Question $3$: The pin$-$ended beam$-$column structure shown in the figure below is subjected to a compressive axial force $P.$ It has a non$-$uniform cross$-$section, whose second moment of area is equal to $I_0,5I_0$ and $I_0$ for the three segments, respectively. The modulus of elasticity is $E.$ Determine the buckling load $P_{cr}$ by assuming the bending deflection function $y(x)=$asin$(\frac{x}{L}).$