A simply supported column is loaded with a transverse load Q

A simply supported column is loaded with a transverse load Q and a compressive axial load P. The Young\'s modulus is E, and the cross-section is rectangular with base b and height h. Find an expression of the maximum deflection. For L = 20 in, Q = 50 lb, sigma_0 = 50 times 10^3 psi, h = b = 1 in. and E = 30 times 10^6 psi, calculate the maximum allowable axial load. Plot P versus v(x = L/2) and identify the critical load.

Solution

area of cross section of beam is h*b, not h/b

total stress is due to bending and compressive.