Question

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.

Answer 1

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

`L=k(wd^2)/(l)`

In our case

l=10ft

w=4in

d=8in

L=960lbs

Then we substitute the values

`960=k((4)(8)^2)/(10)`

Then we isolate the constant

`k=(960(10))/((4)(8)^2)=37.5`

Then for the other case

l=16ft

w=3.5in

d=5in

We substitute in the formula

`L=37.5((3.5)(5)^2)/(16)=205.08\text{lbs}\approx205`

ANSWER

L=205 pounds