Appendix BTorsion Properties of Thin-Walled Open Cross-Sections

Cross-section Shear center O Torsion constant J Warping constant Cw
Schematic illustration of a Torsion Property of Thin-Walled Open Cross-Sections. upper J equals StartFraction 2 italic b t Subscript f Baseline Superscript 3 Baseline plus italic h t Subscript w Superscript 3 Baseline Over 3 EndFraction upper C Subscript w Baseline equals StartFraction t Subscript f Baseline h squared b cubed Over 24 EndFraction
If t = tf = tw
upper J equals StartFraction t cubed Over 3 EndFraction left-parenthesis 2 b plus h right-parenthesis
Schematic illustration of a Torsion Property of Thin-Walled Open Cross-Sections. e equals h StartFraction b 1 cubed Over b 1 cubed plus b 2 cubed EndFraction upper J equals StartFraction left-parenthesis b 1 plus b 2 right-parenthesis t Subscript f Superscript 3 Baseline plus italic h t Subscript w Superscript 3 Baseline Over 3 EndFraction upper C Subscript w Baseline equals StartFraction t Subscript f Baseline h squared Over 12 EndFraction StartFraction b 1 cubed b 2 cubed Over b 1 cubed plus b 2 cubed EndFraction
If t = tf = tw
upper J equals StartFraction t cubed Over 3 EndFraction left-parenthesis b 1 plus b 2 plus h right-parenthesis
Schematic illustration of a Torsion Property of Thin-Walled Open Cross-Sections. e equals StartFraction 3 b squared t Subscript f Baseline Over 6 italic b t Subscript f Baseline plus italic h t Subscript w Baseline EndFraction upper J equals StartFraction 2 italic b t Subscript f Superscript 3 Baseline plus italic h t Subscript w Superscript 3 Baseline Over 3 EndFraction
If t = tf = tw If t = tf = tw If t = tf = tw
If t = tf = tw If t = tf = tw

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