Section: Solid Mechanics | Marks: 2
Two bars of different Young's moduli, $E_1$ and $E_2$, but with the same cross sectional area, $A$, and coefficient of thermal expansion, $\alpha$, are attached together at one end and fixed at the other as shown in the figure. The construction of this setup was carried out at an ambient temperature of $25^\circ\text{C}$. The stress in the bars when the temperature is uniformly increased by $10^\circ\text{C}$ is
- A. $\sigma = 10\alpha(E_1 + E_2)$
- B. $\sigma = 20\alpha(E_1 + E_2)$
- C. $\sigma = 20\alpha\left(\frac{E_1 E_2}{E_1 + E_2}\right)$
- D. $\sigma = 10\alpha\left(\frac{E_1 E_2}{E_1 + E_2}\right)$