Question

A vertical steel beam in a building supports a load of 6.0×10⁴. If the length of the beam is 4.0m and it's cross-sectional area is 8.0×10^-3m². Find the diameter of the beam which is compressed along its length

Answer 1

DL = 1.5*10^-4[m]

Step-by-step explanation:

First we will determine the initial values of the problem, in this way we have:

F = 60000[N]

L = 4 [m]

A = 0.008 [m^2]

DL = distance of the beam compressed along its length [m]

With the following equation we can find DL

`(F)/(A) = Y*(DL)/(L) \\where:\\Y = young's modulus = 2*10^(11) [Pa]\\DL=(F*L)/(Y*A) \\DL=(60000*4)/(2*10^(11) *0.008) \\DL= 1.5*10^(-4) [m]`

Note: The question should be related with the distance, not with the diameter, since the diameter can be found very easily using the equation for a circular area.

`A=(\pi)/(4) *D^(2) \\D = \sqrt{(A*4)/(\pi) } \\D = \sqrt{(0.008*4)/(\\pi ) \\\\D = 0.1[m]`