Design equations for steel beams explicitly subject to torsional moment? 7

[CivilSigma]

Suppose you have a laterally unsupported, simply supported wide flange beam subject to a uniform load. At mid span you also have a torsional moment due to a point load eccentricity.

Design equations in the Canadian code (CSA S16) tell you how to calculate Mr as related to uniform loading only.
How do you verify that the beam can also resist the torsional moment applied?

I know that you can perform a detailed finite element analysis using the Vlasov theory to determine the true Mr of the beam under the above loading conditions.

But is there a simpler "code" approach to the design? Is it reasonable to consider the total factored moment in the beam as: M_f = M_uniform + M_torsion , and then make sure Mr > Mf using the code design equations?

 

[WARose]

How do you verify that the beam can also resist the torsional moment applied?

For hand calcs, I typically use AISC's Design Guide 9. (I don't know the equivalent of that in Canadian codes.)

EDIT: By the way, we recently kicked around alternate methods in this thread here:

https://www.eng-tips.com/viewthread.cfm?qid=472982

 

[CivilSigma]

Wow perfect, thank you for the reference. It's exactly what I needed.

I find it weird how we don't have anything like this in the Canadian codes. Our code simply says that combined stresses should not exceed Fy (Clause 14.10.4 CSA S16)

 

[WARose]

You are welcome. By the way, if you look in that thread I linked to, it links to another thread that has a spreadsheet you should be able to download.

Whatever code you are using, it makes a good sanity/back check.

 

[Logan82]

Hi!

I highly recommend this AISC Education video in relation to the AISC Design Guide 9.

https://www.youtube.com/watch?v=y71tWRmnCZg&ab_channel=AISCEducation

It helps a lot to understand the concept of torsion support types.

 

[JoshPlumSE]

CivilSigma -

While AISC (and the British guys) have design guides on the subject, I don't think either code handles torsion of I shaped members any better than the Canadian code does.

There is just a real gap between what the "theoretically correct" analysis is and what engineers believe actually happens in real structures. I'm not qualified enough to definitively say who's right and who's wrong. I think it probably lies somehwere in the middle.

For what it's worth, I really like using the WT analogy that this 2nd thread talks about. I like teaching it to young engineers because it helps them to really understand the type of stress that torsional warping creates. Really giving them a phyiscal explanation for the concept.

Therefore, anyone who starts down this road, I always tell them to take a look at that analogy and run some calcs that way. Just to get a ball park estimate of what's happening.

 

[human909]

Thanks Logan82! That video looks really good though I'm only a quarter way into it.

I had a quick question though regarding steel connection detailing for yourself or anybody else who wants to answer. Is the ideal shear plate connection inside or outside the web of a channel. I've always thought it was INSIDE. But based on the shear centre this would imply it is outside. Any thoughts?

 

[Enable]

Kulak and Grondin discuss the applicability of torsion and S16 in their book Limit States Design in Structural Steel (endorsed by CISC)

IIRC they treat the torsional moment as an equivalent force couple acting at the flange tips and decompose the stresses into the following:

stress = Mx / Sx + My / Sy + Beta*Mfl / 0.5*Sy

But my copy is up North at the moment. If you can wait a few days I can scan the relevant pages.

 

[CivilSigma]

Thanks everyone for your input.


@Enable, that would be nice, thank you.

 

[Yao1989]

I second Enable. I’ve used the method described in Kulak and Grondin to design a few steel beam in torsion before.

Basically the you resolve torsion into a horizontal equal and opposite force for the top and bottom flange, then check combined normal stress on the flange due normal bending + bending about weak axis.

You also need to check combined shear stress + st.Vincent stress due to torsion.

Be sure to also check your boundary condition and make sure your torsion is properly restrained by your support connection.

 

[JoshPlumSE]

Enable -

Doesn't that equation limit the maximum stress to yield stress?

That's generally the issue I have with the AISC specification as it relates to torsion. You get a huge disparity in code check on a member that has a very small torsion than on one that has a zero..... Solely because you're then obliged to limit your weak and strong axis bending to the yield stress.

When I do this by hand, the way I combine it is the following:

1) Using the WT analogy, I come up with a "warping stress" in the flange of the Tee. This stress is very similar to the flexural stress in the flange of a WF due to weak axis bending.
2) I convert this "warping stress" to an "equivalent" weak axis bending moment that would produce that same bending stress.
3) I then add this weak axis moment to the regular weak axis bending moment in the Wide Flange, and use that for the combined stress codes checks.

Note: I also check shear stress in the web is caused by the torsion. But, that is not usually as big of an issue.

 

[PEFLWI]

I think a good analysis program can do all the design checks for you at least as a sanity check to your hand calculations. I personally trust RISA 3D for a design using the AISC specification. RISA has the Canadian code. You can down load a trial version for free, but I don't know if it will allow you to use the Canadian code.

 

[Enable]

Doesn't that equation limit the maximum stress to yield stress?

It does. But I don't view it as unnecessarily penalizing since this is a serviceability check rather than a ultimate states checks (though I am slightly confused how your 1-2-3 procedure differs from Kulak's approach). In addition, Canadians are bound by CL 14.10.4 which kinda hamstrings us to use it! See below

...For members subject to torsion or to combined flexure and torsion, the maximum combined normal stress, as determined by an elastic analysis, arising from warping torsion and bending due to the specified loads shall not exceed Fy

CivilSigma: See pages attached which should help! BTW the book is worth buying and I highly recommend it to you.

BTW: To all check out this research report from UofA that discusses S16 and Torsion (CL 2.2.3). Even talks about applicability of Kulak + Grondin's approach (Grondin is an author of this research report).

 

[CivilSigma]

Thank you @Enable. The book is out of stock, maybe they're going to publish the next itteration. I definetly will be buying it.

 

[Logan82]

human909, it's an excellent question. I have just posted a specific thread on the question you asked me:

https://www.eng-tips.com/viewthread.cfm?qid=485224