Elasticity
12.0 Thermal Stress & Strains
12.0 Thermal Stress & Strains
When there is increase or decrease in the temperature, it causes the body to expand or contract. If the body is allowed to expand or contract freely, then with the increase or decrease in temperature no stress will be produced in the body. But if the deformation of the body is restricted then stress is developed in the body and the stress is known as thermal stress.
When there is increase or decrease in the temperature, it causes the body to expand or contract.
If the body is allowed to expand or contract freely, then with the increase or decrease in temperature no stress will be produced in the body. But if the deformation of the body is restricted then stress is developed in the body and the stress is known as thermal stress.
When the temperature is increased body expands, so the FBD is shown as in Fig. E. 26 (a).
When temperature is decreased body contracts, so the FBD is shown as in Fig. E. 26 (b).
When the temperature is increased or decreased, then change in length of the rod is given by,
$$\begin{equation} \begin{aligned} \Delta l = l\alpha \Delta T \\ Strain = \frac{{\Delta l}}{l} = \alpha \Delta T \\\end{aligned} \end{equation} $$
As we know,
$$\begin{equation} \begin{aligned} Y = \frac{{Stress}}{{Strain}} \\ Stress = Y \times Strain \\ \frac{F}{A} = Y\alpha \Delta T \\ F = AY\alpha \Delta T \\\end{aligned} \end{equation} $$
where,
$A$= Area of cross section of rod
$Y$= Young’s modulus of rod
$\alpha $= Coefficient of linear expansion of rod
$\Delta T$= Change in temperature
