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

Overview

• Load-Deformation Response– KI and Vu

– Backbone Curve

– Hysteretic Model

• Damage Analysis– Cracking Behavior

– Empirical Fragility Model

– Analysis-Based Fragility Model

Monotonic Wall Response

-50

0

50

100

150

200

250

300

350

400

450

-0.005 0 0.005 0.01 0.015 0.02 0.025 0.03

Drift Ratio

Force/Length of Wall

Major failures, e.g., pulling away of sheetrock from the frame, buckling etc.

Nail popping

Diagonal Cracking

Vu

0.6Vu

Keff

Shear Stiffness Model

Effective Shear Area

Keff = Geff tl* / h

√√↵

+=

connwalleff GGC

G

111

Calibrated Coefficients:

C = 1.1

Gwall = 16 ksi

Gconn = gconn

= conn. density (c/sq.ft.)

gnail = 14 ksi

gscrew = 24 ksi

Stiffness Comparison

Test Conn. conn

(conn/sq ft)

Calculated Stiffness Meas. Keff

(kips/inch) 

Geq (ksi) Keff (k/in)

Oliva N8 1.3 9.0 4.6 5.8

SJSU 1 N8 1.3 9.0 14.8 12

SJSU 2 S16 0.65 8.3 13.6 13.3

SJSU 3 S16 0.65 8.3 13.6 14.3

SJSU 4 S8 1.3 11.3 18.5 15.8

SJSU 5 S16 0.65 8.3 13.6 12.6

SJSU 6 S16 0.65 8.3 13.6 14.9

SJSU 7 S16 0.65 8.3 13.6 12.0

SJSU 8 N8 1.6 9.8 16.3 16.0

SJSU 12 w/window

S16 0.8 9.2 11.7 12.9

Stiffness Comparison (cont’d)

Force Transfer Mechanisms

V

C

B

TD

V = C + B < VTD

Shear Strength Model

Effective Shear Area

Vu = (Co + C1l* + B < VOT

Calibrated Coef. (2 sided ½ in):

Co = 350 plf (S16); 350 plf (N8)

C1 = 250 plf (screw)

* = - 0.65 (screw/sf)

B = (3500 lb) ladj/h < 3500 lb

VOT by analysis

Note – UBC Table 25-1 gives Vallow = 200 lb/foot (2 sided, ½ in)

reduce 50% for seismic and 25% long term

Shear Panel Strength

Spec.# Conn. l* (ft) Co (lb) C1 (lb) B (lb) Vu,calc. (lb) Calc./Meas.

Oliva N8 8.0 1600 0 0 2800 0.88SJSU 1 S16 13.2 4620 2145 3500* 10265 1.66*SJSU 2 S16 13.2 4620 0 3500 8120 1.54**SJSU 3 S16 13.2 4620 0 3500 8120 0.92SJSU 4 S8 13.2 4620 2145 3500 10265 0.90SJSU 5 S8 13.2 4620 0 3500 8120 0.97SJSU 6 S8 13.2 4620 0 3500 8120 1.01SJSU 7 S8 13.2 4620 0 3500 8120 1.63**SJSU 8 N8 13.2 4620 3500 8120 0.96SJSU 10 S16 10.2 3570 383 1313 5265 0.92SJSU 11 S16 10.2 3570 383 1313 5265 1.02SJSU 12 S16 10.2 3570 383 1313 5265 0.84

* Bearing strength limited by boundary element failure

** Strength limited by uplift/overturning

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 2 3 4 5 6 7 8 9 10 11 12

Test Specimen

Vcalc

/Vmeas Bearing

C1

CoC

Shear Panel Strength

Failed

boun

dary

membe

r

Uplift Upli

ft

Backbone Load-Deflection Curves

K1

K2

Force

Displacement

K4

K3=0

u1 u3

Pmax

Fig 2.7 Modified Trilinear Model 1(b)

P0=Pmax

K1

Kp=0

K4

u3

Different Shapes due to different shape parameter n

Fig 2.9 Modified Power Model

P0Forc

e

Displacement

K4

K1

Fig 2.10. Unloading Slope Exponential Model

Shape depends on the parameter n

Power Model vs. Test Data

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 0.5 1 1.5 2 2.5 3 3.5 4

Drift (Inches)

Force (Pounds)

SJSU #5 SJSU #6

Using calculated Keff and Pu and average plot coefficients;

n= 8.5(K2/Keff)+1.2, K2 = 220 lb/in/ft, uunload = 0.01H, Kunload = -110 lb/in/ft)

Hysteretic Model (SJSU #7)

Rule-based Model with 14 parameters (pinching, energy dissipation etc., following Rahnama & Krawinkler, 1993)

-5 -4 -3 -2 -1 0 1 2 3 4 5-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

(trailing cycles omitted for clarity)

Crack Growth Fragility Analysis

2

3

1P,

Two Approaches:

• Simple Empirical ( versus a from test data)

• Analysis-Based Empirical

-Test Data (P, , a) FEM Analysis Prob.Dist.(Kic & Geff)

-Prob.Dist.(Kic & Geff) FEM Analysis Fragility( , a)

Crack Initiation

Length (a)

Test # 5 Front of Wall

y = 55.353x - 10.163

0

5

10

15

20

25

30

35

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Drift (Inches)

Crack Length (Inches)

a

SJSU #6

Empirical Fragility Curves

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8

Drift Ratio (%)

Probability

1 in.

5 in.

10 in.

15 in.

20 in.

Crack Lengths

Analysis-Based Fragility

1 in.

12 in.

1 in.

12 in.

Drift Ratio (%)

Pro

babi

lity

Pro

babi

lity

0.1 0.2 0.3 0.4 0.5

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