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