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UPSC Civil Service Exam Questions - Engineering

Q1:

A simply supported beam of span l and flexural rigidity EI, carries a unit point load at its centre. The strain energy in the beam due to bending is

A

B

C

D

ANS:C -

The formula is = integral (M^2 dx/2EI).

M= WL/4 (as we know point load is given at the centre then the maximum bending moment is wl/4).
W= 1 (Unit load assume this value).

Substitute and Integrate using the formula:

You will get = (W^2 X L^3)/(96 EI).
Therefore the answer is = (L^3)/96EI.