Problem $2$

Consider the axial member that is shown below. This member is circular with a radius of $2\mathrm{.}0$ in and is fixed at one end. The member is made out of a material with a modulus of elasticity of $29000$ ksi and a linear coefficient of thermal expansion of $\backslash (0\mathrm{.}000006451/\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ).$

$($a$)$ Calculate the reactions when this axial member is subjected to a $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$ increase in temperature.

$($b$)$ Calculate the displacement of point B $,$ relative to point A $,$ when this axial member is subjected to a $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$ increase in temperature.

$($c$)$ Consider an applied axial force at point $\backslash ($ B $\backslash ).$ What is the value of this axial force that would result in the same displacement of point $\backslash ($ B $\backslash ),$ relative to point $\backslash ($ A $\backslash )$ that was solved for in part a$.$ Notes:

$1)$ In addition to providing a magnitude for this axial force, make sure you state if the axial force is tension or compression.

$2)$ In part c$,$ the member is subjected to an applied axial load only, not a combined axial load and temperature differential.