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Transverse Stiffeners - Torsion
6

Transverse Stiffeners - Torsion

Transverse Stiffeners - Torsion

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

RE: Transverse Stiffeners - Torsion

2
The stiffeners are flexible out-of-plane so wouldn't do much, if anything to help with warping.  I don't see how stiffeners would help with pure torsion either, so I don't think they'd do anything for torsion.  This assumes a member with regular proportions.  If the member has very high b/t, then the stiffeners might prevent distortion.

RE: Transverse Stiffeners - Torsion

I don't know.  But, since the beam will be restrained from warping at the stiffeners, I can picture the beam rotating more to compensate.  As 271828 notes, the stiffenrs add nothing to pure torsion resistance.  My hypothesis is that the stiffeners will cause the beam to rotate more but not add anything to its torsional resistance (perhaps a worse condition).

RE: Transverse Stiffeners - Torsion

Teguci, how will the beam be restrained from warping at the stiffeners?  Warping not the same as "distortion," which I think is what you're referring to.  See the AISC Design Guide 9 Figure 2.2.  Stiffeners would do next to zero to restrain this type of deformation.

A plate added to restrain warping would have to be rotated 90 deg. to the usual orientation of a stiffener.  See Figure 3.3(a).  These plates are rotated in the direction that would restrain warping deformations.

Stiffeners = no help for torsion of regular rolled shapes, as far as I know.  It would be cool if they did, so if someone has a reference, I'd be very interested in seeing it.

RE: Transverse Stiffeners - Torsion

i think they'd help in making the entire section work as one, stiffening the joint between the flanges and the web.

RE: Transverse Stiffeners - Torsion

In other words, controlling distortion, right? LOL

RE: Transverse Stiffeners - Torsion

i think the weak point for an open section in torsion is the joint between the flanges and the web.  Stiffening that would improve the torsional stiffness of the section and the torsional capacity of the beam.

LOL?

RE: Transverse Stiffeners - Torsion

I just thought it was funny because I thought we were talking about the same thing.  Sorry.

The OP was talking about regular steel beams because he said "wideflange."  Design Guide 9 shows how to compute stresses and deformations for those, and stiffeners wouldn't come into the picture.  For that particular type of section, I don't think they'd do anything.

I could be wrong, though, so if someone has a reference, I'd like to see it.

RE: Transverse Stiffeners - Torsion

I think the issue is trying to resolve the shear flow in the flanges that's induced by torsion.  The shear flow in flanges flow in opposite directions creating a couple acting about the shear center of the beam.  In order to resist the torsion, you need to resist the shear flow couple that develops.

The stiffeners would not be able to resist that couple.  Once the shear flow goes into the stiffener, it would creates a couple within the stiffener, where the stiffener is connected to the flanges, and since the stiffener is unsupported at one edge, a resisive couple would not develop.

The only thing the stiffener might do is resist any possible distorsions in the flange as 271828 notes.

That's my thought...Let me know if anyone agrees.

RE: Transverse Stiffeners - Torsion

The kind of stffeners that would reduce warping are the kind that convert the W section into a closed shape.  i.e. welding plates from flange to flange or welding the open side of channels to the web.  If I remeber correctly AISC DG 9 has an example of attaching a channel to the web (open side against the web and running parrallel to the axis of the beam for a short distance).

I am not aware of any research that supports this but maybe DG 9 has more information.  I don't have a copy available.

Jim

RE: Transverse Stiffeners - Torsion

That's why the shapes bestr recognized to resist torsion are tubes and cylinders, not I sections.

Mike McCann
MMC Engineering

 

RE: Transverse Stiffeners - Torsion

(OP)
And here I thought I had a silly, almost embarrassing question.
I find myself agreeing with 271828 as far as the out-of-plane stiffness of the stiffeners being inadequate as far as reducing warping.  

RE: Transverse Stiffeners - Torsion

jtx - I agree totally with your post.  Stiffeners don't do much of anything for torsion.

 

RE: Transverse Stiffeners - Torsion

I agree that full depth stiffeners don't offer much in terms of torsional resistance, but intuitively I think that if a number of these stiffeners are provided along the length (at a close enough spacing), then it should have some benefit.

RE: Transverse Stiffeners - Torsion

(OP)
slick-
i thought the same and i am now trying to talk myself out of it

RE: Transverse Stiffeners - Torsion

jtx: are you referring to full depth or partial depth stiffeners?

RE: Transverse Stiffeners - Torsion

Slickdeals: Full depth stiffeners assuming they are connected to both flanges and the web, leaving one side unsupported.

RE: Transverse Stiffeners - Torsion

Toad- can you explain your exact situation?

RE: Transverse Stiffeners - Torsion

I think Teguci has come closest to the resulting behavior.
Without the stiffeners the WF will both distort and rotate.
By adding the stiffeners, this prevents distortion to occur in the vicinity of the pair of stiffeners without causing a corresponding deflection in the stiffeners.
The added stiffeness would be in the resistance of the stiffeners to bending in their strong axis.
The top fla would try and deflect laterally in one direction while the bottom fla would try to deflect laterally in the other
putting the stiffeners in double curvature, assuming stiffeners are welded into both top and bottom flanges.
It would be difficult to quantify the added resistance.

RE: Transverse Stiffeners - Torsion

If anybody's interested, the following journal paper is relevant to this discussion.  

http://ascelibrary.org/sto/resource/1/jsendh/v121/i7/p1119_s1

The author refers to a 1983 ASCE Jnl of SE paper by Szewczak et al.  On Page 1639, 3rd Paragraph, the researchers state:

Quote:

As noted by previous researchers and shown in Fig. 3(b), the transverse stiffener has very little torsional stiffening abilities and shows rotations and warping normal stresses approximating those of the unstiffened member.

Note however that this section of the paper only addresses stiffeners at the ends.  The remainder of the paper looks at other types of stiffeners--see the first full sentence on Page 1641.

In these two papers, the authors go through quite a lot, looking at relatively exotic and very expensive options.  Why would they be looking at these if all one has to do is add transverse stiffeners?

Blodgett shows a funny little experiment on Page 2.10-18, Figure 33.  The twisting angles are compared for a web plate, a web plus flanges plus closely spaced transverse stiffeners, and diagonal stiffeners.  The the web plate twisted 10 deg.  The web+flanges+stiffeners twisted 9 deg.  The diagonal stiffeners helped a great deal, and it twisted only 0.25 deg.  Take that experiment for what it's worth, though, because there is no warping stress generated using those boundary conditions.

Unless someone produces a reference that shows that transverse stiffeners add significant torsional strength or stiffness, I'm convinced that they don't help with torsion of wide flange beams.

RE: Transverse Stiffeners - Torsion

Stiffeners may add incrementaly to torsional stiffness but not to strength because the torsional strength of the beam between stiffeners is unaffected by their presence.

BA

RE: Transverse Stiffeners - Torsion

BA true....but if I space the stiffeners closer together so that
their area of influence reaches from stiff to stiff then that would address your point.
Granted, this is doing it the hard way and not very efficient in addressing torsion....but as an answer to the original OP...yes, I believe the transverse stiff do add increased resistance/stiffeness in the case of torsion....how much?..intuitively, I would not expect a significant increase...could be wrong though as it becomes a very complicated theoretical problem and hard to get a handle on.

RE: Transverse Stiffeners - Torsion

For all practical purposes, stiffeners do not add to torsional strength or stiffness.  The only area of influence a stiffener has is the thickness of the stiffener, assuming it is fillet welded on both sides to the web and flanges.  

Between the stiffeners, the beam is subjected to the full torsion resulting in stresses determined by the soap bubble or membrane analogy.  The volume under the membrane is unchanged by stiffeners.

Beyond the elastic limit, the "sand heap" analogy would be used and again, the volume under the sand heap is unchanged by stiffeners.

BA

RE: Transverse Stiffeners - Torsion

Not using the membrane theory ie.
By preventing the top fla deflecting laterally in relation to the bottom fla deflecting laterally in the opposite direction by the strong-axis bending stiffeness of the stiffeness. This has set up a different mechanism to resist the torsion.
One of the reasons an open section behaves so poorly in torsion is that the web typically has such little resistance to the above deflection.
I think the membrane theory applies to closed sections.

RE: Transverse Stiffeners - Torsion

With torsion, the entire cross section of a WF rotates uniformly.  Stiffeners do not prevent that rotation except for the thickness of the stiffener where you have essentially a rectangular section of b*d where b is the flange width and d is the depth.  But it is over such a short length that the torsional stiffness of the total beam length is altered negligibly.

The flanges do not deflect laterally, although there is a lateral component to their deflection.   They deflect rotationally about the centroid.  The stiffeners rotate with the cross section and offer no resistance to torsion in the space between stiffeners.

The critical torsional moment for a beam with stiffeners is precisely the same as the same beam without them.

Quote:

I think the membrane theory applies to closed sections.
Membrane theory applies to shells and is a different thing entirely.  Membrane analogy applies to open or closed sections.  If you have a copy of 'Design of Welded Steel Structures' by Blodgett, look at page 2.10-25 (Fig. 45) to see the shape of the membrane for various shapes including a channel and a WF.

Here are a couple of other references:

http://ocw.mit.edu/courses/aeronautics-and-astronautics/16-20-structural-mechanics-fall-2002/lecture-notes/unit11.pdf

http://www.clear.rice.edu/mech400/soap_film_lectureUC_D.pdf

BA

RE: Transverse Stiffeners - Torsion

You are correct about the membrane analogy, sorry, was working from memory.
The stiffeners, as you said don't prevent the WF section rotating as awhole, but I believe they help to prevent the distortion of the web.
Torsion causes a lateral force in the top and bott fla in opposite directions.
Now if we look at the fla separately as a beam with this force on it. This bm would then have spring supports at each stiffener location. The stiffeness of the springs would be the strong-axis
bending stiffness of the stiffeners.
So we would be comparing a case where this beam would have a very weak continous spring support represented by the web stiffeness alone(when no stiffeners are present) to the case outlined above.
If one looks at the typical deflected shape of a WF due to torsion..the web has a double curvature deflection(distortion)in addition to the rotation of the section as awhole.
 

RE: Transverse Stiffeners - Torsion

I think Toad lost interest in his own post :)

RE: Transverse Stiffeners - Torsion

3
See attachment. If the stiffeners are not hold by something (that can be the loading wall or whatever transversal  stiffness in place) in such a way that they are preventing their rotation, stiffeners by themselves do nothing but to enhance the worse rotational response of double tee members by enforcing efficiently the transmission of the torque.

So stiffeners out of themselves must not (to the light of the  investigated example in the attachment) be used to forestall torsion.

Other particular setups of the beams may vary the usefulness of the stiffeners to such purpose, that can be investigated in akin way.

RE: Transverse Stiffeners - Torsion

ishvaaag,

Whilst stiffeners my not enhance torsional resistance, I fail to see they could give worst output results in your attachment.

Care to explain please.

Kieran
 

RE: Transverse Stiffeners - Torsion

As I understand what the FEM models reveal, it means that through adding stiffeners the structure finds (and needs to meet) the kind of deformation shown because the energy of deformation is such way minimum, i.e., the lower energy of deformation available within the restraints, loadings, and actual configuration present in every separate case.

Perhaps the first pair is easier to understand; when adding the stiffeners, with the pair of forces applied as a torque, this torque is efficiently transmitted to the whole section, that then, trough the stouter open box-like short segments passes efficiently the torque to the following and so on. In the case when there are no inner stiffeners, you have basically in each flange one force to be resisted by the respective flange, and the mechanism is less a torsional one than two separate bendings. The fact that the FEM program shows be the case *** should *** mean that for the loading that I have imparted in the way I have imparted it, it finds to have less energy of deformation taking the load in that bending way than resourcing to some other (theoretical) more torsional in behaviour output.

The contrary is the case, relatively, when we add the stiffeners: now each flange cannot work as separately to meet its own lateral load through bending in the flange plane, and lamentably for a maxwellian daemon that would love to keep the former mechanism, the presence of the stiffeners ensure and forces that the torsional mode, and not one where the flanges bend in their respective plane, prevails. So we have forced through our stiffeners the structure to go for some particular way of deformation, which, again, since the solution of the model in FEM, should be the one having less energy of deformation to meet the loads as it is.

We could model now stiffeners less and less thick; at one given moment their addition would be irrelevant when compared to the overall stiffness of the beam itself, and then the model would revert to the situation where bending in each flange is predominant.

More, these are elastic models. Imagine that by whatever the reason we lose the stiffeners or separate them softly, then, I agree with you, the overal section is there and no less than what it provides is to be expected from it (rolling secondary stresses etc being ignored etc). When looking at these results, that fortunately mostly remain under the yield stress of the material, we must not forget that when dealing with a strength case we could account with some plasticity that also would show at least the minimum strength that you expect of the overall bare beam. So having some particular zones with a bigger stress when the analysis and material are in the model just elastic may well not reveal the final strength issues; making the model with elasto-plastic material when the forces engage some plastic regions would again show that you are right (again, residual stresses etc apart) in expecting no less than the basic beam provides.

But as long as the model is right (on which I am open to any contrary illustration) and the program as well, it leads you to ascertain that having stiffeners quite likely in the service levels will make the beam enter a more torsional response and then as per the op question, this is not precisely what one would be trying to do.

RE: Transverse Stiffeners - Torsion

It's as clear as mud.

BA

RE: Transverse Stiffeners - Torsion

I'll try a bit more.

For the first pair of examples, when you add the stiffeners you disable the bending action scheme dealing with the loads when there are not stiffeners. This happens because the stiffeners bring the flanges torsionally out of its original plane and then the structure needs to resource mainly to torsional behaviour (instead of flange bending) to meet the loads. The torsional stiffness is not as big as the bending stiffness, hence to meet the loads the lateral deflection when the torsional mechanism prevails is bigger.


  

RE: Transverse Stiffeners - Torsion

ishvaaag,

I am not convinced of your argument, but I am also not convinced of Sail3's description of the deflected shape of a WF in torsion.

It does not make sense to me that the addition of stiffeners makes any material difference to torsional strength, stiffness or deformation.  I believe there is something wrong with your FEM analysis...don't ask me what because I don't know.

BA

RE: Transverse Stiffeners - Torsion

I would agree 100% with BAretired.  But climbing up out of the theoretical mud - adding stiffeners like that would be really wasting money as they do so LITTLE to help your torsional stiffness or strength.  Why even bother.  Reduce the rotation by 0.00003 degrees by spending lots of money.  Makes no sense.

RE: Transverse Stiffeners - Torsion

Really BAretired is right in the thing that ALL models (even our cherished Timoshenko beam) fail to represent -always pushing the envelope of accuracy- reality; how not more with too worded explanations of what simply is the establishment of equilibrium with a FEM model with specific restraints, basical assumptions, ways of application etc that even further pretends through a pair of instances to devise the answer some quite more general issue  like the general problem of the influence of adding stiffeners in torsion.

Yet to the particularities of the FEM model (even inf keeping most if not all of its assumptions) we can do more by just making equivalent models in other program; obviously, exactly equal answers we shouldn't expect, at least to some degree of accuracy, and particularly when the models are at enough variation, but the procedure may reassure all those looking the questions on the validity of the first model and the insight gained there, that, of course and as said, may be limited to only a set of situations like the examples described.

I'll try (I hope) later the same models in RISA 3D. Now I won't be checking if the models are good enough to represent the influence of adding stiffeners in torsion, just if they are at qualitative variance of what Algor, er,  Autodesk Simulation models come to show for the behaviour.

Even if it was, I am not at all convinced that the response shown by Autodesk Simulation for the problems set in the models is incorrect. I, like many of the older people here is one that still has from when a child direct experience of the physical strength of anything we could do with our hands and arms. I push the stiffened beam with my mental child finger at center and I see it forced to take a more rotational response than when not and so a softened response in terms of rotation, even if it has to show ancillary localized bigger stresses on the coercions then occurring. So let's meet with some further model.

 

RE: Transverse Stiffeners - Torsion

Torsion causes a lateral force in the top and bottom fla in opposite directions.
Case 1..no stiffeners
Check the fla as a bm with this load on it. It will have supports at each end. Inbetween it will have a continous spring support whose spring stiffeness is equal to the bending stiffeness of the web in double curvature. Find max deflection.

Case 2...add transverse stiff.
Same model as case 1 but add conc spring supports at each stiffener location whose spring stiffeness is equal to the strong-axis bending stiffeness of the stiffeners in double curvature. Find max deflection.

The reduction in deflection between case 1 and 2 is a measure of the added resistance of the transverse stiffeners. QED(maybe!)   

RE: Transverse Stiffeners - Torsion

Thanks, BAretired, JAE and SAIL3, I will also be considering the matter with your insights.

For now the addition of models in RISA 3D supports the common wisdom that adding stiffeners will be benefitial to get diminished responses, both in terms of stress and deflection. Thanks so for pointing that could be the case.

I still want to clear the subject to where I can push it (maybe not to the pace till now) and will be further reviewing the AS models and matter.

I am finding (I hope temporal) problems in uploading the attachment, so I'll post it later.

RE: Transverse Stiffeners - Torsion

I ponder this all the time and agree that stiffeners do nothing for the global torsional resistance.  I do think SAIL3 is correct about stiffeners helping with distortion of the web though.    

Consider a simply supported (for torsion)wide flange beam with a uniform torsional moment applied only to one of the flanges.  The only way for this moment to flow into the entire section is through out of plane bending of the web.  This is the load path, right?

If the uniform torsion was more than the Fy*tw^2/6, wouldn't the web start to yield?  Wouldn't stiffeners help with this?

RE: Transverse Stiffeners - Torsion

Quote:

Torsion causes a lateral force in the top and bottom fla in opposite directions.
That is an inaccuracy.  Torsion causes a force in the top and bottom flange in opposite directions.  The forces are not lateral.  They are parallel to the flange in the rotated position. Together, they form a couple.

Quote:

Case 1..no stiffeners
Check the fla as a bm with this load on it. It will have supports at each end. Inbetween it will have a continous spring support whose spring stiffeness is equal to the bending stiffeness of the web in double curvature. Find max deflection.
This is not a valid procedure.  The direction of the flange force is constantly changing throughout the beam span.

Furthermore, the web is not in double curvature.  It remains straight but rotated.  To be in double curvature, there would need to be an applied moment top and bottom of opposite direction to the applied torsion.

Quote:

Case 2...add transverse stiff.
Same model as case 1 but add conc spring supports at each stiffener location whose spring stiffeness is equal to the strong-axis bending stiffeness of the stiffeners in double curvature. Find max deflection.
Again, not a valid procedure.  The stiffeners are attached to a beam which has rotated but the cross section is otherwise unchanged, so stiffeners have no effect.

BA

RE: Transverse Stiffeners - Torsion

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.

RE: Transverse Stiffeners - Torsion

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.

RE: Transverse Stiffeners - Torsion

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.

RE: Transverse Stiffeners - Torsion

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.

RE: Transverse Stiffeners - Torsion

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

RE: Transverse Stiffeners - Torsion

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?  

RE: Transverse Stiffeners - Torsion

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.

RE: Transverse Stiffeners - Torsion

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

RE: Transverse Stiffeners - Torsion

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).

RE: Transverse Stiffeners - Torsion

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

RE: Transverse Stiffeners - Torsion

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

RE: Transverse Stiffeners - Torsion

(OP)
the OP is back baby!!!

RE: Transverse Stiffeners - Torsion

(OP)
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.  

RE: Transverse Stiffeners - Torsion

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.

RE: Transverse Stiffeners - Torsion

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.

RE: Transverse Stiffeners - Torsion

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.   

RE: Transverse Stiffeners - Torsion

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.

RE: Transverse Stiffeners - Torsion

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.  

RE: Transverse Stiffeners - Torsion

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.

RE: Transverse Stiffeners - Torsion

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.  

RE: Transverse Stiffeners - Torsion

Sorry, either I don't understand your scenario or I don't see how it runs the e gauntlet.  Please clarify.

RE: Transverse Stiffeners - Torsion

It may also be a gross example for the question asked for 271828, but may be useful to show the idea. Take a plate of constant thickness supporting some loads, simply supported at all edges. Imagine some party thinks it will be deflecting too much, and he decides to increase the thickness to counteract such excessive deflection; depending on from where we are starting, and to where we bring the thickness, it may well result that the overall deflection increases, and the structure in general be even worse than it initially was due to the addition of weight overcoming any gains in strength and stiffness coming from the addition of structural material.

I understand that in this case the addition wouldn't be judicious in the proposed extent, and what we have been (and somewhat are still) elucidating here is if such is the case with the addition of stiffeners, if not economically, from an structural viewpoint.

RE: Transverse Stiffeners - Torsion

I may also reconvert the example by Teguci to your satisfaction. Imagine our original cantilever is a symmetrical tee. So, instabilities apart, zero torsion and zero lateral deflection by design. Now imagine by whatever the not very reasonable reasons we decide to reinforce it by just adding a parallel plate welded to just one of the sides. Inmediately the asymmetry shows and the responses in terms of lateral deflection and torsion appear, so, augment. It is normally an unreasonable proposition, as was above to thicken so much the plate, but this is what we are thinking about at least theoretically in part of this thread, whether  adding stiffeners may or not in some case make the structure to enter one of such pitfalls out of its modified setup.

RE: Transverse Stiffeners - Torsion

Quote:

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?

Consider a WF laterally unbraced with uniform gravity load acting on it.  The addition of a thin, deep vertical steel plate welded to the middle of the top flange would relieve the stresses in the beam but could cause lateral torsional buckling because the plate cannot resist the fiber stresses due to bending.

BA

RE: Transverse Stiffeners - Torsion

I should have clarified the gauntlet.  Monitor the same DOF for the before and after.  Other than the variable plate, the other examples are introducing an asymmetry, so there is movement in some other DOF.  The original DOF stiffness was unchanged or increased.

As for the variable plate, the stiffness for the same DOF certainly went up.

The gauntlet is worded with one DOF monitored because that is lime the problem at hand.

RE: Transverse Stiffeners - Torsion

Well, I have made a line (frame element) model in SAP2000 and I find it less than informing for our matter, and requiring some spreadsheet or worksheet element to add to my judgement so after trying I suspend the thing for the moment in that path. It also seems that fixing the ends of the beam does not introduces restraint to warping there, to be verified.

So I return and rebuild anew entirely the Autodesk Simulation models that have no stiffener, and, essentially, I find no error in my previous trials that the new models have discovered. I can still remake as well those with stiffeners, but the likelihood is that my former conclusions of the stiffeners making the outfit show a bigger torsional response likely will stand as per AS seems to be seeing the thing. My heart is with AS in this matter, but I won't make professional statement on it till further clearance of the same. Algor was a package with all the certifications for the nuclear industry etc, and I have read that with the purchase by autodesk the buyers were at a loss to understand the pipepack module because those that made it were not already to explain. Knowledge is delicate matter to keep. This must not make in the eyes of anyone see that I am dismissing the two other programs' results nor stance in my own eyes. It is simply making a bet on who will be right.

See attachment.

You can make your own models with your own programs, I'll be happy to read of your results. I may use these two cases for benchmark with other FEM programs when I'll use them. The sooner may be the Inventor linear built-in solver, that I have used in some occasion a pair of times, or the old visualNastran if I have some PC with it still installed. For others (generic FEM packages), It will take me more time, have not used them.

Essentially, the benchmark problems are


1.
CONCENTRATED TORQUE AT MIDLENGTH
HEB 300 beam 7 m long, fixed at both ends, a pair of 1.9 tonne forces applied at midlength on flanges to create a concentrated torque

2.
UPPER FLANGE EDGE LOAD
Same HEB 300 beam 7 m long, fixed at both ends, but now with an edge distributed load at one of the edges of the upper flange of 3 tonnes on each meter.

Then I have introduced for the stiffened cases (quite proportionally thick) 15 mm complete stiffeners.
 

RE: Transverse Stiffeners - Torsion

... the stiffeners separated 50 cm on center, starting at the center.

RE: Transverse Stiffeners - Torsion

(OP)
Ok-I'd like to have my post back

Does anyone have a reference for torsional analysis of a wideflange with a cap channel?  

RE: Transverse Stiffeners - Torsion

BA has been talking about classical Saint-Venant torsion; this assumes that the angle of twist is small, the elastic limits of the material are not exceeded, and that the shape of the cross section does not change.  The section just rolls (rotates), but retains it shape, and this is generally true for most WF shapes, or distortions in shape are so small they can be neglected, thus the web stiffeners we are talking about will not appreciably improve the torsional capacity of these beams.  If some of the member components are thin or tall and slender, such as some webs, plate girders, the shape of the cross section is likely to distort due to the warping torsional moment, just as SAIL3 suggests.  This is called the 'Goodier-Barton effect' of web distortion, and in some shapes and cases might have to be considered.  (See J.N. Goodier and M.V. Barton, "The Effects of Web Deformation on the Torsion of I-Beams," Journal of Appl. Mechanics, 11, MAR1944).

St. Venant torsion assumes that the cross section shape doesn't change, but is free to warp, this is a uniform or pure torsion, represented by St.Venant's soap film analogy.  But, since most members are not free to warp under torsion, normal stresses exist or are induced, particularly in the flanges, due to the bending of the flanges.  Thus, both St. Venant (shear stresses) and warping torsional stresses (normal & shear stresses) occur together in the member.  In addition, there will be the regular normal and shear stresses in the member due to bending as a beam, gravity loaded, about its shear center.  All of these stresses must be combined, in appropriate fashion, to start to approach the output of a FEA.  And, on a problem like this the FEA is incredibly sensitive to the way the model is put together; the types of elements used, the boundary conditions, the types of constraints employed, etc. etc.  You certainly better know the limitations and idiosyncrasies of the program you are using.  And, it may be quite edifying to run the same problem with several different programs, as Ishvaaag has, to start to understand what these infallible programs are doing to our thinking and understanding.  You want to model this problem with small solid elements, but can't afford to; but to model it as a beam or smaller plate elements may be missing half the detail at the important locations.

I pretty much agree with BA and 271828 that these type web stiffeners shouldn't do much to improve the torsional strength of the WF shape, except preventing the shape from distorting in the immediate area of the stiffener.  And, given Ishvaaag's FEA they may actually cause some high, but quite localized stress points, if not detailed very carefully.  I would have to see much more detail on the FEA input and output and the way it was modeled, the actual stress output, etc.  I assume Ishvaaag's model didn't show the stiffeners clipped at the radius btwn. the web and flg. and I'll bet that is one of the places where the max. stresses occur, as a triaxial stress condition no less.  The fixity at the end reactions is suspect for high stresses too.

Some of my thoughts, or food for thought, RE: Ishvaaag's models and results:

1.    The first model with the 1.9 tonne point load applied at the center of the beam and out at the tip of the flgs.: I have two questions; are there two point loads, one at each flg. tip, one on each side of the beam, the near side, up, on the top flg. and the far side, down, on the bottom flg.; thus the torsional moment would be (1.9)(300mm)?  I'm having trouble with the orientation of the load and the distorted shape of the beam, on the third page, his 24JUL11, 13:48 post, seem bass-ackwards; the visible load should be pointing upward for the distortion shown.  This is actually a pretty complex problem from the Theory of Elasticity standpoint, and we should remember Saint-Venant's principle as relates to stress conditions and our simplified methods near point loads and reactions, but there aren't any structural detail anomalies which would cause a high von Mises stress, except at the application of the loads and the reaction points at the ends.  Funny enough, Saint-Venant is also associated with BA's soap film analogy for representing torsional shear stress.  The point loads cause canti. plate type bending in the vert. direction in the flgs., but torsionally cause the flg. to bend in its strong direction in the plane of the flg.  This latter bending, or the torsional shear forces associated with it, is what causes the WF section rotation, but this torsional loading is distributed over some considerable length of the WF, about the beam center, in inputting the total torsional moment.  I suspect the von Mises stress and the Max. Principal stress will exist in the area of the flg. tips or flg./web connection near the load application, or at the end reaction plates and beam flg. tips.

2.   In the second example with the 15mm thick stiffeners at 500mm o/c, one pair of stiffeners is at the center of the beam, right at the load application, and that torsional moment is input to the whole WF right there at length/2 from the reactions, not over some beam length, thus the rotational angle and displacements will be significantly greater in this case.  I think this is about what Ishvaaag is trying to say in his 24JUL11, 18:26 post, but I think the results have more to do with the abrupt input of the torsional moment to the whole WF section at a max. distance from the reactions, thus a max. rotational angle, rather than any great change in the flg. lateral bending.
 
3.   The third and forth examples, a distributed torsional loading over the full length of the beam, and on only one side is an apples vs. oranges comparison to the first two examples.  Quite a different loading condition and a much larger total load on the beam.  Despite the larger total load, it might well cause relatively smaller deformations and stresses per unit of loading given the way it is applied, and when applied over the full length of the beam.  In the first two cases the moment is applied at the center of the beam, and has the full half length in which to induce the angle of rotation; in case 1 gradually through flg. bending, and in case 2 harshly and abruptly through two stiffeners.  In cases 3 & 4 the distributed load induces less regular beam bending and also less rotation per unit of load since part of the load is nearer the reactions.

I am always floored by the fact that when all else fails in our ability at comprehension, we go to FEA for the ultimate solution.  But, then are unable to explain how that actually works, how it should be modeled, or what the results mean, and we sight a von Mises stress and a Max. Principal stress, but can't see where they are, the volume over which they act, or their orientation, and we take them as gospel.  Not giving much of a second thought to the fact that they might be (probably are) caused by the way the structure was modeled at a few nodes or at one boundary or point of intersection of two or three plane elements.  And, we can't seem to square the FEA results with our gut feelings, or the simplified solutions which we were taught years ago and which seemed to have work without disaster for so many years.  I'm all for seeing your (more exact?) solution, but not when it doesn't square with what I know has worked for years.  I expect FEA to refine my detailed solutions and assist me in refining my gross analysis, not to reinvent the Theory of Elasticity.  Ishvaaag may be doing us a service here by forcing us to consider that the first FEA solution may not be better, or more correcter, than our gut feeling, our simplified solution, and we better think twice about taking all FEA results for the gospel.  Thanks for the effort Ishvaaag.
 

RE: Transverse Stiffeners - Torsion

I would think you could still use AISC design guide #9.  The only thing is you would have to figure out what J and Cw are.  I am not sure if they are in the 13th edition manual, but a descent software program that analyzes cross-sectional shapes should be able to give these to you.

RE: Transverse Stiffeners - Torsion

Well, dhengr, thanks. Now I will explain how I modeled the torque for the concentrated torque cases.

In AS I first introduced a small bump antymmetrical in the center of the flanges where I later put the total amount of the 1.9 tonnes as a traction in +X and -X (rounded to kN) so its average point of application was at midheight of the flanges. The ugly minor bump I put because one of the things that can be ameliorated in AS I think is introduction of the loads, it is not very clement on it for those accustomed to enter ordinary hypotheses at ease.

Then, when making the RISA-3D models I took care to specify the height of the web between the midheight of the flanges, i.e., 281 mm once you deduce two half flange thickness, that is of 19 mm. So when putting there the 1.9 tonne loads there it was at the same point, only that without the to kN rounding.

Then, for the SAP2000 models, all the geometry was OK except that the fillets were beveled to excess of material (and I accepted the end stiffeners to be like the others "to axes" against the AS models. Since I had 2 joints at the incumbent flange sections and flanges, I used two 0.95 tonnes at the atop flange, and two contrary in the bottom flange, so for the same resultant at midheight.

For the line model the torque was directly entered as a torque itself.

And the last AS models to verify the former ones, I took the liberty of using just 1 node per flange to enter the load, i.e., I put the 19 tonne or more really, the 19000 kN force at just two nodes to form the torque. Really I could have made the same than in SAP2000, since I have also 2 nodes available.

In general I have proceeded at ease not looking for entire agreement but the behaviour.



Now I will add a further example of how the modification of the structure may introduce a variation of some particular kind of response that we want controlled. It is the well known structural type of strong colum-weak beam. If you have a well tuned system to such intent, you may alter the required characteristics of the system by increasing the stiffness of the beams.

In general, as work that is, inner work is the integration of products of stresses of strains. For some given inner work, you may have more stress and less strain, or more strain and less stress; the attribution of which to every case to be got by the pertaining laws governing the case.

So it may turn that some modification of some particular aspect of one structure causes a perturbation on some kind of response, stress of strain (or its more visible or accountable correspondent solicitations and displacements) that we want controlled.

In fact we as animals use it continously: when we are to fall we extend a leg or arm to precisely modify the response.

RE: Transverse Stiffeners - Torsion

errata, 1.9 tonne, of course. It came from that the flanges were 1.9 cm thick , used a bump length of 10 cm so I had 19 cm2 where I would be putting a simple pressure (called traction) of 100 kgf/cm2 for a total, of 1900 kgf, or 1.9 tonne.

RE: Transverse Stiffeners - Torsion

(OP)
BA-
Thanks.
I think I have that PDF somewhere, but thanks for pointing it out for me!
I hope the constants match those that are required for AISC 13th calcs

RE: Transverse Stiffeners - Torsion

100000e's Torsion Experiment FWIW.  

Objective: Determine the effect of regular transverse stiffeners on torsional stiffness and warping normal stresses for a typical W-shape beam subject to point moment at midspan.

Test Beam
• W18x35
• 20 ft long, 40 kip-in. concentrated torque at midspan
• Simply supported at ends

SAP Model Details
• Shell elements
• 1 in. mesh everywhere
• Flange shells at d-tf=17.7 in. – 0.425 in. apart, measured to centerlines.
• Lateral restraint at end nodes at each flange-web junction.
• Vertical restraint at end nodes at bottom flange-web junction.
• Longitudinal 0.1 kip/in. spring at left end, bottom, flange-web junction.

Unstiffened Beam Model (and closed-form solution verifications)
• Beam subject to strong-axis load of 20 kip at midspan.  Monitor displacement at midspan.
oApply the 20 kip at each of the 17 midspan nodes, so 1.1765 kip each
o First order analysis
o Shear deflection from virtual work: 0.0207 in.
o Flexural deflection from virtual work: 0.3895 in.
o Total deflection: 0.4101 in.
o SAP2000 total deflection: 0.4158 in.  Speculate that the increased deflection is due to compressive deformations near the reactions.
o SAP2000 modification: add axially rigid, otherwise flexible member at the end supports.  New deflection is 0.4107 in.

• Weak-axis natural frequency of the beam (self mass only)
o Closed form solution = 6.61 Hz
o SAP2000 first mode = 6.61 Hz

• Apply 40 kip-in. concentrated torque at midspan.
o DG9 analytical solution for Case 3, Page 110.
o In SAP, apply 2.3148 kip laterally, as a couple to the nodes at the flange-web junctions.
o First-order solution in SAP.
o J=0.51 in.4, a=76.1 in., Wno=25.9 in.2, alpha=0.5
o Rotation at midspan = 10.06 deg. from the equation on Page 110; SAP2000 flange displacement = 1.657 in. which translates into 10.86 deg (8% higher than closed-form solution)
o Warping normal stress = 31.7 ksi from DG9 Eq. 4.3a.  (Second derivative of theta equation using Mathcad); SAP2000 max flange stress = 33.2 ksi (5% higher than closed-form solution)
o Note that the model does not have quite as much material as the W-shape due to its lack of k-area material at the web-flange junction.  The model has slightly more rotation and slightly higher stress, both of which make sense.

• Closed form solutions are close enough to the analytical solutions to conclude that the model is behaving well enough to use as a basis for comparison.
o Midspan rotation = 10.86 deg.
o Max warping normal stress = 33.2 ksi

Stiffened Beam Models (1/2 in. transverse stiffeners)
• Unstiffened: rotation=10.9 deg., stress=33.2 ksi
• One pair of stiffeners at each end: rotation=9.78 deg. (-10.3%); stress=31.5 ksi (-5.12%)
• Five pairs of stiffeners at each end, 12 in. o.c. spacing: rotation= 7.89 deg. (-27.6%); stress=27.8 ksi (-16.3%)
• Stiffeners at 12 in. the entire beam length: rotation= 7.13 deg. (-34.6%); stress= 23.6 ksi (-28.9%)

Conclusion
• For this beam, modest decreases in the rotation angle and warping normal stress may be attained by adding typical transverse stiffeners, especially if they'e closed spaced.

Experiment Mode Off / Editorial+Opinion Mode On (LOL)

I was pleasantly surprised that the stiffeners helped as much as they did.  While other types of stiffeners, such as those shown in DG9, are undoubtedly far, far more efficient, these do offer a small help.  For example, if torsional rotation is only slightly too much, perhaps it can be dropped 10% or so just by adding or considering (perhaps they're already there) stiffeners at the ends.  In general, I think the initially visualized behavior was correct: the stiffeners bend out-of-plane near the beam ends, providing some restraint to warping, but not a lot.   

RE: Transverse Stiffeners - Torsion

A star from me.

RE: Transverse Stiffeners - Torsion

And one from me.

BA

RE: Transverse Stiffeners - Torsion

Well, now the results of the models in Inventor, also confirmatory of slight benefitial action. Also the table of comparison of results, updated. Those signaled in ellipse are the first ones that signaled what is becoming an statistic anomaly and I will try still to repair if feasible to commonality.

Thankyou to everyone for pushing the clarification so far.

RE: Transverse Stiffeners - Torsion

And the reconciled Algor Simulation models. I took no chances varying a number of things whilst preserving the shape and intent of the models and quite likely the use of a finer mesh (even if the former was a fine one) did. So, friends, all my pairs of FEM models say now that the addition of stiffeners signify a slight improvement against rotation.  

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