Problem $10\mathrm{.}14$

A $25$ mm square aluminum strut is maintained in the position shown by a pin support at A and by sets of rollers at $B$ and $C$ that prevent rotation of the strut in the plane of the figure. Consider only buckling in the plane of the figure and use $E=71\mathrm{.}7$GPa. Knowing that $L_{AB}=1$ meter, determine

a$)$ the largest values of $L_{BC}$ and $L_{CD}$ that can be used if the critical buckling load $P_{cr}$ is to be as large as possible,

b$)$ the magnitude of the corresponding critical load.