength to ?v
  • Shear at yield and ultimate increases with
    vertical reinforcement ratio?

? Background ? Validation ? Coupling Beams ?
Coupled Walls ? Conclusions
45
Vector2 Compressive Stresses
46
Vector2 Crack Patterns
ZHAO MCB4 Specimen
Vector2 Model
47
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?

48
VecTor2 Model Parameters

Popovics Concrete Model
Vecchio Wong, (2006), VecTor2 User Manual
49
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

50
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.

51
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.

52
Coupling 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
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