List of top Solid Mechanics Questions on Thermal stresses

A bar of length \(L = 1 \, m\) is fixed at one end. Before heating, its free end has a gap of \(\delta = 0.1 \, mm\) from a rigid wall. The bar is then heated, resulting in a uniform temperature rise of \(10^\circ C\). The coefficient of linear thermal expansion of the material is \(\alpha = 20 \times 10^{-6}/^\circ C\), and the Young’s modulus of elasticity is \(E = 100 \, GPa\).

Assume that the material properties do not change with temperature.
The magnitude of the resulting axial stress on the bar is ............ MPa (in integer).

A solid shaft and a hollow shaft have the same cross-sectional area. The hollow shaft: $D_o = 150 \, mm$, $D_i = 120 \, mm$. Both are subjected to same torque. Find ratio $\dfrac{\tau_h}{\tau_s}$.

At room temperature of 25°C, a gap of 1 mm exists between the ends of the rods 1 and 2 as shown. Given the cross section area \( A \) of the rods is \( 1500 \, \text{mm}^2 \), Young's modulus \( E = 75 \, \text{GPa} \), and the coefficient of thermal expansion \( \alpha = 23 \times 10^{-6} \, \text{°C}^{-1} \). When the temperature has reached 150°C, the magnitude of normal stress in each of the rods (in MPa, rounded off to two decimal places) is \(\underline{\hspace{2cm}}\).
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