# St Venant's torsion constant

1. ### derryck1234

56
Hello

I am a Junior Structural engineer and need to know how St Venant's torsion constant is calculated. It appears in structural steel tables, but without knowing how to calculate it, I cannot find its value for non-standard steel sections.

Please, can somebody help.

Regards

Derryck

2. ### SteamKing

8,625
Staff Emeritus
This is a topic which is covered in advanced strength of materials courses. The general calculation of J for an arbitrary cross-section involves solving a partial differential equation, usually by means of a finite element method.

For thin-wall cross sections, various approximate formulas and methods have been developed to calculate J for closed and open sections. These methods are usually covered in texts dealing with aircraft or ship structures.

For open sections of the type usually found in construction, the formulas in the attached article may be used:

http://www.cisc-icca.ca/files/technical/techdocs/updates/torsionprop.pdf

3. ### AlephZero

7,300
This might help. http://www.cisc-icca.ca/files/technical/techdocs/updates/torsionprop.pdf

Bear in mind that the mathematical notion of a torsion constant is only an approximation to the real behavior of the object (except for circular sections) and the formulas for complicated shapes are approximate.

One might hope that the values quoted in structural steel tables for standard sections were validated against measurements, not just calculated theoretically, so don't worry too much the formulas don't give exactly the same values as the tables.

If the shape of your non-standard sections don't match any of the formulas, probably the easiest way would be to make a finite element model of a length of section, apply some loads to twist it, and find the displacements.

EDIT: That must be a good reference if two people recommended it independently

4. ### henneh

7
If you have an open section (e.g. I-beam, parallel flanged changed, equal angle i.e. with a closed flow of shear flows within the walls of a section) this formula will give you a good enough approximation:

J = bt^3/3 where b is the always the longer side. e.g. for a rectanngle

J = breadth * depth^3/3

For an I-beam or indeed other section you can simply add all the bt^3/3 i.e. for an I-beam,

J = (1/3)*(bTF*tTF^3+dweb*tweb^3 + bBF*tTF^3)

It should be noted that the formulaa begins to break down where b isn't >> t. To get a better approximate there are various tables that give you a factor k to multiply the torsion constant with thats a function of b/t

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