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.)
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.