End Plate with hole? how to size?

[BurgoEng]

Here is a crazy plate design I am trying to work out.

I have a square (10"x10") end/cap plate with a 2"dia hole at the center. The plate will be welded on 4 sides to a steel "box". Through the hole is a bolt with a washer/nut on the back-side. This bolt will be tensioned so that the 10x10 plate will want to bow outward.

How do I go about sizing this plate, and getting reactions at the perimeter for sizing the welds?

 

[DaveAtkins]

So, AISC says the washer thickness should be 1/3 the rod diameter? 1/4" thick washers for 3/4" anchor rods? I doubt that will happen!!!

DaveAtkins

 

[271828]

Dave, why is that a strange washer size? Of course, they're thinking of plate washers at the huge oversized holes.

haynewp, say there's a plate washer there. I'm having a hard time envisioning a pull-through failure. He might also have a leveling nut and washer underneath, sandwiching the end plate. With a regular hardened washer, I can envision pull-through.

I think the most troublesome issue is overall deformation because that doesn't come out of the YL analysis and because treq might be pretty thin. Elastic deflection is the only thing that IS easy to get from a FE model. I really like using YLA for strength and FE for deflection.

 

[Tomfh]

If you really want to make this problem simple you can halve the load and solve strength and deflections for a one-way case.

 

[csd72]

Use a strip method.

Treat it as a square hole and apply load along four sides.

Take this load onto a 2" wide strip and analyse this as a beam. 4 beams total but all are identical.

This will be conservative, but I would think that your time to put this into an analysis would not be justified by the cost of the plate.

csd

 

[271828]

csd, but that's no fun at all! After all, that's why we do this, right?!

 

[miecz]

271828-

Using the yield line theory formula presented above, and neglecting local effects, I get a required plate thickness of .175 inches for a 3 kip load. Is that what the formula says? Seems a bit thin.

 

[271828]

I get 0.208" for a 3 kip load and 36 ksi. Not sure if that seems thin to me for 3 kips.

Want to re-emphasize that the formula is NOT guaranteed for design use and was provided for verification purposes only. I feel pretty good about it, though.

 

[csd72]

271828,

Yes, it is certainly not because it pays well!

 

[miecz]

271828-

I'm not designing this. I'm just trying to get a handle on yield line theory, as it looks like a valuable tool. I was using 50 ksi. For comparison, I modeled this up with a crude elastic finite element model. With a .208 thick plate, and a 3 kip load, I get stresses near 90 ksi. Of course, these are near the hole, where finite elements tend to find stress risers. To get stresses below yield, I would need a 3/8" plate. Just from a gut level though, 3/8" feels a lot better than 3/16" for a 3 kip factored load.

 

[271828]

jmiec, I would expect large stresses like that from the FE model. In reality, they wouldn't exist and load would distribute, eventually ending up with a collapse mechanism like assumed in the yield line analysis. We're definitely focusing on "the end of the line" strength, excluding strain hardening that is.

3/8" just *feels* better because we use them more in applications like this. In reality, I'd probably bump up the plate size to that anyway in this case, not because of 3 kips because that's small.

For one thing, perhaps there are other loads, gravity loads for example, that might push the plate size up.

Deflection is still an issue too. Your FE model is perfect for checking that.

There could also be constructability issues, like moments on the BP during construction.

Definitely some issues to think about. I just like YLA because it gives a rational way to check the strength limit state without some hokie approximation. Then I can go figure out how to deal with the others.