First slide

Thermal expansion

Question

Coefficients of linear expansion of two rods A and B are in the ratio 2 : 3. The rods are fixed between two rigid walls. If the young's modulii of the materials of the rod are in the ratio 2:1 and temperatures of the rods are increased by $15^{o} C$ , the thermal stresses developed in the rods will be in the ratio

Easy

A

3 : 2
B

4 : 3
C

3 : 1
D

3 : 4

Solution

Thermal stress $σ_{t} = Y α Δ θ$
$∴ \frac{{(σ_{t})}_{A}}{{(σ_{t})}_{B}} = \frac{Y_{A}}{Y_{B}} . \frac{α_{A}}{α_{B}} = (\frac{2}{1}) (\frac{2}{3}) = \frac{4}{3}$

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