AISI Design Methods for Sheathing Braced Design

,2 AISI Specification

1962 AISI Design Manual

$ 78he safe load-carr5ing capacit5 of a stud ma5 (e computed on the (asis that the #all material or sheathing 9attached to the stud: furnishes ade;uate lateral support to the stud in the plane of the #all' pro"ided the #all material and its attachments to the stud compl5 #ith the follo#ing re;uirements<= %stener spcing( a( m-st ,e less thn

amax' =

a max /

=

0 EI / k A/ f y/ Lr / /r '




amax' =

a max /

=

0 EI / k A/ f y/ Lr / /r '




amax' = a max / =

%stener*shething sti%%* ness( k ( m-st ,e t lest)

0 EI / k A/ f y/ Lr / /r '

k min =

f y/ aA/ /21 ,111 ,111 I /




amax' = a max / =

%stener*shething sti%%* ness( k ( m-st ,e t lest)

%steners m-st h3e t lest this m-ch strength)

0 EI / k A/ f y/ Lr / /r '

k min =

f y/ aA/ /21 ,111 ,111 I /

F min =

keP

/ EI / k / a − P

Fastener spacing limit >,


$ Design basis < a max , re;uires that #ea6-ais (uc6ling of the stud' including contri(utions from the #all stiffness k' that is de"eloped from fasteners at spacing a, is greater than or e;ual to the s;uash load of the column. P cr / (k @ a ,( KL )/ = L ) ≥ Af y %stener spcing( a( m-st ,e less thn

amax' =

a max /

0 EI / k A/ f y/

Lr / =

/r '

Fastener spacing limit >,


$ Design basis < a max , re;uires that #ea6-ais (uc6ling of the stud' including contri(utions from the #all stiffness k' that is de"eloped from fasteners at spacing a, is greater than or e;ual to the s;uash load of the column. P cr / (k @ a ,( KL )/ = L ) ≥ Af y %stener spcing( a( m-st ,e less thn

amax' =

a max /

0 EI / k A/ f y/

Lr / =

P cr / P E

→

/

β id L/

π

P E

Winter 4'5617 sol-tion %or col-mn on  sti%%( contin-o-s( %o-ndtion

con3ert contin-o-s %o-ndtion sti%%ness( β ( to discrete springs( k, nd set P cr /8 Af y

/r ' sol3e %or a( 9o- get

Af y /

/

π EI L

=

/

/k a L/

π π / EI L/

Fastener spacing limit >2


$ Design basis < a max 2 re;uires that #ea6-ais (uc6ling of the stud o"er a length of 2a 9t#ice the fastener spacing: must (e greater than the strong-ais (uc6ling o"er the entire length. P cr / (k = 1 , ( KL )/ = /a ) ≥ P cr ' (( KL )' = L ) %stener spcing( a( m-st ,e less thn

amax'

a max /

=

0 EI / k

A/ f y/ Lr /

=

/r '

Fastener spacing limit >2


$ Design basis < a max 2 re;uires that #ea6-ais (uc6ling of the stud o"er a length of 2a 9t#ice the fastener spacing: must (e greater than the strong-ais (uc6ling o"er the entire length. P cr / (k = 1 , ( KL )/ = /a ) ≥ P cr ' (( KL )' = L ) %stener spcing( a( m-st ,e less thn

amax'

a max /

=

E:-ting P cr ' nd P cr / implies

( KL )'

0 EI / k

A/ f y/

r '

/r '

r /

Ins-re .e!*+is ,-c!ling o3er /a does not control

L

Lr / =

=

( KL )/

sol3e %or a( 9o- get

r '

=

/a r /

minimum stiffness k


$ Design basis: kmin is the same as the a max , design chec6. P cr / P E

→

/ π

β id L/

Af y /

P E

/

π EI / L

=

/

/k a L/

π π / EI / L/

4%rom Winter '5617

%stener*shething sti%%* ness( !( m-st ,e t lest) s-, in %or E nd π( sol3e %or k

k min =

(

f y/ aA/ /21 ,111 ,111 I /

(

)

)

fastener strength


$ Design basis < forces de"eloped in an imperfect' (ut stiff continuous foundation under the design load P ' should (e carried (5 the fasteners' plus Winter adds some interesting empirical corrections. Winter 4'5617 de%ines %orces de3eloped in  sti%% con* tin-o-s %o-ndtion s-pporting n imper%ect col-mn

sreq = d o

β id

' − β id β act F min = sreq a /

= /k a F min = e

k id ' − k id k act


F min =

keP

/ EI / k / a − P

fastener strength 9continued:


F min = e

k id ' − k id k act

gin( Winter -ses the sol-tion %or ,-c!ling o%  col-mn on  sti%% contin-o-s %o-ndtion( this time to %ind the idel sti%%ness βid 4k id 7)

P cr / P E

=

id

/

/

β id L

π

P E

.hich res-lts in

nd

= /k id a

P E = π / EI / / L/ P cr / = P

(

k id = P / / EI / a

)

/

%ter s-,stit-tion nd rerrnging( .e %ind

F min =

ek act P / / EI / a k act


k id − P

F min =

keP / EI / k / a − P

fastener strength 9continued: F min =


k id − P

'; ss-me k act 8k id onl9 -nder %irst denomintor term /; remo3e / -nder the rdicl in %irst term s .ell <; remining k act 8 k

res-lts in


=rce %orces res-lting %rom E+mple '' o% '56/ design mn-l note k act 801k id

F min =


fastener strength 9continued:


F min =


k id − P

'; ss-me k act 8k id onl9 -nder %irst denomintor term /; remo3e / -nder the rdicl in %irst term s .ell <; remining k act 8 k /@ $r-le&

1;1/

?min4 P7


1;1'>

P ?min/4 P7

res-lts in

=rce %orces res-lting %rom E+mple '' o% '56/ design mn-l note k act 801k id

1;1'

P

F min =

1;11>

1 1

/111

2111

6111

0111

' .'1

2



Summar5 of ,2 Specification $ 8he fastener-sheathing stiffness must insure the follo#ing condition is met P cr / (k @ a , ( KL )/ = L ) ≥ Af y

$ 8he fastener-sheathing strength must insure the follo#ing condition is met F min = e

k k / k id − '

.here

k id = P / a 0 EI /

$ In addition to insure ade;uate performance in the face of potential defects P cr / (k = 1 ,( KL )/ = /a ) ≥ P cr ' (( KL )' = L )

$ If the a(o"e conditions are met P cr ? P cr1 9strong-ais:.


Criti;ue of ,2 Specification $ 8he fastener-sheathing stiffness must insure the follo#ing condition is met P cr / (k @ a , ( KL )/ = L ) ≥ Af y

useful, but arbitrary, does not even insure that strong axis controls

$ 8he fastener-sheathing strength must insure the follo#ing condition is met F min = e

k k / k id − '

couched in something theoretical, but in the end empirical, not wholly consistent with current approaches

$ In addition to insure ade;uate performance in the face of potential defects P cr / (k = 1 ,( KL )/ = /a ) ≥ P cr ' (( KL )' = L )

arbitrary, realistic?

$ If the a(o"e conditions are met P cr ? P cr1 9strong-ais:. Underlying theory not directly applicable, no torsional-flexural buckling

1980 to 2004 AISI Spec.

,! to 2/ AISI Specification $ Also 6no#n as the Simaan and %e6@ method' or the shear diaphragm model' or the 7D/ method=. 1isted from ,! to 2/ in Spec. Section D/. A(andoned in fa"or of a return to Winter4s method' more or less. $ Wh5 #as the method a(andoned $ What can #e learn from the 7mista6es=


%ractical limitations of D/ method $ 78he design epressions are comple. 8he design epressions do not gi"e credit to the presence of supplementar5 steel (ridging #hich is t5picall5 installed in order to align mem(ers and to pro"ide necessar5 structural integrit5 during erection and in the completed structure. %ro"ided there is ade;uate steel (ridging' the imperfect sheathing approach in Section D/ 9a: can produce a lo#er capacit5 than an all steel approach. 8he most popular sheathing' g5psum #all(oard' is seen (5 some as too moisture and load c5cle sensiti"e to act as a relia(le structural (race for the ser"ice life of a structure. Other restrictions in Section D/ 9a: are for the most part impractical for t5pical use.= 98restain 22:.


8heoretical limitation of the D/ Method $ For the most part Winter4s method ma5 conceptuall5 (e understood as a column supported (5 discrete springs<

$ 8he D/ method has ne"er (een presented #ith an e;ui"alent mechanical model' instead it is al#a5s descri(ed as a summation of energies 9column (ending  shear distortion of diaphragm:' #hat is underneath the hood


Consider the shear energ5 term

sher energ9

$sher& ngle

D s =

' /

α ( z ) =

∫

L

1

Q[α ( z )] dz /

d ( z ) dz

= θ y ( z )


Consider the shear energ5 term

sher energ9

$sher& ngle

D s =

' /

α ( z ) =

∫

L

1

Q[α ( z )] dz /

d ( z ) dz

= θ y ( z )

e:-i3lence .ith rottionl spring %o-ndtion)

D s =

' /

L

∫

1

Qθ y dz = D β = /

' /

∫

L

1

/

β α θ y dz


Consider the shear energ5 term mechnicll9 e:-i3lent model to sher diphrgm

sher energ9

$sher& ngle

D s =

' /

α ( z ) =

∫

L

1

Q[α ( z )] dz /

d ( z ) dz

considering discrete %steners

= θ y ( z )

e:-i3lence .ith rottionl spring %o-ndtion)

D s =

' /

L

∫

1

Qθ y dz = D β = /

' /

∫

L

1

/

β α θ y dz


D/ method summar5 $ 8he method #as a(andoned for numerous practical reasons' and no# can (e seen to ha"e a serious theoretical limitation $ o#e"er' lots of great and complicated mechanics in the D/ method. 8orsional-fleural (uc6ling is treated thoroughl5 9e"en for dissimilar and one-sided sheathing:. $ 8he role of shear in deforming the sheathing is real' (ut ha"e to (e careful #ith ho# that actuall5 (races the stud

2007 AISI-COFS all Stu! Stan!a"! #S211$

20 AISI-S2,, Wall Stud Standard $ 7Wall stud assem(lies using a sheathing (raced design shall (e designed assuming that identical sheathing is attached to (oth sides of the #all stud and connected to the (ottom and top horiontal mem(ers of the #all to pro"ide lateral and torsional support to the #all stud in the plane of the #all.= $ 7Both ends of the stud shall (e connected to restrain rotation a(out the longitudinal stud ais and horiontal displacement perpendicular to the stud ais.= Further' in B,.29(: it is prescri(ed that the glo(al (uc6ling load of a stud' #ith fasteners spaced distance 7a = apart shall (e determined ignoring an5 sheathing contri(ution 9i.e. k ? : o"er a distance of 2a ' i.e.< P cr k = 1 , ( KL ) x = L , ( KL ) y = /a , ( KL )t = /a


P cr (5 AISI-S2,,-0 $ It is assumed that the sheathing pro"ides enough stiffness that P cr ignoring the sheathing o"er a length e;ual to t#ice the fastener spacing' a ' is al#a5s less than P cr considering the sheathing< ,-c!ling cross  de%ecti3e %stener

assmed

<

,-c!ling o% the st-d engging ll %steners


P cr (5 AISI-S2,,-0 $ It is assumed that the sheathing pro"ides enough stiffness that P cr ignoring the sheathing o"er a length e;ual to t#ice the fastener spacing' a ' is al#a5s less than P cr considering the sheathing< ,-c!ling cross  de%ecti3e %stener

min

P cry k = 1 , ( KL ) y = /a P cr!F (k = 1 , ( KL ) x = L , ( KL )t = /a )

assmed

<

assmed

<

,-c!ling o% the st-d engging ll %steners min P cry k @ a ,( KL ) y = L P cr!F (k = 1 ,( KL ) x = L" k @ a , ( KL )t = L )


P cr (5 AISI-S2,,-0 $ It is assumed that the sheathing pro"ides enough stiffness that P cr ignoring the sheathing o"er a length e;ual to t#ice the fastener spacing' a ' is al#a5s less than P cr considering the sheathing< assmed

,-c!ling cross  de%ecti3e %stener min

<

P cry k = 1 , ( KL ) y = /a

assmed

P cr!F (k = 1 , ( KL ) x = L , ( KL )t = /a )

<

,-c!ling o% the st-d engging ll %steners min P cry k @ a ,( KL ) y = L P cr!F (k = 1 ,( KL ) x = L" k @ a , ( KL )t = L )

3lidit9 o% ss-mption depends on the sti%%ness !( s ! 1 de%initel9 not  3lid ss-mption


AISI-S2,,-0 Commentar5 $ Wall Stud Standard pro"ides onl5 minor guidance' primaril5 #all stud design is left to rational anal5sis. $ o#e"er' the commentar5 pro"ides one such rational anal5sis method' rel5ing primaril5 on the 2E rule for fastener demands. $ et us re"isit the classic deri"ation to (etter understand the implications of the 2E rule.


2E rule in AISI-S2,,-0 Commentar5 $ Consider the (asic deri"ation 9supplementing the commentar5:


2E rule in AISI-S2,,-0 Commentar5 $ Consider the (asic deri"ation 9supplementing the commentar5: ?inll9 sol3ing %or the ,rcing %orce)

note( '@P( not /@P( ,-t ,rce %orce is  %-nction o% k nd do cn ,e higher or lo.er


Comparison of ,2 and 20 methods


Anal%&e an% !esign

'"esc"i(e! )ailu"e *o!e

AISI /11B 4S/''*1B7 P cr = min P cry , P cr!F

AISI '56/ P cr = P crx (( KL ) x = L ) C

.here P cry k = 1 , ( KL ) y = /a

s-,Dect to P cry k = 1 , ( KL ) y = /a ≥ P crx (( KL ) x = L )

P cr!F (k = 1 ,( KL ) x = L , ( KL )t = /a )

P cry (k @ a , ( KL ) y = L ) ≥ Af y

nd /@ P %or %steners

nd E/@ P %or %steners C It is importnt to note tht AISI '56/ did not incl-de torsionl*%le+-rl ,-c!ling nd P cr!F F P crx tho-gh s torsionl resistnce is incresed P cr!F .ill s9mptote to P crx;

oo6ing to#ards ne# methods..

imit states 9a(ridged: $ Stud + Glo(al (uc6ling 9F' 8' F8 + including sheathing: $ should the stud (e chec6ed assuming defecti"e fastener

+ ocal (uc6ling 9pro(a(l5 ignore sheathing: + Distortional (uc6ling 9pro(a(l5 including sheathing: $ should the stud (e chec6ed assuming a defecti"e fastener

$ Connections + Stud-fastener-sheathing connection + 8rac6-fastener-sheathing connection + Stud-to-trac6 connection

$ Sheathing $ Construction loads 9re;uires all-steel chec6:

imit states 9a(ridged:

stte o% de3elopment;;;

$ Stud + Glo(al (uc6ling 9F' 8' F8 + including sheathing: $ should the stud (e chec6ed assuming defecti"e fastener

+ ocal (uc6ling 9pro(a(l5 ignore sheathing: + Distortional (uc6ling 9pro(a(l5 including sheathing: $ should the stud (e chec6ed assuming a defecti"e fastener

$ Connections + Stud-fastener-sheathing connection + 8rac6-fastener-sheathing connection + Stud-to-trac6 connection

$ Sheathing $ Construction loads 9re;uires all-steel chec6:

Hp to date #or6 on (racing a stud

Sheathing k y

τ & y %

=

$θ & y %

x4 y 7 = sin4

θ 4 y 7 =

d x4 y 7 dy

τ 4 y 7 = #

x

=

$ ⋅ π L

π ⋅ y L

π L

7

⋅ cos4

⋅ cos4

π ⋅ y L

π ⋅ y L

7

7

Sheathing k y

F & y % = & τ / − τ ' % ⋅ #t / n

τ & y %

=

$θ & y %

k =

x

#

k = /'

$#t  π a  sin  Ln  / L 

F 4 y 7 x4 y 7

When sheathing k matters $ If k s(eat(in) ,k fastener ... pro(a(l5 matters ! totl ( α ) :=

' ' ! %stener

+

' ! shething( α )

k fastener 1;0

! totl 4 α 7

%stener

1;6

shething

! %stener 1;2

1;/

1 1;'

'

'1 ! shething 4 α 7

'11

Getting past fleure... $ Support of the stud eists for other DOF as #ell' and in some cases preliminar5 characteriation has (een done

O"er"ie# $ %art of the AISI-COFS funded pro&ect on the design of sheathed #alls #ith dis-similar sheathing. $ %resentation de"eloped from a report of the same name $ %ro&ect updates' including full report a"aila(le at ###.ce.&hu.edu)(schafer)sheathed#alls $ *eport co"ers + Design methods "ia ,2' ,!-2/' 20 AISI + 1amination of sheathing stiffness 3k4 + Initial summar5 of 6no#n demands and limit states on a sheathed #all stud in compression

A** for no#, !(ank yo+++

Cu""ent Mo!eling

St"ess !ist"i(ution at 'ea+ ,oa! #"a% colo" "ep"esents %iel!ing - connections$

,a(  ene"al /ie 1

AISI Design Methods for Sheathing Braced Design

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