Question

A steel bar 300 mm long and having 24 mm diameter, is turned down to 18 mm diameter for one third of its length. It is heated 30°C above room temperature, clamped at both ends and then allowed to cool to room temperature. If the distance between the clamps is unchanged, the maximum stress in the bar $(\alpha =12.5\times {10}^{-6}per°C$ and $E=200GN/m^2)$ is

• A. $25MN/m^2$
• B. $50MN/m^2$
• C. $75MN/m^2$
• D. $100MN/m^2$

Answer 1

The correct option is D $100MN/m^2$

Change due to temperature
$\Delta L=L_1{\alpha }_1\Delta T+L_2{\alpha }_2\Delta T$

$\Delta L^{\prime }=\frac{P{L}_1}{A_{1}E}+\frac{P{L}_2}{A_{2}E}$
$\Delta L+\Delta L^{\prime }=0$ (Because both ends fixed)
$P+2.69kN$
${\sigma }_{max}=\frac{P}{A}=\frac{2.69\times {10}^3}{\frac{\pi }{4}(18{)}^2}$
$\simeq 105MPa$