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.

 

[Tomfh]

NASTRAN: 0.753 (PLP) (No minor axis or flange restraint at ends, no twist restraint at lateral brace)

What about FLF? Similar?

 

[Tomfh]

though AS4100 doesn't explicitly take this into account

Isn't this the kr factor?

An unrestrained minor axis is unrealistic in a single span scenario

Why?

 

[human909]

What about FLP? Similar?

Full twist restraint at one end would make some difference. But each scenario would be different.

Isn't this the kr factor?

No the kr factor is dealing with rotation around the Z-axis of the beam. The flange restrains F,P,L,U etc are all to do with z-axis rotation. y-axis rotation is different and may or may not be restrained by z-axis restraints. LTB by nature is focused on z-axis.

An unrestrained minor axis is unrealistic in a single span scenario
Why?

Most moment conections offer rigidity in the x-axis and the y-axis. It would moment connection in the x-axis and pinned in the y-axis is fairly contrived unless it is representing a continuous beam.

 

[Tomfh]

Full twist restraint at one end would make some difference. But each scenario would be different.

Sorry that was a typo. I meant FLF. I.e. fixed both ends.

No the kr factor is dealing with rotation around the Z-axis of the beam

Z-axis being parallel with the beam? I thought kr concerned rotation around beam weak axis?

It would moment connection in the x-axis and pinned in the y-axis is fairly contrived unless it is representing a continuous beam.

Hmm. I'm not sure I agree with that. How can you assume the y-axis to be a fixed connection? What about a simply suppported beam spanning between two columns, connected by cleat? There is no lateral rotational restraint at the ends.

Likewise with continuous beam, each span can buckle in opposite directions, which is the same effective length as a single span.

 

[human909]

I thought kr concerned rotation around beam weak axis?

No. As per the code, the restraints flange restrains F,P,L,U etc are all to do with z-axis rotation and thus so is kr. z-axis being parellel with the beam. (x-axis being major axis, y-axis being minor axis)

Hmm. I'm not sure I agree with that. How can you assume the y-axis to be a fixed connection?

I'm not assuming y-axis to be fixed. I'm simply saying that for a END connection when X is fixed, y is normally fixed too. Though of course I could contrive a vertical pin that fixes x-axis and pins y-axis.

What about a simply suppported beam spanning between two columns, connected by cleat?

That isn't a moment connection in the x-axis.

connected by cleat? There is no lateral rotational restraint at the ends.

A cleat connection does provide partial lateral rotational restraint.

Likewise with continuous beam, each span can buckle in opposite directions, which is the same effective length as a single span.

Yep which is why I have said a continuous beam is often effectively pinned along y-axis and behaves like a moment connection at the x-axis.

 

[Tomfh]

My understanding of kr factor is that it represents minor axis (y-axis) fixity at supports, as this reduces the effective lateral bracing length, similar to a fixed ended column having a reduced effective height.

You appear to be saying kr concerns z-axis rotational fixity?

 

[human909]

My understanding of kr factor is that it represents minor axis (y-axis) fixity at supports, as this reduces the effective lateral bracing length, similar to a fixed ended column having a reduced effective height.

It specifically says rotation, aka twist rotation as defined earlier regarding a rotation of the cross section (aka the z plane, perpendicular to the z-axis) F,P,L,U are undefined regarding y-axis restraint, they are only defined in terms or z-axis fixity.

You appear to be saying kr concerns z-axis rotational fixity?

That is precisely what I'm saying. Look at the definitions in AS4100 regarding the restraints. They are all defined as cross sections of the beam. These restraints just deal with the 'T' for torsion in LTB. Even if restraints in the y-axis make a significant difference, they are largely not considered.

 

[Settingsun]

K_r is as Tomfh is saying. Figure 5.4.2.3 is clear about what 'lateral rotation' means.

 

[Settingsun]

EG: 46m 610UB101 with single lateral brace at the top flange in the centre
LOAD FACTORS:
AS4100: 1.01 (PLP & FLF)
NASTRAN: 0.753 (PLP) (No minor axis or flange restraint at ends, no twist restraint at lateral brace)
NASTRAN: 0.757 (PLP) (No minor axis or flange restraint at ends, twist restraint at lateral brace)
NASTRAN: 2.59 (FLF) (Full end restraint, twist restraint at lateral brace)

In the second and third cases (Nastran with 0.75x factor), do the end restraints consist of lateral and twist restraint both acting at the centroid?

In the third and fourth cases, the lateral brace also has twist restraint. Wouldn't this make an F restraint at midspan?

I don't think the fourth case is apples:apples to what you called AS4100 FLF in the first case. The fourth case sounds like FF with k_r<1.0, probably k_r~0.7 if an ideal rigid restraint has been modelled.

[Ignore the box below. There's not meant to be any attachment.]

 

[human909]

Sorry Tomfh. Thanks steveh49 for hitting me over the head with the truth.

 

[human909]

In the second and third cases (Nastran with 0.75x factor), do the end restraints consist of lateral and twist restraint both acting at the centroid?

The end restraints are lateral restrains in X,Y,Z axis at the web. It rotational restrain in the X-axis only. Not full flange restraint hence a P restraint.

In the third and fourth cases, the lateral brace also has twist restraint. Wouldn't this make an F restraint at midspan?

Good point. The lateral brace was at the flange edge only. So I would say no, but I can see the point being argued.
"....may be considered to be laterally restrained when the restraint effectively prevents lateral deflection of the critical flange (see Clause 5.5) but is ineffective in preventing twist rotation of the section"
(The twist restraint was at the lateral brace on the flange edge. It did not provide effectict twist restraint to the section.

I don't think this is apples:apples to what you called AS4100 FLF in the first case. This sounds like FF with k_r<1.0, probably k_r~0.7 if an ideal rigid restraint has been modelled.

Only in the last one 2.59 would have kr<1.0. The rest would be kr=1.0. So yes for the last one it isn't apples:apples.

What about FLF? Similar?

Yep. FLF is almost the same as PLP in the model examined earlier. 1.5% difference, when you lack the minor axis rotation constraint.
(Sorry again it too so long to slap me with the facts for me to get that point you were making about the kr factor.)

 

[Tomfh]

In the third and fourth cases, the lateral brace also has twist restraint. Wouldn't this make an F restraint at midspan?

Agree. If the brace provides twist restraint and is attached to top flange then it qualifies as F restraint. Figure 5.4.2.1 (b) Critical Flange restraint, Partial Twist restraint.

L restraint should be a pinned connection to the critical flange.

 

[human909]

Dammit! Tomfh and Steveh49. Could you please stop proving me wrong and making me look bad! [sub](But thanks, being corrected is learning.)[/sub] I got halfway through my rebuttal until I realise that my investigation disproved my own arguments. What I was going to say was:

The written requirement is to meet a F is to "effectively prevents twist rotation" or "partially prevents twist rotation". These are qualitative requirements and aren't quantative. So it is perfectly valid for us to have different interpretations on this qualitative requirement.

My assessment is that a twist restrain on the tip on the flange in my view does not 'partially prevent twist rotation'. OOPS! However, my own FEA modelling suggest that I am incorrect. Buckling of the cross section at the restrain switches for torsional to minor axis rotation.

 

[Tomfh]

So what are the revised numbers when you release the twist restraint at the lateral brace?

 

[human909]

As per previously stated:
NASTRAN: 0.753 (PLP) (No minor axis or flange restraint at ends, no twist restraint at lateral brace)
NASTRAN: 0.757 (PLP) (No minor axis or flange restraint at ends, twist restraint at lateral brace)

 

[Tomfh]

Is there a result for FLF, no minor axis restraint, no twist restrint at lateral brace?

 

[Tomfh]

Does anyone feel the Mastan results are unreliable? E.g. that they are underestimating the true theoretical buckling loads?

 

[KootK]

Does anyone feel the Mastan results are unreliable? E.g. that they are underestimating the true theoretical buckling loads?

1) I would have liked to have seen much better agreement between the Mastan prediction and the Nastran prediction. That concerns me. Similar buckled shapes is useful but being off by 100% is troublesome. Over the holidays, I may attempt to replicate Human909's work in a student edition of Nastran. Or I may not. Kinda depending on how onerous the install is on my virtual machine and how good the skiing is.

2) I do not presently have the wherewithal to verify Mastan's output for our test case by hand. My academic training in FEM was extensive but did not venture into the development of the kind of warping torsion endowed line elements that Mastan uses. The fellow that authored the software also authored a companion book that is freely available however. Over the holidays, I may also attempt to see if I can find out a bit more about that.

3) In the quoted statement below, I described how I actually feel that something like Mastan is a more appropriate tool than something like plate/shell element FEM for determining theoretical buckling loads. I acknowledge, however, that more sophisticated FEM, properly used, is surely the better tool for predicting real world behavior, particularly outside of the elastic range.

4) The authors of Mastan developed it specifically for the purpose of exploring stability problems as they relate to modern code provisions and stability theory. As Agent666 mentioned on several occasions, and via some interesting graphs, Mastan has been shown to be spot on in its theoretical buckling predictions for a lot of common situations, none of which are our exact situation to my knowledge. Our situation isn't really that exotic and I've no doubt that it's been played with extensively in the past. I just don't personally know where to find any examples of it.

5) Celt83 prompted an investigation earlier where we compared Mastan results to hand calculations run using Yura's proposed Cb values that were developed for beams with the same disposition of bending moments and accounting for the beneficial effect of the L-restraints. We had to modify the loading condition to approximate a uniform load rather than a point load, however, as Yura didn't have anything for a point load. I would consider Yura's method to yield something close to a theoretically correct result for the situation that I described. The Mastan number came out at 93% of the Yura value which I consider to be very close, particularly given that the uniform load had to be approximated as 7 point loads owing to Mastan limitations.

6) A good program's only as good as the person wielding it of course. It was always my hope that Agent666 would be scrutinizing my work but, by and large, I don't believe that things panned out that way. So my work has gone largely unvetted I'm afraid. If anybody else feels like taking up the mantle with Mastan and doing some QC on my work, I would absolutely welcome that. I've posted all of my models and would be happy to post them again. That said, somebody else starting from scratch might make for a more meaningful QC check.

7) I have always been concerned about how little I/we know about the character of the Nastran modelling. In my past experiences messing with full blown FEM software (ANSYS, ABAQUS, etc) there have always been gobs of user selected pre-processing and post-processing variable involved that drastically affected the results. And I don't know what any of those are here. Moreover, my attempts to tease that information out of Human909 have gone very badly, leading to accusations that my requests are superfluous and that I've not been carrying my share of the load when it comes to research effort. More concerning, my queries have led to Human909 withdrawing from the conversation in frustration which is not healthy for either Human909 or the discussion. So I'll not be going back to that well again.

In my opinion, Mastan is actually a better tool than full blown FEM for what we've been trying to do in this thread. Full blown FEM surely is a more accurate representation of reality but, I would argue, reality isn't really what were trying to parse out here. Instead, it seems to me that we're mostly trying to reconcile code provisions with the underlying LTB theory that informed them. And that underlying theory was linear elastic bifurcation buckling, just what we've been doing with Mastan but with a slightly higher degree of sophistication. In this respect, I feel that full blown FEM kind of "overshoots" things in making direct comparisons to code provisions less meaningful. That said, it is of great value here to be able to use Nastran to corroborate the modes shapes and capacities predicted by Mastan. Were Nastran mode shapes wildy different that the Mastan modes shapes then I would definitely be concerned.

 

[Tomfh]

I tend to agree.

I suspect the Mastan is doing more or less the right thing, but I’m not entirely convinced, as it’s a bit black boxy.

What I’d really like to see is experimental bucking results of laterally restrained beams subject to moment reversals. I want to see what the beams actually do in t

 

[KootK]

What I’d really like to see is experimental bucking results of laterally restrained beams subject to moment reversals. I want to see what the beams actually do...

Ditto. That would be the very best form of corroboration. In my travels, however, I've often found it shocking how much has been extrapolated from relatively small amounts of testing on, often, relatively small specimens. I'm sure that the statisticians have all of the similitudes and confidence intervals sorted to the nuts but I'll not be holding my breath lying in wait for a sexy set of moment reversal LTB testing with L-bracing. I'll be first in line to offer a star and some radar love to the first person to post some though.