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 Quake Summit 2010, NEES & PEER Annual Meeting, Oct-9, San Francisco

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

Force-based v.s. Displacement-based Design 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 Displacement-based Design Concept pioneered by Priestley (1998) Displacement  damage indicator / seismic performance For concrete and steel buildings

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

Force-based v.s. Displacement-based Design Force-based Displacement-Based 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 R

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  Soft-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%

NEESWood Capstone Building 60 ft 40 ft 9ft 8ft 55.7 ft 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 Photo credit: Courtesy of Simpson Strong-Tie

Performance Expectations Inter-Story Drift Limit Design Objectives Performance => 1) inter-story drift limit 2) hazard level 3) non-exceedance probability Level Seismic Hazard Performance Expectations Description Exceedance Prob. Inter-Story Drift Limit NE Prob. Level 1 Short Return Period Earthquake 50%/50yr 1% 50% Level 2 Design Basis Earthquake (DBE) 10%/50yr 2% Level 3 Maximum Credible Earthquake (MCE) 2%/50yr 4% 80% Level 4 Near Fault 7%

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

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

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

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

Wall Model Deformation Animation

Example Shear Wall Database (per unit Width) Consider only full-height shear wall segments Backbone force Design drift Drift (%) Wall Height (ft) Wall Type/ Sheathing Layer Edge Nail Spacing (in) Ko (kip/in per ft) Fu (kip per ft) Backbone Force at Different Drift Levels (kip per ft) Wall Drift 0.5% 1.0% 2.0% 3.0% 4.0% 9 Standard 2 3.95 2.17 1.33 1.83 1.87 1.57 3 3.24 1.46 0.99 1.29 1.45 1.24 1.02 4 2.76 1.12 0.79 1.00 1.11 0.94 0.77 6 1.98 0.56 0.69 0.75 0.65 0.54 Midply 5.03 4.22 2.04 3.18 3.64 3.06 4.38 2.86 1.63 2.38 2.81 2.43 2.06 3.84 2.18 1.35 1.90 2.11 1.56 3.16 1.49 1.43 1.25 1.07 GWB 16 0.14 0.13 0.09 0.06 0.03

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

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

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

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

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

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

Periods and Mode Shapes Model M-SAWS SAPWood Test Mode Initial Stiffness Tangent Stiffness at 0.15% Drift Initial Period 1 2 3 0.38 0.36 0.32 0.54 0.51 0.44 0.40 0.39 0.42 0.41 - Mode 1 T1=0.54s Mode 2 T2=0.51s Mode 3 T3=0.44s

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

Test versus Design Drifts Level Test Inter-Story Drift Design Limit 1 2 3 ~0.75% ~1.30% 3.08% (max) 1% 2% 4%

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 Probability Median Sa @ Tn (g) Collapse fragility curve Incremental Dynamic Analysis

Summary DDD procedure 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)

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

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. Design Variable

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

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