Thick Steel Plate (10" x 13" x 3/4") Under load (about 12000 lb in total)

[kaffy]

Hello guys,

I am designing a steel plate (which will be welded on all four sides) and load will be acting at 8 location (uniform load acting over a small circular area, represented by the blue circles). I was planning to use Roark's formula 8b (also shown in attached file) but it only works with one load
To idealize, Initially I was planning to apply the full load (sum of all 8 loads) at small centre (without blue boundary) and then use the 8b. What do you guys suggest?
Also Is my idealization correct for assuming it as all edges fixed as it will be welded??

I have access to solid works simulation. I can run a very basic FEA but for post processing, what is the outcome I should compare with yield stress, Is it principle stress or vin mises?
Thank You
Newbie

 

[centondollar]

What is "sigma_b" in the document you provided? A quick glance tells me that the table in question is not enough for design. In addition, your sketch does not make clear how the clamped boundary conditions are enforced in practice; roughly 50% of each of the short sides of the plate seem to be free from restraints. Full penetration welds along all edges will make it clamped, but once again, your sketch does not indicate weld thickness, weld continuity (stitch or continuous) and how exactly the plate is supported, so I cannot give any definitive advice regarding that.

This problem can be solved with Galerkin or Rayleigh-Ritz method, using Kirchoff plate model. Assume a kinematically admissible displacement trial function that is a polynomial which gives a second derivative and mixed second derivative of deflection that is at least a quadratic polynomial (otherwise moment and shear distributions will be very inaccurate); alternatively, use a trigonometric displacement trial function. Apply the load as point loads (conservative) or as a uniform equivalent area load (perhaps also conservative) in the area in question, integrate the load potential and plate strain energy, solve the unknown parameters, insert the parameters into the displacement trial function and use the plate definition of stresses to find stress components. Finally, extract (with some reasonable spacing, e.g. 100x100 or 200x200 grid) and plug the values into the von Mises equation (can be done using e.g. Excel) to solve the critical stress and check your design.

For your last question, I recommend you to read about principal stresses and von Mises stresses. They are not comparable, and only one of them is relevant for the problem in question.

PS. You should stay away from FEA until you know what stress values are of interest in a simple plate bending problem.

 

[le99]

I suggest using the superposition principle with Roark's formula for a plate with two long edges fixed and the other two edges free, then compare to the result from the FEM analysis. No, you can't assume all 4 sides are fixed.

 

[JStephen]

I would treat it as a beam spanning across the short dimension, simply supported.
You could analyze it great detail, but unless you have a large quantity, it won't be worthwhile to do so.

 

[WARose]

It's got a lot of openings.....so I'd suggest (since you have it) using FEA and seeing what the Von Mises stress is. (Along with the localized shear stresses and so on.)

I'd vary your support conditions unless you are modeling the support itself as well. Maybe one run with the supports as pinned.....and another with it fixed. (Taking the worst case for each. I.e. likely the max plate stresses will bee in the pinned run.....while the worst stresses on the weld will be in the fixed support run)

 

[JoelTXCive]

Try this software...... It has a 30 day free trial period.

It's called Visual Plate by IES. I find all their software very easy to use.

https://www.iesweb.com/vp/index.html

 

[PEinc]

I would simplify the problem like JStephen suggested. This is similar to designing bearing plates for a non-gravity, retaining wall's tieback anchors on double channel walers where you very frequently have a short span for a small, unwelded plate with a single hole in the plate and a very much higher design load. I would look at it as a simple span where there are two line loads each totaling 6,000 pounds each. No matter how you analyze the plate it should not be very thick. Don't skimp on the plate size. I would not expect more sophisticated analyses to be required unless this is a high volume application where a small material cost savings per plate would significantly add up over time.

http://www.PeirceEngineering.com

 

[kaffy]

Awesome. Thank you very much guys. So much information