SOLUTION: The strength of a rectangular beam varies jointly as its width and the square of its depth. If the strength of a beam 2 inches wide by 10 inches deep is 1000 pounds per square inch
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Question 1118836: The strength of a rectangular beam varies jointly as its width and the square of its depth. If the strength of a beam 2 inches wide by 10 inches deep is 1000 pounds per square inch, what is the strength of a beam 4 inches wide and 8 inches deep Found 2 solutions by josgarithmetic, greenestamps:Answer by josgarithmetic(39630) (Show Source):
The other tutor derived the specific formula for calculating the strength of a beam, using the given information to calculate the constant of variation. So they didn't answer your question; but they made it easy for you to plug in numbers to get the answer.
In relatively simple problems like this, I find it more difficult and time-consuming to find the constant of variation the way the other tutor did.
Instead, I find it easier to apply factors to the given information to find how the strength is changed with the new information.
The load limit is 1000 pounds per square inch when the beam is 2 inches wide and 10 inches deep. In the new beam, the width is 4 inches (times 2) and the depth is 8 inches (times 4/5).
Then since the variation is jointly with the width and the square of the depth, the new load limit is
The load limit of the new beam is 1280 pounds per square inch.
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