1. Task 1.4.6 Seismic Performance of Gypsum Walls – Analytical Study Gregory G. Deierlein & Amit Kanvinde Stanford University CUREe-Caltech Woodframe Project Meeting January 12-13, 2001

2. Overview Load-Deformation Response –K I and V u –Backbone Curve –Hysteretic Model Damage Analysis –Cracking Behavior –Empirical Fragility Model –Analysis-Based Fragility Model

3. Monotonic Wall Response Major failures, e.g., pulling away of sheetrock from the frame, buckling etc. Nail popping Diagonal Cracking VuVu 0.6V u K eff

4. Shear Stiffness Model Effective Shear Area K eff = G eff  t  l * / h Calibrated Coefficients: C = 1.1 G wall = 16 ksi G conn =  g conn  = conn. density (c/sq.ft.) g nail = 14 ksi g screw = 24 ksi

5. Stiffness Comparison TestConn.  conn (conn/sq ft) Calculated StiffnessMeas. K eff (kips/inch) G eq (ksi)K eff (k/in) OlivaN81.39.04.65.8 SJSU 1N81.39.014.812 SJSU 2S160.658.313.613.3 SJSU 3S160.658.313.614.3 SJSU 4S81.311.318.515.8 SJSU 5S160.658.313.612.6 SJSU 6S160.658.313.614.9 SJSU 7S160.658.313.612.0 SJSU 8N81.69.816.316.0 SJSU 12 w/window S160.89.211.712.9

6. Stiffness Comparison (cont’d)

7. Force Transfer Mechanisms V C B TD V = C + B < V TD

8. Shear Strength Model Effective Shear Area V u = (C o + C 1    l * + B < V OT Calibrated Coef. (2 sided ½ in): C o = 350 plf (S16); 350 plf (N8) C 1 = 250 plf (screw)  * =  - 0.65 (screw/sf) B = (3500 lb) l adj /h < 3500 lb V OT by analysis Note – UBC Table 25-1 gives V allow = 200 lb/foot (2 sided, ½ in) reduce 50% for seismic and 25% long term

9. Shear Panel Strength * Bearing strength limited by boundary element failure ** Strength limited by uplift/overturning

10. Shear Panel Strength Failed boundary member Uplift

11. Backbone Load-Deflection Curves K1K1 K2K2 Force Displacement K4K4 K 3 =0 u1u1 u3u3 P max Fig 2.7 Modified Trilinear Model 1(b) P 0 =P max K1K1 K p =0 K4K4 u3u3 Different Shapes due to different shape parameter n Fig 2.9 Modified Power Model P0P0 Force Displacement K4K4 K1K1 Fig 2.10. Unloading Slope Exponential Model Shape depends on the parameter n

12. Power Model vs. Test Data SJSU #5SJSU #6 Using calculated K eff and P u and average plot coefficients; n= 8.5(K 2 /K eff )+1.2, K2 = 220 lb/in/ft, u unload = 0.01H, K unload = -110 lb/in/ft)

13. Hysteretic Model (SJSU #7) Rule-based Model with 14 parameters (pinching, energy dissipation etc., following Rahnama & Krawinkler, 1993) (trailing cycles omitted for clarity)

14. Crack Growth Fragility Analysis 2 3 1 P,  Two Approaches: Simple Empirical (  versus a from test data) Analysis-Based Empirical -Test Data (P, , a)  FEM Analysis  Prob.Dist.(K ic & G eff ) -Prob.Dist.(K ic & G eff )  FEM Analysis  Fragility( , a) Crack Initiation Length (a)  a SJSU #6

15. Empirical Fragility Curves Crack Lengths

16. Analysis-Based Fragility 1 in. 12 in. 1 in. 12 in. Drift Ratio (%) Probability 0.1 0.2 0.30.40.5

17. Final Remarks Load-Deflection Models Crack Growth –typically occurs between  /H = 0.1% to 0.8% –fairly linear with load and displacement in this range –potential as indicator of drift demand Remaining Work –incorporate remaining SJSU test data –fracture analysis-based fragility curves –complete Final Report