sheathing braced design of wall studs july 2010 update for aisi committee on framing standards...

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