Question $1$: $[$Temperature$-$Induced Stresses$]$

$1$ Figure $1,$ below, shows a bolt and pipe assembly. The bolt is made of steel and has a diameter of $15$ mm $.$ The pipe is made of aluminium with an outside diameter of $35$ mm and inside diameter of $25$ mm $.$ note the lengths, and the thickness of the washers in the figure.

Calculate the following:

$1\mathrm{.}1$ The magnitude and nature of the stresses induced in each material due to a temperature change of $\backslash (35^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ by cooling the assembly.

Note that the nut and bolt head restrict free expansion.

$1\mathrm{.}2$ The magnitude and nature of the stresses induced in each material if tightening the nut causes a total change in length of $\backslash (0,33\backslash$mathrm$\{$~mm$\}\backslash )$

Note: exclude temperature change here.

$1\mathrm{.}3$ The resultant stresses in the assembly when considering the temperature change and the tightening of the nut. Question $4$: $[$Thin Cylinders and Mohr's Circle$]$

$4$ The inside diameter of a cylindrical pressure vessel is $2$ m $,$ the internal pressure must not exceed $2\mathrm{.}1$ MPa $,$ the hoop stress in the in the material is $80$ MPa and the longitudinal joint efficiency is $\backslash (75\backslash \%.\backslash$mathrm$\{$E$\}=180\backslash$mathrm$\{$GPa$\}\backslash )$ and Poisson's ratio $\backslash (=0,29\backslash ).$

$4\mathrm{.}1$ Calculate the required thickness.

$4\mathrm{.}2$ Assume that the thickness is $38$ mm and calculate:

$4\mathrm{.}2\mathrm{.}1$ The circumferential strain.

$4\mathrm{.}2\mathrm{.}2$ The longitudinal strain

$4\mathrm{.}2\mathrm{.}3$ The change in length due to the internal pressure, if the original length is $1$ m $.$