I wouldn't think torsion applied to WF or I sections is ever governed by capacity, i.e. shear capacity although it is a fairly simple calculation. It is usually governed by acceptable rotation, also fairly simple to calculate.
WF's will typically have warping stresses and shear stresses. The combination of bending and torsional shear stresses do not normally control but sometimes bending stress added to warping stress may control. Acceptable rotation may also control.
For torsion on wide flanges I always use the "equivalent tee" analogy as a starting point. The reason why I like it is becasue it gives a good physical explanation for where those warping stresses are coming from.
Here is the procedure:
1) For torsion, think of the I beam as having been split at the center. Hence forming two Tee beams.
2) If the original beam was warping restrained at the ends, then your tee beam will be a fixed-fixed beam. If your original beam did NOT restrain warping, then your tee beams will be simply supported.
3) Break your torsional load into a force couple applied at the centroid of the Tee. Apply these point load or distributed load to each tee beam individually and analyze using simple beam theory.
4) The simple beam theory will develop weak axis bending moments (and flange bending stresses) in the Tee that are similar to the warping stresses that you'd get from a more rigorous analysis.
This analogy is relatively simple and should always be conservative... at least compared to the actual warping stresses in the flanges. Therefore, there is little danger to using it.
One of the things that I like it this method can be expanded out in situations where the rigorous methods become too difficult. Such as when you want to model a boundary condition that is somewhere between warping fixity and a warping pin. Or, when you have multiple unusual loading conditions.
JoshPlum...otherwise known as the "flexural analogy" which is described (including an example and illustrations) in Salmon and Johnson (p443-445 in 4th edition).
This is the method I generally use as well...though I just think of it as a plate since the stem of the "T" is useless.
Josh... thanks for the reply. this seems a good and simple approach and I'd like to hear if anybody has any concerns about this approach. i guess in closed sections i.e. box sections, this approach is even more conservative as it neglects the resistance provided by the 2 other sides of the box section-but fine if a rigourous approach is acceptable.
if there is bending in the beam too, do you think it is satisfactory to sum the stresses (from bending) and the stresses calculated above (from torsion ) and check that is doesn't overstress the steel. I'm thinking this approach neglects the effects of lateral torsional buckling....
Following on from my last response. to calculate torsional deflection using the T-section analogy-this could be done using simple beam deflection formulae (for the flange plate of the T-section) and will give a conservative answer-any thoughts?
For I-Beams and other open sections get a copy of "Design Guide 9: Torsional Analysis of Structural Steel Members" from AISC. It's a little intimidating to use at first, but there's actually only a couple of formulae that apply to warping stresses. I think it's free for members and $60 for non-members. I got a free copy from Bethlehem Steel in 1976 and still use it, even though it's falling apart.
One of the more recent design guides from AISC, 22 - Facade Attachments to Steel-Framed Buildings, goes into a comparison of the torsion on a spandrel beam, based on FEM and equations provided previously to calculate rotation, etc. for restraints in this specific application of SOMD and facade system.
It is pretty interesting.
Appendix A - Results of FEM to study the effect of Slab/Deck translational restraint on spandrel beams.
Some info to read.
RC
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Edmund Burke
I would be surprised if the web actually does anything in torsion. Just like you ignore the flanges for calculating vertical shear stress I ignore the web when calculating torsion. It makes the calculations much easier too!
