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UPSC Civil Service Exam Questions

Q1: Two simply supported beams B1 and B2 have spans l and 2l respectively. Beam B1 has a cross-section of 1 x 1 units and beam B2 has a cross-section of 2 x 2 units. These beams are subjected to concentrated loads W each at the centre of their spans. The ratio of the maximum flexural stress in these beams is

A 4

B 2

C

D

ANS:A - 4

Flexural stress = MY/I,
M1=WL/4, y1=1/2, I1=1(1^3)/12 put values u will get stress 1=3wl/2
M2 = w(2L)/4=wL/2, y2=2/2=1 , I2= 2(2)^3/12=4/3
Hence stress2 =3wl/8.
Now stress1/stress 2 = 3wl/2 ÷ 3wl/8 = 3wl/2*8/3wl = 4.



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