Problem $4(30$ points$)$:

The following bar is made of $6061-$T$6$ aluminum alloy with yield strength of $260$ MPa and Young's modulus of $70$ GPa $.$ Given the three forces applied to the bar, determine:

a$)$ Normal and shearing stresses at point $a,b,$ and $c.$

b$)$ If the direction of the axial force $10-kN$ was reversed will the bar buckle or not $($ignore $750$ N and $500$ N $)?$ If yes, which axis will it be about?

c$)$ If the axial force in question $4($b$)$ was also allowed to increase, will this bar fail due to buckling or yielding?