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, I. A wooden beam 3 in. wide. 6 in. deep, and 11 ft long holds up 1213 lb. What load would a beam 6 in. wide. 3 in. deep and 12 ft long of the same material support? (Round off your answer to the nearest pound.)

Answer 1

The formula for the safe load, L, of the wooden beam can be written as:

L = k * w * d^2 / I

where k is the constant of variation.

We are given that a wooden beam 3 in. wide, 6 in. deep, and 11 ft long holds up 1213 lb. Plugging these values into the formula, we get:

1213 = k * 3 * 6^2 / 11

Simplifying, we find:

k = 1213 * 11 / (3 * 6^2)
k = 181.87

Now, we can use this value of k to find the safe load for a beam 6 in. wide, 3 in. deep, and 12 ft long:

L = 181.87 * 6 * 3^2 / 12
L = 181.87 * 6 * 9 / 12
L = 818.42

Therefore, the load that a beam 6 in. wide, 3 in. deep, and 12 ft long can support is approximately 818 lb.