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Theory of Structures - Engineering

Q1:

A compound bar consists of two bars of equal length. Steel bar cross-section is 3500 mm2 and that of brass bar is 3000 mm2. These are subjected to a compressive load 100,000 N. If Eb = 0.2 MN/mm2 and Eb = 0.1 MN/mm2, the stresses developed are:

A σb = 10 N/mm2, σs = 20 N/mm2

B σb = 8 N/mm2, σs = 16 N/mm2

C σb = 6 N/mm2, σs = 12 N/mm2

D σb = 5 N/mm2, σs = 10 N/mm2

ANS:A - σb = 10 N/mm2, σs = 20 N/mm2

As it is a compound bar strain produced will be the same in both bars...

PsL/AsEs = PbL/AbL.

L will be cancelled out.
So
Ps/3500*2 = Pb/3000*.1 , Ps/700 = Pb/300.
Or Pb = 0.428ps.
Now P = PB +Ps = 0.428ps +ps = 1.428Ps.
100000=1.428Ps or Ps= 70000N and Pb = 30000N.
Stress = load/ area. stress in steel = 70000/3500 =20N.
Stress in brass = 30000/3000 =10N.