1. Direct Displacement Design Methodology for Woodframe Buildings
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. Overview 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. Force-based v.s. Displacement-based Design
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
Displacement-based Design
Concept pioneered by Priestley (1998)
Displacement  damage indicator / seismic performance
For concrete and steel buildings

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

5. Force-based v.s. Displacement-based Design
Force-based Displacement-Based
Actual nonlinear backbone curves
Numerical model or full-scale test
Response Modification Factor (R-factor)
A yield point is assumed
Displacement is a good damage indictor
Force is not a good damage indictor R

6. Direct Displacement Design (DDD)
Objectives:
1) Optimize distribution of story stiffness over the height of the building
2) Minimize the probability of a weak story 
Soft-story
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%

7. NEESWood Capstone Building
60 ft
40 ft
9ft
8ft
55.7 ft
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

8. Performance Expectations Inter-Story Drift Limit
Design Objectives
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%
Level 3
Maximum Credible Earthquake (MCE)
2%/50yr 4%
80%
Level 4
Near Fault 7%

9. Design Response Spectra
Typical Southern California seismic hazard
Site Class D (Stiff Soil)
5% damping

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

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

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

13. Wall Model Deformation Animation

14. Example Shear Wall Database (per unit Width)
Consider only full-height shear wall segments
Backbone force
Design drift
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
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
0.56
0.69
0.75
0.65
0.54
Midply
5.03
4.22
2.04
3.18
3.64
3.06
4.38
2.86
1.63
2.38
2.81
2.43
2.06
3.84
2.18
1.35
1.90
2.11
1.56
3.16
1.49
1.43
1.25
1.07
GWB 16
0.14
0.13
0.09
0.06
0.03

15. Far-field Ground Motion
Lognormally Distributed
βEQ
Far-field Ground Motion
ATC-63 , 22 bi-axial ground motions
MCE Level 3 Ground motion
Uncertainty ≈ 0.4
Lognormally Distributed
βEQ ≈ 0.4
0.4

16. Target Inter-story Drift Distribution
Non-exceedance probability adjustment factor, CNE
Total Uncertainty
βR= √( βEQ2+ βDS2)
=√( ) ≈ 0.75
2.13%
80%
4 % drift
50%
4% drift at 80% NE
Level 3
80% NE Level 3
1.88

17. Substitute Structure (SDOF)
Vertical distribution factors (function of displacement)
Effective height
Effective seismic weight
Weff ≈ 0.8 total weight w6
o1
o2
o3
o4 hs
F1=Cv1Vb
F2=Cv2Vb
heff
eff w4 w3 w2 w1
F3=Cv3Vb
F5=Cv5Vb
Original Multi-story Building w5
F4=Cv4Vb
F6=Cv6Vb
o5
o6
Vb = Cc
Mo = Ft heff Ft
Weff
Ft = Cc Weff
eff
Keff
Substitute Structure

18. Capacity Spectrum Approach
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. Design Forces Step 9: Design forces
Base Shear
Design base shear coefficient  effective weight
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. Numerical Models
Nonlinear Time-history Analysis (NLTHA) to verify the design
Diaphragm
Nonlinear Spring
M-SAWS

21. Periods and Mode Shapes
Model
M-SAWS
SAPWood
Test
Mode
Initial Stiffness
Tangent Stiffness
at 0.15% Drift
Initial Period 1 2 3
0.38
0.36
0.32
0.54
0.51
0.44
0.40
0.39
0.42
0.41 -
Mode 1
T1=0.54s
Mode 2
T2=0.51s
Mode 3
T3=0.44s

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%
<4%
<2%
<7%
Uniform Drift Profile

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

24. 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
Median Tn (g)
Collapse fragility curve
Incremental Dynamic Analysis

25. Summary DDD procedure 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)

26. Thank you
Contact Information:
Weichiang Pang

27. Shear Wall Model Design Variable 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.
Design Variable

28. Capacity Spectrum Approach
Step 8: Design base shear coefficient
Level 3 (MCE)
eff Cc
Design spectrum at 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

29. Damping Step 7: Damping reduction factor ASCE/SEI- 41 Ks/Ko
Effective damping = Intrinsic + Hysteretic damping
0.21
Ks/Ko