Question $1(5$ marks$)$ A single axial load of magnitude $P=70kN$ is applied at end C of the rod ABC. Knowing that the modulus of elasticity $E=105$GPa and Poisson's ratio $v=0\mathrm{.}31,$ the diameter of part $AB$ is $30$ mm $,$ determine:

$(1)$ the normal stress in part $AB.$

$(2)$ the strajn in part $AB$ along the rod.

$(2)$ the strain $in$ part $AB$ along the rod.

$=\frac{70{10}^{3}1\mathrm{.}2}{4}=1\mathrm{.}131{10}^{-3}$

$40{10}^{-3}$

$(3)$ the lateral strain along the diameter of part $AB.$

$6$

$(3)$ the lateral strain along the diameter $of$ part $AB.$

${}_{\text{l}\text{a}\text{t}}$

${}_{\text{l}\text{o}\text{n}\text{g}}=\frac{}{{}_{\text{l}\text{o}\text{n}\text{g}}}=0\mathrm{.}31=-\frac{{}_{1at}}{9\mathrm{.}425{10}^{-4}}=9\mathrm{.}425{10}^{-4}$

$(4)$ the reduction $in$ diameter $of$ part $AB.$

$(4)$ the reduction in diameter of part $AB.$

$+{}_{\text{l}\text{a}\text{t}}=d+\frac{1}{31{10}^{-3}-2\mathrm{.}92{10}^{-4}}=8\mathrm{.}39{10}^{-4}$

$(5)$ the diameter $d$ of portion $BC$ for which the deflection of point $C$ will be $5$ mm $.$

$5{10}^{-3}=\frac{70{10}^{3}0\mathrm{.}8}{\frac{x}{4}(d{)}^2({10\mathrm{.}5910}^9)},a_{81}^d=0\mathrm{.}01165m$