$(20pts)A$ rod is used as a pinned machine part loaded as a column with F$.$S$.=2$; The rod size is $32$ in long, and $2$ inch of diameter; The rod is made of A$992$ steel, with the relevant appendix table is given as below.

$(4$ pts$)$ Of the column, what is the effective length factor $K[$unitless$]?$

$(4$ pts $)$ Of the column cross$-$sectional area, what is the radius of gyration $r_G[in]?$

$(4$ pts$)$ Prove whether the column is intermediate or slender?

$(4$ pts$)$ Calculate the allowable stress ${}_{\text{a}\text{l}\text{l}}[ksi]$

$(4$ pts$)$ Calculate the allowable load $P_{\text{a}\text{t}\text{l}}[kips]$