Q1: A square column carries a load P at the centroid of one of the quarters of the square. If a is the side of the main square, the combined bending stress will be

ANS:C -

Total stress=direct stress+bending stress due to eccentricity at x-x axis And y-y axis.
Here, find the maximum bending stress.

So bending stress (maximum)
= {(p.ex)/z + (p.ey)/z}.......(1no.)

So here,( ex = b/4) ,and (ey=b/4). ( Z=I/y ,)
So,
I= b^4/12 and y= b/2.

So, Z ={(b^4/12)x(2/b)}=(b^3)/6.

Then put the value ...(1no.) eq.
={Px(b/4)}/{(b^3)/6}+{Px(b/4)}/{(b^3)/6}
={pb/4x6/(b^3)}+{pb/4x6/(b^3)}
={3p/(2b^2)}+{3p/(2b^2)}
=2x{3p/(2b^2)}
={3p/(b^2)} answer.