AISC Design Guide 9: Why torsionally-pinned design examples calculate warping stresses? 1

Pardon me if I get something slightly incorrect here, it's been a while since I've rectified this.

But the general idea is that even when the boundary conditions themselves do not provide torsional restraint, the change in torsion along the length of a member provides its own sort of "restraint" which allows warping stresses to develop.

My Q&A with AISC on this issue:

Q: In design guide 9, sections 4.1.2 and 4.1.3 state that when a member is allowed to warp freely, shear stresses and normal stresses due to warping do not develop. However, this is only true at the ends of the member - warping stresses develop in the member between the supports. This is also confirmed in the worked examples, as well as the graphs of torsional functions in Appendix B for members pinned torsionnally at both ends. Can you clarify this point?

A: Your statement, that warping stresses develop in the member between the supports, is correct for all practical conditions. The discussions in Design Guide 9 Sections 4.1.2 and 4.1.3 are also correct. However, members are allowed to “warp freely” only for the conditions shown in Appendix B Case 1, which is of academic interest only because those loading and boundary conditions do not occur in building design.

In effect, they say warp freely and not torsionnally pinned.

jochav5282 said:

That design guide says that warping stresses can't develop when the section is not restrained from warping, as would be the case when it's "torsionally-pinned".

Click to expand...

This mostly comes down to the somewhat confusing meaning of "torsionally pinned". It does not mean that the beam ends are free to rotate. Rather, it just means that warping is not restrained at the beam ends (the cross section is allowed to distort such that lateral bending stresses develop in the various parts of the cross section.

The sketch below shows how a torsionally pinned beam still resists twist via warping. It's a view of a wide flange section from the top. Simple span with twist restraint at each end.

Hmmm, this seems almost self evident to me.... It' for the same reason a simply supported beam with no moment restraint at the ends can develop moment at mid span.

If it helps to understand warping stresses thing of them using the WT analogy. If I at a point torque at midspan of a torsionally pinned beam. The torque could be replaced by equal and opposite point loads applied to the two flanges of the WF beam.

The warping stresses are like the flexural stresses that develop in those flanges...

Torsional fixity in comparison to my previous post.

This is the closest think I can think of to a practical situation wherein one would have no warping torsion restraint anywhere within a beam span. And it's not very practical.