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Transverse Stiffeners - Torsion 6
- Thread starter ToadJones
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1
- #21
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.
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.
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
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
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.
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.
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.
Here are a couple of other references:
BA
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.
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:
BA
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.
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.
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3
- #28
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.
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.
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.
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.
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.
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.
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
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
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.
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.
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.
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!)
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!)
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.
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.
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?
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?
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.
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.
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
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