Thermal Stresses in Simple Bars

Q. A copper bar of $25cm$ length is fixed by means of supports at its ends. Supports can yield (total) by $0.01cm$. If the temperature of the bar is raised by ${100}^{o}C$, then the stress induced in the bar for ${\alpha }_c=20\times {10}^{-6}{}^{o}C$ and $E_e=1\times {10}^{6}kg/c{m}^2$ will be

1. $2\times {10}^{2}kg/c{m}^2$
2. $4\times {10}^{2}kg/c{m}^2$
3. $8\times {10}^{2}kg/c{m}^2$
4. $16\times {10}^{2}kg/c{m}^2$

Q. 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

1. $25MN/m^2$
2. $50MN/m^2$
3. $75MN/m^2$
4. $100MN/m^2$

Q. The length, coefficient of thermal expansion and Young's modulus of bar A are twice that of bar B. If the temperature of both bars is increased by the same amount while preventing any expansion, then the ratio of stress developed in bar A to that in bar B will be

1. $2$
2. $4$
3. $8$
4. $16$

Q. A square plate (a $\times$ a) rigidly held at three edges is free to move along the fourth edge. If temperature of the plate is raised by temperature 't', then the free expansion at the fourth edge will be (coefficient of thermal expansion of the material = a, modulus of elasticity of the material = E and its Poisson's ratio = μ)

1. $a\alpha t\mu$
2. $a\alpha t(1+\mu )$
3. $a(\alpha t+\frac{\alpha t\mu }{E})$
4. $a\alpha t(1-\mu )$

Q. A metallic bar of diameter 20 mm is shown in figure.


Modulus of elasticity of bar is $2\times {10}^{5}MPa$, coefficient of thermal expansions is $12\times {10}^{-6}{/}^{\circ }C$. The temperature of metallic bar is increased by ${100}^{\circ }C$, then what is the reaction generated at right support if the right supports yields by 0.1 mm is ___ kN

1. 12.56