direct displacement design methodology for woodframe buildings

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 performanceFor 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 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


R

Force-based Displacement-BasedResponse 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)

Forc

e (k

ip)

Test M47-01M-CASHEW Model

-100 -80 -60 -40 -20 0 20 40 60 80 100

-60

-40

-20

0

20

40

60

Displacement (mm)

Forc

e (k

N)

Actual nonlinear backbone curves• Numerical model or full-scale test

Displacement is a good damage indictor

6

Direct Displacement Design (DDD)

Simplified Direct Displacement DesignUsed 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

8ft8ft

55.7 ft

8

Design Objectives

Performance => 1) inter-story drift limit 2) hazard level 3) non-exceedance probability

LevelSeismic 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

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)

Spe

ctra

l Acc

eler

atio

n, S a (g

)

Design Response Spectra - ATC-63 High Seismic Hazard Region

44% DBEDBEMCE

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 WallNail 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 force Consider only full-height shear wall segments

15

Far-field Ground MotionLognormally DistributedβE

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 @ Tn = 0.63sScaled Median Sa = 1.419 @ Tn = 0.63s

Period (s)

Spe

ctra

l Acc

eler

atio

n (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

ndar

d D

evia

tion

of ln

(Sa)Median

80%-tileDesign Spectrum

Median80th %tileDesign Spectrum

Lognormally DistributedβEQ ≈ 0.4

0.4

160 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

Cum

ulat

ive

Pro

babi

lity

of In

ter-s

tory

Drif

t

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 34% 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

WW

C

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/Weff

TS

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

Backbone Force (kN)

0 1 2 3 4 50

100

200

300

400

500

600X-Direction

Backbone Force (kip)

Inter-story Drift (%)

Floor 1Floor 2Floor 3Floor 4Floor 5Floor 6

0 1 2 3 4 50

500

1000

1500

2000

2500

Backbone Force (kN)

0 1 2 3 4 50

100

200

300

400

500

600Y-Direction

Backbone Force (kip)

Inter-story Drift (%)

Floor 1Floor 2Floor 3Floor 4Floor 5Floor 6

(a)

Design Forces

Step 9: Design forces

j

N

bj 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 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 Stiffness Tangent 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

600z-

axis

(Ele

vatio

n)

Mode 3T3 = 0.443 s

y-axisx-axis -500 0 500 1000

0

200

400

600

800

Mode 3T3 = 0.443 s

z-ax

is (E

leva

tion)

x-axis

0 200 400 600 800

0

200

400

600

800

Mode 3T3 = 0.443 s

z-ax

is (E

leva

tion)

y-axis0 500 1000 1500

0

200

400

600

800

x-axis

y-ax

is

Mode 3T3 = 0.443 s

BaseDiaphragm 1Diaphragm 2Diaphragm 3Diaphragm 4Diaphragm 5Diaphragm 6

0200

400600

0200

400600

8000

200

400

600

z-ax

is (E

leva

tion)

Mode 3T3 = 0.443 s

y-axisx-axis -500 0 500 1000

0

200

400

600

800

Mode 3T3 = 0.443 s

z-ax

is (E

leva

tion)

x-axis

0 200 400 600 800

0

200

400

600

800

Mode 3T3 = 0.443 s

z-ax

is (E

leva

tion)

y-axis0 500 1000 1500

0

200

400

600

800

x-axis

y-ax

is

Mode 3T3 = 0.443 s


-2000

200400

600

0200

400

0

200

400

600

z-ax

is (E

leva

tion)

Mode 1T1 = 0.537 s

x-axisy-axis -500 0 500 1000

0

200

400

600

800

Mode 1T1 = 0.537 s

z-ax

is (E

leva

tion)

x-axis

-200 0 200 400 600

0

200

400

600

800

Mode 1T1 = 0.537 s

z-ax

is (E

leva

tion)

y-axis0 500 1000

-200

0

200

400

600

800

x-axis

y-ax

is

Mode 1T1 = 0.537 s


-2000

200400

600

0200

400600

8000

200

400

600

z-ax

is (E

leva

tion)

Mode 2T2 = 0.505 s

y-axis x-axis -200 0 200 400 600 800

0

200

400

600

Mode 2T2 = 0.505 s

z-ax

is (E

leva

tion)

x-axis

0 200 400 600

0

200

400

600

Mode 2T2 = 0.505 s

z-ax

is (E

leva

tion)

y-axis0 200 400 600 800 1000 1200

0

200

400

600

x-axis

y-ax

is

Mode 2T2 = 0.505 s


-2000

200400

600

0200

400600

8000

500

z-ax

is (E

leva

tion)

Mode 2T2 = 0.505 s

y-axis x-axis -200 0 200 400 600 800

0

200

400

600

Mode 2T2 = 0.505 s

z-ax

is (E

leva

tion)

x-axis

0 200 400 600

0

200

400

600

Mode 2T2 = 0.505 s

z-ax

is (E

leva

tion)

y-axis0 200 400 600 800 1000 1200

0

200

400

600

x-axis

y-ax

is

Mode 2T2 = 0.505 s


-2000

200400

600

0200

400

0

200

400

600

z-ax

is (E

leva

tion)

Mode 1T1 = 0.537 s

y-axis

x-axis

-500 0 500 1000

0

200

400

600

800

Mode 1T1 = 0.537 s

z-ax

is (E

leva

tion)

x-axis

-200 0 200 400 600

0

200

400

600

800

Mode 1T1 = 0.537 s

z-ax

is (E

leva

tion)

y-axis0 500 1000

-200

0

200

400

600

800

x-axis

y-ax

is

Mode 1T1 = 0.537 s


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-ax

is (E

leva

tion)

Mode 3T3 = 0.357 s

y-axis x-axis-500 0 500 1000

-100

0

100

200

300

400

500

600

700

800

Mode 3T3 = 0.357 s

z-ax

is (E

leva

tion)

x-axis

0 200 400 600 800

-100

0

100

200

300

400

500

600

700

800

Mode 3T3 = 0.357 s

z-ax

is (E

leva

tion)

y-axis-500 0 500 1000

0

100

200

300

400

500

600

700

800

x-axis

y-ax

is

Mode 3T3 = 0.357 s


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)

Collaps

e Pro

bability

Unadjusted Collapse Fragility Curve for NEESWood Capstone Building (6-story Woodframe)

ATC-63 Far-field Ground Motions Model: M-SAWS = 5%

Colla

pse

Prob

abilit

y

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 [email protected]

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 0.91.70.

0.9

4

1

14 247

8

eff

NE XS

NE X

c

C SB

C SgC

B

ef

f

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

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/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

direct displacement design methodology for woodframe buildings

Documents