Question

A steel column is 3 m long and 0.4 m diameter. It carries a load of 50 MN so that 5.967 mm is elongates more. Find the modulus of elasticity. Please show your work in details, write formulas clearly, and plug in values properly.

Answer 1

Answer:

$E=2.0*10^{11}N/m^{2}$

Explanation:

Relation between stress and Force:

$\sigma=\frac{F}{A}=\frac{F}{\pi*d^{2}/4}$

Relation between stress and strain:

Young's modulus is defined by the ratio of longitudinal stress σ , to the longitudinal strain ε:

$E=\frac{\sigma}{\epsilon}$

$\epsilon=\frac{\Delta l}{l}$

So:

$E=\frac{F*l}{\pi*d^{2}/4*\Delta l}=\frac{50*10^{6}*3}{\pi*(0.4^{2}/4)*5.967*10^{-3}}=2*10^{11}N/m^2$