Problem $6$

From the text problem $11\mathrm{.}39$

Links $2$ and $3$ are pinned together at $B$ and a constant $P=800kN$ vertical load is applied at $B.$ Link $2$ is fixed in the ground at A and link $3$ is pinned to the ground at $C.$ The length of link $2$ is $8m$ and it has a $150-mm$ solid square cross$-$section. The length of link $3$ is $0\mathrm{.}5$ m and it has a solid circular cross$-$section with diameter $D.$ Both links are made from a steel with a modulus of elasticity E$=207$ GPa and a compressive yield strength Syc$=200$ MPa. Using the theoretic values for the end condition constants of each link, determine: $($a$)$ the slenderness ratio, the critical load, and the factor of safety guarding against buckling of link $2$; and $(b)$ the minimum diameter of link $3$ if the static factor of safety guarding against buckling is to be $N=2.$

Ans D$=$Djohnson$=72$ mm