Civil Engineering - UPSC Civil Service Exam Questions - Discussion

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.

@Mudra ...

It's because on LHS it is UDL and on RHS it is Point load.
Total load by UDL = w x L.

@Chhaya : Why L^4 and not L^3. From your eqn I have understood, it's the equation for deflection.

Please give the clear explanation of the answer.

Here wL^4/8EI = WL^3/3EI.
W = 3wL/8.

Option B is the correct answer.