Topic: Strength of Materials
A rod of length L and area of cross section A has a modulus of elasticity E and coefficient of thermal expansion $\alpha$. One end of the rod is fixed and other end is free. If the temperature of the rod is increased by $\Delta T$, then
- A. Stress developed in the rod is $E\alpha\Delta T$ and strain developed in the rod is $\alpha\Delta T$
- B. Stress developed in the rod is zero and strain developed in the rod is $-\alpha\Delta T$
- C. Stress developed in the rod is zero and strain developed in the rod is $\alpha\Delta T$
- D. Stress developed in the rod is $E\alpha\Delta T$ and strain developed in the rod is zero
Answer: C. Stress developed in the rod is zero and strain developed in the rod is $\alpha\Delta T$
Explanation: Since one end of the rod is free, it can freely expand upon heating. Because the expansion is completely unconstrained, no internal resisting forces develop, so the thermal stress is zero. The rod will undergo a thermal strain given by $\epsilon_{T} = \alpha\Delta T$.