wood frame design

1. •WeiChiang Pang, Clemson University
•David Rosowsky, Rensselaer Polytechnic Institute
•John van de Lindt, University of Alabama
•Shiling Pei, South Dakota State University
Quake Summit 2010, NEES & PEER Annual Meeting, Oct-9, San Francisco

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

3. 3
Displacement-based Design
 Concept pioneered by Priestley (1998)
Displacement  damage indicator / seismic performance
For concrete and steel buildings
Force-based Design
Elastic fundamental period
Response of woodframe structures is highly nonlinear
Force is not a good damage indictor
No guarantee damage will be manageable

4. 4
Force-based Displacement-Based
x
a tT C h
• period estimate based on building
height and building type
 Approximate elastic fundamental period  Direct period calculation
• Actual mass and stiffness
• Capacity Spectrum Approach
Sa
T
Ta
Location 1
Location 2
eff
TS
TL
Design spectrum
(demand)
Capacity spectrum
Keff

5. 5
R
Force-based Displacement-Based
 Response Modification Factor (R-factor)
A yield point is assumed
 Force is not a good damage indictor
-4 -3 -2 -1 0 1 2 3 4
-15
-10
-5
0
5
10
15
Displacement (in)
Force(kip)
Test M47-01
M-CASHEW Model
-100 -80 -60 -40 -20 0 20 40 60 80 100
-60
-40
-20
0
20
40
60
Displacement (mm)
Force(kN)
 Actual nonlinear backbone curves
• Numerical model or full-scale test
 Displacement is a good damage indictor

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

7. 7
 Plan Dimensions: 40x60 ft
 Height: 56ft (6-story wood only)
 23 apartment units
 Weight : ~2734 kips (wood only)
 Shear Wall Design:
Direct Displacement Design (DDD)
 Tested on E-defense (Miki) Shake
Table in July-2009
Photo credit: Courtesy of Simpson Strong-Tie
60 ft 40 ft
9ft
8ft
8ft
8ft
8ft
8ft
55.7 ft

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

9. 9
0 0.5 1 1.5 2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Period, T (s)
SpectralAcceleration,Sa
(g)
Design Response Spectra - ATC-63 High Seismic Hazard Region
44% DBE
DBE
MCE
 Typical Southern California seismic hazard
 Site Class D (Stiff Soil)
5% damping

10. 10
 4 Apartment Units
 Midply walls
 carry high shear
demand
 Reduce torsional
effect
Midply Shearwall
Standard Shearwall
Partition/ non-Shearwall
39.8 ft
59.5 ft
Y
X
Unit 3
Unit 3
Unit 2
Unit 1
Elevator
Shaft
N
Stairway
Stairway
A B D E
1
2
4
6
8
10
11
Midply Wall
Midply Wall

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

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

13. 13
13

14. 14
Drift (%)
Wall
Height
(ft)
Wall Type/
Sheathing
Layer
Edge Nail
Spacing
(in)
Ko
(kip/in
per ft)
Fu
(kip per ft)
Backbone Force at Different Drift
Levels (kip per ft)
Wall Drift
0.5% 1.0% 2.0% 3.0% 4.0%
9
Standard
2 3.95 2.17 1.33 1.83 2.17 1.87 1.57
3 3.24 1.46 0.99 1.29 1.45 1.24 1.02
4 2.76 1.12 0.79 1.00 1.11 0.94 0.77
6 1.98 0.77 0.56 0.69 0.75 0.65 0.54
Midply
2 5.03 4.22 2.04 3.18 4.22 3.64 3.06
3 4.38 2.86 1.63 2.38 2.81 2.43 2.06
4 3.84 2.18 1.35 1.90 2.11 1.83 1.56
6 3.16 1.49 1.02 1.35 1.43 1.25 1.07
GWB 16 1.29 0.14 0.13 0.13 0.09 0.06 0.03
Design drift
Backbone force
Consider only full-height
shear wall segments

15. 15
 ATC-63 , 22 bi-axial ground motions
 MCE Level 3 Ground motion
 Uncertainty ≈ 0.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
1
2
3
4
5
6
Response Spectra
Group Scale Factor = 2.337
Unscaled Median Sa
= 0.607 @ Tn
= 0.63s
Scaled Median Sa
= 1.419 @ Tn
= 0.63s
Period (s)
SpectralAcceleration(g)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
StandardDeviationofln(Sa)
Median
80%-tile
Design Spectrum
Median
80th %tile
Design Spectrum
Lognormally
Distributed
βEQ ≈ 0.4
0.4

16. 16
0 1 2 3 4 5 6 7 8 9 10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CumulativeProbabilityofInter-storyDrift
Peak Inter-story Drift (%)
2.13%
80%
4 % drift
50%
1
exp[ ( ) ]NE t RC NE 
 
 Non-exceedance probability adjustment factor, CNE
Total Uncertainty
βR= √( βEQ
2
+ βDS
2)
=√( 0.42
+ 0.62) ≈ 0.75
1
exp[ (0.8)0.75]
1.88

 

80% NE Level 3
4% drift at 80% NE
Level 3
1.88

17. 17
 Vertical distribution factors (function of displacement)
 Effective height
 Effective seismic weight
j
j
v
j
i
i
o
oi
W
W
C



0.7 total heighteffh 
Weff ≈ 0.8 total weight
w6
o1
o2
o3
o4
hs
F1=Cv1Vb
F2=Cv2Vb
heff
effw4
w3
w2
w1
F3=Cv3Vb
F5=Cv5Vb
Original Multi-story Building
w5
F4=Cv4Vb
F6=Cv6Vb
o5
o6
Vb = Cc
Mo = Ft heff
Ft
eff
Vb = Cc
Weff
Ft = Cc Weff
eff
Keff
Substitute Structure
Mo = Ft heff
heff
effeff

18. 18
 Design base shear coefficient
eff
Cc= 0.98
Design spectrum (5% damping)
Sd, Δ
Sa,
Ft/Weff
TS
TL
Design spectrum (demand) adjusted for damping and
target NE probability of drift limit
Capacity spectrum
Keff

19. 19
0 1 2 3 4 5
0
500
1000
1500
2000
2500
BackboneForce(kN)
0 1 2 3 4 5
0
100
200
300
400
500
600
X-Direction
BackboneForce(kip)
Inter-story Drift (%)
Floor 1
Floor 2
Floor 3
Floor 4
Floor 5
Floor 6
0 1 2 3 4 5
0
500
1000
1500
2000
2500
BackboneForce(kN)
0 1 2 3 4 5
0
100
200
300
400
500
600
X-Direction
BackboneForce(kip)
Inter-story Drift (%)
Floor 1
Floor 2
Floor 3
Floor 4
Floor 5
Floor 6
(a)
 Step 9: Design forces
j
N
b
j i
v
s
is CV V

 
b effcV WC Design base shear coefficient  effective weightBase Shear
Story Shear
 Step 10: Select shear wall
nail spacing
 Assume no torsion
 Direct summation of the wall stiffness
 Full-height shear wall segments
Level 3
Story Shear
Requirements

20. 20
Diaphragm
Nonlinear Spring
 NonlinearTime-historyAnalysis (NLTHA) to verify the design
M-SAWS

21. 21
Model M-SAWS SAPWood Test
Mode Initial Stiffness
Tangent Stiffness
at 0.15% Drift
Initial Stiffness Initial Period
1
2
3
0.38
0.36
0.32
0.54
0.51
0.44
0.40
0.39
0.32
0.42
0.41
-
0
200
400
600
0
200
400
600
800
0
200
400
600
z-axis(Elevation)
Mode 3
T3
= 0.443 s
y-axis
x-axis
0
200
400
600
0
200
x-axis -500 0 500 100
0
200
400
z-axis(Elevati
x-axis
200 400 600 800
Mode 3
T3
= 0.443 s
y-axis
0 500 1000 15
0
200
400
600
800
x-axis
y-axis
Mode 3
T3
= 0.443 s
Base
Diaphragm 1
Diaphragm 2
Diaphragm 3
Diaphragm 4
Diaphragm 5
Diaphragm 6
-200
0
200
400
600
0
200
400
0
200
400
600
z-axis(Elevation)
Mode 1
T1
= 0.537 s
x-axisy-axis
-500 0 500 1000
0
200
400
600
800
Mode 1
T1
= 0.537 s
z-axis(Elevation)
x-axis
-200
0
200
400
600
0
200
400
600
800
0
200
400
600
z-axis(Elevation)
Mode 2
T2
= 0.505 s
y-axis x-axis -200 0 2
0
200
400
600
T
z-axis(Elevation)
200
0
200
400
600
x-axis -200 0 200 400 600 800
0
200
400
600
z-axis(Elevation)
x-axis
400 600
de 2
.505 s
xis
0 200 400 600 800 1000 1200
0
200
400
600
x-axis
y-axis
Mode 2
T2
= 0.505 s
Base
Diaphragm 1
Diaphragm 2
Diaphragm 3
Diaphragm 4
Diaphragm 5
Diaphragm 6
-500 0 500 1000
0
200
400
z-axis(Elev
x-axis
0 500 1000
-200
0
200
400
600
800
x-axis
y-axis
Mode 1
T1
= 0.537 s
Base
Diaphragm 1
Diaphragm 2
Diaphragm 3
Diaphragm 4
Diaphragm 5
Diaphragm 6
Mode 1
T1=0.54s
Mode 2
T2=0.51s
Mode 3
T3=0.44s
0 500 1000
x-axis
0 500 1000
x-axis
Mode 3
T3
= 0.357 s
Base
Diaphragm 1
Diaphragm 2
Diaphragm 3
Diaphragm 4
Diaphragm 5
Diaphragm 6

22. 22
 Levels 1-3: ATC-63 Far Field Ground Motions (22 bi-axial)
 Level 4: CUREE Near-fault Ground Motions
Design Requirement
Level 4
Level 3
Level 2
Level 1
Uniform Drift
Profile
<7%
<4%
<2%
<1%

23. 23
Level
Test Inter-Story
Drift
Design
Limit
1
2
3
~0.75%
~1.30%
3.08% (max)
1%
2%
4%

24. 24
0 1 2 3 4 5 6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SMCE
= 1.50 g
SCT
= 2.57 g, Pf
= 0.5
CMR = 1.71
Pf
= 0.04
Median ST
@ Tn (g)
CollapseProbability
Unadjusted Collapse Fragility Curve for NEESWood Capstone Building (6-story Woodframe)
ATC-63 Far-field Ground Motions
Model: M-SAWS
 = 5%
CollapseProbability
Median Sa @ Tn (g)
 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 fragility curve
 Incremental Dynamic Analysis

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

26. 26
Thank you
Contact Information:
Weichiang Pang
wpang@clemson.edu

27. 27
 M-CASHEW model (Matlab)
 11.9mm (15/32”) OSB, 2x6 studs
 10d common nails (3.76mm dia.), nail spacing
 12.7mm (½”) Gypsum wallboard
 31.75mm long #6 drywall screws 406mm (16”) o.c.
u
Fb()
Displacement, 
Force, Fb( )
r2Ko
r1Ko
Ko
Fo
Fu
DesignVariable

28. 28
 Step 8: Design base shear coefficient
 
2
1
2 2
1.88 1.5
1.65
1.71
min
9.81 1.88 0.9
1.70.
0.9
4
1
14 247
8
eff
NE XS
NE X
c
C S
B
C Sg
C
B

 

 

 
    
         
ef
C
c
Design spectrum at 5% damping
Sd, Δ
Sa,
Ft/Weff
TS
T
L
Design spectrum (demand) adjusted for
damping and target NE probability of drift
limit
Capacity spectrum
Keff
Level 3 (MCE)

29. 29
 Step 7: Damping reduction factor
4
5.6 ln(10 )
.71
0
1
eff
B

 

ASCE/SEI- 41
int 26%5% 21%hysteff      
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Ks
/Ko
hyst
Hysteretic Damping Model
(FPI) Standard S34
(FPI) Midply M47-01
(FPI) Midply M46-01
(CUREE) Task 1.4.4 12A
(APA) T2003-22 Wall 7
(APA) T2004-14 Wall 8dcom
0.32exp( 1.38 )hyst s ok k  
0.21
Ks/Ko
Effective damping = Intrinsic + Hysteretic damping