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UPSC Civil Service Exam Questions

Q1:

A short column of external diameter D and internal diameter d, is subjected to a load W, with an eccentricity 'e', causing zero stress at an extreme fibre. Then the value of 'e' must be

A

B

C

D

ANS:C -

As we know the formula for Z for ext and int dia is Z= 3.14(D^4-d^4)/32D and we also know that (D^4-d^4)= (D^2-d^2)(D^2+d^2) and we also know the area A= (3.14(D^2-d^2))/4
e=Z/A.

e=(3.14(D^4-d^4)/32D)/(3.14(D^2-d^2))/4.

Hence e will comes after solving.
e= (D^2+d^2)/8D.



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