Transverse Stiffeners - Torsion 6

[ToadJones]

Do transverse stiffeners do anything for the torsional capacity of a wideflange?
Intuitively I would think they would help locally with warping.

 

[ishvaaag]

And this one the models with edge loads, and ongoing conclusions.

As you will see I am not yet entirely satisfied that Autodesk Simulation has not discovered something of interest and so will be further investigating the thing.

I tried to combine the things to ease the comparison in a single pdf but exceeding 5 MB it seems the file storage system rejects it.

 

[jtx]

Since this is such an interesting and polarizing topic with different opinions shared by everone here, I asked the AISC Steel Solution Center to see what they think. When I get a response, I will post it here.

 

[ishvaaag]

Update: I have made a solids model for SAP2000, and for the torque model without stiffeners it gives values akin to RISA 3D. Hence all points to the models without stiffeners in AS suffering from a defect, that I will try to identify and correct later.

So, as provisional conclusion (going against my former statement in the matter based in the models I had available then) the addition of stiffeners seem to slightly improve the torsional response under torque. For close and proportionally thick stiffeners and taking the RISA 3D models as representative, worse stresses may be reduced maybe between 10 and 20% and maximum lateral displacement on torsion between 20 and 30%.

I may post something more on the matter but for me, except identifying the culprit errors in my AS models the thing is becoming settled.

 

[Teguci]

ishvaag, your first model (AS) matches my hypothesis that the addition of stiffeners would increase the shape rotation but not increase the overall beam capacity. The Risa Model shows a reduction in rotation of approx 20% and a decrease in stresses with the use of stiffeners. I don't think anyone has guessed that outcome. If anything, the RISA model is suspect.

What are the dimensions of the beam you used? I was hoping to run a hand calc.

 

[271828]

How can the addition of stiffeners possibly make the member more flexible for torsion or anything else for that matter? Am I understanding incorrectly?

 

[Teguci]

OK, by hand I'm getting 3.9 mm lateral deflection with a 18.6 kN couple force at the center of a 7m beam, HEB300. Have to say the AS model is probably wrong (by an order of magnitude) and my hypthesis is probably wrong (but I'm still holding out hope).

In return, 271828, how do you get a 20% reduction in lateral deflections by adding stiffeners?

One possible problem with the models (all of them) is the forces are global not local. As the beam twists, the flanges go out of plane. Do the forces go out of plane with the flanges or do they push against a rotated flange?

 

[SAIL3]

The energy of distortion in this case is composed of the distortion of the web and rotation of the cross section as awhole.
If we assume that the transverse stiffeners eliminate(or reduce) the distortion of the web, then all(or more) of the energy of distortion goes into the total rotation of the cross section.
I would expect a slight increase in this rotation when the transverse stiffeners are present. Instead, the 20% reduction in this rotation shown in the RISA model was not something I would have expected. Can not rule it out, though.
Perhaps, the presence of these stiffeners sets up a different mechanism to resist the torsion ie. Vert stiffeners and diagonal
tension struts provided by a portion of the web itself.
An earlier post mentioned an experiment by Blodgett(2.10-18, Fig 33) using diadgonal struts that resulted in a marked reduction in rotation...so maybe, afterall, the RISA model is correct.
Not an outcome I would have thought off.

 

[271828]

Teguci, I wouldn't. I would expect a minute increase in stiffness from adding stiffeners.

 

[ishvaaag]

Teguci I am going now to sleep. Tomorrow I will provide whatever you need; I still see the AS model might have something to it, but now SAP2000 and RISA are against it; still to review. Respect the shape dimensions you have in the first attachment, within, it is HEB 300 (300 mm tall and wide).

 

[ishvaaag]

Quite likely the forces keep the initial orientation, yet as well to check. They draw them keeping the direction, even.

 

[BAretired]

Upon further consideration, SAIL3 has a valid point. The rotation of the beam per unit length is [θ] = Mt/JG where J = [∑]bc³/3 for the web and flanges.

If J(flange) = J(web) then there should be no bending in the web because all three elements rotate identically when resisting torsion. If J(flange) > J(web) as is the more usual case, then the web will bend in double curvature and the addition of stiffeners should effectively cause the web to act as a stiffer element in the cross section.

So, I guess web stiffeners would likely have a beneficial effect on torsional rotation and strength, but I agree with JAE that it is not a very practical way to achieve it.

BA

 

[ToadJones]

the OP is back baby!!!

 

[ToadJones]

I thought I was walking the proverbial plank when I posted this seemingly stupid question. I figured the responses would be something like "man, what an idiot".
Clearly others have pondered this.
I'll have to wait until I get more time to read through all the posts.

 

[ishvaaag]

Here I attach the central torque models resumé without and with stiffeners in SAP2000 models, in general agreement with the RISA 3D models, and, for the case with stiffeners, as well with the Autodesk Simulation model. So again everything points to an error in the models for the cases without stiffeners in Algor Simulation, that I hope to rebuild anew this afternoon to see if I can find them in agreement with the other programs' models.

 

[271828]

ishvaaag, I skimmed your responses for an indication that you also generated an exact analytical solution for the case without stiffeners. Unless I missed it, it's not there. Did you perform such a calculation? If not, then it's highly recommended. Otherwise, your models are suspect. Using multiple programs doesn't alleviate this concern because a modeling mistake could be repeated in all models. The model without stiffeners should have an overall rotation almost equal to the closed form solution. Otherwise, it forms no basis for comparison IMO.

Verification #2 is that the overall rotation must decrease with the additon of stiffeners. For it to increase makes no sense from a mechanics standpoint IMO.

 

[271828]

ishvaaag, sorry. I didn't mean for that to sound harsh. Let me rephrase appropriately: Your comparisons will be greatly strengthened by the addition of a closed form solution to back up your model.

 

[ishvaaag]

I have not made the analytical check you refer to, and I may well make it as well, program, closed form or whatever. Yours is certainly as well a welcome advice, since it may shorten effort and clarify the sooner the matters. Anyway, I certainly am (not in relation with the post only) trying to investigate the use of the advanced FEM tools to learn more about their usefulness, so anything is worth the try in such intent; not to forget that FEM is not but other mathematical procedure leading solution to the mechanical problem, and hence the insight gained through the programs is as valid as the way you suggest once you manage to produce a valid model and analysis. That this may be more difficult I agree and that is the struggle.

Respect the second statement, once the loads are imparted in one specific way to one structure, in my view the main requirement is that the energy of deformation invested in the structure stays at the minimum value at which it can get in equilibrium with the loads. If, coming from a previous structure, we add the stiffeners, the structure is now different, and so even if subject to the same loads it *** might *** turn out that the minimum energy of deformation happens for some enhanced responses in some terms and less response in others, when compared to the ones they had prior to adding the stiffeners.

So even if in general reasonable addition of structural material may be in concordance with a decrease of the interesting responses -as seems be the case with the addition of the stiffeners from the latest analyses I have-, I think it is not neccesarily warranted that a particular kind of response decreases when the shape of the structure gets changed even with some thought to be reasonable addition of structural material.

A correct mechanical solver must be able to identify the equilibrium, that needs be in satisfaction of the minimum energy of deformation, and for such cases show an unexpected increase of some particular response; it is the integrated amount of energy of deformation that must stay minimal, no their component terms.

 

[ishvaaag]

No prob. 271828, it is always great to have illustrious companyons that enhance our understanding of things, I am very well aware I am not atop the ladder seeing the literature out there, and the interventions of so many of you here are of such character that I see I am far behind in so many matters that I hereby thank you all for so generously coming and teaching, whatever the wordings one may be using in the intent.

 

[271828]

Can you provide an example of a simple structure for which the addition of a piece of material (that will have stresses generated with the addition of load) causes an increase in deflection?

Let's use a uniformly loaded cantilever beam tip reflection for example. If we add a spring support anywhere, the deflection goes down. This can be formulated with real work, virtual work, stiffness, etc., obviously. Let's talk stiffness -- the stiffness matrix remained unchanged except for the _addition_ of some new terms. I think that borders on proof that the deflection cannot go down, but I am not quite there yet.

I can't seem to think of a counter example. Please provide one if you don't mind.

 

[Teguci]

The reason counterintuitive options become open with torsion is that we are dealing with a non-constant matrix. The shape does not remain planar, 2nd order effects are prevalent. Any distortion will change the beam shape.

As for your guantlet, consider the cantilevered beam with a bottom flange tee offset to one side that moves the neutral axis to the side and causes torsional rotation. As soon as we rotate the cantilevered beam our bending capacity drops through the floor due to weak axis bending.