The safe load, L, of a wooden beam supported at both ends varies jointly as the width, w, the square of the depth, d, and inversely as the length, l. A wooden beam 9 in.

Question

The safe load, L, of a wooden beam supported at both ends varies jointly as the width, w, the square of the depth, d, and inversely as the length, l. A wooden beam 9 in. wide, 9 in. deep, and 17 ft long holds up to 3903 lb. What load would a beam 10 in. wide, 2 in. deep and 16 feet long of the same material support? (Round your answer off to the nearest pound.)

Answer 1

L = kwd² / L

3903 = k(9)(9)² / 17

Solve for k, then plug in 10 for w, 2 for d, and 10 for L.