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

Un

idir

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on

alL

oad

ing

Bid

irec

tio

nal

Lo

adin

g

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




Model: Galano P05Monotonically Loaded






Model: Galano P07Cyclically Loaded




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



Simulation vs. Experimental Results

Background Validation Design Analysis Conclusions

Model: Tassios CB2BCyclically Loaded

Diagonally Reinforced


Experimental Test Program

Moment – Shear RatioSSI

BoundaryConditions

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oad

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Bid

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Lo

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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

go

nal

Rei

nfo

rcem

ent

Rat

io

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

performance-based design and nonlinear modeling of coupled shear walls and coupling beams

Documents

coupled wall tests

coupled wall configuration

coupled wall system

coupled wall specimens

wall flexu

coupled wall research

typical coupled wall

coupled shear walls