TGPSC HMWSSB Manager 2015 Paper 2 · Question 102
Question 102 of the TSPSC Manager (Engineering), HMWSSB, 2015: Paper 2 (Civil Engineering) (1 November 2015). Try it first, then open the answer and explanation.
A cantilever beam of uniform flexural rigidity with span L and depth D is subjected to temperatures T_1 on the upper face and T_2 on the lower face. If T_1 < T_2 and α is the coefficient of linear expansion for the material, the deflection at the free end of the beam is ______.
- α (T_2 - T_1) L²/2D (upward)
- α (T_2 - T_1) L²/D (upward)
- α (T_2 - T_1) L/2D (upward)
- α (T_2 - T_1) L²/2D (downward)
Show answer
Answer: (1) α (T_2 - T_1) L²/2D (upward)
The temperature difference across the depth gives a uniform curvature κ = α(T_2 − T_1)/D; the hotter lower face expands more, so the cantilever curls upward. Free-end deflection = κL²/2 = α(T_2 − T_1)L²/(2D), upward.