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 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.

7. 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.

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 Hinges 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. Zones of different Reinf. Ratios & Reinf. Orientation Discrete Truss-Bar Elements 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 Conventionally Reinforced Tassios, Maretti and Bezas (1997) ACI Structural Journal 97 (6)

21. Vu δu δue Vue K1.5 δye δy Vye Ku K1.5e Kue Kye Vy Ky Results for Complete Coupling Beam Evaluation Study

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, Vuexceeding 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 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. NEESR Wall 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.  Background Model Evaluation Coupling Beams  Coupled Walls  Conclusions 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.