Method of Design for Floor Plate on Platform

[aljosa_90]

Hello everybody, I hope you're all doing well.

I would really appreciate some input and wisdom on how to approach a structural design problem I am dealing with.

I'm in the middle of designing a floor plate that's going to be the ground floor of a maintenance platform. The plate will be ASTM A1011, Grade 36 Type 1 Hot Rolled Carbon Steel (yield strength = 36.3 ksi; E = 29,000 ksi), and will carry an evenly-distributed load of 115.6 lb/ft². The plate will be 3/8" thick with dimensions of 8' x 1.67'. I will have beams and joists at the boundaries of those dimensions, and will mechanically fix the plate to them.

My question is, how should I go about determining the bending stress, shear stress and deflection for this plate?

I had modeled the problem on paper using the LRFD method from AISC 360 (2016 ed.), using Section F.11 for the bending and Section G.4 for the shear. But I am positive my results are incorrect because my solution considers only a two-dimensional cross-section that is fixed on two sides whereas I really have a plate that's fixed on four sides. My calcs are attached.

I've done some research and found: (1) that plate theory is hard, and (2) that W.T. Moody published some neat tables that describes variations of different types of loading on flat plates under various boundary conditions. That being said, the length-to-width ratio in this particular instance is ~0.208 and I wasn't able to find a table in the Moody book that corresponds to those dimensions.

My belief is that the stresses I calculated in the attached sheets are going to be significantly higher than those in reality because the plate is fixed on four sides, and those fixtures will absorb much of the stresses from the applied load. However, I really want to show this on paper.

So what methods do structural engineers use to solve this problem? I assume it's rather common since maintenance platforms are often designed to have flat plates for the flooring, but right now I'm at a loss. I really think this is a valuable learning exercise and I'd love to get to the bottom of it. Any help is appreciated!

Floor Plate Calcs

 

[r13]

Two way action is usually insignificant when aspect ratio (long side/short side) beyond 4. Your plate is dominated by one way action, with a design span length of 1.67'. If you want more precise reactions, you shall use FEM instead of simple hand calculation.

 

[jayrod12]

Roark's formulas for stress and strain have formulae for plate bending with 4 sides fixed. But as retired indicated, your plate is dominated by the short direction. I would be analyzing it in a per foot of length spanning the short direction.

At service level loads that means you have M=116*1.67^2*0.125 = 40.34 ftlbs/ft. For 3/8" thick plate you have a section modulus of 0.281 in^3/ft. Therefore your bending stress is 1723 psi. Quick napkin math by the way, you'll have to run the numbers.

 

[JLNJ]

A few more comments to add onto the others you have received:

Be careful when considering things "fixed". Few supports provide full fixity (i.e. perfect rotational restraint). It is properly conservative to consider these as pinned supports. Roark's methods sometimes have scenarios where the edges are "held down". This may or may not apply to your condition. Plates have a tendency to deflect upwards along some portion of some edges. If the plate is welded to the supports you might consider it "held down", but otherwise consider upward support only. As you can probably visualize, holding the plate edges down lowers the deflection and changes the internal stresses a bit compared to plates with edges free to deflect upwards.

If you want to do a few hand calcs, consider a point on two strips which intersect in the middle of the plate. This point deflects the same for the short span as the long span. The load carried by each strip varies by the strip's stiffness. Because the stiffness is proportioned by the cube of the span, you can see that the short span is 100 times as stiff as the long span. The short span does 99% of the work. This is why jayrod12's calc above is a reasonable approximation. It considers the short side only.

Another thing to look for in floor plates is deflection. The deflection can get uncomfortable for a person walking long before the plate itself is overstressed. People are very perceptive to deflections and vibrations on walking surfaces.

 

[aljosa_90]

Thanks everybody for answering my questions and steering me in the right direction. After reading your comments, I realized that I was using the wrong cross-section when calculating for moment and shear. The calcs have been revised, so I'm attaching them once again. (Good news, I can use 1/4" plate now).

I have AutoCAD Robot at home and I played around with it last night. I am still getting the hang of it, and will most-likely only use it to check my work.

Thanks again!

Floor Plate Calcs (Revised)

 

[dold]

OP, your calculation of plastic section modulus, Z, should read: bh²/4, not bh³/4. That will help quite a bit.

 

[aljosa_90]

Oh boy... how did I do that. It does help, thank you!