Direct Displacement Design Methodology for Woodframe Buildings

Report
•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
Gravity Load
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

Non-exceedance probability adjustment factor, CNE
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
[email protected]
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
Design spectrum (demand) adjusted for
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
(CUREE) Task 1.4.4 12A
(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

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