The strength of a beam

Question

The strength of a beam is directly proportional to its width and the square of its depth but inversely proportional to its length. If a beam that is 55 inches wide, 88 inches deep, and 55 feet long can support a weight of 512 pounds, how much weight could the same type of beam that is 55 inches wide, 44 inches deep, and 10 feet long support?

 

The beam can support _____ pounds

 

 

Answer 1

When you cut the depth in half, you cut the strength in one fourth, if everything else stays the same. Thus, just changing that part, you will be able to support 512/4 = 128 pounds. However, you then reduce the length to 2/11 of its original, which increases the strength by 11/2. Therefore, we multiply (11/2)*(128) = 11*64 = 704 pounds.

A more formal approach goes like this. First we write an equation: S = kWD^2/L When W=55, D=88 and L=55, we have S=512. Plugging all of those in, you can solve for k. Once you have k, you can rewrite the equation, using k that you found, and new values for D and L. You can then calculate S in a straightforward manner.