### Direct Displacement Design Methodology for Woodframe Buildings

```•WeiChiang
•David
•John
Pang, Clemson University
Rosowsky, Rensselaer Polytechnic Institute
van de Lindt, University of Alabama
•Shiling
Pei, South Dakota State University
Quake Summit 2010, NEES & PEER Annual Meeting, Oct-9, San Francisco

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
2
 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
3
Force-based
Displacement-Based
 Approximate elastic fundamental period
Ta  Ct h
 Direct period calculation
• Actual mass and stiffness
x
• Capacity Spectrum Approach
• period estimate based on building
height and building type
Sa
TS
Design spectrum
(demand)
Location 1
Location 2
Capacity spectrum
TL
Keff
Ta
T
eff
4
Displacement-Based
 Response Modification Factor (R-factor)
A yield point is assumed
 Force is not a good damage indictor
 Actual nonlinear backbone curves
• Numerical model or full-scale test
 Displacement is a good damage indictor
-100
15
-80
-60
Displacement (mm)
-20
0
20
-40
40
60
80
10
Force (kip)
R
100
60
Test M47-01
M-CASHEW Model
40
5
20
0
0
Force (kN)
Force-based
-20
-5
-40
-10
-60
-15
-4
-3
-2
-1
0
1
Displacement (in)
2
3
4
5
 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%

6
8ft
8ft
8ft
55.7 ft
8ft
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)

8ft

9ft
60 ft

Tested on E-defense (Miki) Shake
Table in July-2009
40 ft
Photo credit: Courtesy of Simpson Strong-Tie
7

Performance => 1) inter-story drift limit
2) hazard level
3) non-exceedance probability
Seismic Hazard
Level
Description
Performance Expectations
Exceedance Inter-Story
Prob.
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%
8
 Typical Southern California seismic hazard
 Site Class D (Stiff Soil)
Spectral Acceleration, Sa (g)
Design Response Spectra - ATC-63 High Seismic Hazard Region
1.6
44% DBE
1.4
DBE
1.2
MCE
1
5% damping
0.8
0.6
0.4
0.2
0
0
0.5
1
Period, T (s)
1.5
2
9
B
A
E
D
1
Midply Wall
Stairway
2
Unit 3
Unit 1

4 Apartment Units

Midply walls
 carry high shear
4
59.5 ft
Elevator
Shaft
N
6
demand

Reduce torsional
effect
8
Standard Shearwall
Unit 3
Unit 2
Midply Wall
10
Y
Partition/ non-Shearwall
Stairway
X
11
39.8 ft
Midply Shearwall
10
Standard /Conventional Shear Wall
Stud
Sheathing
Nail in Single-shear
Drywall
406mm
16 in
406mm
16 in
406mm
16 in
Midply Shear Wall
Nail in Double-shear
Sheathing
Drywall
406mm
16 in
406mm
16 in
Construction concept developed by Forintek (Varoglu et al. 2007)
11


M-CASHEW model (Matlab)
Shear Wall Backbone database for different nail spacings
Force-Displacement Response
Framing
nails
Contact
element
Hold-down Element
End-nail
Panel-to-frame nails
12
13
13
Consider only full-height
shear wall segments
Backbone force
Design drift
Wall Wall Type/ Edge Nail
Ko
Fu
Height Sheathing Spacing (kip/in
(kip per ft)
(ft)
Layer
(in)
per ft)
Standard
9
Midply
GWB
2
3
4
6
2
3
4
6
16
3.95
3.24
2.76
1.98
5.03
4.38
3.84
3.16
1.29
2.17
1.46
1.12
0.77
4.22
2.86
2.18
1.49
0.14
Drift (%)
Backbone Force at Different Drift
Levels (kip per ft)
Wall Drift
0.5% 1.0% 2.0% 3.0% 4.0%
1.33
1.83
2.17
1.87 1.57
0.99
1.29
1.45
1.24 1.02
0.79
1.00
1.11
0.94 0.77
0.56
0.69
0.75
0.65 0.54
2.04
3.18
4.22
3.64 3.06
1.63
2.38
2.81
2.43 2.06
1.35
1.90
2.11
1.83 1.56
1.02
1.35
1.43
1.25 1.07
0.13
0.13
0.09
0.06 0.03
14
 ATC-63 , 22 bi-axial ground motions
Response Spectra
 MCE Level 3 Ground motion
Group Scale Factor = 2.337
Unscaled Median S a = 0.607 @ Tn = 0.63s
 Uncertainty ≈ 0.4 Scaled Median S = 1.419 @ T = 0.63s
a
n
1
Median
80 th %tile
80%-tile
Design Spectrum
Design
Spectrum
Spectral Acceleration (g)
5
3
0.8
0.7
Lognormally
Distributed
βEQ ≈ 0.4
4
0.9
0.6
0.5
0.4
0.4
2
0.3
Standard Deviation of ln(Sa)
6
0.2
1
0.1
0
0
0.2
0.4
0.6
0.8
1
1.2
Period (s)
1.4
1.6
1.8
0
2
15

CNE  exp[1 ( NEt )R ]
1
 exp[ 1 (0.8)0.75]
80% NE Level 3
Total Uncertainty
βR= √( βEQ2+ βDS2)
=√( 0.42+ 0.62) ≈ 0.75
Cumulative Probability of Inter-story Drift
 1.88
0.9
80%
0.8
0.7
0.6
4% drift at 80% NE
Level 3
50%
0.5
1.88
0.4
0.3
0.2
2.13%
0.1
0
4 % drift
0
1
2
3
4
5
6
Peak Inter-story Drift (%)
7
8
9
10
16
 Vertical distribution factors (function of displacement)
heff  0.7 total height
 Effective height
 Effective seismic weight
Cv j 
W j o j
i Wi oi
Weff ≈ 0.8 total weight
Original Multi-story Building
w6
F6=Cv6Vb
w5
F5=Cv5Vb
Ft
hs
F1=Cv1Vb
w1
eff
Ft = Cc Weff
eff

eff
Weff
o3
w2
F2=Cv2Vb
o5
o4
w3
F3=Cv3Vb
heff
eff
w4
F4=Cv4Vb
Substitute Structure
o6
o2
Keff
heff
eff
o1
Vb = Cc
Mo = Ft heff
Vb = Cc
Mo = Ft heff
17
 Design base shear coefficient
Sa,
Ft/Weff
TS
Design spectrum (5% damping)
Design spectrum (demand) adjusted for damping and
target NE probability of drift limit
Capacity spectrum
Cc= 0.98
TL
Keff
eff
Sd, Δ
18

Step 9: Design forces
Base Shear
Vb  CcWeff
Design base shear coefficient  effective weight
X-Direction
i
 Cv j Vb
2500
2500
Floor 1
Floor 2
500
Floor 3 500
Floor 4
Floor 5 400
400
Floor 6
(a)
j i
 Step 10: Select shear wall
nail spacing
 Assume no torsion
 Direct summation of the wall stiffness
Backbone Force (kN)
2000
2000
1500
1500
300
300
1000
1000
200
200
Level 3
100
Story Shear 100
Requirements
500
500
 Full-height shear wall segments
00
00
1
3
2
Inter-story Drift (%)
4
00
55
Backbone Force (kip)
Story Shear V 
s
600
600
Ns
19

Nonlinear Time-history Analysis (NLTHA) to verify the design
Diaphragm
Nonlinear Spring
M-SAWS
20
200
0
500
Model
z-axis (Elevati
z-axis (Elevation)
400
1000
400
200
M-SAWS
SAPWood
200
Tangent Stiffness0
600 Stiffness
Mode
Initial
Initial Stiffness
3
600 Mode 400
200
at
0.15%
Drift
T
=
0.357
s
200
400
-500
0
500 0
1000
0200
0
x-axis
-500
0
0
0.38
0.54
0.40
x-axis
x-axis 1
200
-200
0
200
400
600
800
Mode 1
0.36
0.51
0.39
x-axis
Mode 32
T1 = 0.537 s
de 2
Mode 2
T = 0.443
s
.505 s3
T2 = 0.505 s 0.32
0.32
0.44
800 3
x-axis
0
Test
Initial Period
3
600
-200
600
600
0
z-axis (Elevation)
400
y-axis
0
500
x-axis
800
600
400
200
0
400
200
y-axis
0
-200
0
200
400
6001000
400
200
0
800
600600
400
400
200
200
0
x-axis
y-axis
600
x-axis
0
-200
600
z-axis (Elevation)
T1 = 0.537 s
x-axis
Base
Diaphragm 1
Diaphragm
Mode
32
TDiaphragm
=0.44s 3
3
Diaphragm 4
Diaphragm 5
Mode 1
Diaphragm
6 0.537 s
T =
y-axis
y-axis
500 Mode 1
0
1
2 Mode 2 400
3T =0.51s
2
200
4
Mode 2
1000
Diaphragm
5 T2 = 0.505 s
0
0
Diaphragm 6
800
z-axis (Elevation)
0
z-axis (Elevation)
y-axis
Mode 1
T1=0.54s
200
600
Base
Base
Diaphragm
Diaphragm
400 1
Diaphragm 2
Diaphragm
Diaphragm
3
Diaphragm 4
Diaphragm
200 5
Diaphragm
Diaphragm
6
Diaphragm
400
200
100
800
600
400
xis
0.42500
x-axis
Mode0.41
3
T3 = 0.443- s
800
600
Base
Diaphragm
Diaphragm
Diaphragm
Diaphragm
Diaphragm
Diaphragm
Mode1 3
T3 = 0.443 s
1000
1200
0
500
x-axis
400 400
200
200
0
800
0 600600
400
400
200
200
y-axis
x-axis
-500
400
00
0
1
2
3
4
5
6
T
600
200
x-axis500
x-axis
z-axis (Elevation)
z-axis (Elev
600
400
600
1000
15
400
200
0
-200
1000
21
0
2


Levels 1-3: ATC-63 Far Field Ground Motions (22 bi-axial)
Level 4: CUREE Near-fault Ground Motions
Level 1
<1%
Level 2
<4%
<2%
<7%
Level 3
Level 4
Design Requirement
Uniform Drift
Profile
22
Test Inter-Story Design
Level
Drift
Limit
1
2
3
~0.75%
~1.30%
3.08% (max)
1%
2%
4%
23
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
Unadjusted Collapse Fragility Curve for NEESWood Capstone Building (6-story Woodframe)
1
0.9
Probability
Collapse
Collapse Probability

0.8
 Collapse fragility curve
CMR = 1.71
0.7
 Incremental Dynamic Analysis
0.6
0.5
S CT = 2.57 g, P f = 0.5
0.4
0.3
0.2
0.1
0
ATC-63 Far-field Ground Motions
Model: M-SAWS
 = 5%
S MCE = 1.50 g
P f = 0.04
0
1
2
3
4
Median S T @ Tn (g)
Median
Sa @ Tn (g)
5
6
24
Summary

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)
25
Thank you
Contact Information:
Weichiang Pang
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26

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
Force, Fb( )
Fu
r2Ko
r1Ko
Fo
Fb()
Ko
u
Displacement, 
27
 Step 8: Design base shear coefficient



Cc  min 
 g
 4 2 
eff

Sa,
Ft/Weff
CNE S XS 1.88 1.5 

 1.65
B
1.71
2
 CNE S X 1 
9.81  1.88  0.9 

  2


B
1.7
1
4

0.
247





TS
 0.981
Level 3 (MCE)
Design spectrum at 5% damping
damping and target NE probability of drift
limit
Capacity spectrum
C
c
T
Keff
L
ef
Sd, Δ
28
 Step 7: Damping reduction factor B 
4
 1.71
5.6  ln(100 eff )
Effective damping = Intrinsic + Hysteretic damping
ASCE/SEI- 41
 eff   int   hyst  5%  21%  26%
0.4
Hysteretic Damping Model
(FPI) Standard S34
(FPI) Midply M47-01
(FPI) Midply M46-01
(APA) T2003-22 Wall 7
(APA) T2004-14 Wall 8dcom
0.35
0.3
hyst
0.25
 hyst  0.32exp(1.38 ks ko )
0.2
0.21
0.15
0.1
Ks/Ko
0.05
0
0.1
0.2
0.3
0.4
0.5
Ks /Ko
0.6
0.7
0.8
0.9
1
29
```