Question

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

Answer 1

Given that,

Radius $r=10mm$

Length $l=1.0m$

Force $F=100kN$

Young modulus $Y=2.0\times {10}^{11}N{m}^2$

Now, the stress is

Stress $=\frac{100\times {10}^{3}N}{3.14\times {10}^2{m}^2}$

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

Now, the elongation is

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

$\Delta L=\frac{3.18\times {10}^8\times 1}{2.0\times {10}^{11}}$

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

$\Delta L=1.59mm$

Now, the strain is

Strain

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

$=\frac{1.59\times {10}^{-3}}{1.0}$

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

Hence, this is the required solution.