Torsion 9 xls

"TORSION9" --- SIMPLIFIED TORSION ANALYSIS FOR STEEL BEAMS Program Description "TORSION9" is a spreadsheet program written in MS-Excel for the purpose of simplified analsis and code chec!ing of steel eams su#ected to torsional loading$ Specificall% Specificall% six &'( different eam and loading configurations can e anal)ed * code chec!ed per t he +IS, 9th Edition +llowale +llowale Stress esign &+S( Manual$ .oth actual and allowale stresses are computed% with the f inal result eing a computed "stress ratio" of actual stress*allowale stress$ /inall% /inall% the total angle of twist resulting from the torsional loading is determined$ This program is a wor!oo! consisting of se0en &1( wor!sheets% descried as follows2

!ors#eet Name

Description

oc ,antile0er 0er - Ecc$ ,o ,onc$ 3oad Simp Simple le Spa Span n - Ecc$ Ecc$ ,onc ,onc$$ 3oad 3oad ,ont ,ont$$ Span Span - Ecc$ Ecc$ ,onc$ ,onc$ 3oad 3oad

This documentation sheet ,antil tile0er .e .eam wi with Eccen centric ric ,o ,oncen centra trated ted 3o 3oad at at /r /ree En End Simp Simple le Spa Span n .ea .eam m wit with h Ecce Eccent ntri ric c ,on ,once cent ntra rate ted d 3oad 3oad +ppl +pplie ied d at Mids Midspa pan n ,ont ,ontin inuo uous us .eam .eam with with Ecc Eccen entr tric ic ,onc ,oncen entr trate ated d 3oad 3oad +pp +ppli lied ed at +ll +ll Mids Midspa pans ns

,antile0er - Ec Ecc$ 4nif$ 3o 3oad Simple Sp Span - Ecc$ 4n 4nif$ 3oad

,antile0er .eam with Ec Eccentric 4niforml istriuted 3oad Simple Sp Span .e .eam wi with Eccen centri tric 4n 4nifor forml istr striuted ted 3o 3oad

,ont ,ont$$ Spa Span n - Ecc$ Ecc$ 4nif 4nif$$ 3oa 3oad d

,ont ,ontin inuo uous us .eam .eam with with Ecce Eccent ntri ric c 4ni 4nifor forml ml  istr istri iut uted ed 3oad 3oad on +ll +ll Spa Spans ns

Program Ass$mptions Ass$mptions an% Limitations 5$ The simplified torsion analsis used is this program is ased on the following reference2 4SS Steel esign Manual &5965(% ,hapter 12 Torsion &/igures 1$9 7 1$58% pages 51-5'9(% 2 R$3$ .roc!enrough 7 .$:$ ;ohnston <$ This program is 0alid for +IS, =% S% M% and >? shapes$ @$ This program uses the dataase of memer dimensions dimensions and section properties properties from the "+IS, Shapes ataase"% Aersion @$8 &<885( as well as the +IS, 9th Edition &+S( Manual &5969($ B$ This program follows the procedures and guidelines guidelines of the +IS, 9th Edition +llowale Stress &+S( Manual Manual &5969($ $ =hen the 0alue of C3C is input D 8 &or actuall D 5$8 ft$(% this program will use a 0alue D 5$8 ft$ '$ This program utili)es an "+llowale "+llowale Stress Increase /actor" &+SI/( which is a multiplier of an of the calculated allowale allowale stresses /a% /x% and / and also the Euler column uc!ling stresses /Cex and /Ce$ /Ce$ It is used and appears ON3F ON3F in the stress ratio calculation$ Tpicall Tpicall a 0alue of 5$8 ma e used$ >owe0er% >owe0er% a 0alue of 5$@@@ ma ma e used for load cominations which include wind or seismic seismic loads$ loads$ 1$ This program does not not calculate or chec! shear or deflection in memer 6$ This program does not not consider deduction for holes in memers su#ected to tension$ 9$ This program contains numerous Gcomment oxesH which which contain a wide 0ariet of information including explanations of input or output items% euations used% data tales% etc$ &Note2 presence of a Gcomment oxH is denoted  a Gred triangleH triangleH in the upper right-hand corner of a cell$ Merel mo0e the mouse pointer pointer to the desired cell to 0iew the contents of that particular "comment ox"$(

"TORSION9$xls" ?rogram Aersion 5$8

SIMPLIFIED TORSION ANALYSIS FOR STEEL BEAMS

;o Name2 ;o Numer2

&anti'e(er Beam )it# Eccentric &oncentrate% Loa% App'ie% at Free En% For !* S* M* an% +P S#apes an% Per AIS& 9t# E%ition ,ASD Man$a' Su#ect2 Originator2 ,hec!er2

Inp$t Data Mem.er Si/e Select2

f*&
=6x
=BB

Mem.er Loa%ing ?D 8$988 e D 5<$8888

3c D 3u D 3*rt D fa*/ D Mx D fx D Is 3D3cL Is d*twDallowL Is *tD'*SRT&/(L Is *t9*SRT&/(L En$ /5-52 /x D En$ /5-@2 /x D En$ /5-2 /x D Reference for Torsion +nalsis2 /5-'2 /x D 4SS Steel esign ManualEn$ &5965( En$ /5-12 ,hapter 12 Tor sion &/ igures 1$9 7 1$58( /x D /x D 2 R$3$ .roc!enrough 7En$ .$:$ /5-62 ;ohnston /x D 4se2 /x D

Design Parameters / D @'$88 3D '$888 3 D 5<$888 , D 5$88 +SI/ D 5$888 Mem.er Properties + D 1$86 dD 1$9@8 tw D 8$
!ips in$

!si ft$ ft$

in$< in$ in$ in$ in$ in$

Ix D Sx D I D S D ;D ,w D wt$*ft$ D

6<$18 <8$98 56$@8 $'@ 8$@B'

in$B

<9$8

in$'

plf

in$@ in$B in$@ in$B

=B8

Res$'ts 0-a1is Ben%ing Mx D $6@ fx D @$@ 3*rt D 65$6< /x D <5$'8

ft-!ips !si !si

aD Mt D f D / D

Mx D ?J3 P wJ3<*< &w D eam self weight( fx D MxJ5<*Sx Note2 3c D '$6' ft$% 3u D 5$56 ft$ /x D 5<888J,*&3J5
=B8

S$R$ D =B8

Torsion ,Latera' F'ange Ben%ing aD BB$8@ in$ Mt D B$66 ft-!ips f D <8$19 !si / D <1$88 !si

a D SRT&EJ,w*&:J;(( &where2 E D <9888 !si% : D 55<88 !si( Mt D &?JeJa*dfJT+N>&3J5<*a((*5< &where2 df D d-tf( f D MtJ5<*&S*<( Note2 use onl 5*< of S / D 8$1J/

φD =B8 =B8 =B8 =B8

Stress Ratio S$R$ D

=B8

8$9<

S$R$ D fx*&+SI/J/x( P f*&+SI/J/( D 5$8

=B8 =@'

Ang'e o2 T)ist φD

=@'

B$965

deg$

φ D &?JeJa*&;J:(J&3J5<*a-T+N>&3J5<*a(((J568*π

=@' =@'

< of 5@

81*8*<85' 52'255

"TORSION9$xls" ?rogram Aersion 5$8 =@'

@ of 5@

81*8*<85' 52'255


SIMPLIFIED TORSION ANALYSIS FOR STEEL BEAMS Simp'e Span Beam )it# Eccentric &oncentrate% Loa% App'ie% at Mi%span For !* S* M* an% +P S#apes an% Per AIS& 9t# E%ition ,ASD Man$a' ;o Name2 Su#ect2 ;o Numer2 Originator2 ,hec!er2 Inp$t Data Mem.er Si/e Select2

f*&
=6x
=BB

Mem.er Loa%ing ?D <$<8 eD '$8888

3c D 3u D 3*rt D fa*/ D Mx D fx D Is 3D3cL Is d*twDallowL Is *tD'*SRT&/(L Is *t9*SRT&/(L En$ /5-52 /x D En$ /5-@2 /x D En$ /5-2 /x D En$ /5-'2 /x D Reference for Torsion +nalsis2 /5-12 /x D 4SS Steel esign ManualEn$ &5965( En$ /5-62 ,hapter 12 Tor sion &/ igures 1$9 7 1$58( /x D /x D 2 R$3$ .roc!enrough 7 .$:$ ;ohnston 4se2 /x D

Design Parameters / D @'$88 3D <8$888 3 D <8$888 , D 5$88 +SI/ D 5$888 Mem.er Properties + D 1$86 dD 1$9@8 tw D 8$
!ips in$

!si ft$ ft$



6<$18 <8$98 56$@8 $'@ 8$@B'

in$B

<9$8

in$'

plf


=B8

Res$'ts 0-a1is Ben%ing Mx D 5<$B fx D 1$5 3*rt D 5@'$@' /x D 5'$@9

ft-!ips !si !si

aD Mt D f D / D

Mx D ?J3*B P wJ3<*6 &w D eam self weight( fx D MxJ5<*Sx Note2 3c D '$6' ft$% 3u D 5$56 ft$ /x D 5<888J,*&3J5
=B8

S$R$ D =B8

Torsion ,Latera' F'ange Ben%ing aD BB$8@ in$ Mt D @$<' ft-!ips f D 5@$98 !si / D <1$88 !si

a D SRT&EJ,w*&:J;(( &where2 E D <9888 !si% : D 55<88 !si( Mt D &?JeJa*&&3J5<*&
φD =B8 =B8 =B8 =B8


=B8

8$95


=B8 =@'


=@'

1$'<8

deg$

φ D &?JeJa*&&3J5<*&
=@' =@'

B of 5@

81*8*<85' 52'255


 of 5@

81*8*<85' 52'255


SIMPLIFIED TORSION ANALYSIS FOR STEEL BEAMS &ontin$o$s Span Beam )it# Eccentric &oncentrate% Loa% App'ie% at A'' Mi%spans For !* S* M* an% +P S#apes an% Per AIS& 9t# E%ition ,ASD Man$a' ;o Name2 Su#ect2 ;o Numer2 Originator2 ,hec!er2 Inp$t Data Mem.er Si/e Select2

f*&
=6x
=BB

Mem.er Loa%ing ?D B$888 eD 6$8888

3c D 3u D 3*rt D fa*/ D Mx D fx D Is 3D3cL Is d*twDallowL Is *tD'*SRT&/(L Is *t9*SRT&/(L En$ /5-52 /x D En$ /5-@2 /x D En$ /5-2 /x D En$ /5-'2 /x D Reference for Torsion +nalsis2 /5-12 /x D 4SS Steel esign ManualEn$ &5965( En$ /5-62 ,hapter 12 Tor sion &/ igures 1$9 7 1$58( /x D /x D 2 R$3$ .roc!enrough 7 .$:$ ;ohnston 4se2 /x D

Design Parameters / D @'$88 3D 58$888 3 D 58$888 , D 5$88 +SI/ D 5$888 Mem.er Properties + D 1$86 dD 1$9@8 tw D 8$
!ips in$

!si ft$ ft$



6<$18 <8$98 56$@8 $'@ 8$@B'

in$B

<9$8

in$'

plf


=B8

Res$'ts 0-a1is Ben%ing Mx D 1$59 fx D B$5@ 3*rt D '6$56 /x D <5$'8

ft-!ips !si !si

Mx D 8$51J?J3 P 8$86JwJ3< &w D eam self weight( fx D MxJ5<*Sx Note2 3c D '$6' ft$% 3u D 5$56 ft$ /x D 5<888J,*&3J5
aD Mt D f D / D =B8

S$R$ D =B8

Torsion ,Latera' F'ange Ben%ing aD BB$8@ in$ Mt D B$'< ft-!ips f D 59$'9 !si / D <1$88 !si

a D SRT&EJ,w*&:J;(( &where2 E D <9888 !si% : D 55<88 !si( Mt D &?JeJa*&&3J5<*&BJa(((*5< &where2 df D d-tf( f D MtJ5<*&S*<( Note2 use onl 5*< of S / D 8$1J/

φD =B8 =B8 =B8 =B8


=B8

8$9<8


=B8 =@'


=@'

5$6@

deg$

φ D &?JeJa*&;J:(J&3J5<*&BJa(-T+N>&3J5<*&BJa((((J568*π

=@' =@'

' of 5@

81*8*<85' 52'255


1 of 5@

81*8*<85' 52'25<




&anti'e(er Beam )it# Eccentric 3ni2orm'4 Distri.$te% Loa% For !* S* M* an% +P S#apes an% Per AIS& 9t# E%ition ,ASD Man$a' Su#ect2 Originator2 ,hec!er2


f*&
=6x
=BB

Mem.er Loa%ing wD 8$@88 e D 58$8888

3c D 3u D 3*rt D fa*/ D Mx D fx D Is 3D3cL Is d*twDallowL Is *tD'*SRT&/(L Is *t9*SRT&/(L En$ /5-52 /x D En$ /5-@2 /x D En$ /5-2 /x D En$ /5-'2 /x D En$ /5-12 /x D Reference for Torsion +nalsis2 /5-62 /x D 4SS Steel esign ManualEn$ &5965( ,hapter 12 Tor sion &/ igures 1$9 7 1$58( /x D 4se2 /x D 2 R$3$ .roc!enrough 7 .$:$ ;ohnston

Design Parameters / D @'$88 3D '$888 3 D 5<$888 , D 5$88 +SI/ D 5$888 Mem.er Properties + D 1$86 dD 1$9@8 tw D 8$
!ips*ft$ in$

!si ft$ ft$



6<$18 <8$98 56$@8 $'@ 8$@B'

in$B

<9$8

in$'

plf


=B8

Res$'ts 0-a1is Ben%ing Mx D $6@ fx D @$@ 3*rt D 65$6< /x D <5$'8

ft-!ips !si !si

Mx D wJ3<*< P wJ3<*< &w D eam self weight( fx D MxJ5<*Sx Note2 3c D '$6' ft$% 3u D 5$56 ft$ /x D 5<888J,*&3J5
aD Mt D f D / D =B8

S$R$ D =B8

Torsion ,Latera' F'ange Ben%ing aD BB$8@ in$ Mt D B$16 ft-!ips f D <8$@1 !si / D <1$88 !si

&where2 df D d-tf( a D SRT&EJ,w*&:J;((

&where2 E D <9888 !si% : D 55<88 !si(

φD

MtD&w*5&3J5<*a(P5*&&3J5<*a(J,OS>&3J5<*a((-a*&3J5<(((*5<

f D MtJ5<*&S*<( Note2 use onl 5*< of S / D 8$1J/

=B8 =B8 =B8


=B8

8$958


=B8 =@'


=@'

@$59'

deg$

φ D &w*5&3*a(-5*&&3*a(J,OS>&3*a((Pa*&3(((J568* π

=@'

&Note2 in euation ao0e 3 is multiplied  5< to con0ert length from feet t o inches$(

=@'

6 of 5@

81*8*<85' 52'25<


9 of 5@

81*8*<85' 52'25<




Simp'e Span Beam )it# Eccentric 3ni2orm'4 Distri.$te% Loa% For !* S* M* an% +P S#apes an% Per AIS& 9t# E%ition ,ASD Man$a' Su#ect2 Originator2 ,hec!er2


f*&
=6x@5

=BB

Mem.er Loa%ing wD 8$18 e D 58$8888


Design Parameters / D @'$88 3D 58$888 3 D 58$888 , D 5$88 +SI/ D 5$888 Mem.er Properties + D 9$5< dD 6$888 tw D 8$<6 f D 6$888 tf D 8$B@ rt D <$568 d*+f D <$@8

!ips*ft$ in$

!si ft$ ft$



558$88 <1$8 @1$58 9$<1 8$@'

in$B

@5$8

in$'

@5

plf


=B8

Res$'ts 0-a1is Ben%ing Mx D 9$1' fx D B$<' 3*rt D $8 /x D <5$'8

ft-!ips !si !si

Mx D wJ3<*6 P wJ3<*6 &w D eam self weight( fx D MxJ5<*Sx Note2 3c D 6$BB ft$% 3u D <8$5@ ft$ /x D 5<888J,*&3J5
aD Mt D f D / D =B8

S$R$ D =B8

Torsion ,Latera' F'ange Ben%ing aD 8$' in$ Mt D 1$16 ft-!ips f D <8$5 !si / D <1$88 !si


&where2 E D <9888 !si% : D 55<88 !si(

φD

Mt D &w*5&3J5<*&

=B8 =B8 =B8


=B8

8$9B@


=B8 =@'


=@'

@$99

deg$

φ D &w*5&3*&
=@'

&Note2 in euation ao0e 3 is multiplied  5< to con0ert length from feet t o inches$(

=@'

58 of 5@

81*8*<85' 52'25<


55 of 5@

81*8*<85' 52'25<


SIMPLIFIED TORSION ANALYSIS FOR STEEL BEAMS &ontin$o$s Span Beam )it# Eccentric 3ni2orm'4 Distri.$te% Loa% on A'' Spans For !* S* M* an% +P S#apes an% Per AIS& 9t# E%ition ,ASD Man$a' ;o Name2 Su#ect2 ;o Numer2 Originator2 ,hec!er2 Inp$t Data Mem.er Si/e Select2

f*&
=5
Mem.er Loa%ing wD 5$888 eD <$8888 Design Parameters / D @'$88 3D <6$888 3 D 5B$888 , D 5$88 +SI/ D 5$888 Mem.er Properties + D 51$88 dD 5<$<88 tw D 8$@'8 f D 58$888 tf D 8$'B8 rt D <$1<8 d*+f D 5$98

=BB

B1$88 16$88 581$88 <5$B8 <$588

in$B

in$B


@18$8

in$'

=B8

6

plf

!*ft$ in$

!si ft$ ft$



in$@ in$B in$@

Res$'ts 0-a1is Ben%ing Mx D fx D 3*rt D /x D

''$@' 58$<5 '5$1' <5$'8

ft-!ips !si !si

Mx D 8$86JwJ3< P 8$86JwJ3< &w D eam self weight( fx D MxJ5<*Sx Note2 3c D 58$' ft$% 3u D
aD Mt D f D / D =B8

S$R$ D =B8

Torsion ,Latera' F'ange Ben%ing aD ''$@ in$ Mt D 6$<1 ft-!ips f D 9$<6 !si / D <1$88 !si


&where2 E D <9888 !si% : D 55<88 !si(

φD

Mt D &w*5&3J5<*&
=B8


=B8 =B8 =B8


=B8

8$65'


=B8 =@'


=@'

5$615

deg$

φ D &w*5&3J5<*&BJa((((J568*π =@' =@'

5< of 5@

81*8*<85' 52'25<


5@ of 5@

81*8*<85' 52'25<

Torsion 9 xls

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