Torsion of I-Beams: Simplified Bi-moment Method 9

[MegaStructures]

Hello:

I am designing a small frame with significant torsion applied to some members in RISA3D. After going through the help manual I have found that RISA does not account for any torsion in beams, besides torsion caused by frame racking (fixed end condition, point torques at ends), similar to what is found in case 2 of AISC DG9. Of course this means I cannot trust the results from RISA and I need to input my own torsional stresses, so I have set out to figure out how to do the hand calc.

I reviewed some threads here on the forum and see some users suggesting the "equivalent tee" or "bi-moment" method to conservatively approximate the shear and normal stresses from torsional warping as suggested in AISC DG 4.1.4. The DG provides the figure below and says the normal stresses can be found by treating each flange as a beam and using the following equation σ_w= M_f/S_f where; S_f= (t_f*(b_f)²)/6. I assume the flange in the figure below (fig 4.4) is showing the side view of the entire length of the beam.

So, to me this method seems extremely simple and if accurate and conservative I am happy to have found it, because it will take me only minutes to check my beam. I do have a couple questions though and as I am typing this I realize this post might even be more suited for the RISA sub.

1) Is this method accurate enough (conservative is probably a better word) and at what unity ratio from pure torsion should I opt for a more accurate calculation of torsion stresses i.e. if torsion capacity calculated per this simplified method is 50% of the beams flexural capacity, but the beam still passes code checks should I be worried?
2) If this method is so simple and seemingly well suited for an automated calculation, why in the world does RISA not support it as a simple check? The fact that they don't makes me feel like I'm missing something about the usefulness of this method
3) In this review I have looked more at how RISA combines torsion stresses in the interaction equation and it combines torsional warping stress with weak axis moment, which seems to contradict what DG9 is suggesting, since the torsional warping moment found in the equation above is a stress normal to the flanges, or a major axis moment. How can this discrepancy be explained?

**As a bonus question has anyone used a shell element model to study the effects of torsion on I-beams that can speak on the efficacy of that method? I have created an FEA model of my frame with shell elements, the beams are relatively short < 10 ft W21x76's and support a point torque of 48 kip*ft and won't be limited by LTB and I'm not aware of any other buckling modes I need to be aware of (pure torsional buckling in the web?). I have ran a linear-static model and show very favorable stress results, which I am trying to confirm with this hand calc and of course the original RISA results.**

 

[r13]

This is the way I resolve torsion.

 

[WARose]

1) Is this method accurate enough (conservative is probably a better word)....

From everything I have read, the Flexural analogy is conservative.....the problem though is: in some cases it is excessively so. (There is a brief discussion on this in Salmon & Johnson's text on steel design.) For more accuracy, it is typically modified by a β value. (I've heard some people call this the "Beta Method".)

Of course with all the spreadsheets/programs with the differential equation solution programmed in.....all this is not necessary at this point.

**As a bonus question has anyone used a shell element model to study the effects of torsion on I-beams that can speak on the efficacy of that method?

I've made plate models of I-Beams under torsion before to study connection performance (for simple shear connections) and the effect of torsion has on the weld for stiffener plates......but never for the purpose of looking at the flexural analogy.

 

[MegaStructures]

Of course with all the spreadsheets/programs with the differential equation solution programmed in.....all this is not necessary at this point.

You wouldn't happen to have one of these you could share, or point me towards, would you? I'm perfectly OK with extremely conservative as long as my beam passes, these beams are important and I'd much rather over design.

 

[WARose]

See this thread:

https://www.eng-tips.com/viewthread.cfm?qid=243423

The last post is the one I use. (Besides STAAD.)

 

[MegaStructures]

Great thanks WARose. Hope to get answers to my other two questions as well!

 

[r13]

 

[MegaStructures]

What resource is that snippet from retired13?

 

[r13]

Link

 

[WARose]

Hope to get answers to my other two questions as well!

I don't know enough about RISA to answer your other questions (except to say I loathed it when I had to use it years ago).

I have a feeling the answer to #2 is contained in what I said about the accuracy of the method.

 

[human909]

Just out of curiosity how long are your members and why are they receiving torsion. The reason why I ask is because most of the time if torsion on an open section beam matters then deflection will normally control well before strength.

 

[canwesteng]

Does any software support this type of simplified warping check? I know STAAD will do a DG 9 torsion check, but personally I don't trust it to do so with the correct end conditions. Re your question 3, both weak axis and strong axis moment create stress normal to the section. You would normally combine this with weak axis bending since typically you just assume one flange has half the weak axis section modulus of the whole section.

Re: making a shell element, I've never done that but I have done a beam/plate hybrid FEA model of beams under torsion to check stresses, but watch out for inelastic buckling as always with FEA.

 

[JoshPlumSE]

1) Is this method accurate enough (conservative is probably a better word) and at what unity ratio from pure torsion should I opt for a more accurate calculation of torsion stresses i.e. if torsion capacity calculated per this simplified method is 50% of the beams flexural capacity, but the beam still passes code checks should I be worried?

The hand calc method you refer to (as far as I understand) is always conservative.

2) If this method is so simple and seemingly well suited for an automated calculation, why in the world does RISA not support it as a simple check? The fact that they don't makes me feel like I'm missing something about the usefulness of this method

Some thoughts on this:
a) There aren't a whole lot of users requesting improved torsional warping calculations.
b) At one point (before I worked for them) RISA sank a lot of time into researching and developing the torsional warping calculations that they do (case 2 from design guide) which assumes that whatever torsion in the member is due to point torques applied at the ends of the member. User's didn't really care that they were doing this better than competitors. So, they (IMO) became reticent to extend this any further.
c) This method (the one RISA uses) as well as the hand calc method can be very over conservative. One of the issues is quantifying warping restraint at the end of the member. The AISC design guide addresses torsional pins (i.e. warping not restrained at the end) and torsional fixed (i.e. warping restrained). But, in reality (and in FEM program) everything is somewhere in between free and fixed.
d) When I worked there, I got very excited when I found some references that gave what appeared to be accurate and generalized ways to do this properly (the references were cited in MacGuire, Gallagher and Ziemian's Matrix Structural Analysis which can be downloaded from the Bucknell website). No one else at RISA was particularly excited about this. I created an "enhancement ticket" that cited the appropriate articles and such. But, nothing has been done that I know about. Honestly, I'm not even sure I would trust the current version of the company to do it correctly, even if they thought they could make money off of the enhancement.

3) In this review I have looked more at how RISA combines torsion stresses in the interaction equation and it combines torsional warping stress with weak axis moment, which seems to contradict what DG9 is suggesting, since the torsional warping moment found in the equation above is a stress normal to the flanges, or a major axis moment. How can this discrepancy be explained?

I don't think this is a contradiction. In your pictures, you're resolving the torsional load into equal and oppose weak axis load on the flanges of the beam. Right? If you apply those point loads to the WT only (assuming the W beam is split at the center of section) then this produces stresses in the top and bottom flanges that are akin to what you get with weak axis bending of the section. It's just that the stresses in the top and bottom flanges are headed in different direction.

**As a bonus question has anyone used a shell element model to study the effects of torsion on I-beams that can speak on the efficacy of that method?

I believe this method works. I played around with it at one point. But, it was a good bit more difficult to validate and interpret results than I would have liked. You may get results that are comparable to the theoretical results in the Design Guide... But, only with the truly idealized end conditions as soon as you connect your beams to other members, everything changes dramatically.

Note: I worked for RISA for 16 years (before they got acquired by Nemetchek) and was a Vice President. There were some hard feelings when management changed, and I was forced out. Also, I now work for one of their competitors (CSI). Therefore, my opinions expressed here certainly come with some bias against RISA... at least the current RISA managment.

 

[MegaStructures]

So many great comments so far!

Just out of curiosity how long are your members and why are they receiving torsion. The reason why I ask is because most of the time if torsion on an open section beam matters then deflection will normally control well before strength

it's quite a unique structure. The beams in question actually support a center mounted column and base plate. Torsion is transferred through the base plate through bearing and through welded connections at the edges of the plate. The beams are about 6' long. I developed an FEA model with plate elements for the deflection, but since I'm a relatively new FEA user I was worried about blindly trusting the Von Mises stress results, mainly in case I was missing a buckling failure mode like canwesteng pointed out.

but watch out for inelastic buckling as always with FEA.

precisely the type of thing I was worried about, but I am thinking if my FEA model is going to miss inelastic buckling than so is my hand calc. I of course did check LTB by hand and there is no issue there with such short spans and deep beams. I am not sure what other type of inelastic buckling to expect.

JoshPlumSE

It really helps to know the background of why a check like this might have been left out of RISA. I personally think if a program handled torsion in unique cases I would consider switching from RISA just for that functionality. Then of course maybe I should be developing my own spreadsheet for torsion checks if I feel that strongly about it.

 

[IDS]

Following the link at WARose post no.2, I see I posted a link to some spreadsheets to the British code in that thread, but that link no longer works.

The same spreadsheet now seems to be available from:

https://www.theengineeringcommunity.org/steel-beam-design-spreadsheet-to-bs-5950/

Note that that site has a lot of junk links and download buttons. You need to scroll down to near the end where there is a link with the words "Download Link" at the end of the main text.

I'm not sure that the spreadsheet at my link or the one linked in the final post in that thread cover torsional warping effects at all. If they do perhaps someone could point out where to look.

Edit 23 Aug 20:

As WARose notes below, the spreadsheet at the second link does indeed do torsional warping effects, not sure how I missed that. A direct download link is:

https://www.cesdb.com/torsion9.html

Click on the tiny download button inside the spreadsheet image at the top, not the huge "Start Download" button just below it!

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[WARose]

I'm not sure that the spreadsheet at my link or the one linked in the final post in that thread cover torsional warping effects at all. If they do perhaps someone could point out where to look.

The one in the final post does. (I.e. ChipB's link). I back checked it by doing Example 5.1 in AISC's Design Guide 9 and came out with a nearly identical (28 ksi) warping (normal) stress that DG 9 does.

The method used in that sheet is based on a differential equation solution (based on support conditions and loading) in a old USS manual.

 

[Mohanlal0488]

@Megastructures

I have used FEA in many occasions for very complex connections which cannot be designed by hand, many of these have also included torsional effects.

It is very possible to assess torsional effects on beams using FEA analysis, however I do not think this is possible using software like SAP2000, STAAD and most of the generally used structural engineering software(I may be wrong). You may need to look at something Strand7, Lusas, Ansys and so on... There are lower end packages like Mecway that can also do the task very well.

The basic idea is that you develop a shell or brick model (preferably shell) using CAD geometry or manually creating a model. The mesh will need to be very fine. Depending on your loading you may want to adopt non-linear transient dynamic solvers however if it is purely static a non-linear static solver will be perfect.

If loading is very symmetric I would suggest the addition of a small disrupting force to get rid of symmetry. Both non-linear geometry and material would need to be taken into account by the solver.

Once the load increments are setup and a successful solution is achieved you can assess buckling by means of plotting displacement results with respect to a fixed point. In general if there is any form of buckling the displacement results will present a "snap back" thus indicating that buckling has occurred. It is best to plot the nodal rotational displacements. In many cases you can use the deflected shape to assist in finding nodes to plot.

Previously for design of torsional members I have used the AISC360, they also have a good guide which explains everything very nicely.

 

[MegaStructures]

Mahonlal0488

I have an ANSYS model setup with shell mesh and I have run a linear-static analysis, but sadly a non-linear geometric/material analysis is a bit out of my league at the moment and I wouldn't feel comfortable interpreting the results. The only inelastic buckling that I should be worried about as far as I know (maybe this is wrong) is LTB, which I said before was no concern due to beam length, but now I'm realizing that might be misguided since I have possibly significant pure torsion that could contribute greatly to buckling my beam out of plane and invalidate the AISC beam tables for LTB strength.

My version of ANSYS doesn't support non-linear solutions in assemblies, but maybe I can run a stand alone analysis of a single beam with idealized end conditions and loading to get a better idea for how each beam reacts to the torsion. Seeing the boxed geometry I showed above would you agree that it is relatively accurate to model a single beam with fixed ends and an applied torsion at the weld line of the base plate to investigate the non-linear torsional effects?

 

[canwesteng]

Re: Inelastic buckling - you are only really concerned with local flange buckling and LTB. Hand checks can cover these off, I can't recall what DG 9 recommends for adding strong axis moment to torsional effects but that would be where I look.

 

[Mohanlal0488]

@MegaStructures

Can you please upload an image of your FEM model so that I can comment, I do not want to prematurely say something not having all the facts at hand, as I am thinking of the situation as I would model it.

Depending on the extent of what you have modeled may also change the way loads are applied. If you just have the beam of concern modeled then you would need to apply the load at the weld as the loads the weld would see it. Thus you would need to get the distribution of loads on the weld (which is simply from basic hand calculations) and then apply that distribution on the beam at the location of the welds. Alternatively you can use links to distribute the loads as required.

I assume that the torsion is coming from the fact the the "column" has a moment that is transferring as torsion in the supporting beam?

If you can confirm the above I can make a better comment and also build a small model that I can share to show how I would do it.