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

Answer:

DL = 1.5*10^-4[m]

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

$\frac{F}{A} = Y*\frac{DL}{L} \\where:\\Y = young's modulus = 2*10^{11} [Pa]\\DL=\frac{F*L}{Y*A} \\DL=\frac{60000*4}{2*10^{11} *0.008} \\DL= 1.5*10^{-4} [m]$

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.

$A=\frac{\pi}{4} *D^{2} \\D = \sqrt{\frac{A*4}{\pi} } \\D = \sqrt{\frac{0.008*4}{\\pi } \\\\D = 0.1[m]$