Calculating Load Capacity of 96"x48"x6" EPS Foam Board

[dustman]

TL;DR

I need to figure out how much weight a 96"x48"x6" EPS foam board can hold when laid flat and supported at both ends. Tensile psi: 92. Compressive psi: 52.

I need to figure out how much weight a 96"x48"x6" EPS foam board can hold when laid flat and supported at both ends(96" span). Tensile psi: 92. Compressive psi: 52. I believe these figures are for 10 percent deformation. I would like to support temporary 200lb loads at any point on the span, with little to no bending. These would not be point loads so am not worried about "local" deformation. If you can tell me how to calculate this myself I would be grateful.

 

[PhanthomJay]

If the foam board is simply supported at its short ends, and if your load is applied uniformly along the full width of the board but over a small length , then the max stress will occur when this load is applied at the center and the max stress at the center can be approximated using simple beam equations, where max M is PL/4 and max stress is Mc/I. Max compressive stress controls the design. If your load more closely approximates its being spread over just a small area near the center, it is best to use equations listed in the book entitled "Roark's Stress and Strain".

I'm not familiar with stress allowables and deflections in foam, so take this response lightly, please. Disclaimer: Do not use this as a basis for design.
Thank you.

 

[dustman]

If the foam board is simply supported at its short ends, and if your load is applied uniformly along the full width of the board but over a small length , then the max stress will occur when this load is applied at the center and the max stress at the center can be approximated using simple beam equations, where max M is PL/4 and max stress is Mc/I. Max compressive stress controls the design. If your load more closely approximates its being spread over just a small area near the center, it is best to use equations listed in the book entitled "Roark's Stress and Strain".

I'm not familiar with stress allowables and deflections in foam, so take this response lightly, please. Disclaimer: Do not use this as a basis for design.
Thank you.

Thank you for the response.

I had meant point load as in very small point, like the ball of a foot, because I thought people might get hung up on the brittle nature of the foams surface. Basically I need to be able to walk over the panel without it bending or breaking. Yes, I figured that the compression would be the limiting factor. I'm not sure what these terms are: M, PL/4, Mc/I. Would you mind explaining?

 

[PhanthomJay]

Thank you for the response.

I had meant point load as in very small point, like the ball of a foot, because I thought people might get hung up on the brittle nature of the foams surface. Basically I need to be able to walk over the panel without it bending or breaking. Yes, I figured that the compression would be the limiting factor. I'm not sure what these terms are: M, PL/4, Mc/I. Would you mind explaining?

M is the bending moment and at its maximum is equal to PL/4 from basic statics of a simple beam, along the short centerline of the plate for the simplified loading case I noted, where P is 200 pounds, L is 96 inches, and thus M-max is PL/4 or about 5000 in-lb. Then c is just half the board's thickness, or c is 3 inches, and I is the plate's area moment of Inertia, which is equal to bt^3/12, where b is 48 inches and t is 6 inches. You have to be an engineering student taking a course in mechanics of materials to understand all this stuff. Otherwise, it just becomes algebra, and you should get a max stress of about 20 psi. However, this is not your actual case if you are walking along the board, where your full 200 pounds is more like a point load, and stresses could be much higher, maybe double or more. I'll see if i can find one of those plate tables from Roark, I don't have the book.
In terms of its deflection or bending, all materials known to humankind will deflect or deform under load, sometimes a tiny bit,. sometimes a lot. These are harder to calculate, because you need to know of other properties of the foam board, like its elasticity modulus and stress-strain characteristics.

If you walk across the board and it breaks or bends excessively. I take no responsibility. Make sure the ends are fully supported full width along its ends. I've got a feeling that if your allowable stresses are correct, you're going to make it across OK. Just make sure the board is elevated just a few inches off the floor, in case you fall. This isn't a circus act, you know.. And be sure to walk across slowly, to avoid sudden impact loading.