Section slenderness 4

[LR11]

With respect to section slenderness, I have a couple of queries.
(1) This is considered for members subject to bending and compression, the plate element dimensions are modified to work out the Area and Section/Plastic Modulus. What about for torsion, where properties such as Torsion Constant and Warping Constant are used. Are these based on modified plate dimensions? What are your thoughts? Have you seen any textual guidance on this.
(2) Let's say the section is slender. When considering each plate, does the location remain the same, or are the plates moved in together. Refer to sketch below.

 

[BAretired]

The attached article provides torsional properties for various steel sections. The torsional constant J for a WF is just the sum of the torsional constants of the flanges and web.

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

BA

 

[Agent666]

Torsion and warping constants are calculated on the gross section typically.

When evaluating properties like the effective plastic modulus you simply ignore the ineffective bits (keep the rest of the section where it is in your explanation. For an I-Section this results in two tee sections with central part of the web ignored and flange tips ignored based on the applicable slenderness limits. The two ends of the web are effective, so your sketch is slightly wrong in that you're implying the central part is the effective part.

 

[LR11]

Thanks for the responses.
BAretired: I have heard about this reference, this is the third time, and is what I was using actually. It also gives the basis literature in it as well.
Agent666: Yes you are correct regarding the effective and ineffective parts for an I-beam, when calculating the effective plastic modulus. Also with the Torsion Constant and Warping Constant, I have not seen anywhere yet which states to use anything other than the gross section, so will apply as suggested. The reference above does not make any distinction between compact or slender sections.

 

[Guest090822]

LR11 - You should try to acquire any college textbook on steel design. These questions are covered in the fundamental principals of steel design and are way too in-depth to try to post here.

 

[KootK]

My thoughts:

1) Obviously, torsional response is part St.Ventant and part Warping for an open section.

2) For an open section, I would say that St.Venant torsion does not induce plate buckling. That, because shear stresses are running little circuits around all of the plate elements such that the aggregate effect is zero across the full width of the plate at almost all locations.

3) For an open section, I would say that St.Venant torsion is not affected by plate buckling induced by internal forces other than torsion. Basically, if a differential element of any given plate rotates in space, then it develops a St.Venant torsional response. And small displacements resulting from plate compression buckling are unlikely to affect this appreciably.

4) Because of #3, I would argue that neither of your sketches would be accurate for the St.Venant component of torsion. For St.Venant torsion, I believe that the effective cross section is the entire cross section. No reductions for slenderness whatsoever.

5) For an open section, the warping response is of great importance. And, in a wide flange section, this will be almost exclusively the story of what's happening with the flanges. Warping will generate in plane bending stresses which alone may be enough to buckle a flange tip under a compression gradient. Most flanges, of course, will be subject to a bending induced uniform compression and a torsion induced gradient compression simultaneously. To the extent that one wishes to deal with this, I would use the effective cross section method proposed by Agent666 above.

6) In practice, and in some design guides, you will often hear the recommendation that, when dealing torsion, combined stresses ought to be kept within the elastic range. I feel that's sound advice. Trying to evaluate plastic flexure effects, elastic warping torsion effects, and LTB stiffness restraint actions concurrently in a single flange pretty much exceeds the mental capacity of most mortals as far as I'm concerned. To a lesser extent, I'd apply the same logic to slenderness effects. If you have control over the section to be used, just pick one with compact everything. That way you've got a little reserve on buckling even if your combined stresses remain elastic ostensibly.

 

[KootK]

I've noticed that you seem to have a lot of questions related to torsion lately. Back in '09, I had my own little fit of torsion interest, mostly concerning multi-cellular torsion in shear wall groups. Anyhow, by tracking reference after reference, I arrived at what I believe to be the most thorough treatment of engineering torsion on planet earth. The math gets brutal but, if you really want to dig deep, you might consider acquiring a copy. I'll post the table of contents to give you a flavor for it.

I know... the rabbit hole is so deep that I sometime wish that I hadn't peeked into it.

 

[LR11]

Many thanks for the additional information.
KootK, your comments are noted. With respect to warping, it does make sense to use the effective section properties, although I would not protest if someone did use the the entire section, certainly not with my current level of understanding.

With respect to the St Venant component, in considering shear buckling ... the reference "Torsional Analysis of Structured Steel Members" from AISC, when dealing with design provisions, notes that a "shear buckling limit has not been defined".

Cheers for the text reference, I'll have a look through it at some stage.