Question

A metal bar of length $100mm$ is inserted between two rigid supports and its temperature is increased by ${10}^{\circ }C$. If the coefficient of thermal expansion is $12\times {10}^{-6}\text{per}{}^{\circ }C$ and the Young's modulus is $2\times {10}^{5}MPa$, the stress in the bar is

• A. Zero
• B. $12MPa$
• C. $24MPa$
• D. $2400MPa$

Answer 1

The correct option is C $24MPa$

Length of bar =100 mm
Increase in temperature,

$\Delta t={10}^{\circ }C$

Young's modulus,
$E=2\times {10}^{5}MPa$

Coefficient of thermal expansion,
$\alpha =12\times {10}^{-6}\text{per}{}^{\circ }C$

Stress in the bar

$=\frac{E}{L}\times \left(Deflectionprevented\right)$

$=\frac{E}{L}\times L\alpha \Delta t$

$=2\times {10}^5\times 12\times {10}^{-6}\times 10$

= $24MPa$