Expression for Torsion Constant of Varying Thickness Box Section

[Engineering01]

Hello Everyone,

I am after an expression for the torsion stiffness constant of a rectangular hollow section (RHS) with varying wall thickness. I have done some research into finding an expression that allows for four varying wall thicknesses but have not found anything as of yet. The only expressions that are published are of RHS's with two varying thicknesses (Roark's 7th ed, Wiki etc).

If anyone could point me to a resource or present a proof I would greatly appreciate it.

Attached is a sketch of the general shape (excuse the huge image).

Thanks.

 

[SteamKing]

I don't know if what you are looking for exists, in terms of a general formula.

However, if the wall thicknesses can be considered "thin" in relation to the height and width of the section, then you could do a torsional shear analysis on the section.

Sec 6.5 of the following link gives the procedure for doing such a calculation:
http://www.engr.sjsu.edu/mae/faculty/larrosa/AE250_Thinwalledbeams_BauchauCraig_ch6.pdf