Direct Displacement Design Methodology for Woodframe Buildings Wei

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Direct Displacement Design Methodology for Woodframe Buildings • Wei. Chiang • David • John

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

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

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

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

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

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:

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

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

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

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

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

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

Wall Model Deformation Animation 13 13

Example Shear Wall Database (per unit Width) Consider only full-height shear wall segments Backbone

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

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

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

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%

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

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

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

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

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.

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 >

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

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 wpang@clemson. edu 26

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

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 ,

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-

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