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End Plate with hole? how to size?

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BurgoEng

BurgoEng

Structural
Apr 7, 2006
68
US
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?
 
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Look in Roark's book Formulas for Stress and Strain. I'm pretty sure they have formulas for the situation you're describing.
 
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I agreewith nutte - Roark is real handy. You could also check out some of Timoshenko's works.

Mike McCann
McCann Engineering
 
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Ok, I got a Rourke book and will look through it. I've only ever used it for walls of concrete pits, or storage sheds.
 
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Another option is to model the plate on, say, RISA-3D, and analyze for the point load.

DaveAtkins
 
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Good idea Dave. I would model it with the hole and with a ring load of the bearing width of the washer at the edge of the hole. Should be interesting.

Mike McCann
McCann Engineering
 
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Well, I'm not finding anything in Rourke yet. I guess I might need to model it.
 
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This is a pretty easy problem using yield line theory. That's what I'd do for sure.
 
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I doubt Roark has a square plate with round hole. You could treat it as a round plate with round hole and that would likely be close enough. Summing moments about a centerline will get you the average bending moment in it- perhaps that's the yield line theory.
 
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I am not very savvy with finite element modeling but this seems like it would be a good application.
 
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"Summing moments about a centerline will get you the average bending moment in it- perhaps that's the yield line theory."

Nope, not quite. Most good concrete design books have a section on yield line theory. This one should take about 15 min. max to figure out the load to cause the collapse mechanism.
 
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Roarke doesn't have this. I would model this up with finite elements. Be sure to include some of the tube in your model, say 10 inches. That way, you don't have to use pinned or fixed edges at the edge of your plate. Also, I would use rigid links for the weld, so it's easy to extract the weld forces.
 
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Obviously the yield lines should come in from each corner. Depending on the size of the washer/nut I might still do some kind of check in the immediate area of the hole for pull-through.
 
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OK, using AISC LRFD, I get:

treq = sqrt( Pu / (2*phi*Fy) * (B-d) / (B-0.7071d) )

Pu = the factored load at the bolt hole.
phi = 0.9 for bending (if you want ASD, then put Omega=1.67 beside the Pu instead)
B = square plate width
d = bolt hole at the center of the plate

Use this only for comparison for whatever you end up with because it is NOT guaranteed!

Better yet, use it for comparison with your own YLT result!

[Soapbox On]It took very little time to derive this, even symbolically. Probably would've been <5 min. with numbers instead. Serious steel design folks owe it to themselves to take that concrete book home one weekend and become fluent in yield line theory. It is frequently useful and certainly faster and easier to interpret than a FE model.[Soapbox Off]

The only gotcha is that there's no way to get deflections from this. If you have an application that you're concerned with deflection, then you'll have to use a FE model. When I do something like this, I either approximate the deflections using some simplified model or make the FE model for deflections only.
 
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haynewp, that's the way I see it to: the mechanism has YLs coming from the corners, terminating at the edge of the hole.

As for a local check, any suggestions for how to do such a thing? I think I'd just use a bigger washer and forget that one.
 
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I would try an FE model but I am not sure how to model in the stiffening around the hole from the attachment itself (again I am not real good with FE I was 'raised' around old-school guys) or might just put in an oversized washer.



 
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I guess we're the same in that regard. I wouldn't know how to model such a thing.

A simplified model would be easy enough, but I think any realistic model must include difficult items like residual stresses around the hole from hole punching or drilling.
 
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I thought there would be a decent amount of info on pull through of bolts but I am not finding much so far. I think it would also be a function of the distortion of the remainder of the plate and not just in the local area of the washer.

I only found this in Design Guide 10 regarding anchor bolts:

"4.2.5 Anchor Rod Pull or Push Through
The nuts on the anchor rods can pull through the
base plate holes, or when leveling nuts are used and the
column is not grouted, the base plate can be pushed
through the leveling nuts. Both failures occur when a
washer of insufficient size (diameter, thickness) is used
to cover the base plate holes. No formal treatise is presented
herein regarding the proper sizing of the washers;
however, as a rule of thumb, it is suggested that the
thickness of the washers be a minimum of one third the
diameter of the anchor rod, and that the length and width
of the washers equal the base plate hole diameter plus
one inch."
 
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271828,

Pullthough can be checked with YL too. It will probably be a small fan, but you could cheat and do it as a small square, much the original problem.
 
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Tom I was thinking that too but it would seem to me that checking the two yield surfaces (the overall square versus a fan around the hole) independently might not be conservative.


I am trying to imagine how the deflection on the overall square plate influences the angles toward the middle of the plate, possibly a pull-through might occur earlier than what a fan yield line predicts. But I may be wrong.
 
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