Question

A structure steel rod has a radius of $10mm$ and a length of $1.0m$. A $100kN$ force stretches it along its length. Calculate $\left(a\right)$ stress. $\left(b\right)$ elongation. and $\left(c\right)$ strain on the rod. Young's modulus, of stricture steel is $2.0\times {10}^{11}N{m}^{-2}$.

Answer 1

Given that,

Length of rod, $l=1m$

Radius of rod, $r=10mm=0.01m$

Force along its length, $F=100\times {10}^{3}N={10}^{5}N$

(a) Stress,

$\sigma =\frac{force}{area}$

$=\frac{{10}^5}{\pi {\left(0.01\right)}^2}$

$=\frac{{10}^5}{3.14\times {10}^{-4}}$

$=0.318\times {10}^9$

$=3.18\times {10}^{8}N/m^2$

(b) Elongation,

$\Delta L=\frac{F}{A}Y$

$=\frac{3.18\times {10}^8}{2\times {10}^{11}}$

$=1.59\times {10}^{-3}m$

(c) Strain,

$=\frac{\Delta L}{L}$

$=\frac{1.59\times {10}^{-3}}{1}$

$=0.16$