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UPSC Civil Service Exam Questions - Engineering

Q1:

A cantilever beam of uniform EI has span equal to 'L'. An upward force W acts at the mid-point of the beam and a downward force P acts at the free end. In order that the deflection at the free end is zero, the relation between P and W should be

A W = 3P/2

B W = 2P

C W = 16P/5

D W = 5P

ANS:C - W = 16P/5

Deflection at the free end (I.e, P) =PL^3/3EI (downwards).
Deflection at the free end due to W,

W(L/2) ^3/3EI + W(L/2) ^2/2EI * (L/2) = 5WL^3/48EI (upwards).
As given, in order to make deflection at the free end as 0,
Upward deflection=downward deflection 5WL^3/48EI = PL^3/3EI.
P= 5W/16.