Sheathing Braced Design of Wall Studs

July 2010 Update

for

AISI Committee on Framing StandardsDesign Methods Subcommittee

Toronto, ON

CivilEngineeringat JOHNS HOPKINS UNIVERSITY

www.ce.jhu.edu/bschafer/sheathedwalls

Overview

• Performance of sheathed walls

• Development of design method

• Current work

• Work plan and summary

www.ce.jhu.edu/bschafer/sheathedwalls

a) Bare wall with bridging b) Sheathed wall, no bridging

track

stud

bridging

board

Wall Bracing

Compression testing (full-scale walls)

Observed failure modes

Bare-Bare: FT OSB-Bare: FTOSB-Gyp: L + DGyp removed in picture

OSB-Gyp: L OSB-OSB: L

0 0.2 0.4 0.6 0.8 1 1.20

20

40

60

80

100

120

position (in)

load

(ki

p)

Comparison betw een different boards combination

2-BARE-BARE.txt

1-OSB-BARE.txt

11-GYP-GYP.txt

3-OSB-GYP.txt

9-OSB-OSB.txt

Full-scale wall tests (P-D)

Overview

• Performance of sheathed walls

• Development of design method

• Current work

• Work plan and summary

www.ce.jhu.edu/bschafer/sheathedwalls

a) Bare wall with bridging

b) Sheathed wall, no bridging

c) Single column

€

k

d) Spring-column model

track

studbridging

board

€

k

€

k

€

k

€

k

€

kx

€

kφ€

ky

€

kx

€

kφ

€

ky

e) Springs on the cross-section

Sheathed Wall - Idealization

Comparison to design methods

AISI-S100-07

AISI-S100-01

AISI-S210-07

Proposed

Proposed 1-sided

board€

kx

€

kφ€

ky

€

kx

€

kφ

€

ky

Sheathing Restraint - Bracing

xminor-axis bending

global torsion

ymajor-axis bending

flocal torsion

(distortional buckling)

board€

kx

€

kφ€

ky

€

kx

€

kφ

€

ky

Sheathing Restraint - Source

xfastener tilting/bearing

in series with

sheathing diaphragmstiffness

yfastener tilting/bearing

in series with

sheathing bendingstiffness

ffastener pull-out

in series with

sheathing bendingstiffness

board€

kx

€

kφ€

ky

€

kx

€

kφ

€

ky

Sheathing Restraint - Determination

xfastener-board test

in addition to

sheathing diaphragmequation and “APA” values

yfastener tilting/bearing

in series with

sheathing bendingstiffness via “APA” values

fFastener-board test (completed)

in series with

sheathing bendingstiffness equation and

“APA” values

and

Flexural- torsional buckling

Weak axis global

buckling

Local bucklingDistortional

buckling

Sheathing Restraint - ImpactOne-side sheathing only

Sheathing Restraint - ImpactOne-side sheathing only

Sheathing Restraint - PredictionOne-side sheathing only

€

Py 0 0

0 Px 0

0 0 Io /A( )Pφ

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥− P

1 0 yo0 1 −xoyo −xo Io /A( )

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

A1

A2

A3

⎧

⎨ ⎪

⎩ ⎪

⎫

⎬ ⎪

⎭ ⎪= 0€

u = A1 sinπz

L

⎛

⎝ ⎜

⎞

⎠ ⎟

€

v = A2 sinπz

L

⎛

⎝ ⎜

⎞

⎠ ⎟

€

φ=A3 sinπz

L

⎛

⎝ ⎜

⎞

⎠ ⎟

Or you can go back to the classical methods to find the global buckling load

€

Py =π 2EIy

2

L2

€

Px =π 2EIx

2

L2

€

Pφ =A

IoGJ +

π 2

L2ECw

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

€

Io = Ix + Iy + A xo2 + yo

2( )

Sheathing Restraint - PredictionOne-side sheathing only

€

u = A1 sinπz

L

⎛

⎝ ⎜

⎞

⎠ ⎟

€

v = A2 sinπz

L

⎛

⎝ ⎜

⎞

⎠ ⎟

€

φ=A3 sinπz

L

⎛

⎝ ⎜

⎞

⎠ ⎟

Or you can go back to the classical methods to find the global buckling load

€

Py =π 2EIy

2

L2

€

Px =π 2EIx

2

L2

€

Pφ =A

IoGJ +

π 2

L2ECw

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

€

Io = Ix + Iy + A xo2 + yo

2( )

€

Py + kxL2

π 20 kx

L2

π 2yo − hy( )

0 Px + kyL2

π 2−ky

L2

π 2xo − hx( )

kxL2

π 2yo − hy( ) −ky

L2

π 2xo − hx( )

IoAPφ + kx

L2

π 2yo − hy( )

2+ ky

L2

π 2xo − hx( )2 + kφ

L2

π 2

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

− P

1 0 yo0 1 −xoyo −xo Io /A( )

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

A1

A2

A3

⎧

⎨ ⎪

⎩ ⎪

⎫

⎬ ⎪

⎭ ⎪= 0

€

kx

€

kφ€

ky

€

kx

€

kφ

€

ky

Sheathing Restraint - ImpactOne-side sheathing only

pinfix

pin

fixpinfix

K=0.5K=1

a) Contact stud and track

End conditions(comparison to unsheathed specimens)

Sheathing Restraint - ImpactOne-side sheathing only

pinfix

pin

fixpinfix

€

kx

€

kφ€

ky

€

kx

€

kφ

€

ky

ky lowerboundAdd bending stiffnessof sheathing, but non-compositeky upperboundFully composite bending stiffness+ “Ad2” stiffness

Fixed end conditions kx, kf, and ky (lowerbound) found to be consistent with tests

Now, considering again all cases…

AISI-S100-07

AISI-S100-01

AISI-S210-07

Proposed

Proposed 1-sided

Design Method Outline• Determine sheathing restraint

– x, fastener-stiffness test + equations and “APA” for sheathing

– y, equations and “APA” for sheathing or composite test?– f, rotation test or COFS table, + eqn’s and APA for

sheathing• Determine Member Strength

– Global, add kx, ky, kf springs to classical equations or FSM, to findFe (main Spec.) Pcre (DSM)then launder through the column curve to getFn (main Spec.) Pne (DSM)

– Local, ignore spring restraints, determine local-global capacityAeFn (main Spec.) Pnl (DSM)

– Distortional, use kf classical, or kx and kf rational/FSM, to findFd (main Spec. C4.2) Pcrd (DSM)then launder through the distortional strength curve to getPn (main Spec. C4.2) Pnd (DSM)

• Check Fastener Demands

Overview

• Performance of sheathed walls

• Development of design method

• Current Work

• Work plan and summary

www.ce.jhu.edu/bschafer/sheathedwalls

Modeling (for fastener demands)

€

kx

€

kφ€

ky

€

kx

€

kφ

€

ky

imperfections…

Example fastener forces

0.5%Pn

further analysis and comparison with analytical predictions underway

y

f

Overview

• Performance of sheathed walls

• Development of design method

• Current Work

• Work plan and summary

www.ce.jhu.edu/bschafer/sheathedwalls

Basic summary of work plan• Literature summary

– existing methods– existing predictive capabilities

• Computational modeling– to support testing– to support design method creation

• Phase 1 testing– 8’ wall, single stud type, different sheathing configurations, axial only– Fastener translational stiffness/strength tests– Single column with sheathing tests

• Phase 2 testing– Axial + bending tests, 8’ wall, final details TBD– Axial + bending single member tests, w/ sheathing

• Development of new design methods– identify limit states, potential design methodologies, calcs, examples

red = added to initial work plan

Basic summary of work products• Literature summary

– existing methods (summary report, corrections to Simaan and Peköz)– existing predictive capabilities (Mathcad form)

• Computational modeling– to support testing (CUFSM and ABAQUS)– to support design method creation (reliability study on 2a, fastener spacing

studies, fastener demands in bending due to torsion begun)

• Phase 1 testing– 8’ wall, single stud type, different sheathing, axial only (report and

paper posted)– Fastener translational stiffness/strength tests (report and paper posted)– Single column with sheathing tests (report and paper posted )

• Phase 2 testing– Axial + bending tests, 8’ wall, final details TBD (materials ordered)– Axial + bending single member tests, w/ sheathing (materials ordered)

• Development of new design methods– identify limit states, potential design methodologies, calcs, examples

red = added to initial work plan blue = comment on work product

www.ce.jhu.edu/bschafer/sheathedwalls