Rafter without fly brace? 22

[fourpm]

I am designing rafters to AS4100 and wondering what if I don't use fly brace. I understand that with fly brace it will give you full restraint. But if I don't use fly brace, will the purlin above be considered as lateral restraint for rafter under uplift? If so. can I take the purlin spacing as segment and the only factor that changes without fly brace is kt?
I have the same question when it comes the continuous steel floor beam design where Z/C floor joints sit on top of the beam. What segment should I take for the beam near the support? Can I take the floor joists spacing as segment with lateral restraint? Can anyone give me some examples? I have read some manuals but the examples they have are simply supported beams only. Thank you.

 

[KootK]

Oh, I know. And I'm saying that's irrelevant with respect to the discussion of elastic stability. I believe that it serves as a persistent and unecesary distraction in a discussion already nearly too complex for mortal minds to readily decipher.

 

[human909]

Exactly Tomfh. I believe it is completely necessray. As has already been acknowledged, we have no desire to consider ALL buckling modes as part of AS4100 member capacity check, just those that lie within the section capacity.

Human909, what are your end restraints? Are they restrained against minor axis bending? I think others are releasing this. And are both ends restrained longitudunally, so pinned-pinned rather than pinned-roller?

Thanks for clarifying.
My end restraints on the previous model was on the two edges of the web which did give some degree of stiffness in the minor plane. I re-ran the model with no stiffness in the minor plane and got 1845kN Picture below.
(Though having completely restrained in the major axis and completely pinned in the minor axis is a unusual connection!)

Beam restraint viewed from below.
-Full translational restaint Rotationally restrained in the major axis, rotationally unrestrained in the minor axis.
-Lateral restrains on top falnge as described by Kootk

 

[Agent666]

If there was an author, does that mean that the graphs are part of a document that you could either share with me or refer me to so that I might review it myself?

The author of mastan2 was what I meant. The results are part of the stability fun modules, module 4 I believe. The graphs are generated when you undertaking the stability fun module.

@Agent666: as long as I have your attention, can you confirm that your understanding of how AS4100 LTB works matches Tomfh's and Human909's, repeated below? The salient features there being that:

1) The AS4100 procedure checks no particular LTB buckling mode and, rather;

2) Checks all buckling modes at once by ensuring that parameters lie within a set of enveloping curves that encompass numerous individual LTB buckling modes.?

Disagree with 1 & 2, as you are checking the only critical buckling mode. Really this is the mode with the lowest reference buckling moment. That's the whole point, to find the lowest buckling moment, and work this through to a capacity.

When doing it by hand, you are checking the critical buckling mode, it doesn't matter what it is really is the point the others are making (which I agree with). Provided the effective length is correct then it theoretically buckles at the reference buckling moment (Moa) (edit - this is Mo x alpha_m essentially), you could have 101 different beams with all sorts of restraint conditions with the same effective length, and the reference buckling moment (Mo) would be the same. This is what the theory says. Then knowing the theoretical buckling moment you apply code reductions (alpha_s/phi, etc). The factors on effective length have been calibrated against tests, etc.

The point is you don't need to know the buckling mode, or how it fails, it is irrelevant really. The only variable in the reference buckling moment formula is the length that can change.

When you do it by buckling analysis you are solving the fundamental governing equation of LTB for the system and getting to the critical mode of buckling failure directly, if you want you can back calculate out the effective length to understand whats going on you can do so from the fundamental equation. But the actual mechanism of buckling is really irrelevant or redundant as you are essentially skipping over it determining the only (most) critical reference buckling moment which you need for determining the design capacity.



You all need to stop quoting the reference buckling moment directly as a capacity, it isn't! See my post above. If you're quoting capacities based on a buckling analysis then at least work it through using the AS4100/NZS3404/AISC360 provisions for doing so so everyone is comparing apples with apples.

 

[Settingsun]

I don't understand what this envelope check would look like. Isn't it game over after the beam fails when the lowest buckling mode/load is reached? Should I care if there are two more modes < yield and another at 107% of yield after finding a substantially lower LTB load? Is the envelope just the check of the various segments?

I agree with Agent's preceding post but I think that AS4100 is considering a buckling mode when the various factors are determined, at least comparatively to the reference mode. It's built in (but simplified/approximated to the same degree as the method overall) because the factors have come from tests/analyses which did have specific modes.

 

[Settingsun]

Not sure if I've had an epiphany about what KootK wants to understand about AS4100 or whether he'll turn around and say this is obvious and everyone already knows, but here goes.

Yura defined the segment length based on twist restraints. AS4100 places a greater emphasis on lateral restraint. AS4100 technically defines a twist restraint with no lateral restraint as unrestrained, knowing this may be conservative. Not sure how our bridge engineers handle this in long-span bridges but I see that the latest bridge code has added some motherhood statements without providing a design procedure. AU/NZ engineers probably do a buckling analysis or use Yura's 'Fundamentals' article for designing torsional restraints.

For AS4100, an L restraint is as good as an F restraint except that you can't use k_r < 1.0 with L restraints. See the graph I posted 23 Nov 14:27 which shows a case where the L restraint does the job of an F restraint and is better than a twist restraint. I find human909's latest buckling shape image interesting as it appears to match the AS4100 assumption: the bottom flange is only moving near the beam ends where it is in compression and the top flange restraints are ineffective at restraining the bottom flange. It looks straight and along its original alignment in the middle of the beam where it is in tension. The top flange L restraints are acting as F restraints. But this is very different to the Mastan buckled shapes and key to the AS4100 'magic' being correct for moment reversal within segment.

It would be interesting to see whether human909's method (and Mastan) handles reference cases well. Eg take away all the top flange lateral braces and subject the beam to a uniform moment. Does the buckling load match the M_o formula? Then change the loading to midspan point load with end moments equal to midspan moment. Is the buckling load 1.71*M_o?

 

[human909]

AS4100 technically defines a twist restraint with no lateral restraint as unrestrained, knowing this may be conservative. Not sure how our bridge engineers handle this in long-span bridges but I see that the latest bridge code has added some motherhood statements without providing a design procedure.

I was going to disagree with you on this one but rereading 4100, seems to concur with what you have said.

I went through this more than 12 months ago digging through resources. I've been building plent of long span 15-20m gantries. I treat tortional restrains as partial restraints. Though maybe this is quite debatable as far as AS4100 goes. This is from the Steel Designers Handbbook. (GORENC, TINYOU, SYAM)

I typically use plan bracing OR full web stiffeners with deep channel between them. I should run the system through elastic buckling analysis and have a look.

 

[Tomfh]

See the graph I posted 23 Nov 14:27 which shows a case where the L restraint does the job of an F restraint and is better than a twist restraint.

What is that graph based on?

It doesn’t agree with Mastan analyses above, and isn’t very intuitive. I’m not sure how an L can really be as good as F in reality, or how L on non critical flange can do literally nothing...

 

[RFreund]

Thanks Kootk and Tomfh for the recap.

I would concur that the unbraced length should be handled as the distance between columns and Kootk has done an admiral job defending this point.

I would like to define the braces again becasue I think that is important:

F-brace: Lateral deflection and twist are prevented.
P-brace: Lateral deflection of the tension flange is prevented. Twist can occur (i.e. the compression flange can move relative to the top flange)
L-brace: Lateral deflection of the compression flange is prevented
U - Unrestrained: No restraint.

To prevent lateral-torsional buckling you either need to prevent deflection of the compression flange or prevent the rotation of the flanges (i.e. both flanges can translate laterally but cannot rotate).

Now that Human909 removed the weak-axis restraint does the Mastan Model results match?
Curious to how this compares to the nominal capacity allowed by AS4100.

Also curious to find out more about the P-brace. This would apply to buildings with roofs that have continuous/drop beam system (Gerber system) where the beams are continuous but they don't use a stiffener. I know (in the US) this is a fairly big no-no and there are known failures because of this.

EIT

http://www.HowToEngineer.com

 

[Agent666]

Last time I looked I thought NZS3404 allowed just rotational restraints, but re-reading the definition of an 'F' & 'P' restraints it it seems it doesn't as there needs to be some effective/partial lateral restraint of the critical flange. However in reality just rotational restraining the section without lateral restraint is a valid means of increasing it's resistance to LTB. The classic examples is parallel bridge girders constrained to the same rotation with no plan bracing. I.e. all of those examples from the steel designers handbook, except for the last one with the bracing would qualify for this enhancement. I'm not sure if this is the intent of NZS3404 to prevent this type of rotational restraint being used in isolation, I certainly recall some literature showing it being used in a NZ context.

Eg take away all the top flange lateral braces and subject the beam to a uniform moment. Does the buckling load match the M_o formula? Then change the loading to midspan point load with end moments equal to midspan moment. Is the buckling load 1.71*M_o?

Yes it does. I showed this in case#1. This is how clause 5.6.4 requires you to work out alpha_m, and was how I checked alpha_m was actually comparable to the eqn in the table in a following post. If you setup the same uniform conditions for any span L, it should give you Mo. This is in mastan2, I can't say human909s analysis will show this because I'm not familiar with the software he's using and if it's even doing the same type of analysis because it seems FEM based, made from plates, and it raises many questions for me. To the best of my knowledge human just quotes reference buckling moments and not design capacities so it makes it hard to compare results directly.

It would be quite easy to show, for example use one of the cases where alpha_m is given explicitly. Then the reference elastic buckling moment from a buckling analysis should be alpha_m x Mo (derived from Mo eqn).

 

[Agent666]

RFreund, your definitions are off a little, especially in the restraint of twist department for F/P types. Bang on for L/U types though.

Best to see below regarding F/P restraints rather than me trying to re-hash it in my own words.

 

[Agent666]

I would concur that the unbraced length should be handled as the distance between columns and Kootk has done an admiral job defending this point.

Curious how you would defend that position knowing that AISC allows you to use a elastic buckling analysis which accounts for any degree of restraint imaginable.

Does AISC live in a world where if you use the hand method, it's strictly consider LTB between supports (Blue pill).

But if you use a buckling analysis you can consider any imaginable degree of restraint (Red pill).

That just seems a little crazy to me.

This is a serious question, just facilitating your opinion?

 

[KootK]

RFreund will have his own take on things here but I'm going to throw in my own responses for good measure as these questions really do speak to the depth of misunderstanding at play.

Curious how you would defend that position knowing that AISC allows you to use a elastic buckling analysis which accounts for any degree of restraint imaginable.

1) Distance between columns = distance between points of cross section twist restraint.

2) Distance between points of twist restraint makes sense as the LTB buckling length because that is the physical length over which the phenomenon that is LTB occurs. This shows up in:

a) Physical testing.

b) All of our FEM models.

c) Yura's work.

d) Trahair's work.

AISC's allowing you to consider all lateral restraints available doesn't conflict with this definition of Lb when viewed in this way. For the case at hand, the critical buckling mode is as shown below and is what has been referred to as constrained axis buckling. The salient feature being that:

3) It accounts for the beneficial effects of the L-restraints and;

4) It is still an LTB buckling mode that involves the entire length of the beam between supports.

That just seems a little crazy to me.

If there is something that is unintuitive, I would argue that it is AS4100 using something other than the distance between points of twist restraint as the LTB buckling length. That, because using the distance between L-restraints would appear to be the examination of buckling lengths not actually reflective of the physical buckling length. I get that you see all of this differently and that's fine. To cross the divide here however, we're all going to have to find a way to parse out and understand the perspective of the other side.

 

[KootK]

Not sure if I've had an epiphany about what KootK wants to understand about AS4100 or whether he'll turn around and say this is obvious and everyone already knows, but here goes.

I would think that the silver bullet here would almost have to be something that is obvious to some parties and opaque to others.

For AS4100, an L restraint is as good as an F restraint except that you can't use k_r < 1.0 with L restraints.

Yes, if L-restraints are as good or nearly as good as F restraints then this would be a epiphany from my end. It would explain the anomaly, from my perspective, that is AS4100 treating the buckling length as something near to the subsegement lengths (8' here) when the actual, physical length of the LTB phenomenon is the entire beam length (32' here). This will have two dimensions for me:

1) Verifying that this is how AS4100 works and;

2) Justifying that this approach is theoretically appropriate.

Phase two can wait. For now, just having phase one settled would be a massive win for me in the understanding department. Massive. And I see your point, the graph below would suggest that, at least in some situations, An L-brace might be considered effectively an F-brace.

I find human909's latest buckling shape image interesting as it appears to match the AS4100 assumption: the bottom flange is only moving near the beam ends where it is in compression and the top flange restraints are ineffective at restraining the bottom flange. It looks straight and along its original alignment in the middle of the beam where it is in tension. The top flange L restraints are acting as F restraints. But this is very different to the Mastan buckled shapes and key to the AS4100 'magic' being correct for moment reversal within segment.

Mastan and Human909's stuff are both just FEM models. One way or another, they have to be made to agree. In my mind, the differences between software models cannot stand as the "key" to explaining the AS4100 magic. Three things about Human909's model catch my eye and, hopefully, he can speak to them:

1) If I understand the symbology correctly, there is still some degree of weak axis rotational restraint at the beam ends.

2) The bottom flanges buckle in opposite directions. That S-shape suggests that this is something other than first mode behavior. This may be related to my next point.

3) Graphically, it appears that the load may have been applied at a point lower on the cross section than the top flange.

 

[KootK]

P-brace: Lateral deflection of the tension flange is prevented. Twist can occur (i.e. the compression flange can move relative to the top flange)

I think that needs some tightening.

P-brace:

1) lateral deflection of the tension flange is prevented.

2) rotation of the tension flange is prevented by some kind of moment/torsion connection between the brace and the tension flange.

3) rotational restraint of the tensions flange ---> rotational restraint of the entire cross section --> indirect lateral restraint of the compression flange.

4) If the indirect lateral restraint of the compression flange is relatively flexible, then you're talking P-restraint instead of F-restraints. Sometimes the difference will be the absence of a web stiffener which will make the compression flange lateral restraint more flexible by way of something that looks a bit like web sidesway buckling.

Also curious to find out more about the P-brace. This would apply to buildings with roofs that have continuous/drop beam system (Gerber system) where the beams are continuous but they don't use a stiffener.

Normally, with steel joists, the joist connections would not be considered P-braces because the connections between the joist seats and the girders would lack #2 above.

 

[KootK]

You all need to stop quoting the reference buckling moment directly as a capacity, it isn't!

"You all" is a pretty big bucket. Does it include my work? It shouldn't. Two perfectly valid things can be done with the reference buckling moments from FEM:

1) Compare one reference buckling moment to another so suss out the impacts of various changes to the situation.

2) Use a reference buckling moment as an upper bound capacity.

I believe that I carefully placed all of my stuff into one of those two buckets with statements like the one below that I included along with my modelling results.

No imperfections modeled so a high side estimate

In the interest of full disclosure, I would like to trade in adjusted capacities but have not been because:

3) I don't yet know how to do that in a way consistent with what others expect here and;

4) I don't yet know if doing this would represent more of a time expenditure than I can spare.

I invested my Friday evening and my Saturday morning into learning Mastan so that I could help share the modelling load here that I felt was being unfairly shouldered by a small group. As much as I would prefer to deal in "true" capacities, holding off my FEM participation another month until I got that aspect sorted didn't strike me as prudent. You go to war with the army you have, not the army you wish you had.

 

[KootK]

But I now agree that top flange loading at a top flange L restraint should use K_l>1.0 if the bottom flange is going to move sideways.

That's too bad because I've since changed my mind and rescind my concern. This is neat... and cleaner than most things here. Start with a full read of the attached sketch.

Yesterday, you asked for the W27x84 with a single L-restraint at mid-span to be modeled. I did that and thought to myself "Great, I'll run this same model with the load at the shear center and the load at the top flange. The top flange loaded model will buckle earlier and this will support my position that k_l should be greater than unity for that." I did this exercise and the results were just as I expected: capacity is less with the load at the top flange than it is with the load at the shear center. Unfortunately, this was never the right question to ask so the answer was meaningless.

The right question to ask is really this: of the various vertical positions available for the load, which one represents neutral stability? That, because the LTB capacities are calibrated to the neutral stability condition. And the neutral stability position is not, strictly speaking, the beam shear center. Rather, it is the center of rotation for the critical LTB buckling mode. Once the mid-span L-brace is added, that center of rotation becomes the top flange and, therefore, the top flange becomes the neutral load position. Everything shifts up as shown below. As a way to "feel" this, imagine the load applied at point [D} in the sketch below, with the top flange L-restraint in play. Obviously, in this position, the load is actually stabilizing rather than just neutral.

Neat huh? In a way, this dovetails into your hypothesis that, in many cases, L-restraints are effectively F-restraints. It is, after-all, acknowledged by all that the destabilizing effect of a load in a destabilizing position ends at the nearest F-restraint where it gets absorbed into the bracing.

 

[human909]

Last time I looked I thought NZS3404 allowed just rotational restraints, but re-reading the definition of an 'F' & 'P' restraints it it seems it doesn't as there needs to be some effective/partial lateral restraint of the critical flange. However in reality just rotational restraining the section without lateral restraint is a valid means of increasing it's resistance to LTB. The classic examples is parallel bridge girders constrained to the same rotation with no plan bracing. I.e. all of those examples from the steel designers handbook, except for the last one with the bracing would qualify for this enhancement. I'm not sure if this is the intent of NZS3404 to prevent this type of rotational restraint being used in isolation, I certainly recall some literature showing it being used in a NZ context.

Yep. I don't think it is the intent of AS4100 or NZS3404 to prevent this. In fact AS4100 and I would presume NZ3404 has a clause on diaphrams made to restrict rotation. But but rereading things that clause doesn't undo the previous devinitions of P restrains requiring lateral restraint.

This ia something else I'll modelling. And see how it compares to L restraints.


Kootk
1) If I understand the symbology correctly, there is still some degree of weak axis rotational restraint at the beam ends.
No. In the last picture showed there is none.

The bottom flanges buckle in opposite directions. That S-shape suggests that this is something other than first mode behavior. This may be related to my next point.
That was the first mode with the seecond buckling in the opposite S shape. Full mode buckling doesn't have to be full lenght. I'll go back an grab pictures of a bunch of modes if that will help.

3) Graphically, it appears that the load may have been applied at a point lower on the cross section than the top flange.
Loaded on the top flange directly above the web.

 

[Tomfh]

In a way, this dovetails into your hypothesis that, in many cases, L-restraints are effectively F-restraints

I don’t believe it. I’m perplexed by the suggestion (and the graph) that L restraints are as good as F restraint.

It’s one thing to treat L as the same for design purposes, but really and truly just as good?

When a beam buckles the cross sections move and rotate. So how can a pin do the same thing as full restraint?

 

[Tomfh]

Question for everyone: Why do the Mastan models predict Kootk's bottom flange buckle, but human's FEM model (and the graphs) predict localised buckling between lateral restraints?

 

[RFreund]

I had to go back an re-read some stuff, but Celt should have received more stars, just saying. It seems like there is a large discrepancy between the two codes for this case. I'm still unclear what the AS4100 says the unbraced length for the negative moment (bottom flange) should be.

Curious how you would defend that position knowing that AISC allows you to use a elastic buckling analysis which accounts for any degree of restraint imaginable.
Does AISC live in a world where if you use the hand method, it's strictly consider LTB between supports (Blue pill).
But if you use a buckling analysis you can consider any imaginable degree of restraint (Red pill).

I should start by saying that it seems like we are both considering the unbraced length correctly in terms of the code. Meaning that the length between column (i.e. 32' in the example) is correct for AISC. For AS4100 it is not that length, it is shorter. However, I still think it has more to do with the definitions of the braced locations.
As far as the Red/Blue pill - the simple response is... kinda, yeah. Meaning if you're doing it by hand you basically assume LTB even though it is constrained axis buckling in this case. If you want to go through a more rigorous approach, nothing is stopping you.
Also thanks for clarifying the definitions.

Normally, with steel joists, the joist connections would not be considered P-braces because the connections between the joist seats and the girders would lack #2 above.

That's a good point. There are actually some tests out there that show there is some, but that is a different discussion for a different day.

Best way to think of it is as follows, just determine if a flange is in compression at the point of restraint and pickup the appropriate restraint. Noting an F restraint to the tension flange can be a P restraint in terms of the compression flange. But other than the designation changing an F & P are the same analytically for determine the effective length.

Top flange restraints
FLLLLLLLF
F-------F
Bottom flange restraints

So this could be:
FLLLLLLLF
FPP---PPF

I have yet to go through the Mastan results, but it sounds like:
Mastan gives you something above AISC equation because AISC is assuming LTB vs Constrained axis buckling.
Mastan gives you elastic buckling lower than what AS4100 gives you.
I might have this wrong...


EIT

http://www.HowToEngineer.com