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

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

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

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

Stiffness Comparison TestConn.  conn (conn/sq ft) Calculated StiffnessMeas. K eff (kips/inch) G eq (ksi)K eff (k/in) OlivaN SJSU 1N SJSU 2S SJSU 3S SJSU 4S SJSU 5S SJSU 6S SJSU 7S SJSU 8N SJSU 12 w/window S

Stiffness Comparison (cont’d)

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

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)  * =  (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

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

Shear Panel Strength Failed boundary member Uplift

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 Unloading Slope Exponential Model Shape depends on the parameter n

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)

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

Crack Growth Fragility Analysis 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

Empirical Fragility Curves Crack Lengths

Analysis-Based Fragility 1 in. 12 in. 1 in. 12 in. Drift Ratio (%) Probability

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