Concentrated Load into Fully supported Wbeam in Weak Axis

[PSSC]

I have a W12 laying horizontal supported under each flange by a W8. A concentrated load from a W8 is applied to the middle of the web.
I don't believe this is a matter of using the weak axis "I" because it is supported under the flanges the entire length.
Also supposing the web is beam fully constrained at each end seems an oversimplification.
This is an existing design that I need to confirm will handle new loadings.

I have attached a sketch.

Any thoughts?

Thanks in advance for the help.

 

[PSSC]

I should have stated that I am trying to determine the strength of the web.
How much load can the web handle in this configuration.

Thanks

 

[Lion06]

I'm assuming that the W12 is flat and the W8's are strong axis?

If they are positively connected, check shear flow to see if you have a composite section, then do a composite section analysis to get I, Stop, and Sbtm. If it's not composite, then you would simply sum the (W12 Iy) + 2*(W8 Ix) and that will give you the total I. From that you can proportion out how much each beam is taking and do the necessary checks.

I would also check the web of the W12 for that concentrated load, you're likely to get some localized deformation there.
Maybe you can address that problem by providing stiffeners unter the column flanges between the web of the W12 and the top flange of the W8's, and another (full depth) stiffener on each of the W8's.

 

[ishvaaag]

One can start a search for a closed form formula for your case, that likely there may be, but today it is maybe easier just extrude the shapes in the 2D sketch , then place the W shape for load, and pass everything to a 3D FEM model where you can easily control the start of yielding by a Von Mises criteria, that should be a quite conservative estimate for the case. In all this we are forgetting any interaction with the longitudinal stresses in the supporting outfit, that we must not, but you can proceed with more success to control that in the same way with a more ample substructure till at least supports, or maybe beyond.

 

[KootK]

You could check the beam web treating it as a simply supported beam. This may give overly conservative results. However, if it works, you're done. There may also be a punching shear issue to contend with.

If you can spare the time, you could also check it out using a yield line analysis. That should yield a more realistic capacity.

If it were me, and it were physically possible, I'd weld a pair of stiffeners across the upper half of the W12. I'd then weld the flanges of the W8 post thingy to those same stiffeners. That way, your load flows from the flanges of the W8 post directly into the flanges of the flat W12 beam. Then it's a no brainer and you can sleep easy. The original designer probably should have done that anyhow.

 

[KootK]

SEIT: I just realized that you already brought up the stiffeners in your post. What can I say? I guess great minds think alike.

 

[BAretired]

If you are asking only about the strength of web of the W12, you could do a yield line analysis on it, but you could avoid the calculation by reinforcing it.

Can you reinforce the web with a short angle or channel each side of the W8 column? If you are adding more load to the column, that is probably the best approach.

BA

 

[PSSC]

The composite structure I think I have a handle on.
It's the localized stress on the web that has me scratching my head.
Is it a plate fully fixed at both ends?
It is not localized web buckling, so what is it?

 

[Teguci]

I would start with checking the bending in the web. I'd spread the load out at a 45 degree angle from the corners of the W8 column in order to select a width for the web beam. I'd assume a pinned-pinned end condition.

 

[PSSC]

Sorry, you guys must have posted while I was typing.

Adding the stiffeners has been considered and I will probably just do it, there will be a minimal steel cost.
I was just curious in how to go about the calc.

Thanks

 

[Lion06]

The problem with a yield-line analysis in this scenario is that while the web is fixed to the flanges, the flanges can likely rotate, taking away some of that stiffness, so it's probably unconservative to assume a fixed-fixed condition. It's also definitely not a pin, so you're really stuck somewhere in the middle.

 

[KootK]

You could assume a pinned condition AND do a yield line analysis, could you not? That's what I was suggesting.

 

[BAretired]

Kootenay,

I guess the problem is that we were all posting at the same time.

BA

 

[Lion06]

Kootenay -

You could, but it sounded more like he was interested in this from a theoretical perspective. On that front, I was just suggesting that pin-pin isn't what's really there.

 

[KootK]

Gotcha. I suppose that a YL analysis with pin-pin probably wouldn't be much better than a simplified beam analaysis anyhow.

 

[Lion06]

True, a yield line analysis for a pin-pin plate becomes a plastic analysis for a beam.

 

[BAretired]

A web failure would be a localized effect. It is true that the web is not fully fixed at the flange and it is possible the the flanges may rotate inward slightly. But if the flanges of the W12 are welded to the supporting W8 beams in the vicinity of the column, there would be a negative yield line forming near the inside face of each flange. That assumption, in my opinion, would give a reasonable estimate of the critical load.

To consider a hinge along each flange would yield an ultra conservative solution which would be safe but not a good estimate of failure load.

BA