Two rubber pads with thickness $\backslash (($t$=4\backslash$mathrm$\{$~mm$\})\backslash )$ are clamped between a set of three steel plates. The rubber pads are square in cross$-$section with side length equal to $160$ mm $.$ If a loading is applied to the steel plates as shown above with $\backslash ($ P$=30\backslash$mathrm$\{$kN$\}\backslash ),$ answer the following questions.

For this question, calculate all final numerical answers to THREE decimal places and submit these answers into the appropriate field in Blackboard.

a$)(2$ marks$)$ Does the diagram above represent single or double shear? Explain. In order to earn full marks you must provide an explanation, not just either "single" or "double".

b$)(2$ marks$)$ Calculate the magnitude of the average shear stress on the rubber pads. Give your final numerical answer on Blackboard in kPa.

c$)(2$ marks$)$ If the rubber is known to have a Young's modulus of $\backslash ($ E$=0\mathrm{.}25\backslash$mathrm$\{$GPa$\}\backslash )$ and a Poisson ratio of $0\mathrm{.}35,$ calculate the magnitude of the shear strain under the stress condition described above. Give your final numerical answer on Blackboard in $\backslash \%.$

d$)(2$ marks$)$ Calculate the magnitude of the relative displacement for top surface of the pad with respect to the bottom surface of the pad given the shear stress. Give your final numerical answer on Blackboard in mm$.$

e$)(2$ marks$)$ Draw a diagram which shows how the cross$-$section of the rubber pad deforms under the stress. In order to earn full marks your diagram must be fully labelled with relevant quantities such as shear force, strain, displacement etc.

f$)(1$ mark$)$ If the thickness of the pad doubled, would the shear stress go up$,$ down, or remain the same? Input your answer Blackboard in the relevant spot for this part.