$2-$A$)$ There is a column which has length of $3\mathrm{.}5$ m $.$ This column has clamp$-$free supports. The cross section of this column is shown in the figure:

The Young's modulus of the column can be found based on a tensile test. According to this experiment, a sample made of material of the column is under tensile load. The cross section of the sample is $\backslash (4\backslash$times $10^\{-4\}\backslash$mathrm$\{$~m$\}^\{2\}\backslash )$ and applied force is $15\mathrm{.}2$ KN $,$ the corresponding strain of this test is $\backslash (5\mathrm{.}06\backslash$times $10^\{-4\}\backslash ).$ Calculate the buckling load of the column.

B$)$ In this part, the column is the same but boundary condition is pin$-$pin support $($Length is $3\mathrm{.}5$ m $).$ If the tangent modulus of the material in the plastic area is $\backslash (10\backslash \%\backslash )$ of the Young's modulus, find the buckling load in the plastic area $($For this case, assume that there is no buckling in the elastic loading$)$

C$)$ In this case, the boundary condition of the structure is pin$-$pin support and the length is $7$ m $($length of the column in this part is different from parts $\backslash ($ A $\backslash$& B $\backslash )).$ If the linear expansion coefficient of the column is $\backslash (\backslash$alpha$=24\backslash$times $10^\{-6\}\backslash$frac$\{1\}\{\backslash$mathrm$\{$c$\}^\{\backslash$circ$\}\}\backslash )$; what is the critical temperature of the column for buckling? Mitial Temp$=\backslash (27^\{\backslash$circ$\}\backslash ).$