$13-42.$ The ideal column is subjected to the force $F$ at its midpoint and the axial load $P.$ Determine the maximum moment in the column at midspan. EI is constant. Hint: Establish the differential equation for deflection, Eq$.13-1.$ The general solution is $v=C_{1}sinkx+C_{2}coskx-c^2\frac{x}{k^2},$ where $c^2=\frac{F}{2}EI,k^2=\frac{P}{E}$I.

find critical load, maximum moment, Maximum deflection

Prob. $13-42$