Torsion and Flange Warping Restraint 2

A warping unrestrained (i.e. Torsionally pinned) connection means that warping stresses cannot develop at the connections where there is no restraint to prevent warping of the cross section. But, as you suggest, warping stresses can and will develop along the length of the member.

Whenever these types of questions come up, I always like to point people towards figure 4.4 and section 4.1.4 of the design guide. This give you a nice physical analogy for how warping stresses work. And, using this analogy you can come up with really quick approximate calculations rather than the crazy complex ones described in the rest of the design guide. I also use it to calculate warping stresses for situations that just aren't covered in the design guide.... Like situations that are somewhere between warping restrained and warping unrestrained.

Oh, I understand and appreciate the flange lateral bending analogy for warping normal stresses -- definitely easier (both to perform and to explain to a checker).

Still, the question remains -- do warping stresses always apply for I-shape members? And if so, why discuss free or restrained warping at all?

That terminology applies to the CONNECTION and whether the connection restrains warping or not. But, there is always some degree of warping in a wide flange subject to torsion.

Think of a moment connection with warping restraint at the end. This could be a pull pen moment connection with continuity plates in the column. This connection will develop large warping normal stresses at the location of maximum bending stresses.

Alternatively think of a moment connection where the flanges are free to warp. Maybe a case without continuity plates and where the column flange is relatively thin and can't provide much differential restraint to those beam flanges. This warping "unrestrained" moment connection will develop warping stresses in the member more towards the mid-point of the member. That's a location where the bending / flexural stresses are maybe 50% of what they would be at the connection location.

There is a tendency in our profession to ignore warping stress for simply supported beams. Typical example would be a clip angle connection. It provides torsional restraint, but not warping restraint at the end of the beam. There will be warping stresses along the length of that beam. Though many engineers ignore it. Not saying that's right or wrong. Just that I don't see many folks considering this.

To me, it's an engineering judgment call depending on how significant the torsion is. I personally prefer to use the flange bending analogy as a quick check to see how significant it is compared to the flexural stresses. Then I decide whether to include or ignore it.

Alright, I still don't know why AISC DG9 explains it the way it does.

But after some more research, I found the SCI guide for Design of steel beams in torsion, which confirmed that the flange restraint can come from external sources (connection details) or develop internally (cross sections restrain each other when torsion varies along the length of the member). Also had a handful of other useful charts. I recommend it.

Thanks for your help Josh!

Answers to specific questions

Lomarandil said:

do warping stresses always apply for I-shape members?

Click to expand...

Almost, but not quite, always. See the sketch below for a highly contrived example of a beam that is able to warp freely (relatively speaking).

Lomarandil said:

And if so, why discuss free or restrained warping at all?

Click to expand...

For the most part because a discussion of torsional theory would be incomplete without it. To a lesser extent because there are a few, semi-practical cases of unrestrained warping torsion.

Additional commentary

- if a beam is torsionally fixed (encasement, full pen continuity plates, etc) at any point, it will not be able to warp freely and will develop normal and shear stresses as result of warping.

- if a beam is torsionally pinned (conventional shear connections etc) at two or more locations, it will not be able to warp freely and will develop normal and shear stresses as a result of warping. This is the part that throws people. The beam in question will be warping restrained between torsional supports in the same sense that a simply supported beam, symmetric in all respects, is effectively fixed for strong axis bending at mid-span (zero rotation).

- Beams that are able to warp freely are pretty rare. That's why one gets the impression that it's a case hardly worth discussing. Fee warping is generally precluded by one or more of the following:

1) Code specified limitations on where beam rotational restraint must be provided (LTB stuff).
2) Established practices that form the basis of sound detailing.

It's worth noting that the example shown in the sketch below would have a very high effective length factor with regard to lateral torsional buckling capacity. That is a direct consequence of the fact that the detail permits free warping or something close to it. I would expect that to be the case for virtually all open section beams that are allowed to warp freely.



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

Crap. I didn't see your post regarding the SCI info before submitting my post. Same idea, just expressed much, much more succinctly by SCI it seems

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

No worries -- the more clarification, the better.

I guess this seems like asking why beams without moment connections still develope flexural moments - of course they do - it's just zero at the ends.