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the load L a horizontal beam can safely support various jointly at the with w and the square of the depth d and inversely as the length l. If a 10ft beam with a width of 4in and a depth of 8in safely supports 960lbs how many pounds can a 16ft beam that has a width of 3.5in and a depth of 5in be expected to support? round to the nearest pound.

Respuesta :

the load L a horizontal beam can safely support various jointly at the with w and the square of the depth d and inversely as the length, therefore we have the next formula

[tex]L=k\frac{wd^2}{l}[/tex]

In our case

l=10ft

w=4in

d=8in

L=960lbs

Then we substitute the values

[tex]960=k\frac{(4)(8)^2}{10}[/tex]

Then we isolate the constant

[tex]k=\frac{960(10)}{(4)(8)^2}=37.5[/tex]

Then for the other case

l=16ft

w=3.5in

d=5in

We substitute in the formula

[tex]L=37.5\frac{(3.5)(5)^2}{16}=205.08\text{lbs}\approx205[/tex]

ANSWER

L=205 pounds

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