PROBLEM $2\mathrm{.}3-11$

$2\mathrm{.}3-12$ A bar ABC of length $L$ consists of two parts of equal lengths but different diameters. Segment $AB$ has diameter $d_1=100mm,$ and segment

$BC$ has diameter $d_2=60mm.$ Both segments hane

$2.$ a length $\frac{L}{2}=0\mathrm{.}6m.$ A longitudinal hole of diam. a$)$ eter $d$ is drilled through segment $AB$ for one$-$half pi its length $($distance $\frac{L}{4}=0\mathrm{.}3m).$ The bar is made of as plastic having a modulus of elasticity $E=4\mathrm{.}0G{R}_2$ of Compressive loads $P=110kN$ act at the ends of ar the bar.

$($i$)($a$)$ If the shortening of the bar is limited to $8\mathrm{.}0$ ming

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PROBLEM $2\mathrm{.}3-12$

$236$ what is the maximum allowable diameter $d$ of of the hole? $($See figure part a$.)$

$($b$)$ Now, if $d_{\text{m}\text{a}\text{x}}$ is instead set at $\frac{d_2}{2},$ at what distance $b$ from end $C$ should load $P$ be applied to limit the bar shortening to $8\mathrm{.}0$ mm $?($See figure part b$.)$

$($c$)$ Finally, if loads $P$ are applied at the ends and $d_{\text{m}\text{a}\text{x}}=\frac{d_2}{2},$ what is the permissible length $x$ of the hole if shortening is to be limited to $8\mathrm{.}0$ mm $?($See figure part c $.)$

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