Thermal Stress And Thermal Strain - Practice Questions & MCQ

Thermal stress in a  rod which is rigidly fixed : When a rod which rigidly fixed at ends such as to prevent expansion or contraction, when its temperature is increased or decreased. Due to preventing its thermal expansion or contraction, a compressive or tensile stress is developed in it. As the rod try to expand or contracts, then it apply a reaction force on the rigid support. If the change in temperature of a rod of length L is  then - 

                                             Thermal strain $=\frac{\Delta L}{L}=\alpha \Delta \theta \quad\left[\right.$ As $\left.\alpha=\frac{\Delta L}{L} \times \frac{1}{\Delta \theta}\right]$

As, If we know the strain then with the help of Hooke's law, we can find the stress also. If we know the stress , then we can find the force by multiplying cross-sectional area with stress. Both stress and force can be written as - 

So, Thermal stress $=Y \alpha \Delta \theta$
or, Force on the supports $F=Y A \alpha \Delta \theta$