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UPSC Civil Service Exam Questions - Engineering

Q1:

A propped cantilever of span 'l' carries uniformly distributed load of 'w' per unit over its entire span. The value of prop react to keep the beam horizontal is

A

B

C

D

ANS:B -

Let the propped cantilever have a fixed end at A and propped end at B.
For a propped cantilever, deflection at the propped end (B) = 0.

A propped cantilever with a UDL is equivalent to a cantilever with a UDL(1) + a cantilever with an upward reaction at the propped end(2).
So at B, deflection due to case (1) = deflection due to case (2) ----------since total deflection = 0.

Therefore wL^4/8EI = (Rb)L^3/3EI ----------(3).
Where Rb is the reaction at B.

Also we have Ra+Rb = wL (equating forces) ------------(4).
From (3) and (4), Rb = 3wL/8.