Civil
Engineering
at JOHNS HOPKINS UNIVERSITY
Sheathing Braced Design of Wall Studs
July 2010 Update
www.ce.jhu.edu/bschafer/sheathedwalls
for
AISI Committee on Framing Standards
Design Methods Subcommittee
Toronto, ON
Overview
• Performance of sheathed walls
• Development of design method
• Current work
• Work plan and summary
www.ce.jhu.edu/bschafer/sheathedwalls
Wall Bracing
bridging
stud
track
a) Bare wall with bridging
board
b) Sheathed wall, no bridging
Compression testing (full-scale walls)
Observed failure modes
Bare-Bare: FT
OSB-Gyp: L
OSB-Bare: FT
OSB-Gyp: L + D
Gyp removed
in picture
OSB-OSB: L
Full-scale wall tests (P-D)
Comparison betw een different boards combination
120
2-BARE-BARE.txt
1-OSB-BARE.txt
11-GYP-GYP.txt
3-OSB-GYP.txt
100
9-OSB-OSB.txt
load (kip)
80
60
40
20
0
0
0.2
0.4
0.6
position (in)
0.8
1
1.2
Overview
• Performance of sheathed walls
• Development of design method
• Current work
• Work plan and summary
www.ce.jhu.edu/bschafer/sheathedwalls
Sheathed Wall - Idealization
bridging
stud
k
ky
k
kx


k

k


b) Sheathed wall, no
bridging

k
k
x
k
board
a) Bare wall with
bridging


track
k
c) Single column

ky

d) Spring-column e) Springs on the
cross-section
model
Comparison to design methods
Sheathing Restraint - Bracing
y
major-axis bending
ky
x
kx
k
minor-axis bending

global torsion

board

local torsion
(distortional buckling)

kx
k
ky


Sheathing Restraint - Source
y
ky
x
kx
fastener tilting/bearing
in series with
sheathing bending
stiffness
k
fastener tilting/bearing

fastener pull-out
in series with
in series with
sheathing diaphragm
stiffness
sheathing bending
stiffness

kx
board

k
ky


Sheathing Restraint - Determination
y
ky
x
kx
fastener tilting/bearing
in series with
sheathing bending
stiffness via “APA” values
k
fastener-board
test
Fastener-board test (completed)
in addition to
in series with
sheathing diaphragm
equation
and “APA” values

kx
board

k
ky


sheathing bending
stiffness equation and
“APA” values
Sheathing Restraint - Impact
One-side sheathing only
Flexuraltorsional
buckling
Weak axis
global buckling
and
Local buckling
Distortional
buckling
Sheathing Restraint - Impact
One-side sheathing only
Sheathing Restraint - Prediction
One-side sheathing only
Or you can go back to the classical methods to find the global buckling load
z 
z 
z 
u  A1 sin  v  A2 sin    A3 sin 
 L 
 L 
 L 
P
 y
 0
 0


Py 
 2 EI y2
L2
0
P 
x
0
Px 
 1
 

0

P
  0
I o / A P  yo
 2 EI x2
L2
0
0
1
xo
A1 
 
xo A2   0
A 


I
/
A
 o  3 


2
A 
P 
GJ  2 ECw 

I o 
L


yo

I o  I x  I y  A xo2  yo2

Sheathing Restraint - Prediction
One-side sheathing only
Or you can go back to the classical methods to find the global buckling load
z 
z 
z 
u  A1 sin  v  A2 sin    A3 sin 
 L 
 L 
 L 
ky
kx


k
x


L2
L2
 Py  kx
0
k
y

h

o y
x
2
2

 1

L2
L2
 
0
Px  ky 2
ky 2 xo  hx 

 P 0




2
2
2
2
2 
yo
k L y  h  k L x  h  I o P  k L y  h 2  k L x  h 2  k L 
y
y
o
x

x
o
y
y
o
x

 x  2 o
A
2
2
2
 2 



Py 

 2 EI y2
L2
Px 
 2 EI x2
L2



2
A 
P 
GJ  2 ECw 

I o 
L


k
k
 ky


0
yo A1 
 
1
xo A2   0


xo I o / A 
A3 




I o  I x  I y  A xo2  yo2

Sheathing Restraint - Impact
One-side sheathing only
fix
pin
fix
pin
fix
pin
End conditions
(comparison to unsheathed specimens)
a) Contact stud and track
K=1
K=0.5
Sheathing Restraint - Impact
One-side sheathing only
fix
pin
fix
pin
ky
kx
k



k
fix
pin
k
x
ky


ky lowerbound
Add bending stiffness
of sheathing, but noncomposite
ky upperbound
Fully composite
bending stiffness
+ “Ad2” stiffness

Fixed end conditions kx, k, and ky (lowerbound) found to be consistent with tests
Now, considering again all cases…
Design Method Outline
• Determine sheathing restraint
– x, fastener-stiffness test + equations and “APA” for sheathing
– y, equations and “APA” for sheathing or composite test?
 , rotation test or COFS table, + eqn’s and APA for sheathing
• Determine Member Strength
– Global, add kx, ky, k springs to classical equations or FSM, to find
Fe (main Spec.) Pcre (DSM)
then launder through the column curve to get
Fn (main Spec.) Pne (DSM)
– Local, ignore spring restraints, determine local-global capacity
AeFn (main Spec.) Pnl (DSM)
– Distortional, use k classical, or kx and k rational/FSM, to find
Fd (main Spec. C4.2) Pcrd (DSM)
then launder through the distortional strength curve to get
Pn (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)
imperfections…
ky
kx
k



k
k
x
ky



Example fastener forces
0.5%Pn
further analysis and comparison with analytical predictions underway
y

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
www.ce.jhu.edu/bschafer/sheathedwalls
• 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