Final answer:
To find the safe load of a beam with different dimensions, we can use the joint variation formula and solve for the constant k. Once we have the value of k, we can plug in the new dimensions to find the safe load. In this case, the safe load of a beam with a length of 12 in is 960 lb.
Step-by-step explanation:
To solve this problem, we can use the formula for joint variation: P = k * (w * d^2) / l, where P is the load, w is the width, d is the depth, and l is the length of the beam. We are given that the load P is 1440 lb when w = 3 in, d = 16 in, and l = 8 in. To find the safe load when the beam is 12 in long, we can substitute the given values into the formula and solve for k. Once we have the value of k, we can plug in the new values of w, d, and l to find the safe load in pounds.
Substituting the given values into the formula:
1440 = k * (3 * 16^2) / 8
1440 = k * 768 / 8
1440 = k * 96
Divide both sides of the equation by 96:
k = 1440 / 96
k = 15
Now we can use the value of k to find the safe load when l = 12 in:
P = 15 * (3 * 16^2) / 12
P = 15 * 768 / 12
P = 960 lb
Therefore, the safe load of a beam made from the same material, with a width of 3 in, depth of 16 in, and length of 12 in, is 960 lb.