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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
VerificationNonlinear Time History Analyses (NLTHA)ATC-63 Collapse Analysis
Summary
3
Force-based v.s. Displacement-based Design
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
Force-based v.s. Displacement-based Design
Force-based Displacement-Based
xa 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
TTa
Location 1Location 2
eff
TS
TL
Design spectrum (demand)
Capacity spectrum
Keff
5
Force-based v.s. Displacement-based Design
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)
For
ce (
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)
For
ce (
kN)
Actual nonlinear backbone curves• Numerical model or full-scale test
Displacement is a good damage indictor
6
Direct Displacement Design (DDD)
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
NEESWood Capstone Building
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
Design Objectives
Performance => 1) inter-story drift limit 2) hazard level 3) non-exceedance probability
LevelSeismic Hazard Performance Expectations
DescriptionExceedance
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
Design Response Spectra
0 0.5 1 1.5 20
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Period, T (s)
Spectr
al A
ccele
ratio
n, S
a (g)
Design Response Spectra - ATC-63 High Seismic Hazard Region
44% DBE
DBEMCE
Typical Southern California seismic hazard Site Class D (Stiff Soil)
5% damping
10
Example 1st Floor Plan View
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
ElevatorShaft
N
Stairway
Stairway
A B D E
1
2
4
6
8
10
11
Midply Wall
Midply Wall
11
Shear Wall System
406mm16 in
406mm16 in
406mm16 in
Stud Sheathing
Drywall
Standard /Conventional Shear Wall
Nail in Single-shear
406mm16 in
406mm16 in
Sheathing
Drywall
Midply Shear Wall Nail in Double-shear
Construction concept developed by Forintek (Varoglu et al. 2007)
12
Shear Wall Model
Hold-down Element
Contact element
Panel-to-frame nailsEnd-nail
Gravity LoadForce-Displacement Response
Framing nails
M-CASHEW model (Matlab) Shear Wall Backbone database for different nail spacings
13
Wall Model Deformation Animation
13
14
Example Shear Wall Database (per unit Width)
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 1.573 3.24 1.46 0.99 1.29 1.45 1.24 1.024 2.76 1.12 0.79 1.00 1.11 0.94 0.776 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 3.063 4.38 2.86 1.63 2.38 2.81 2.43 2.064 3.84 2.18 1.35 1.90 2.11 1.83 1.566 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 forceConsider only full-height shear wall segments
15
Far-field Ground Motion
Lognormally Distributedβ
E
Q
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 20
1
2
3
4
5
6
Response SpectraGroup Scale Factor = 2.337
Unscaled Median Sa = 0.607 @ T
n = 0.63s
Scaled Median Sa = 1.419 @ T
n = 0.63s
Period (s)
Spectr
al A
ccele
ration (
g)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sta
ndard
Devia
tion o
f ln
(Sa)
Median
80%-tile
Design Spectrum
Median80th %tileDesign Spectrum
Lognormally DistributedβEQ ≈ 0.4
0.4
16
0 1 2 3 4 5 6 7 8 9 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cum
ula
tive P
robabili
ty o
f In
ter-
sto
ry D
rift
Peak Inter-story Drift (%)
2.13%
80%
4 % drift
50%
1exp[ ( ) ]NE t RC NE
Target Inter-story Drift Distribution
Non-exceedance probability adjustment factor, CNE
Total UncertaintyβR= √( βEQ
2+ βDS
2)=√( 0.42
+ 0.62) ≈ 0.75
1exp[ (0.8)0.75]
1.88
80% NE Level 3
4% drift at 80% NE Level 3
1.88
17
Vertical distribution factors (function of displacement)
Effective height
Effective seismic weight
j
jv
j
ii
o
oi
W
WC
0.7 total heighteffh
Weff ≈ 0.8 total weight
Substitute Structure (SDOF)
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
effeff
18
Capacity Spectrum Approach
Design base shear coefficient
eff
Cc= 0.98
Design spectrum (5% damping)
Sd, Δ
Sa,
Ft/WeffTS
TL
Design spectrum (demand) adjusted for damping and target NE probability of drift limit
Capacity spectrum
Keff
19
0 1 2 3 4 50
500
1000
1500
2000
2500
Backbo
ne For
ce (kN
)
0 1 2 3 4 50
100
200
300
400
500
600X-Direction
Backbo
ne For
ce (kip
)Inter-story Drift (%)
Floor 1Floor 2
Floor 3
Floor 4
Floor 5Floor 6
0 1 2 3 4 50
500
1000
1500
2000
2500
Backbo
ne For
ce (kN
)
0 1 2 3 4 50
100
200
300
400
500
600Y-Direction
Backbo
ne For
ce (kip
)
Inter-story Drift (%)
Floor 1Floor 2
Floor 3
Floor 4
Floor 5Floor 6
(a)
Design Forces
Step 9: Design forces
j
N
bj i
v
s
isCV 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 3Story Shear Requirements
20
Diaphragm
Nonlinear Spring
Numerical Models Nonlinear Time-history Analysis (NLTHA) to verify the
design
M-SAWS
21
Periods and Mode ShapesModel M-SAWS SAPWood Test
Mode Initial StiffnessTangent Stiffness
at 0.15% Drift Initial Stiffness Initial Period
123
0.380.360.32
0.540.510.44
0.400.390.32
0.420.41
-
0200
400600
0200
400600
8000
200
400
600
z-a
xis
(E
levation)
Mode 3T
3 = 0.443 s
y-axisx-axis -500 0 500 1000
0
200
400
600
800
Mode 3T
3 = 0.443 s
z-a
xis
(E
levation)
x-axis
0 200 400 600 800
0
200
400
600
800
Mode 3T
3 = 0.443 s
z-a
xis
(E
levation)
y-axis0 500 1000 1500
0
200
400
600
800
x-axis
y-a
xis
Mode 3T
3 = 0.443 s
Base
Diaphragm 1
Diaphragm 2
Diaphragm 3
Diaphragm 4
Diaphragm 5Diaphragm 6
0200
400600
0200
400600
8000
200
400
600
z-ax
is (
Ele
vatio
n)Mode 3
T3 = 0.443 s
y-axisx-axis -500 0 500 1000
0
200
400
600
800
Mode 3T
3 = 0.443 s
z-ax
is (
Ele
vatio
n)
x-axis
0 200 400 600 800
0
200
400
600
800
Mode 3T
3 = 0.443 s
z-ax
is (
Ele
vatio
n)
y-axis0 500 1000 1500
0
200
400
600
800
x-axis
y-ax
is
Mode 3T
3 = 0.443 s
BaseDiaphragm 1
Diaphragm 2
Diaphragm 3
Diaphragm 4
Diaphragm 5Diaphragm 6
-2000
200400
600
0200
400
0
200
400
600
z-ax
is (
Ele
vatio
n)
Mode 1T
1 = 0.537 s
x-axisy-axis-500 0 500 1000
0
200
400
600
800
Mode 1T
1 = 0.537 s
z-ax
is (
Ele
vatio
n)
x-axis
-200 0 200 400 600
0
200
400
600
800
Mode 1T
1 = 0.537 s
z-ax
is (
Ele
vatio
n)
y-axis0 500 1000
-200
0
200
400
600
800
x-axis
y-ax
is
Mode 1T
1 = 0.537 s
BaseDiaphragm 1
Diaphragm 2
Diaphragm 3
Diaphragm 4
Diaphragm 5Diaphragm 6
-2000
200400
600
0200
400600
8000
200
400
600
z-ax
is (
Ele
vatio
n)
Mode 2T
2 = 0.505 s
y-axis x-axis -200 0 200 400 600 800
0
200
400
600
Mode 2T
2 = 0.505 s
z-ax
is (
Ele
vatio
n)
x-axis
0 200 400 600
0
200
400
600
Mode 2T
2 = 0.505 s
z-ax
is (
Ele
vatio
n)
y-axis0 200 400 600 800 1000 1200
0
200
400
600
x-axis
y-ax
is
Mode 2T
2 = 0.505 s
BaseDiaphragm 1
Diaphragm 2
Diaphragm 3
Diaphragm 4
Diaphragm 5Diaphragm 6
-2000
200400
600
0200
400600
8000
500
z-ax
is (
Ele
vatio
n)
Mode 2T
2 = 0.505 s
y-axis x-axis -200 0 200 400 600 800
0
200
400
600
Mode 2T
2 = 0.505 s
z-ax
is (
Ele
vatio
n)
x-axis
0 200 400 600
0
200
400
600
Mode 2T
2 = 0.505 s
z-ax
is (
Ele
vatio
n)
y-axis0 200 400 600 800 1000 1200
0
200
400
600
x-axis
y-ax
is
Mode 2T
2 = 0.505 s
BaseDiaphragm 1
Diaphragm 2
Diaphragm 3
Diaphragm 4
Diaphragm 5Diaphragm 6
-2000
200400
600
0200
400
0
200
400
600
z-ax
is (
Ele
vatio
n)
Mode 1T
1 = 0.537 s
y-axis
x-axis
-500 0 500 1000
0
200
400
600
800
Mode 1T
1 = 0.537 s
z-ax
is (
Ele
vatio
n)
x-axis
-200 0 200 400 600
0
200
400
600
800
Mode 1T
1 = 0.537 s
z-ax
is (
Ele
vatio
n)
y-axis0 500 1000
-200
0
200
400
600
800
x-axis
y-ax
is
Mode 1T
1 = 0.537 s
BaseDiaphragm 1
Diaphragm 2
Diaphragm 3
Diaphragm 4
Diaphragm 5Diaphragm 6
Mode 1T1=0.54s
Mode 2T2=0.51s
Mode 3T3=0.44s
-500
0
500
1000
0200
400600
800
0
200
400
600
800
z-axis
(Elev
ation
)
Mode 3T
3 = 0.357 s
y-axis x-axis-500 0 500 1000
-100
0
100
200
300
400
500
600
700
800
Mode 3T
3 = 0.357 s
z-axis
(Elev
ation
)
x-axis
0 200 400 600 800
-100
0
100
200
300
400
500
600
700
800
Mode 3T
3 = 0.357 s
z-axis
(Elev
ation
)
y-axis-500 0 500 1000
0
100
200
300
400
500
600
700
800
x-axis
y-axis
Mode 3T
3 = 0.357 s
BaseDiaphragm 1
Diaphragm 2
Diaphragm 3
Diaphragm 4
Diaphragm 5Diaphragm 6
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
Design Requirement
Level 4
Level 3
Level 2
Level 1
Uniform Drift Profile
<7%
<4%<2%
<1%
23
Test versus Design Drifts
Level Test Inter-Story Drift
DesignLimit
123
~0.75%~1.30%
3.08% (max)
1%2%4%
24
0 1 2 3 4 5 60
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)
Colla
pse
Prob
abilit
y
Unadjusted Collapse Fragility Curve for NEESWood Capstone Building (6-story Woodframe)
ATC-63 Far-field Ground Motions Model: M-SAWS = 5%
Colla
pse
Pro
bab
ility
Median Sa @ Tn (g)
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 fragility curve Incremental Dynamic Analysis
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
Thank you
Contact Information:Weichiang Pangwpang@clemson.edu
27
Shear Wall Model
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( )
r2Kor1Ko
Ko
Fo
Fu
Design Variable
28
Capacity Spectrum Approach
Step 8: Design base shear coefficient
2
12 2
1.88 1.51.65
1.71min
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 SgC
B
eff
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
Step 7: Damping reduction factor 4
5.6 ln(10 ).71
01
eff
B
ASCE/SEI- 41
int 26%5% 21%hysteff
Damping
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Ks/K
o
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
Recommended