Effects of Intermediate bracing on effective length of large cantilever 2

[StructuralDesigner91]

Hi,

I'm working on a temporary beam that will cantilever 20 meters, I'm looking for information regarding the effective length to use. Most publication only discuss the restraint condition at the tip and the root, but what effects do adding intermediate bracing have on the effective length. Its a built up beam 2500mm deep. I've read Galambos guide to stability design criteria for metal structures but there is no discussion regarding the effect of intermediate stiffeners.

Any guidance or information is appreciated.

 

[Settingsun]

Hi Agent666,
Your results look somewhat like Figure 5 from the UQ paper I posted - shear centre load case. I believe this is for K=0.6 as stated at the top of the figure (rather than 0.1 as stated in the caption). What is the K-value from your model? I suspect K<0.6.

K = sqrt(pi^2*E*Iw/(G*J*L^2))

 

[Agent666]

Its was 610UB101, cantilever length is L=5486mm. So K = 1.62?

 

[Settingsun]

I suspected wrong then. Figure 3 actually shows little dependence on K from 0.1 to 1.0 so maybe this extends to 1.6 also.

 

[Agent666]

The relative ratios between shear ctr loading do look like a reasonable match for the overarching behaviour I noted (compared to figure 5 for example) in terms of both rotational restraint and translational restraint cases more or less being a similar number, full restraint case being approx 50-60% more.

 

[human909]

Is your rotational restraint:

1) rotational restraint of the top flange (as stated) or;

2) effective rotational restraint of the entire cross section?

It would need to be #2 to fit my definition of "the best kind of cantilever".

If it's #1, you could initiate a buckling mode that starts of as web sidesway buckling at the cantilever tip.

This is probably just semantics but, then, semantics are a big deal in these discussions. It may well be that your top flange rotational restraint is also whole section rotational restraint (stiffeners etc).

Thanks for asking. And yes it is 1) as stated, so it doesn't meet your definition of "the best kind of cantilever". (Sorry for misrepresenting your definition.) And you are absolutely right about the buckling mode possibility. And no it isn't just semantics in this case. (Despite a major in mathematics, my mathematical grasp on the expected buckling behaviour isn't as good as it could be. However my visual grasp on the expected behaviour is reasonably good.)

 

[human909]

Ok for what its worth, I found the results of doing a simple case in mastan2 quite interesting to quantify relative effects. It showed a rotational restraint at the tip wasn't a hell of a lot better than the unrestrained case, and by far the best benefit gained is by preventing the lateral deflection of both flanges (which also prevents twist).

Thank you very much Agent666!

I don't have access to mastan2 currently. If you can at all be bothered and do a 7 case:
Case 7 Twist restraint on top flange ONLY and lateral restraint to top flange ONLY at tip

I'd give you 1000 internet points!

My reason. That is the cantilever I have hanging up at site currently and now I'm curious. (Curious not concerned.) Though I'll keep pulling on this thread myself regardless.


If people are interested I can even put up the design. It is a bit 'different' as it is cantilevered off a tension brace. Which given the position of the support and the points of lateral restraints it doesn't really fit nicely into the code requirements if taken at the letter. However given the restraints it has, the worst that could realistically occur is an elastic buckling sag. (Again, no calculations or modelling to go with that prior assessment, just visualisation.) I'll follow this up though because not I am curious!

 

[Agent666]

That was case 6.

 

[human909]

That was case 6.

Oh. Ok!

I interpreted Case 6 as full rotational restraint rather than just top flange rotation restraint. (I should have looked at your picture for case 6.)

Again thanks for following this through. It started as a dispute I initiated. I certainly have learnt from it. I hope you have found it productive too.

 

[KootK]

That was case 6.

I'm not convinced that it really was in a meaningful way. I suspect that human909 may have been effectively correct with this assessment:

I interpreted Case 6 as full rotational restraint rather than just top flange rotation restraint. (I should have looked at your picture for case 6.)

Two sources of my skepticism:

1) the deformed shape shows no apparent acknowledgement of web distortion (or it's just too small to see).

2) the applied load ration values for case 3 and case 6 are virtually identical which somewhat suggest that they are virtually equivalent in terms of modelling.

If I still don't get it we should move on! The poor OP's had his thread well and truly hijacked at this point!

For what it's worth, the "let's agree to disagree" business is -- and will always be -- a waste of words with me. I simply don't have that setting. And I consider it OP's prerogative to guide the discussion as he sees fit. In my opinion, he's already received all of the straight forward guidance here that he's likely to get and should consider the ensuing debate to be a valuable bonus.

 

[KootK]

It showed a rotational restraint at the tip wasn't a hell of a lot better than the unrestrained case

I've come to question the validity of this as well and offer the following up for consideration, none of which is definitive on its own:

1) Obviously, this isn't a good fit with long standing practice and assumptions. We've been believing in the whole "roll beam" thing for a while now.

2) The result isn't consistent with intuition or, at the least, not my intuition. True LTB instability requires that the load do work. In this case, that means the load moving vertically downwards. And all that I'm seeing appears to be lateral movement. I'll offer an explanation for this next.

3) For Mastan to do its thing, it requires some manner of "perturbation" to get the model moving. Whatever that perturbation is, I'm guessing that it encourages lateral movement and scales up with the applied load ratio just as the primary load does. So what we're seeing here may actually be:

a) Instability as represented by a loss of lateral stiffness rather than lateral torsional stiffness (LTB) and;

b) A lateral motion inducing perterbation that may be scaling up in a manner not consistent with real world conditions.

 

[KootK]

Twist is only one part of the complex web of elastic buckling, warping stiffness, torsional stiffness and residual stresses all play a role. To boil it down to just twist reduction is perhaps overly simplistic.

That statement strikes me as internally inconsistent. All of the complex web stuff that you listed as evidence that it's more than just twist in fact do point to twist in my opinion. Consider:

1) Warping stiffness. All about twist and the resistance to it.

2) Torsional stiffness. All about twist and the resistance to it.

3) Residual stresses. Residual stresses will mean a premature degradation of warping stiffness which circles back to #1.

To boil it down to just twist reduction is perhaps overly simplistic.

Truly, I believe that it is that simplistic even if the "twist" bucket contains, within it, many complex nuances. Do keep in mind that, when I reference "twist", I'm always speaking of rotation about a point coincident with the web but not necessarily within the depth of the cross section (usually above or below the cross section really). I'm starting to wonder if, when I say "twist", you might really be hearing "twist about the centroidal axis".

 

[KootK]

...but you're essentially saying its a by product of laterally restraining the section that twist is perhaps reduced or eliminated.

Yes! Take out the wishy washy "perhaps" and you've got my position down exactly. I believe that all LTB is twist and that all lateral bracing is an attempt to eliminate one or more modes of twist as instability mechanisms.

In case 2 I posted, the twist rotation is still there you will observe at the point where I restrained the tip, even though the critical tension flange is restrained laterally only. This goes back to the compression flange still being unstable in this state and wanting to kick out.

I see it but, in my opinion, this doesn't change the fact that it's still a failure of twisting. In adding the top flange lateral brace, you've simply exchanged twisting about a point far below the bottom flange for twisting about a point less far above the top flange. In making that trade we are, of course, moving to a higher energy state which implies a higher load capacity, just as your investigation indicates.

 

[KootK]

To play devil advocate I'm curious how the following observations sit with your theory regarding the reduction of twist?
If I observe the reported twist along the member at the tip it's actually 3+ times higher at the tip when you add the lateral restraint than with the unrestrained section:-
Case 1 with unrestrained end: x_twist = 0.0002218
Case 2 with top flange lateral restraint only: x_twist = 0.0007423

Fun. I shall be the devil then.

I would rationalize that observation as follows:

1) The two cases represent deformation states at two different load levels. I'd think that they would need to be at the same load levels for an apples to apples comparison.

2) The numbers that you're quoting represent twist about the centroidal axes rather than twist about the point in space about which LTB is occurring (usually well above or well below the cross section). As such, the lateral sway component of LTB is not being captured in the twist numbers. And that's important as lateral sway is an important part of the LTB mechanism and is, in fact, the very reason why cantilevers can go so wrong, so fast.

I should note that I don't much care for the common description of LTB where it's split into centroidal torsion + lateral sway as a means of making LTB intuitive for text book & code readers. When you look at the math it becomes clear that it really is not centroidal torsion + lateral sway as that would produce no downward movement on a centroidally applied load, no reduction in potential energy and, thus, no instability. I understand why Steve prefers to stick to the "common" language to avoid confusion but, for me, the common language is really imprecise language that leads to the kind of misunderstandings that we're having here. "Rotation about a point in space coincident with the web but often beyond it" is the precise way to define LTB motion.

3) In going from mastan case #1 to case #2, we're preventing the cantilever sway component of LTB and forcing the section to, instead, rotate a about a point in space that is both:

a) above rather than below the cross section and:
b) much closer to the centroidal axis of the cross section.

Intuitively, those suggest to me that:

c) The capacity of the member will be higher and;
b) Resistance will tend to be expressed, in larger proportion, via ceentroidal twist rather than lateral sway.

So the results are consistent with intuition and sit well with me in this respect.

 

[KootK]

The optimum full-restraint location plotted on Figures 3 & 4 (which you highlighted in the conclusion) wasn't any real surprise. If you're going to introduce an additional restraint, you should make it so you have two segments each with shorter effective length than the total length of the cantilever.

Well, if it wasn't any surprise for you then that speaks well of your grasp on the situation. My money says that nine out of ten north american engineers would have guessed that the best place to brace a cantilever was at the cantilever tip. That's invariably what you see in practice but, then, there are surely other reasons for that as well (diaphragm chords etc). I might be able to make use of this in practice. I've encountered a couple of instances where architects wanted to be able to "express" the cantilever rather than just seeing a rim piece.

 

[Settingsun]

I probably got the right answer for the wrong reason by oversimplifying. Just seemed that adding the restraint at the tip creates a single segment that's restrained at both ends with effective length equal to cantilever length - the base case. If the restraint is instead very slightly before the tip, there are two segments. I'm not concerned with the segment from restraint to tip because its very short length overcompensates being unrestrained at one end. The other segment from support to restraint is now shorter than the base case. The moment distribution is less favourable (no longer zero at one end) but you'd have to be unlucky to introduce a restraint that shortens the effective length and make things worse. Keep moving the restraint closer to the support until the tip segment becomes a problem and you've maximised the capacity.

I'm still digesting your other recent posts but my current thinking is the differing understanding/language may be between restraints that restrict twist vs restraints that completely prevent twist.

 

[KootK]

my current thinking is the differing understanding/language may be between restraints that restrict twist vs restraints that completely prevent twist.

I'm of a similar mind but would say it a little differently:

differing understanding/language may be between restraints that restrict one or more modes of twist about points in space coincident with the axis of the web but not necessarily coincident with the centroid vs restraints that completely prevent all modes of twist about all possible points in space.

I'm obviously bending over backwards to be precise here and realize that nobody speaks this way in real life.

 

[dauwerda]

I am not going to add to this in any meaningful way, but I would like to say:
Discussions like this are why I love frequenting eng-tips.
Thank you to all participants

 

[Settingsun]

Two sources of my skepticism:
1) the deformed shape shows no apparent acknowledgement of web distortion (or it's just too small to see).

2) the applied load ration values for case 3 and case 6 are virtually identical which somewhat suggest that they are virtually equivalent in terms of modelling.

1) Should we expect to see web distortion? If I've understood correctly, the actual model is just the line on the member centroid. Agent666 added the I-sections but they don't really contribute to the analysis. Although there may be a small contribution in this instance (because the restraints are applied to the I), won't the load's position below the restraint tend to restore the web towards vertical if it did try to kick sideways?

2) Agent666 did note that they are almost equivalent when he posted the mastan results. I know you're not fond of references to codes, but the A/NZ codes treat these two cases very similarly. Case 3 is Full restraint whereas case 6 is Partial (IMO*) resulting in a very small increase of effective length for case 6.

* - The code commentary acknowledges that the difference between F & P restraints is only defined qualitatively in the code, so it's always a matter of opinion.

True LTB instability requires that the load do work. In this case, that means the load moving vertically downwards. And all that I'm seeing appears to be lateral movement. I'll offer an explanation for this next.

The explanation could be as simple as the posted results have the vertical deflection component removed. It appears to me that none of the plots shows the tip deflecting vertically. Cases 3 & 6 show this clearly. The mastan result matches the analysis in the UQ paper. They didn't do any twist-restraint-only experiments though - probably quite hard to restrain twist without also some measure of lateral restraint.

Agent666 said the case 5 result was hardly better than case 1, but it's actually a 40% improvement. The best possible restraints only doubled the capacity (cases 3 & 6). Maybe the relative contributions of Iy and (Iw & J) are just similar for this particular geometry.

I should note that I don't much care for the common description of LTB where it's split into centroidal torsion + lateral sway as a means of making LTB intuitive for text book & code readers. When you look at the math it becomes clear that it really is not centroidal torsion + lateral sway as that would produce no downward movement on a centroidally applied load, no reduction in potential energy and, thus, no instability.

I'm going to request some of your precise/bent over backwards/twisted into a pretzel language. How does this tally with loads applied at restraint points like cases 3 & 6?

PS: While the common definition of twist restraint being fully-effective twist restraint (eg web that starts vertical must remain vertical) probably does come from the textbook definition of the mathematical boundary condition (phi = zero), I personally wouldn't call differential equations, that run to four differentiations deep, 'intuitive'.

I guess I also wouldn't say centroidal twist is the common definition. Figure 5.4.1 posted by Agent in the 18th post shows two unrestrained sections. Neither is twisting about the centroid.

 

[KootK]

Discussions like this are why I love frequenting eng-tips. Thank you to all participants

Thanks for this. I feel the same and it's good to know that the conversation is of value to more than just the active participants.

Should we expect to see web distortion? If I've understood correctly, the actual model is just the line on the member centroid.

We should certainly expect it if sidesway buckling is being accounted for which was human909's concern with case 6. If you're correct that it's a line member, as was the case a decade ago when I used tinker with Mastan then, without doubt, sidesway buckling is not being accounted for as it would be quite impossible with a line member.

Although there may be a small contribution in this instance (because the restraints are applied to the I), won't the load's position below the restraint tend to restore the web towards vertical if it did try to kick sideways?

No. That would be the case if the restraint were a vertical restraint but it's not. I see no reason why load applied below a rotational restraint would tend to straighten out the web.

The explanation could be as simple as the posted results have the vertical deflection component removed.

That explanation would be simple. And implausible in my opinion. I don't see why Mastan or Agent666 would bother to do this. I'll leave this one alone unless Agent666, or someone else, can supply some evidence to indicate that this is actually the case an worth discussing further.

It appears to me that none of the plots shows the tip deflecting vertically.

In my opinion, case 1 clearly shows rotation about a point below the cross section which, by definition, implies

​

vertical movement.

It appears to me that none of the plots shows the tip deflecting vertically. Cases 3 & 6 show this clearly.

I'm fairly certain that what is happening is that the vertical deformations included in all the plots are simply dwarfed by the lateral movements that represent the buckling. The buckling, after all, is movement without bound, right? So this dwarfing should not come as a surprise.

I should note that I don't much care for the common description of LTB where it's split into centroidal torsion + lateral sway as a means of making LTB intuitive for text book & code readers. When you look at the math it becomes clear that it really is not centroidal torsion + lateral sway as that would produce no downward movement on a centroidally applied load, no reduction in potential energy and, thus, no instability.

I'm going to request some of your precise/bent over backwards/twisted jester2 into a pretzel language. How does this tally with loads applied at restraint points like cases 3 & 6?

Quite naturally. The cross section clearly flips over towards weak axis over a portion of the member over which internal moments are present. The result of will obviously be that vertical deflections are increased, whether or not they are too small to see compared to the gross, lateral movements.

 

[KootK]

Agent666 said the case 5 result was hardly better than case 1, but it's actually a 40% improvement. The best possible restraints only doubled the capacity (cases 3 & 6).

My real concern with this is not about how much improvement is there but, rather, that the buckling shape does not seem to have switched to a higher energy mode as it has with some of the other models and as I would expect it to here. It still very much looks like the first mode, lateral sway pattern that we've come to know and love about free cantilevers. And if there's no vertical movement associated with that, I question it's validity.

Anyone who's dabbled in the coding of these things will know that what the bot will register as "instability" in a non-linear analysis like this is really instances of stiffness diminishing to zero. In the context of case 5, it seems to me that this could occur via:

1) Loss of vertical stiffness at the point of load application as we would hope or;

2) Loss of lateral stiffness at the point of application of the perturbation mechanism which the model doesn't show us.

So, unless we fully understand the perturbation mechanism and how its being applied and scaled, I think that it is sensible to put a question mark on this particular result. Certainly, that is the case for me personally since I struggle to reconcile the Mastan result with my own intuition and the model that I that I carry around in my head.

Additionally, with case 5, what are we saying the final result is that would bring the load to ground? Lateral motion alone won't get the job done. Or are we saying that the thing bends around like a U-bolt until torsional flexibility becomes it's undoing?

I'll add that I do not dispute that perturbations represent real world imperfections. The most definitely do. But, as with many things, I think that the question becomes one of how the perturbations are applied and scaled and whether or not those things are adequate reflections of real world perturbations. Accurate modelling of the real world has turned out to be quite a challenge. Mastan is a great leap forward relative to our day to day FEM tools but, still, it's not a god program and our own intuition and understanding should not take a back seat to it.

This probably deserves it's own thread at some point but I consider the hierarchy of information quality in our field to be as follows, working from lowest quality to highest.

1) What is gleaned from our computer modelling tools "teaching" us things.

2) What we forensically piece together from what code writers choose to tell us.

3) What is gleaned from laboratory testing and real world failures.

4) What our own intuition and understanding of the physical universe is.

I assign value to all four sources and I'm sure that everyone's list is a little different. I sometimes flip flop on the order of #3 & #4. Ultimately, though, I see it as Einstein and Sheldon Cooper did. The ultimate laboratory is the laboratory of the mind and most of our best innovations will always come from there.