Problem $1.$ Determine and plot the axial force$-$moment interaction diagram about $x$ axis for the following column cross$-$section. When obtaining diagrams, determine the capacities for i$)$ pure compression, ii$)$ pure tension, iii$)$ pure bending, iv$)$ balanced failure v$)$ at least one point for tension failure and vi$)$ at least two points for compression failures. Please also submit your data of $N_r-M_r$ pairs in a table. Materials C$32/$ B$500$C and d$\text{'}($mm$)=50$mm