A cantilever beam of length L and depth h is subjected to a uniform temperature rise along its length. At any section, however, the temperature increases linearly from t_{1} on the undersurface of the beam to t_{2} on its upper surface. If the coefficient of linear expansion of the material of the beam is α, calculate the deflection at its free end.
Ans. \alpha\left(t_{2}-t_{1}\right) L^{2} / 2 h .