Problems

$2\mathrm{.}4-2$ A cylindrical assembly consisting of a brass core and an aluminum collar is compressed by a load $P($see figure$).$ The length of the aluminum collar and brass core is $350$ mm $,$ the diameter of the core is $25$ mm $,$ and the outside diameter of the collar is $40$ mm $.$ Also, the moduli of elasticity of the aluminum and brass are $72$ GPa and $100$ GPa $,$ respectively.

$($a$)$ If the length of the assembly decreases by $0\mathrm{.}1\%$ when the load $P$ is applied, what is the magnitude of the load?

$($b$)$ What is the maximum permissible load $P_{\text{m}\text{a}\text{x}}$ if the allowable stresses in the aluminum and brass are $80$ MPa and $120$ MPa $,$ respectively? $($Suggestion: Use the equations derived in Example $2-6.)$

PROB. $2\mathrm{.}4-2$