Eccentric Load- Torsion

[ToadJones]

Theoretical question....
If you had a wide flange beam, simple span, torisally restrained at supports.
You have a point load at the center of the beam span, but the load is eccentric to the center line of the beam (not thru the shear center)
This will obviously cause torsion on the beam, but is there a way to accurately calculate the web bending due to the eccentric load.
In other words, the bending moment on the web is not simply P*e, correct?
We are talking about a matter of relative stiffness, are we not?

 

[Teguci]

Most of the torsion for I shape beams are resisted by warping torsion, Tw. In this case, the top flange bends in one direction and the bottom the other. This warping torsion can be illustrated as a lateral point force couple (top and bottom opp dir) through the flange. This lateral deflection can be estimated by modeling the flange as a beam end to end with the appropriate end support conditions.

A minor amount of the torsion will be resisted by rotational stiffness of the beam. Tr / G J = rotation.

Given all of the factors, this drops into a diff eq in order to determine the sharing between warping and rotation:

Ttot = GJ dr/dz - E Cw d3r/dz3

 

[jimstructures]

AISC Design Guide No. 9. - Torsional Analysis of Structural Steel Members will give methods of estimation the physical rotation of the members as well as the stress in the various parts of the members as it rotates, twists, bends and deflects.

This is available from the AISC website free to members or for a fee.

Jim