UPSC Civil Service Exam Questions - Engineering

Q1:

A simply supported beam of span 'L' carries a concentrated load 'W' at mid-span. If the width 'b' of the beam is constant and its depth is varying throughout the span, then what should be its mid-span depth, when design stress is 'f' ?

A

B

C

D

ANS:C -

M/I = f/y.
y = fI/M.
y = d/2.
d/2 = f*(bd^3/12)/(WL/4).
1/2 = f*(bd^2/3)/WL.
d^2 = 3WL/2fb.
d = sqrt[3WL/2fb].