huangyhg

warping constant cw
i'm have trouble finding how to calculate the warping constant of a doubly-symmetric cruciform shape.
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i did a paper in grad school which on the theory of torsion on structural shapes such as i and t beams and tubes... developing warping constant values is not an easy thing to do it involves a lot of calculus and assumptions.
however, if your 'flanges' (for lack of a better term) are sufficiently thin, say bf/tf > 10... i don't believe warping needs to be considered (don't quote me on that though- you'll need to check literature to confirm that). you can essentially treat it the same as a thin closed tube (ie calculate a jeff value: sum(bt^3/3)).
if your 'flanges' are thick... then your in trouble (just kidding)...
in either case you will want to search through some papers on this subject... i'm sure this has been researched... some key words you will want to use: warping function, sectorial area and restrained warping.

cw of a cruciform section is approximately 0.
i think willisv is right. if anybody has a ref for how to calc cw for a cruciform, angle, or other similar section, i'd be interested in reading it.
strictly speaking for slender 'flanges' saying cw = 0 implies warping exists and the section provides no resistance, therefore angle of twist and warping normal stress tend towards infinity. i think its more appropriate to say warping is neglected.
i believe warping can be neglected because all 'legs' (as long as they are sufficiently thin) of the cruciform pass through the shear center... where as with i beams (flanges) or angles (legs), which are offset from the shear center, can develop significant warping.
i developed expressions for torsion of thin-open sections, i'd be happy to share it with anyone who is interested.
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