# Direct Displacement Design Methodology for Woodframe Buildings Wei

• Slides: 29

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

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

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

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

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

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

NEESWood Capstone Building 8 ft 8 ft 55. 7 ft 8 ft Plan Dimensions: 40 x 60 ft Height: 56 ft (6 -story wood only) 23 apartment units Weight : ~2734 kips (wood only) Shear Wall Design: Direct Displacement Design (DDD) 8 ft 9 ft 60 ft Tested on E-defense (Miki) Shake Table in July-2009 40 ft Photo credit: Courtesy of Simpson Strong-Tie 7

Design Objectives Performance => 1) inter-story drift limit 2) hazard level 3) non-exceedance probability Seismic Hazard Level Description Performance Expectations Exceedance Inter-Story Prob. Drift Limit NE Prob. Level 1 Short Return Period Earthquake 50%/50 yr 1% 50% Level 2 Design Basis Earthquake (DBE) 10%/50 yr 2% 50% Level 3 Maximum Credible Earthquake (MCE) 2%/50 yr 4% 80% Level 4 Near Fault 7% 50% 8

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

Example 1 st Floor Plan View B A E D 1 Midply Wall Stairway 2 Unit 3 Unit 1 � 4 Apartment Units � Midply walls � carry high shear 4 59. 5 ft Elevator Shaft N 6 demand � Reduce torsional effect 8 Standard Shearwall Unit 3 Unit 2 Midply Wall 10 Y Partition/ non-Shearwall Stairway X 11 39. 8 ft Midply Shearwall 10

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

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

Wall Model Deformation Animation 13 13

Example Shear Wall Database (per unit Width) Consider only full-height shear wall segments Backbone force Design drift Wall Type/ Edge Nail Ko Fu Height Sheathing Spacing (kip/in (kip per ft) (ft) Layer (in) per ft) Standard 9 Midply GWB 2 3 4 6 16 3. 95 3. 24 2. 76 1. 98 5. 03 4. 38 3. 84 3. 16 1. 29 2. 17 1. 46 1. 12 0. 77 4. 22 2. 86 2. 18 1. 49 0. 14 Drift (%) Backbone Force at Different Drift Levels (kip per ft) Wall Drift 0. 5% 1. 0% 2. 0% 3. 0% 4. 0% 1. 33 1. 83 2. 17 1. 87 1. 57 0. 99 1. 29 1. 45 1. 24 1. 02 0. 79 1. 00 1. 11 0. 94 0. 77 0. 56 0. 69 0. 75 0. 65 0. 54 2. 04 3. 18 4. 22 3. 64 3. 06 1. 63 2. 38 2. 81 2. 43 2. 06 1. 35 1. 90 2. 11 1. 83 1. 56 1. 02 1. 35 1. 43 1. 25 1. 07 0. 13 0. 09 0. 06 0. 03 14

L o g n o r m a l l y D i s t r i b u t e d β E Q Far-field Ground Motion Ø ATC-63 , 22 bi-axial ground motions Ø MCE Level 3 Ground motion Ø Uncertainty ≈ 0. 4 Lognormally Distributed βEQ ≈ 0. 4 15

Target Inter-story Drift Distribution � Non-exceedance probability adjustment factor, CNE 80% NE Level 3 4% drift at 80% NE Level 3 50% 1. 88 Total Uncertainty βR= √( βEQ 2+ βDS 2) =√( 0. 42+ 0. 62) ≈ 0. 75 2. 13% 4 % drift 16

Substitute Structure (SDOF) Vertical distribution factors (function of displacement) Effective height Effective seismic weight Weff ≈ 0. 8 total weight Original Multi-story Building w 6 F 6=Cv 6 Vb w 5 F 5=Cv 5 Vb Ft hs F 1=Cv 1 Vb w 1 eff Ft = Cc Weff Weff o 3 w 2 F 2=Cv 2 Vb o 5 o 4 w 3 F 3=Cv 3 Vb heff w 4 F 4=Cv 4 Vb Substitute Structure o 6 o 2 Keff heff o 1 Vb = Cc Mo = Ft heff 17

Capacity Spectrum Approach Design base shear coefficient 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 Sd , Δ 18

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

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

Periods and Mode Shapes Model Mode 1 2 3 M-SAWS SAPWood Tangent Stiffness Initial Stiffness at 0. 15% Drift 0. 38 0. 54 0. 40 0. 36 0. 51 0. 39 0. 32 0. 44 0. 32 Mode 1 T 1=0. 54 s Mode 2 T 2=0. 51 s Test Initial Period 0. 42 0. 41 - Mode 3 T 3=0. 44 s 21

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% <2% <4% <7% Uniform Drift Profile 22

Test versus Design Drifts Test Inter-Story Design Level Drift Limit 1 2 3 ~0. 75% ~1. 30% 3. 08% (max) 1% 2% 4% 23

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 q q Collapse fragility curve q Incremental Dynamic Analysis Median Sa @ Tn (g) 24

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

Thank you Contact Information: Weichiang Pang [email protected] edu 26

Shear Wall Model q M-CASHEW model (Matlab) q 11. 9 mm (15/32”) OSB, 2 x 6 studs q 10 d common nails (3. 76 mm dia. ), nail spacing q 12. 7 mm (½”) Gypsum wallboard q 31. 75 mm long #6 drywall screws 406 mm (16”) o. c. Design Variable 27

Capacity Spectrum Approach Step 8: Design base shear coefficient Level 3 (MCE) 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 T Keff L ef Sd , Δ 28

Damping Step 7: Damping reduction factor Effective damping = Intrinsic + Hysteretic damping ASCE/SEI- 41 0. 21 Ks/Ko 29