SOLUTION: The maximum load of a horizontal beam that is supported at both ends vari<bes jointly as the width and the square
of the height and inversely as the length between the supports. A
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Question 1106811: The maximum load of a horizontal beam that is supported at both ends vari
of the height and inversely as the length between the supports. A beam 6 m long, 0.1 m wide, and 0.06 m high
supports a load of 360 kg. What is the maximum load supported by a beam 16 m long, 0.2 m wide, and 0.08 m high?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The information tells us that the mass m that can be supported by a beam of length l, width w, and height (thickness) h is
where k is a constant.
The value of the constant can be determined from the given information: When the length is 6m, the width is 0.1m, and the height is 0.06m, the maximum load is 360kg. So
Then using this constant with the new beam measurements,
That is a general method for solving problems like this. But if the numbers are fairly simple, as in this case, I find it easier just to modify the given mass according to each changed dimension of the beam.
The length of the beam changes from 6m to 16m; since the mass varies inversely as the length, the maximum load decreases by a factor of 6/16 = 3/8.
The width doubles from 0.1m to 0.2m; since the mass varies directly with the width, the maximum load increases by a factor of 2.
The height changes from 0.06m to 0.08m; since the mass varies directly with the square of the height, the maximum load increases by a factor of (0.08/0.06)^2 = (4/3)^2 = 16/9.
Then the new maximum load is
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