# Thermal Stress (तापीय प्रतिबल)

### Thermal Stress in a Rod fixed between two rigid supports

In this article we are going to discuss about thermal stress produced in a rod which is fixed between two rigid supports.

Consider a rod of length L0 with Young’s modulus Y is fixed between two rigid supports. Let it is heated for some time and its temperature increases by ΔT. Now the rod tries to expend in length(due to thermal expansion) but since it is fixed between rigid supports, so a stress is produced in the rod.

This stress is called Thermal Stress (तापीय प्रतिबल).

Now stress is given by = F/A

Also from the concepts of elasticity Young’s modulus :-

Y = Thermal Stress/Thermal Strain $\displaystyle \Rightarrow Y=\frac{F/A}{\Delta L/L}$ $\displaystyle \Rightarrow \frac{F}{A}=Y\left( \frac{\Delta L}{L} \right)=Y\alpha \Delta T$

Hence,

 Thermal Stress(F/A) = YαΔT

And the force which is responsible for this stress :-

 Force (F) = YAαΔT

Example :- A steel rod 50 cm long has cross-sectional area of 0.8 cm2. What force would be required to stretch this rod by the same as the expansion produced by heating it through 10ºC. For steel it is given that

α = 10-5 K-1 , Y = 2×1011 Nm-2.

Solution. Thermal Stress (F/A) = YαΔT

⇒ F = YAαΔT

⇒ F = (2×1011)×(0.8×10-4)×(10-5)×(10)

⇒ F = 1.6×103 N 