Calculating Load from Modulus of Rupture

[utslam]

Homework Statement

There is a structure with four legs. each leg is 6" x 6" square. The bottom of each leg is 6"W x 6"L x 3/4" H. Each leg has a foot which is 4" x 4" x 4". The foot is placed in the center of the leg. The question is how much weight can the legs support before the bottom of the leg collapses.

The Modulus of Rupture of the leg bottom is 1100 lbs/in^2

Homework Equations

Modulus of Rupture = (3 x P x L)/(2 x b x d^2)

P = breaking load
L = distnace between knife edges
b = width
d = depth

The Attempt at a Solution

I rearranged the above formula to

P = M x 2 x b x d^2/ 3 x L

P = 1102 x 2 x 6 x 0.75^2/ 3 x 6 = 413 lbs.

However, I think this is assuming all of the load is applied on one square inch. Since the load is applied acrross four square inches. Does that mean each leg can support 4 x 413 lbs (1,653 lbs. So the whole sturcture can support 6,612 lbs?

 

[utslam]

Actually, I think the formula should be

M = 3 x P x (L-Li)/(2 x b x d^2)

since there is not a single point of pressure.