Suspended Continuous Beam Unbraced Length Question (Yes I know...another one)

[polskadan]

Alright Ladies and Gents,

I've looked through just about all the old unbraced length threads and yet I still feel someone unsatisfied. I was hoping that I could get some opinions from some of the people here on this board. I am also familiar with what AISC says on inflection points as well as Yura's take on unbraced lengths.

I have a situation where I will be having a monorail that is suspended by cables at every 10' in length. This monorail is continuous for lets say 60' in length (moment developed at splice locations). The connection to the cables that are located at every 10' will simply be a lug with shackle attachment and thus provide no lateral restraint in any direction. Their will be a trolley hoist that rides along the bottom of the monorail. So my question is...What is the unbraced length of both the top flange and bottom flange?

I feel like using the full unbraced length of 60' for both flanges and then applying a Cb factor isn't appropriate for this scenario and likewise blows any W-beam monorail scenario out of the water. After reading through some AISC modern steel q&a's it seems like AISC alludes to using the longest distance between supports for the unbraced length of the negative flange.

Let's look at even a regular pin supported beam where a top flange is unrestrained. If there was a continuous beam that went on for infinity distance, had supports at 10' O.C., and the top flange was unrestrained for the infinity distance, then the old answer of take the full unbraced length & use a Cb factor can't apply.

I have my own engineering judgement of ignoring Cb in its entirety and using the longest unbraced span/distance between inflection points as my unbraced length for this scenario however I would really appreciate some opinions from the ol' engtips community.

Thank you all in advance and hope you all have a great memorial day weekend!

 

[KootK]

The use of inflection points as bracing has been out of vogue for a while. It just doesn't check out theoretically.

Without any rotational support along the length of your beam, your unbraced length isn't just 60', it's infinity.

The only rotational restraint that your beam has is the fact that the loads are applied to the bottom while the supports are applied to the top. In summary, my answer is that your un-braced length is 10' but you have to find some way to demonstrate that you've got torsional restraint at each 10' o/c support.

In the interest of improving torsional restraint at each of the hangers, I would be tempted to weld some 2' long channels to the top of your beam and then attach your cables to those. That will greatly increase the amount of torsional restraint available.



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[BAretired]

I think KootK put his finger on a very important point. The beam is loaded from the bottom and suspended from the top. If only one span is loaded, I believe that the unbraced length of the loaded span is 10'. For the unloaded spans, it is not possible to determine the unbraced length without some knowledge of the moment diagram.

BA

 

[polskadan]

I appreciate the quick responses and tend to agree with what both of you are saying. Would you also treat the example of a continuous beam with pinned supports the same way?

Imagine a beam with infinty length and with pinned supports to the bottom flange at every 10'. The bottom flange unbraced length is 10' however the top flange unbraced length is infinity due to being contuous....It is hard for me to believe that I really need to use infinity for the top flange unbraced length as AISC would suggest. What would you take the unbraced length of the top flange to be in this example?

 

[BAretired]

If the supports are truly pinned such that there is no torsional restraint, and if the beam is loaded on top of the top flange, the beam is unstable by inspection. The whole thing can simply rotate about all of the pins. As a minimum you would need to provide torsional restraint at two supports and preferably at every support. If you did the latter, the unbraced length would be 10'.

BA

 

[KootK]

In your original scenario, assuming that you achieve rotational restraint at the cables, I think that you effectively just have a bunch of 10' simple span beams. The cables will be incapable of tying the beam down and restraining uplift. Your only continuity will come from the beam self weight.

I think that your distinction between top flange and bottom flange bracing may be leading you astray. When it comes to LTB, there's only one kind of bracing that is relevant: rotational/side sway restraint bracing. Sometimes that is best achieved through top flange bracing. Sometimes it is best achieve through bottom flange bracing. Sometimes, such as at supports, both are required.

No matter what, you won't ever have separate unbraced lengths for the two flanges. Rather, you'll simply have a single unbraced length that applies between points of rotational/sway restraint.


I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[XR250]

@Kootk;

If what you are saying is true, wouldn't all crane spreader bars be failing?

 

[polskadan]

@Kootk

I disagree with your last post 100%. AISC has stated previously that there is a difference between bracing of flanges. There are even well known distances from either flange that a member shall fall within to be consider bracing that flange for LTB. Sure some people will consider both flanges braced for LTB when you also add a stiffener at a brace point of one flange but this doesn't also mean that at any given situation both flanges are braced for LTB given that you brace only one flange. Think about deep roof girders...why do you think we add kickers that tie to the bottom flange? We want to brace the bottom flange for LTB given an uplift condition (and still have am economical shape at that). Most analysis programs also have separate inputs for bracing of top flange and bottom flange for this reason (RISA provides good illustrations about what it considers rules of thumb for bracing of flanges are).

 

[SAIL3]

looking at it from a loading point of view......if the total length of the bm is only supported/hung by cables @ 10' spacing, then there is no moment in the bm beyond the span where the the load is present and based on that I would use 10' as the unbraced length...it's basically a 10ft bm pinned @ each end..the remaining length of the bm just goes along for the ride....

 

[BAretired]

looking at it from a loading point of view......if the total length of the bm is only supported/hung by cables @ 10' spacing, then there is no moment in the bm beyond the span where the the load is present and based on that I would use 10' as the unbraced length...it's basically a 10ft bm pinned @ each end..the remaining length of the bm just goes along for the ride....

I don't agree that the rest of the beam goes along for the ride. Suppose the beam weighs w #/' and the only load on the system is a concentrated load of P at mid-span of the third span. Outside the loaded span, there is a 20' cantilever at one end and a 30' cantilever at the other.

The simple span moment in the third span is PL/4 + wL[sup]2[/sup]/8. The Fixed End Moment is PL/8 + wL[sup]2[/sup]/12 at each support.

The cantilever moment is w(2L)[sup]2[/sup]/2 at one end and w(3L)[sup]2[/sup]/2 at the other. If the cantilever moment is less than the loaded beam's FEM, then the cantilever may fail in lateral torsional buckling. The cable supports cannot resist compression hence cannot provide a downward reaction.

BA

 

[KootK]

If what you are saying is true, wouldn't all crane spreader bars be failing?

Rigging isn't really my domain of expertise but I see three common possibilities.

1) some spreader beams are loaded only axially. No LTB issues.

2) some transversely loaded spreader beams are designed such that they are loaded weak axis or Ix = Iy. Again, no LTB issues.

3) for spreader beams loaded transversely about their strong axes, end rotational restraint is provide by the load and supports being on opposite sides of the beam as I have described above for the OP's interesting case.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[MikeHalloran]

Am I understanding that your long monorail beam will be suspended by a single vertical cable every ten feet?

If so, that could have some interesting dynamics, when:

- somebody drags the hook laterally to lift a load that's not directly under the beam.

- the trolley is moving fast when it hits an end stop.

You might want to specify some flexibility in associated electrical connections to the beam.





Mike Halloran
Pembroke Pines, FL, USA

 

[KootK]

@polskadan: for good measure, please read my signature at the bottom before continuing.

AISC has stated previously that there is a difference between bracing of flanges.

Yes. That is precisely what I meant by this statement:

Sometimes that (LTB rotational bracing) is best achieved through top flange bracing. Sometimes it is best achieve through bottom flange bracing. Sometimes, such as at supports, both are required.

.

Sure some people will consider both flanges braced for LTB when you also add a stiffener at a brace point of one flange but this doesn't also mean that at any given situation both flanges are braced for LTB given that you brace only one flange.

It's a bit misleading when when we talk of "bracing flanges" in the context of LTB. Flanges don't need to be braced per se because LTB has nothing to do with flange buckling. Rather, we restrain flanges as a means of rotationally bracing entire beam sections against rotation about a fixed point in space.

This is why, whenever LTB equations are derived in textbooks, you see sketches like the one shown below. Lateral torsional buckling has absolutely nothing to do with flange buckling. They are two entirely separate phenomenon. As an interesting example, consider cantilever beams. Cantilever beams are best braced against LTB by restraining the tension flange.

Think about deep roof girders...why do you think we add kickers that tie to the bottom flange? We want to brace the bottom flange for LTB given an uplift condition

We add kickers in this scenario to create discrete points of rotational beam restraint. That rotational restraint is developed by preventing translation of the top flange via the roof deck / OWSJ and preventing the translation of the bottom flange via the kickers that you mentioned. All of this is completely consistent with the definition of LTB unbraced length that I outlined previously.

Most analysis programs also have separate inputs for bracing of top flange and bottom flange for this reason (RISA provides good illustrations about what it considers rules of thumb for bracing of flanges are).

Of course our programs have separate input for the top and bottom flanges. We -- and our software -- need to know at what locations the top and bottom flanges are prevented from lateral translation so that we can answer the more important question for LTB: at what locations can we consider our beams to be braced against whole section rotation about a fixed point in space.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[polskadan]

@KootK, again I must disagree, "LTB has nothing to do with flange buckling"?

Then why do we consider the radius of gyration of the flanges when considering strength w.r.t. LTB? I feel like with the advent of the 13th and 14th AISC editions & imperial design we may have strayed a little too far off of the path of true mathematics and understanding how the equations were originally derived...I.E. AISC 9th editions and previous.

 

[KootK]

Then why do we consider the radius of gyration of the flanges when considering strength w.r.t. LTB?

We don't really. r_ts can just conservatively be approximated that way. The real definition of r_ts is dependent on I_y, C_w, and S_x. An each of those is a whole section parameter. Granted the resistance to twist in a wide flange beam is dominated by the contribution of the flanges.

I attended AISC's stability night school cause this spring. One of the more interesting bits was an exercise where we modelled beams using initial imperfections and non-linear line element analysis to predict LTB with astonishing accuracy. Because we were using line elements rather than shells etc, the software really had no "awareness" of the flanges other than indirectly, via I_y and C_w.



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[MacGruber22]

To reiterate and affirm some of what KootK has said:

The compression flange need not be restrained to resist LTB. You only need a torsional lever arm long enough, combined with bracing strength and stiffness, to resist the LTB effect. The lever arm of the LTB bracing can usually be achieved by a depth within the web area.

There are numerous possible sections with compact flanges and a large ratio of Ixx/Iyy that will exhibit LTB beyond a given unbraced length. Compact flanges will not exhibit local buckling. Therefore, LTB does not depend on the local buckling of the compression flange.

"It is imperative Cunth doesn't get his hands on those codes."