TASK $3$:

A$.$ A solid piece of metal of volume $\backslash (8500\backslash$mathrm$\{$~mm$\}^\{3\}\backslash )$ is compressed by a pressure of $90$ MPa $.$ Determine the bulk modulus given that the elastic modulus E is $\backslash (70$ G P a $\backslash )$ and Poisson's ratio $\backslash ($ v$=0\mathrm{.}33\backslash ).$ Determine the change in volume.

B$.$ One of the two steel structures $(4$ m long$),$ which are suggested by the company's design group, will be used under water as a container for underwater research project equipment. The pressure in the depth that this structure will work is $120$bar. The steel has Modulus of Elasticity $215$GPa and Poisson$`$s ratio $0\mathrm{.}31.$ Calculate the bulk modulus and the reduction in volume.

C$.$ Calculate the total volumetric change $($consider volumetric change due to pressure and volumetric thermal expansion or contraction together$)$ in the structures in task B if:

i$.$ Temperature of water has dropped by $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

ii$.$ Temperature of water has increased by $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

Assume that volumetric thermal expansion coefficient for steel is $\backslash (21\mathrm{.}6\backslash$times $10^\{-6\}\backslash ),$ write a short report, show your calculations and evaluate from engineering perspective.