Normal Stress in orthogonal Directions
Normal Stress in orthogonal Directions
(OP)
I have a case where there is a balcony which is supported from cantilevered steel floor beams. The floor beams tos are flush with their supporting girder steel beams. To provide continuity for the floor beams the flanges are CJP welded to the steel girder.
The top flange of the girder is in compression at the intersection with the floor beam (mid simple span). The top flange of the cantilevering floor beam is in tension.
I'm assuming I cannot have both the girder and floor beam both be at full capacity at the same location, and I can use Mohr's circle to understand what stresses are in the beam, but I'm not sure if there are any interaction provisions our design methods prescribed by AISC.
Any thoughts? Thanks in advance.

Edit: Here's the plan view.

The top flange of the girder is in compression at the intersection with the floor beam (mid simple span). The top flange of the cantilevering floor beam is in tension.
I'm assuming I cannot have both the girder and floor beam both be at full capacity at the same location, and I can use Mohr's circle to understand what stresses are in the beam, but I'm not sure if there are any interaction provisions our design methods prescribed by AISC.
Any thoughts? Thanks in advance.

Edit: Here's the plan view.







RE: Normal Stress in orthogonal Directions
Dik
RE: Normal Stress in orthogonal Directions
Edit: Specifically the top chord of the girder at that intersection. If it is at it's maximum compessive capacity in compression from the Girder, does that limit the amount of tension in the direction parallel to the floor beam.
For example, say it's 50 ksi material. If have it be in 45 ksi (0.9 * 50) compression, what is the maximum transverse tension that it could be in?
If I were to do this based on my own understanding of the mechanics, I'd find the maximum tension that will cause shear failure from Mohr's circle. Say it fails at 0.9*(0.6*50 ksi)=27 ksi. This would occur at only 9 ksi in transverse tension [45 - (-9) ] / 2 = 27 ksi.
RE: Normal Stress in orthogonal Directions
why is the floor beam hogging while the cantilever is sagging ? isn't the down load applied to the floor, collected by the floor beam and given to the cantilever support beam ?
"The top flange of the girder is in compression at the intersection with the floor beam (mid simple span)." ok, but the sketch shows the cap of the floor beam is cut by the cantilever; so the cantilever is not mid-span, but between two short spans.
I'd consider your floor beams as short spans between the cantilevers, applying shear to the cantilevers.
another day in paradise, or is paradise one day closer ?
RE: Normal Stress in orthogonal Directions
Hopefully the plan view helps
RE: Normal Stress in orthogonal Directions
RE: Normal Stress in orthogonal Directions
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The name is a long story -- just call me Lo.
RE: Normal Stress in orthogonal Directions
You will have a stress condition which is tough to justify, with that detail, if all the members can be at their max. stress at the same time. You will have some high principle stress conditions, two very high normal stress fields, both in the plane of the flgs.. If you were to run that framing system and detail through some FEA software, you would end up with a big red blotch in the immediate area of the intersection of the flanges and the ‘k’ areas of the members. Without knowing much more about the whole situation, loading conditions, member sizes, dimensions, why the top of beams must be the same elev., etc., etc. You guys just don’t seem to get it, but this type of info. helps experienced engineers get some early feeling for the magnitude of the problem. Why keep it a secret? Can you increase the size of the girder and beam, at least at the center beam line? Can you put a cover pl. over, but not welded to, the girder, which reduces the canti. flg. stresses and carries part of the moment over the girder? Can you lower that girder by a few inches, so the canti. flg. can pass over it? Can you change to two canti. and back span beam lines (not three) so that concentrated load and nasty crossed flgs. detial doesn’t occur at the middle of the girder? Can you put cover pls. on the girder flgs. to significantly reduce those flg. stresses? Then, finally, those crossed flg. details are a real bitch to weld (CJP or otherwise) without ending up with a really awful weld termination condition at the edges of the canti. and back span flgs., which also happen to be a reentrant corners.
RE: Normal Stress in orthogonal Directions
If 45 ksi is your design capacity, I'd be very cautious about having any tensile stress in the transverse direction. As Deker mentioned a few posts above, the von Mises criterion is commonly applied:
(f*x)^2 + (f*y)^2 - f*x.f*y + 3(v*)^2 < (phi.F)^2
where f* = normal stress (x & y are orthogonal directions); v* = shear stress; and phi.F = design capacity.
Since f*x and f*y are opposite signs (compression and tension), you can't max out one of them and still have stress in the transverse direction.
If I were to do this based on my own understanding of the mechanics, I'd find the maximum tension that will cause shear failure from Mohr's circle. Say it fails at 0.9*(0.6*50 ksi)=27 ksi. This would occur at only 9 ksi in transverse tension [45 - (-9) ] / 2 = 27 ksi.
I can't provide a reference for plates, but 27 ksi would be the shear capacity with a small normal stress. It reduces as the normal stress approaches yield stress as in this case.
RE: Normal Stress in orthogonal Directions
providing a dedicated loadpath like this (either straps or fittings) allows you to separate the tension stress from the cantilever from the compression stress of the girder. Note the RH floor beam isn't a true SS beam, it should be considered to be fixed at it's LH end (the RH end of the cantilever) ... it's more of a propped cantilever.
another day in paradise, or is paradise one day closer ?
RE: Normal Stress in orthogonal Directions
Ignoring the jab, I "kept it a secret" because that information is irrevelant to my question. I was simply wondering about how one would calculate the capacity of this connection. If you would like to know the context, I work as an engineer for a steel construction company. This detail showed up in another engineering firm's contract drawings for a building that we are erecting. I didn't design this, I was just involved in some construction calculations for the building and this detail peaked my curiousity.
Regardless, I do appreciate the recommended alternatives you gave.
RE: Normal Stress in orthogonal Directions
I do not believe we are REQUIRED to check interaction of the stresses by code, perhaps because it typically seems to work, even if neglected.
However, I totally agree with the suggestion of using a tie plate--it is a better detail in my opinion (no von Mises stresses, no counting on a weld to hold up a cantilever, etc.).
DaveAtkins
RE: Normal Stress in orthogonal Directions
another day in paradise, or is paradise one day closer ?
RE: Normal Stress in orthogonal Directions
RE: Normal Stress in orthogonal Directions
then it sounds like you have the combined stress state in the girder upper flange, as you suspected and maybe a von Mises check is warranted. and does the weld pass with tension loading ?
but "you guys" work with prescribed allowables (something like allowable bending stress is 60% ftu ?). does that protect your specific design ?
another day in paradise, or is paradise one day closer ?
RE: Normal Stress in orthogonal Directions