3.1.6 Torsional Constant

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for B>D

BEAM D B A I SA Sthk EQ.(in) Fw C(ext) Use, C(ext) C(int) Use, C(int)

IDEN mm mm mm mm!" mm mm in D B Int(in) Ext(in) Ext(in!")# Ext(in!")$ (in!") (mm!") Int(in!")# Int(in!")$ (in!") (mm!")

B% &'' '' .''E*'& .&E*'+ ."'E*'& &' %' %+. . &-.'+ ." %."E*'" .+-E*'" .+-E*'" %."E*%' .%-E*'" .-E*'" .-E*'" %.&&E*%'

B '' -'' ".'E*'& %.E*%' .E*'& &' %' . -.& .+' "%." .-E*'" &.%E*'" &.%E*'" ."E*%' ."E*'" .+E*'" .+E*'" .-E*%'

B '' -&' ".&'E*'& %.&E*%' .'E*'& &' %' . +.& -. ".% .''E*'" .E*'" .E*'" .-E*%' .+"E*'" -.%E*'" -.%E*'" .%-E*%'

B" '' %''' .''E*'& %.'E*%' ".'E*'& &' %' . +.- +.& &.%& ".%-E*'" %.%'E*'& %.%'E*'& ".&E*%' &."E*'" %.E*'& %.E*'& &.%'E*%'

B& '' %'' -.'E*'& .%E*%' &.-E*'& &' %' . "-." %'.- %.' &.%%E*'" %."&E*'& %."&E*'& .'E*%' .%E*'" %.'E*'& %.'E*'& ."E*%'B '' %&'' +.''E*'& .-'E*%' -.'E*'& &' %' . &+.'& %%.+ -. .&%E*'" %.+E*'& %.+E*'& .%E*%' .+E*'" .%&E*'& .%&E*'& .+E*%'

B- '' ''' %.'E*' .'E*%' +.'E*'& &' %' . -.-" %-%. +.& .&E*'" .E*'& .E*'& %.%E*%% %.%"E*'& .'E*'& .'E*'& %.E*%%

B '' %'' %.E*' .-E*%' %.'%E*' &' %' . . %-+.% +." +.E*'" .''E*'& .''E*'& %.&E*%% %.%+E*'& .-E*'& .-E*'& %.E*%%

B+ '' "'' %.""E*' ".E*%' %.%&E*' &' %' . +"."+ '.- %'.- %.'-E*'& .&E*'& .&E*'& %."-E*%% %.-E*'& .E*'& .E*'& %.&+E*%%

B%' -&' '' .''E*'& .%E*%' ".'E*'& &' %' +.& %.&' . &%.% .E*'" %.%&E*'& %.%&E*'& ".-E*%' -.+E*'" %.&E*'& %.&E*'& &.'E*%'

B%% -&' &' .E*'& .++E*%' &.%'E*'& &' %' +.& ." .% &.%& .&E*'" %.E*'& %.E*'& &."+E*%' -.+%E*'" %."E*'& %."E*'& &.+E*%'

B% -&' %''' -.&'E*'& .&E*%' .''E*'& &' %' +.& +.- +." &+.'& .&"E*'" %.E*'& %.E*'& -.'E*%' +.-+E*'" %.+&E*'& %.+&E*'& .%E*%'

B% -&' %'' +.''E*'& ".E*%' -.'E*'& &' %' +.& "-." %%".%- .+ %.'E*'& .&'E*'& .&'E*'& %.'"E*%% %.E*'& .&E*'& .&E*'& %.%'E*%%

B%" -&' %&'' %.%E*' &.-E*%' +.''E*'& &' %' +.& &+.'& %-.-+ -.-" %."E*'& .&%E*'& .&%E*'& %."E*%% %.'E*'& .-'E*'& .-'E*'& %.&"E*%%

B%& -&' ''' %.&'E*' -.'E*%' %.'E*' &' %' +.& -.-" %--.% +." %.+E*'& &.'E*'& &.'E*'& .%-E*%% .E*'& &."&E*'& &."&E*'& .-E*%%

B% -&' %'' %.&E*' -.E*%' %.E*' &' %' +.& . %&.'" %'. .'+E*'& &.&"E*'& &.&"E*'& .%E*%% .E*'& &.'E*'& &.'E*'& ."E*%%

B%- '' %&'' %.'E*' ."'E*%' +.'E*'& &' %' %.&' &+.'& %+.- '.-% %.--E*'& ".%E*'& ".%E*'& %.-E*%% %.+E*'& ".E*'& ".E*'& %.'E*%%

B% '' ''' %.'E*' .&E*%' %.E*' &' %' %.&' -.-" %-+.% %''.+ .&'E*'& .%E*'& .%E*'& .&-E*%% .-&E*'& ."E*'& ."E*'& .E*%%

B%+ '' "'' %.+E*' %.'E*%% %.&"E*' &% %' %.&' +"."+ %'.&+ %%.%' .'E*'& -.E*'& -.E*'& .E*%% .E*'& .%E*'& .%E*'& .E*%%

B' %''' %'' %.'E*' %.''E*%% +.'E*'& &' %' +.- "-." %".' -.-- .E*'& "."E*'& "."E*'& %.+E*%% .E*'& ".-+E*'& ".-+E*'& %.++E*%%

B% %''' ''' .''E*' %.-E*%% %.'E*' &' %' +.- -.-" %-.'% %'.- &."+E*'& %.%'E*' %.%'E*' ".'E*%% &.-"E*'& %.%E*' %.%E*' ".-'E*%%

B %''' "'' ."'E*' .''E*%% %.+E*' &' %' +.- +"."+ %.&' %".' .+E*'& %."E*' %."E*' &.+E*%% -.%+E*'& %."&E*' %."&E*' .'E*%%

B %&'' %&'' .&E*' ".E*%% %.'E*' &' %' &+.'& &+.'& %-. %'.- %.%&E*' %.&%E*' %.&%E*' .'E*%% %.%-E*' %.&E*' %.&E*' .E*%%

B" %&'' ''' .''E*' &.E*%% ."'E*' &' %' &+.'& -.-" '.+ %-.+& %.+"E*' .-E*' .-E*' %.%+E*% .+E*' .+E*' .+E*' %.%E*%

for D>BD B A I SA Sthk Sthk EQ.(in) Fw C Use, C C(int) Use, C(int)

mm mm mm mm!" mm mm in D B Int(in) Ext(in) Ext(in!")# Ext(in!")$ (in!") (mm!") Int(in!")# Int(in!")$ (in!") (mm!")

B% &'' "'' .''E*'& ".%-E*'+ %.'E*'& &' %' %+. %&.-& "%." &.&+ .'E*' %.+E*'" %.+E*'" &.--E*'+ %.E*'" %.-E*'" %.-E*'" .+-E*'+

B '' &' %.&'E*'& ".&'E*'+ %.'E*'& &' %' . +." ." . -.+&E*' -.+&E*' -.+&E*' .%E*'+ .-E*' %.%%E*'" %.%%E*'" ".%E*'+

B '' '' %.'E*'& &."'E*'+ %.""E*'& &' %' . %%.% -."' &.&+ +."E*' %.%E*'" %.%E*'" ".-'E*'+ +.+-E*' %."&E*'" %."&E*'" .'E*'+

B" '' "'' ."'E*'& -.'E*'+ %.+E*'& &' %' . %&.-& "&. +.& %."E*'" .'E*'" .'E*'" ."E*'+ %.E*'" .E*'" .E*'" +.+E*'+

B& '' '' .'E*'& %.'E*%' .E*'& &' %' . . %.' -."' &.'-E*' ".'E*'" ".'E*'" %.-'E*%' .'&E*'" ".E*'" ".E*'" %.-E*%'

B -&' '' %.&'E*'& -.'E*'+ %.'E*'& &' %' +.& -.- &." -.& +.%E*' .E*' +.%E*' .E*'+ +.%E*' %.%E*'" %.%E*'" ".-'E*'+

B- -&' '' .&E*'& %.'&E*%' %.'E*'& &' %' +.& %%.% ".% %.&' %."E*'" %."E*'" %."E*'" .E*'+ %.%+E*'" %.+E*'" %.+E*'" .%-E*'+

B -&' "'' .''E*'& %."%E*%' ."'E*'& &' %' +.& %&.-& &%.% &." .'E*'" .+E*'" .+E*'" %."E*%' %.%E*'" .'E*'" .'E*'" %.-E*%'B+ -&' &'' .-&E*'& %.-E*%' .''E*'& &' %' +.& %+. &+.'& +.- .+%E*'" ".-E*'" ".-E*'" %.++E*%' ."E*'" &.'E*'" &.'E*'" .%%E*%'

B%' -&' '' ".&'E*'& .%%E*%' .'E*'& &' %' +.& . .+ ".% .+E*'" .E*'" .E*'" .E*%' .-&E*'" -.%E*'" -.%E*'" .+E*%'

B%% -&' -'' &.&E*'& ."E*%' ".'E*'& &' %' +.& -.& -".' "-." .+E*'" .+E*'" .+E*'" .-%E*%' &.&E*'" +.%%E*'" +.%%E*'" .-+E*%'

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B% '' &'' ".''E*'& .%E*%' .'E*'& &' %' %.&' %+. %.' "%." ."-E*'" &.&E*'" &.&E*'" .E*%' .&&E*'" &.&E*'" &.&E*'" .&E*%'

B% '' '' ".'E*'& .&E*%' ."E*'& &% %' %.&' . . "&." ".%E*'" -.-+E*'" -.-+E*'" ."E*%' .++E*'" .'-E*'" .'-E*'" .E*%'

B%" %'' %'' %.""E*' %.-E*%% %.%&E*' &' %' "-." "-." %%.+ ".& .+E*'& ."E*'& ."E*'& .'E*%% ".&E*'& ."E*'& ."E*'& .'E*%%

B%& %''' '' .''E*'& &.''E*%' ".'E*'& &' %' +.- . -.-- &.%& -.+E*'" %.%&E*'& %.%&E*'& ".-+E*%' ".+E*'" %.%E*'& %.%E*'& ".+E*%'

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for B>D

BEAM D B A I SA Sthk EQ.(in) Fw C(ext) Use, C(ext)

IDEN mm mm mm mm!" mm mm in D B Int(in) Ext(in) Ext(in!")# Ext(in!")$ (in!") (mm

B% &'' '' '''''.'' .&E*'+ "''''.'' &' %' %+. . &-.'+ ." %."E*'" .+-E*'" .+-E*'" %."E

B &'' &' &'''.'' .--E*'+ ''''.'' &' %' %+. &.&+ %.' &." %.&&E*'" ."-E*'" ."-E*'" %.""E

B &'' -'' &''''.'' -.+E*'+ ''''.'' &' %' %+. -.& ".+ -."' %.-E*'" .+-E*'" .+-E*'" %.&E

B" &'' -&' -&'''.'' -.%E*'+ '''''.'' &' %' %+. +.& .+' +.- %.'E*'" "."-E*'" "."-E*'" %.E

B& &'' '' "'''''.'' .E*'+ ''''.'' &' %' %+. %.&' -. "%." %.+E*'" ".+-E*'" ".+-E*'" .'-EB &'' &' "&'''.'' .&E*'+ "''''.'' &' %' %+. ." -.-- ".% .'&E*'" &."-E*'" &."-E*'" .E

B- &'' +'' "&''''.'' +.E*'+ ''''.'' &' %' %+. &." '.-% "&. .%-E*'" &.+-E*'" &.+-E*'" ."+E

B &'' +&' "-&'''.'' +.+'E*'+ ''''.'' &' %' %+. -."' ".& "-." .'E*'" ."-E*'" ."-E*'" .+E

B+ &'' %''' &'''''.'' %.'"E*%' "'''''.'' &' %' %+. +.- .& "+.% ."E*'" .+-E*'" .+-E*'" .+'E

B '' &' +''''.'' %.%-E*%' %'''.'' &' %' . &.&+ ".+ +.- .&E*'" ".+&E*'" ".+&E*'" .'E

B '' -'' "''''.'' %.E*%' '''.'' &' %' . -.& .+' "%." .-E*'" &.%E*'" &.%E*'" ."E

B" '' -&' "&''''.'' %.&E*%' ''''.'' &' %' . +.& -. ".% .''E*'" .E*'" .E*'" .-E

B& '' '' "''''.'' %.""E*%' "'''.'' &' %' . %.&' -.-- "&. .E*'" -.&"E*'" -.&"E*'" .%"E

B '' &' &%''''.'' %.&E*%' "''''.'' &' %' . ." '.-% "-." ."-E*'" ."%E*'" ."%E*'" .&'E

B- '' +'' &"''''.'' %.E*%' "'''.'' &' %' . &." ".& "+.% .-'E*'" +.-E*'" +.-E*'" .EB '' +&' &-''''.'' %.-%E*%' "&'''.'' &' %' . -."' .& &%.% .+E*'" %.'%E*'& %.'%E*'& ".E

B+ '' %''' '''''.'' %.'E*%' "''''.'' &' %' . +.- +.& &.%& ".%-E*'" %.%'E*'& %.%'E*'& ".&E

B%' -&' '' '''''.'' .%E*%' "''''.'' &' %' +.& %.&' . &%.% .E*'" %.%&E*'& %.%&E*'& ".-E

B%% -&' &' -&''.'' .++E*%' &%''''.'' &' %' +.& ." .% &.%& .&E*'" %.E*'& %.E*'& &."+E

B% -&' %''' -&''''.'' .&E*%' '''''.'' &' %' +.& +.- +." &+.'& .&"E*'" %.E*'& %.E*'& -.'E

B% -&' %'' +'''''.'' ".E*%' -''''.'' &' %' +.& "-." %%".%- .+ %.'E*'& .&'E*'& .&'E*'& %.'"E

B%" -&' %&'' %%&'''.'' &.-E*%' +'''''.'' &' %' +.& &+.'& %-.-+ -.-" %."E*'& .&%E*'& .&%E*'& %."E

B%& -&' ''' %&'''''.'' -.'E*%' %'''''.'' &' %' +.& -.-" %--.% +." %.+E*'& &.'E*'& &.'E*'& .%-E

B% -&' %'' %&-&'''.'' -.E*%' %''''.'' &' %' +.& . %&.'" %'. .'+E*'& &.&"E*'& &.&"E*'& .%E

B%- '' %&'' %'''''.'' ."'E*%' +''''.'' &' %' %.&' &+.'& %+.- '.-% %.--E*'& ".%E*'& ".%E*'& %.-E

B% '' ''' %'''''.'' .&E*%' %''''.'' &' %' %.&' -.-" %-+.% %''.+ .&'E*'& .%E*'& .%E*'& .&-E

B' %''' %'' %'''''.'' %.''E*%% +''''.'' &' %' +.- "-." %".' -.-- .E*'& "."E*'& "."E*'& %.+E

B% -&' %&'' %%&'''.'' &.-E*%' +'''''.'' &' %' +.& &+.'& %-.-+ -.-" %."E*'& .&%E*'& .&%E*'& %."E

B %''' "'' "'''''.'' .''E*%% %+''''.'' &' %' +.- +"."+ %.&' %".' .+E*'& %."E*' %."E*' &.+E

B %&'' %&'' &''''.'' ".E*%% %'''''.'' &' %' &+.'& &+.'& %-. %'.- %.%&E*' %.&%E*' %.&%E*' .'E

B" %&'' ''' ''''''.'' &.E*%% "'''''.'' &' %' &+.'& -.-" '.+ %-.+& %.+"E*' .-E*' .-E*' %.%+E

B& '' %'' -''''.'' .%E*%' &-'''.'' &' %' . "-." %'.- %.' &.%%E*'" %."&E*'& %."&E*'& .'E

B& '' %&'' +'''''.'' .-'E*%' -''''.'' &' %' . &+.'& %%.+ -. .&%E*'" %.+E*'& %.+E*'& .%E

B -&' '' %+&''''.'' +.%"E*%' %&''''.'' &' %' +.& %'. "."% %.'& .E*'& -.E*'& -.E*'& .'%E

for D>B OR D=B

D B A I SA Sthk Sthk EQ.(in) Fw C Use, C

mm mm mm mm!" mm mm in D B Int(in) Ext(in) Ext(in!")# Ext(in!")$ (in!") (mm

B% &'' "'' '''''.'' ".%-E*'+ %''''.'' &' %' %+. %&.-& "%." &.&+ .'E*' %.+E*'" %.+E*'" &.--E

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B '' &' %&''''.'' ".&'E*'+ %''''.'' &' %' . +." ." . -.+&E*' -.+&E*' -.+&E*' .%E

B '' '' %''''.'' &."'E*'+ %""'''.'' &' %' . %%.% -."' &.&+ +."E*' %.%E*'" %.%E*'" ".-'E

B" '' "'' "''''.'' -.'E*'+ %+'''.'' &' %' . %&.-& "&. +.& %."E*'" .'E*'" .'E*'" ."E

B -&' '' %&''''.'' -.'E*'+ %''''.'' &' %' +.& -.- &." -.& +.%E*' .E*' +.%E*' .E

B- -&' '' &'''.'' %.'&E*%' %''''.'' &' %' +.& %%.% ".% %.&' %."E*'" %."E*'" %."E*'" .E

B -&' "'' '''''.'' %."%E*%' "''''.'' &' %' +.& %&.-& &%.% &." .'E*'" .+E*'" .+E*'" %."E

B+ -&' &'' -&'''.'' %.-E*%' '''''.'' &' %' +.& %+. &+.'& +.- .+%E*'" ".-E*'" ".-E*'" %.++E

B%' -&' '' "&''''.'' .%%E*%' ''''.'' &' %' +.& . .+ ".% .+E*'" .E*'" .E*'" .EB%% %''' %''' %''''''.'' .E*%' '''''.'' &' %' +.- +.- %'.- .+' %.%E*'& .'"E*'& .'"E*'& %.E

B% '' &'' "'''''.'' .%E*%' ''''.'' &' %' %.&' %+. %.' "%." ."-E*'" &.&E*'" &.&E*'" .E

B% '' '' "''''.'' .&E*%' "'''.'' &' %' %.&' . .+' "&. ".E*'" -.-+E*'" -.-+E*'" ."E

B%" &'' &'' &''''.'' &.%E*'+ '''''.'' &' %' %+. %+. "+.% +.& +.'-E*' %.+-E*'" %.+-E*'" .%+E

B%& %''' '' '''''.'' &.''E*%' "''''.'' &' %' +.- . -.-- &.%& -.+E*'" %.%&E*'& %.%&E*'& ".-+E

B% '' &'' '''''.'' +.''E*'+ "''''.'' &' %' . %+. &.%& ." %.E*'" .'+E*'" .'+E*'" %.+E

B%- -&' & %-&'.'' -.+%E*'+ %&'''.'' &' %' +.& . -."' .&" %.'"E*'" +.E*' %.'"E*'" ".E

B% "'' '' %''''.'' %.'E*'+ +'''.'' &' %' %&.-& %%.% +.& %-.- .E*' "."-E*' "."-E*' %.E

B%+ &'' '' %&''''.'' .%E*'+ %''''.'' &' %' %+. %%.% ." %.& .E*' -.E*' -.E*' .E

B' '' '' ''''.'' %.'E*%' '''.'' &' %' . . %.' -."' &.'-E*' ".'E*'" ".'E*'" %.-'E

B% -'' '' %''''.'' .&E*'+ %'''.'' &' %' -.& %%.% "%." +.& %.%E*'" %."-E*'" %."-E*'" .%E

B -&' -'' &&'''.'' ."E*%' "''''.'' &' %' +.& -.& -".' "-." .+E*'" .+E*'" .+E*'" .-%E

B '' '' %''''.'' .&E*'+ %'''.'' &' %' %.&' -.- -."' +.& %.'%E*'" +.E*' %.'%E*'" ".E

B" %''' '' '''''.'' %.-E*%' %''''.'' &' %' +.- -.- "&. -."' %.+E*'" %.'E*'" %.+E*'" &.-+E

B& %''' &'' &'''''.'' ".%-E*%' "'''''.'' &' %' +.- %+. .+' "+.% &.-E*'" -.'E*'" -.'E*'" .%E

B %'' %&'' -'''''.'' -.+E*%% %''''.'' &' %' -'.- &+.'& %-+.% %'.' %.-E*' .E*' .E*' +.+E

B- ''' &'' %''''''.'' .E*%% '''''.'' &' %' -.-" %+. %'.- .& %.-'E*'& %.+E*'& %.+E*'& -.&E

B ''' '' %'''''.'' &.E*%% %''''.'' &' %' -.-" %.&' %%.+ %''.+ &."%E*'& .E*'& .E*'& ."E

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C(int) Use, C(int)

Int(in!")# Int(in!")$ (in!") (mm!") m!"

.%-E*'" .-E*'" .-E*'" %.&&E*%' %.&&E'

.E*'" ".E*'" ".E*'" %.-E*%' %.-E'

.&&E*'" ".&E*'" ".&E*'" .'E*%' .'E'

.-E*'" &."%E*'" &."%E*'" .&E*%' .&E'

.+E*'" &.+-E*'" &.+-E*'" ."+E*%' ."+E'.%%E*'" .&E*'" .&E*'" .-E*%' .-E'

.'E*'" -.%'E*'" -.%'E*'" .+&E*%' .+&E'

."E*'" -.E*'" -.E*'" .%+E*%' .%+E'

.-E*'" .E*'" .E*'" ."E*%' ."E'

."E*'" &.-E*'" &.-E*'" ."'E*%' ."'E'

."E*'" .+E*'" .+E*'" .-E*%' .-E'

.+"E*'" -.%E*'" -.%E*'" .%-E*%' .%-E'

".E*'" .&"E*'" .&"E*'" .&E*%' .&E'

".&E*'" +."-E*'" +."-E*'" .+"E*%' .+"E'

".E*'" %.'"E*'& %.'"E*'& ".E*%' ".E'&.%E*'" %.%E*'& %.%E*'& ".-%E*%' ".-%E'

&."E*'" %.E*'& %.E*'& &.%'E*%' &.%'E'

-.+E*'" %.&E*'& %.&E*'& &.'E*%' &.'E'

-.+%E*'" %."E*'& %."E*'& &.+E*%' &.+E'

+.-+E*'" %.+&E*'& %.+&E*'& .%E*%' .%E'

%.E*'& .&E*'& .&E*'& %.%'E*%% %.%'E'%

%.'E*'& .-'E*'& .-'E*'& %.&"E*%% %.&"E'%

.E*'& &."&E*'& &."&E*'& .-E*%% .-E'%

.E*'& &.'E*'& &.'E*'& ."E*%% ."E'%

%.+E*'& ".E*'& ".E*'& %.'E*%% %.'E'%

.-&E*'& ."E*'& ."E*'& .E*%% .E'%.E*'& ".-+E*'& ".-+E*'& %.++E*%% %.++E'%

%.'E*'& .-'E*'& .-'E*'& %.&"E*%% %.&"E'%

-.%+E*'& %."&E*' %."&E*' .'E*%% .'E'%

%.%-E*' %.&E*' %.&E*' .E*%% .E'%

.+E*' .+E*' .+E*' %.%E*% %.%E*''

%.-&E*'& %.'E*'& %.-&E*'& -.-E*%' -.-E'

."E*'& .%&E*'& ."E*'& +.-"E*%' +.-"E'

-.E*'& -.&E*'& -.E*'& .E*%% .E'%

C(int) Use, C(int)

Int(in!")# Int(in!")$ (in!") (mm!") m!"

%.E*'" %.-E*'" %.-E*'" .+-E*'+ .+-E'

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