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Direct Displacement Design Methodology for Woodframe Buildings

WeiChiang Pang, Clemson University David Rosowsky, Rensselaer Polytechnic Institute John van de Lindt, University of Alabama Shiling Pei, South Dakota State University. Direct Displacement Design Methodology for Woodframe Buildings. Overview. Background on Displacement-based Design

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Direct Displacement Design Methodology for Woodframe Buildings

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  1. WeiChiang Pang, Clemson University David Rosowsky, Rensselaer Polytechnic Institute John van de Lindt, University of Alabama Shiling Pei, South Dakota State University Direct Displacement Design Methodology for Woodframe Buildings Quake Summit 2010, NEES & PEER Annual Meeting, Oct-9, San Francisco

  2. Overview • Background on Displacement-based Design • NEESWood Capstone Building • Design Objectives • Shear Wall System (Database) • Design Procedure • Verification • Nonlinear Time History Analyses (NLTHA) • ATC-63 Collapse Analysis • Summary

  3. Force-based v.s. Displacement-based Design • Displacement-based Design • Concept pioneered by Priestley (1998) • Displacement  damage indicator / seismic performance • For concrete and steel buildings • Force-based Design • Elastic fundamental period • Response of woodframe structures is highly nonlinear • Force is not a good damage indictor • No guarantee damage will be manageable

  4. TS Design spectrum (demand) Capacity spectrum TL Keff eff Force-based v.s. Displacement-based Design Force-based Displacement-Based • Direct period calculation • Actual mass and stiffness • Capacity Spectrum Approach • Approximate elastic fundamental period • period estimate based on building height and building type Location 1 Location 2 Sa Ta T

  5. Force-based v.s. Displacement-based Design Force-based Displacement-Based R • Actual nonlinear backbone curves • Numerical model or full-scale test • Response Modification Factor (R-factor) A yield point is assumed • Displacement is a good damage indictor • Force is not a good damage indictor

  6. Direct Displacement Design (DDD) • Objectives: • 1) Optimize distribution of story stiffness over the height of the building • 2) Minimize the probability of a weak story • Simplified Direct Displacement Design • Used to design the NEESWood Capstone Building • Does not require modal analysis (1st mode approximation) • Can be completed using spreadsheet • Drift limit NE probability other than 50%  Soft-story

  7. NEESWood Capstone Building 8ft 8ft • Plan Dimensions: 40x60 ft • Height: 56ft (6-story wood only) • 23 apartment units • Weight : ~2734 kips (wood only) • Shear Wall Design: Direct Displacement Design (DDD) • Tested on E-defense (Miki) Shake Table in July-2009 8ft 8ft 55.7 ft 8ft 9ft 60 ft 40 ft Photo credit: Courtesy of Simpson Strong-Tie

  8. Design Objectives • Performance => 1) inter-story drift limit 2) hazard level 3) non-exceedance probability

  9. Design Response Spectra • Typical Southern California seismic hazard • Site Class D (Stiff Soil) 5% damping

  10. Example 1st Floor Plan View E B A D Midply Wall 1 Stairway • 4 Apartment Units • Midply walls • carry high shear demand • Reduce torsional effect 2 Unit 3 Unit 1 4 N Elevator Shaft 6 59.5 ft 8 Unit 3 Unit 2 10 Midply Wall Standard Shearwall Y Stairway 39.8 ft Midply Shearwall X 11 Partition/ non-Shearwall

  11. Shear Wall System Standard /Conventional Shear Wall Sheathing Stud Nail in Single-shear Drywall 406mm 16 in 406mm 16 in 406mm 16 in Nail in Double-shear 406mm 16 in 406mm 16 in Midply Shear Wall Sheathing Drywall Construction concept developed by Forintek (Varoglu et al. 2007)

  12. Gravity Load Force-Displacement Response Contact element Hold-down Element End-nail Panel-to-frame nails Shear Wall Model • M-CASHEW model (Matlab) • Shear Wall Backbone database for different nail spacings Framing nails

  13. Wall Model Deformation Animation

  14. Example Shear Wall Database (per unit Width) Consider only full-height shear wall segments Backbone force Design drift Drift (%)

  15. Lognormally Distributed βEQ Lognormally Distributed βEQ ≈ 0.4 Far-field Ground Motion • ATC-63 , 22 bi-axial ground motions • MCE Level 3 Ground motion • Uncertainty ≈0.4 0.4

  16. 2.13% Target Inter-story Drift Distribution • Non-exceedance probability adjustment factor, CNE 80% Total Uncertainty βR= √( βEQ2+ βDS2) =√( 0.42+ 0.62) ≈ 0.75 4% drift at 80% NE Level 3 80% NE Level 3 50% 1.88 4 % drift

  17. Original Multi-story Building Substitute Structure w6 o6 F6=Cv6Vb eff w5 o5 Ft = Cc Weff F5=Cv5Vb Weff Ft eff w4 o4 F4=Cv4Vb w3 F3=Cv3Vb o3 Keff heff heff w2 F2=Cv2Vb o2 eff hs w1 o1 F1=Cv1Vb Vb = Cc Vb = Cc Mo = Ft heff Mo = Ft heff Substitute Structure (SDOF) • Vertical distribution factors (function of displacement) • Effective height • Effective seismic weight Weff≈ 0.8 total weight eff eff

  18. Sa, Ft/Weff TS Design spectrum (5% damping) Design spectrum (demand) adjusted for damping and target NE probability of drift limit Capacity spectrum Cc= 0.98 TL Keff eff Sd, Δ Capacity Spectrum Approach • Design base shear coefficient

  19. Design Forces • Step 9: Design forces Base Shear Design base shear coefficient  effective weight Story Shear • Step 10: Select shear wall nail spacing • Assume no torsion • Direct summation of the wall stiffness • Full-height shear wall segments Level 3 Story Shear Requirements

  20. Diaphragm Nonlinear Spring Numerical Models • Nonlinear Time-history Analysis (NLTHA) to verify the design M-SAWS

  21. Mode 3 T3=0.44s Mode 1 T1=0.54s Mode 2 T2=0.51s Periods and Mode Shapes

  22. Verification: Expected Peak Inter-story Drifts • Levels 1-3: ATC-63 Far Field Ground Motions (22 bi-axial) • Level 4: CUREE Near-fault Ground Motions <1% <4% <2% <7% Uniform Drift Profile

  23. Test versus Design Drifts

  24. Collapse Analysis (ATC-63 Methodology) • Adjusted CMR = SSF x CMR = 2.09 > 1.88 (passed ATC-63 requirement) • Unadjusted collapse margin ratio (CMR) is 2.57/1.50 = 1.71 • Spectral Shape Factor (SSF) = 1.22 • Collapse fragility curve • Incremental Dynamic Analysis Collapse Probability Median Sa @ Tn (g)

  25. Summary • Simplified direct displacement design (DDD) • Optimize distribution of story stiffness (avoid week story) • Focus on “performance” (i.e. control the drifts) • NLTHA not needed (optional) • Can consider multiple performance requirements • DDD procedure • A viable design method for tall woodframe buildings • Confirmed by NLTHA and full-scale shake table test • The collapse margin ratio of the Capstone Building passed the ATC-63 requirement • Next Step: • 1) Include rotation/torsional effects • 2) Modified for retrofitting purpose (pre-1970s buildings)

  26. Thank you • Contact Information: • Weichiang Pang • wpang@clemson.edu

  27. Shear Wall Model Design Variable • M-CASHEW model (Matlab) • 11.9mm (15/32”) OSB, 2x6 studs • 10d common nails (3.76mm dia.), nail spacing • 12.7mm (½”) Gypsum wallboard • 31.75mm long #6 drywall screws 406mm (16”) o.c.

  28. Sa, Ft/Weff TS Design spectrum at 5% damping Design spectrum (demand) adjusted for damping and target NE probability of drift limit Capacity spectrum Cc TL Keff eff Sd, Δ Capacity Spectrum Approach • Step 8: Design base shear coefficient Level 3 (MCE)

  29. Damping • Step 7: Damping reduction factor ASCE/SEI- 41 Effective damping = Intrinsic + Hysteretic damping 0.21 Ks/Ko

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