Single Angle in Bending Unbraced Length

[Serhiy2]

Good day,

I'm dealing with a situation where I have cantilevering single angle supporting a point load at the cantilever end. The angle is oriented in such a way that the toe of the angle pointing in the same direction as the point load and is in compression. The angle is anchored to concrete wall with two anchors. Attached is the sketch which should help to understand the setup.

I'm trying to analyze lateral-torsional buckling moment using the F10.2 (2) of AISC 360-16 and it has the unbraced length term Lb. There is no explanation on what this Lb is other than the general explanation it being the distance between the lateral supports. The way I intend to connect the angle to the wall leaves the angle toe in compression technically unbraced at all. I'm looking for some advice as to what I should be using for Lb in my situation. Thanks

 

[shacked]

I would think that the unbraced length is the 350 dimension. Have you ran the numbers using that dimension for the angle size you want to use?

 

[Harbringer]

Use your judgement, if you think that the leg is unbraced check it as such. If your loading is actually buckling an unbraced L4x4x3/8 you probably to revise this detail to include a brace up to a roof or floor diaphragm. Can the wall actually resist the out of plane moment you are adding? Also your edge distance seems quite small (I'm assuming the dimensions are in mm).

 

[milkshakelake]

I'd use 450 mm for the lower part and 1350mm for the upper part. I would consider those bolts to be bracing it, even if one flange is technically unbraced. It's a bit wishy-washy and based more on judgment than code. If you're going the route of using the lower part unbraced length only, I disagree that it should be 350mm because the cantilever is 450mm.

By the way, I'd consider the bending to be around the geometric axis, not x or y axis. If you were to use a double angle, I'd use x axis. But that's also up to engineering judgment.

 

[dik]

The 450 length is the one that's most likely to twist...

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[SWComposites]

I disagree, the critical length is longer than 450 mm. The max bending moment is ~ at the first fastener (450 mm dimension), so the max compression stress at the outer fiber of the upstanding angle leg is at the 450 mm location, but the stress decays past that point for some distance. And it is the area where compression stress is significant where there is a potential for instability. So, I would use an unsupported length, Lb, of 450 mm + 3 * (leg height), where the "3" value is an eye ball "guess-timate" of the length that will have compression stress in the leg. Or you could build a FEM of this detail and run a buckling analysis.

 

[BAretired]

By definition, the unbraced length is 1350 with a moment varying from 0 to 450F.

 

[dik]

but that's not likely where the failure will occur.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[canwesteng]

Doesn't the angle have two toes? Which one is in compression? In any case, members are supposed to be rotationally restrained at supports, in which case you have one unbraced length of 1.35m to check, and one unbraced cantilever of 450 to check. Neither case has an Lu of 450

 

[BAretired]

but that's not likely where the failure will occur.

We don't know that...the 4x4x3/8 angle seems to be bearing tight against a concrete wall. If the back span is very short because the wall prevents its deflection, perhaps the bottom anchor pulls out. It is a terrible detail and should not be used for any serious value of force F.

If a separator is used between the wall and the angle at each anchor, such that the angle is free to deflect between anchors, I believe that the most critical span of the angle is the 1350mm back span.

Either way, it looks like a potential problem if force F is large.

 

[driftLimiter]

If you get some room for the angle to deflect like BAretired is saying then you really have two spans to check.

Lb is the maximum unbraced length at some location of interest on the beam. Your moment capacity may be higher in one location along a span than another so you check the capacity at each location vs the moment demand at each location.

Normally it isn't too hard to find the worst location, in this case maximum moment occurs at the lower support, but that support is shared by the adjacent spans, so one can determine the controlling span by inspecting the LTB equations as a function of Lb (higher Lb means lower capacity).

 

[milkshakelake]

I agree that there seem to be bigger issues than the angle buckling. Either way, even if the angle has two legs, the bending will be about the geometric axis so there wouldn't be two different unbraced lengths for each leg.

 

[dik]

That's the 'kicker' right there. With the cantilever, the unsupported length of the angle would be approx 2x the cantilever length or 900mm and failure would likely be a lateral torsional buckling mode of this element, I suspect. I also suspect this loading effect would be much more critical than the section secured with the two bolts.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[human909]

That would be my starting point for hand analysis. But I'd also consider the original point that the compression leg isn't actually fully restrained at the support.

So potentially it could be worse. However both because of the thickness of the angle and due to what is effectively continues twist restrain of the tension I would not be surprised if the section at the bolt and beyond behaves like a continuous twist restraint. (This twist restraint could play a significant role in reduce the effective length to less than 900mm.)

I think this calls for some quick Nastran analysis.

 

[dik]

Not fully restrained, but somewhat restrained against rotation... like a 'stubby post' fixed at the bottom.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[PMR06]

What magnitude load is "F"?

L4x4x3/8 w/ ~18" cantilever, (1) anchor bolt @ ~4" edge distance... my guess is the latter may govern before the angle bending anyway

 

[human909]

What magnitude load is "F"?

L4x4x3/8 w/ ~18" cantilever, (1) anchor bolt @ ~4" edge distance... my guess is the latter may govern before the angle bending anyway

True. Not to mention that I believe yielding will govern before LTB.

But the academic question still remains and has piqued my interest. I'm keen to explore more if I can make time to do a suitably thorough analysis. (I did a little bit of computational buckling analysis following my previous post but then got distracted and I have a busy week ahead so I won't promise that I'll do any more than conjecture....)

 

[Tomfh]

Buckling length is 450.

The angle will be stiff enough at the support to act as a restraint; the plate slenderness is around 9 which is fairly stocky.

Buckling aside, unrestrained angles have a nasty tendency to twist into their weak axis as they bend about a strong axis.

 

[dik]

Sorry Tom... I disagree... if you were to change the second fastener distance to 450, you would have identical buckling distances of 450, with the same bending moment diagrams. The two conditions are dramatically different. Have a re-think...

It could be that yielding may be the failure mode... off the top I would have thought with the weakness of the angle in torsion that it would have been a torsional buckling.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[Tomfh]

What are you disagreeing with specifically? Reading your posts I thought you agreed the 450 cantilever is critical?