Rroblem $3(20)($Ci$.$o $6,$ ri$.$o i$)$

Consider a column $A$ B havine a uniform rectangular cross section with b $-50,mm,h=100mm$ and Iength $L=2m.$ The columa material has the modulus elasticity of $E$~~ $100$GPa and the yield stress of ${}_r=150$ MPa. The safery factor is $2.$

Determine the maximum axial load $P$ of the column for each of the following two cases

$($a$)$ If the supports at A and $C$ are pins as shown in Figure $3($a$),$

$($b$)$ If additional pin support is added at $B$ as shown in Figure $3($b$)$ such that the column is restrained in the plane of the figure $($plane $(Cz)$ but is able to deflect perpendicularly to he plane of the figure $($plane $yCz)$