Why is the maximum sagging moment being used in the LTB checks when I have restrained the top flange?

[BA123]

Hi,

I'm posing this question, as it seems that Tekla Structural Designer is using the maximum moment when checking the LTB of the bottom flange, for a fixed ended beam, this max moment in the section can be a sagging moment (i.e. bottom flange in tension), if it has the greater magnitude.
I would have thought the logical moment to use for checking LTB of the bottom flange is the hogging moment, where the bottom flange is in compression. There is a tekla support article (which can be found by googling my thread title), that references "Annex G for BS 5950 and Section 6.3.2.4 of EN 1993", but I'd like to know why the max moment is used regardless of which flange is in tension/compression and not just "this is the code".

Can anyone explain the reasoning behind this?

Thank you

 

[Tomfh]

Post some screen shots of bending moments diagrams, restraints, etc

 

[Smoulder]

I don't know EN or BS but other codes use factors to adjust for shape of bending moment diagram. 1.0 factor is uniform moment along whole segment. Simply supported beam with UDL is 1.13 because not much better than uniform moment. Midspan point load is 1.35. For your case need to check factor is correct for max sagging > max hogging. Factor should be more than 2.4 I think. But basically answer is what you said. Just how code is written. Use max moment and use consistent adjustment factor. If used max hogging moment (smaller moment) then adjustment factor would be smaller (smaller capacity) but give same utilisation.

 

[human909]

Smoulder. While I can't speak for every code including whichever one that you use... The moment modification factor (or whatever you code calls it), which adjusts for the shape of the moment curve, is not intended to directly address the difference between hogging and sagging moments.

If the answer is indeed "because that is how the code is written" then the code is wrong. The local moment should be checked against the local conditions.

BA123's question seems like a legitimate question. Assuming this is a software/code issue rather than a user error.

(Certainly for AS4100 we check the local moment against local conditions.)

 

[Smoulder]

First, I assumed continuous restraint to top flange because BS5950 Annex G qas referenced and talk about one flange buckling.

@human909 Don't know what local conditions means here. LTB is failure over some length. Codes use single maximum bending moment in my experience plus adjustment factor which is like weighted average. Bending moment far from restraint is weighted more than moment close to restraint. You are correct that adjustment normally doesn't cover sag vs hog because it doesn't matter for discrete restraints. Don't think AS4100 covers case with continuous restraint top flange except yes/no for sagging (no LTB if continuous restraints).

I looked up BS5950 and it uses maximum moment which could be bottom flange tension. Adjustment factor for continuous top flange restraint accounts for whether max moment is sagging or hogging.

You can do it how @BA123 was expecting but factor will be different. Yura does that in "
BUCKLING OF BEAMS WITH INFLECTION POINTS". But I don't think a code would because would need to redefine design moment for special case. I think codes would try to match discrete restraint design like BS5950 did.

 

[human909]

@human909 Don't know what local conditions means here. LTB is failure over some length.

Local means exactly that. If a beam is 20m long and has a high moment in a location where it is well restrained then all is well and good. If it has a high moment where it is unrestrained from LTB then there might be issues.

Specifically when it comes to AS4100 the phrasing used is segments and even sub-segments. The code treats considers the LOCAL restraints and the local moment.

Codes use single maximum bending moment in my experience plus adjustment factor which is like weighted average.

I will plead ignorance here on other codes but using maximum bending moment seems to assess a member in a location well away from the maximum bending moment seems totally perverse. Though if that is how North American codes approach things then that would explain why us Aussies and Europeans are confused.

Bending moment far from restraint is weighted more than moment close to restraint. You are correct that adjustment normally doesn't cover sag vs hog because it doesn't matter for discrete restraints. Don't think AS4100 covers case with continuous restraint top flange except yes/no for sagging (no LTB if continuous restraints).

I'm not sure quite what you are saying here but AS4100 certainly does reject restraints continuous or otherwise of the top flange if they are considered suitable restraints to prevent LTB. To quote 5.5.1 "The critical flange at any cross-section is the flange which in the absence of any restraint at that section would deflect the farther during buckling." There is further detail, but I think that quote is enough. Top flange restraint is ignored in areas of hogging moment.


I'm happy to discuss more. Eng-Tips has had some very lively discussions on LTB and the way various codes address it.

 

[Smoulder]

@human909 I am in Australia now so know AS4100 best but sometimes use other codes. I don't think there is massive disagreement, we just meant different things by local. E.g. if 20m beam is one segment with max moment at support (restraint point) you still check using max moment even if can't move there. Alpha_m will be >>1.0 to account for lower moment where movement actually happens. If 4 segments then each is 5m. You called that local but I called it "over some length". We're talking about same thing though. At least I think.

A huge discussion here gets mentioned sometimes and I've skimmed it. Think that's what you meant by lively discussions. Also think it found blind spots in AS4100 with lateral restraints on one flange and reverse curvature. Look at BS5950 Appendix G and Yura' article. They're downloadable. Situations that aren't covered by AS4100 except using buckling analysis.

 

[Smoulder]

"I'm not sure quite what you are saying here but AS4100 certainly does reject restraints continuous or otherwise of the top flange if they are considered suitable restraints to prevent LTB. To quote 5.5.1 "The critical flange at any cross-section is the flange which in the absence of any restraint at that section would deflect the farther during buckling." There is further detail, but I think that quote is enough. Top flange restraint is ignored in areas of hogging moment."


Forgot to respond to this. Agree that sag/hog and location of restraint is used to break beam into segments and for effective length. But alpha_m specifically doesn't care whether hog/sag for discrete restraints.

 

[HTURKAK]

that references "Annex G for BS 5950 and Section 6.3.2.4 of EN 1993", but I'd like to know why the max moment is used regardless of which flange is in tension/compression and not just "this is the code".

I have BS 5950-1 2000. AFAIK , BS 5950 addresses the use of m-factor method .In your case there since there is loading
between the restraints, it is necessary to calculate mLT ( equivalent uniform moment factor ) Pls look 4.3.6.6 ,Table 18.

 

[BA123]

Thanks all, just for clarification I have a beam with fully restrained top flange, unrestrained bottom flange.
The beam is fixed ended, and so goes into hogging.

I am using Tekla Structural Designer, and there is an article here which gives some more explanation https://support.tekla.com/article/w...-in-the-ltb-checks-when-i-have-restrained-the
I was hoping there was some further logic as to why the maximum moment is used to check for LTB of the bottom flange, when the maximum moment could occur where the bottom flange is in tension.
You can see this in the screenshots.



I can't wrap my head around why the hogging moment isn't used for the LTB of the bottom flange (i.e. when it's in max compression).
If for example the maximum hogging moment was 0.0001kNm (e.g. a tiny bit of fixity at beam ends) then the beam bottom flange would still fail in LTB using this approach, which is clearly a nonsense.

Thank you

 

[BA123]

To further demonstrate my point, I've changed the fixity at the ends to reduce the hogging moment to something nominal (circa 1kNm):


and as expected I'm getting massive failure in the bottom flange, as now it's using the max moment of 490kNm in the LTB check for the bottom flange...



Is this incorrect or am I missing something?

 

[Tomfh]

Your model assumes the entire beam length as the lateral torsional buckling (LTB) length—are you certain the beam is completely unrestrained along its full span?

In this case, the “local” zone, or segments, or whatver you want to call it, is the entire beam, that being the unrestrained length. Buckling design is governed by the worst-case moment in that zone, be it positive or negative. If there are truly no restraints along the beam, then the sagging moment will control the design.

 

[Smoulder]

Not sure if Tekla is considering top flange restraint. Euro code reference should be Appendix BB and not 6.3.2.1? Regardless I reckon result would be wrong for case with -1.0kNm end moments. You have made situation very slightly different to simply supported. Might get passing result (not sure) but capacity would be conservative. Engineering judgement would be applying simply supported provisions like I think you're saying. So continuous restrained and capacity equals section capacity.

Happens because LTB is hard to write simple rules for. Too many variables. Rules try to cover common cases but might be conservative or unconservative (hopefully not) for uncommon cases. Like I said before I dont think AS4100 covers this case except using buckling analysis. BS and Euro codes give some rules but don't go as far as very small hogging moment. Then on top you have software applying rules with no judgement filter anymore. Still part of job to detect issues like this one and decide whether worth doing more analysis, making judgement call or increasing beam size. Know you didn't want this answer but it is just that code says to do it that way unless you do more advanced analysis.

 

[Tomfh]

Like I said before I dont think AS4100 covers this case except using buckling analysis.

What do you mean by this?

 

[Agent Coconut]

Your model assumes the entire beam length as the lateral torsional buckling (LTB) length—are you certain the beam is completely unrestrained along its full span?

In this case, the “local” zone, or segments, or whatver you want to call it, is the entire beam, that being the unrestrained length. Buckling design is governed by the worst-case moment in that zone, be it positive or negative. If there are truly no restraints along the beam, then the sagging moment will control the design.

I was about to says this and already found someone saw the same thing.
Based on the calculation, your beam length is 7793mm but lateral length is the same.
That's mean you defined your beam is retrained but Tekla do not capture it.

Your another question: "why the maximum moment is used to check for LTB of the bottom flange, when the maximum moment could occur where the bottom flange is in tension."
No you get it wrong, this maximum moment occurred at one particular section, where due to this moment, it will have compression at top and tension at bottom in that particular section(for this sagging moment) which I believe you are understand the concept already. It doesn't mean it solely used to calculate LTB of the bottom flange only
But since Tekla calculation shows there Length of LTB is still your full span, hence, LTB still occurred at top flange of your center of beam.

 

[Smoulder]

@Tomfh Continuous restraint of one flange but with compression for part of opposite flange. AS4100 calls it either full lateral restraint or unrestrained. Compare with US and British/Europe literature which give design rules. Personallt I think AS4100 assumed simply supported so unconservative in cases that qualify as full restraint but others have design rules.

 

[Tomfh]

Yes AS4100 considers it either lateral restraint or no restraint depending on which flange is critical. But why wouldn’t that work in this case? Once you’re in the sagging zone, lateral restraint on the top flange set your effective length. How do you end up with this odd situation where effective length = full beam length, unless there are indeed no restraints at all?

 

[Smoulder]

Are you saying you take segment length as length in hogging moment? I don't think that's right. Maybe close enough since will follow trend but not sure good enough for critical designs.

 

[Tomfh]

Assuming we are talking about the segment at the start of the beam, that segment length is the length from the start of beam, to the first restraint within the sagging zone, assuming we are following the common convention of taking the compression flange as the critical flange.