$5.$ The air receiver for a small compressor with an internal pressure of $3\mathrm{.}45$ MPa has $900$ mm diameter. Use ASME chart for material code SA$-516-70,$ pressure vessel shell thicknesses $($attached in the formula section$),$ design the air receiver and determine:

i$.$ Wall thickness

ii$.$ State whether this is a thin or thiek cylinder.

iii. Hoop stress $($use mean diameter if this is a thin cylinder$).$

iv$.$ Longitudinal strain.

v$.$ State whether the design is safe or not.

$\backslash (\backslash$mathrm$\{$E$\}=200\backslash$mathrm$\{$GPa$\}\backslash ).$ Poisson's ratio $\backslash (=1/3\backslash ).$

Note: For thin cylinder, $\backslash (\backslash$boldsymbol$\{$t$\}<mi>\backslash </mi>$mathbf$\{120\}\backslash$times O D $\backslash )$ for thick cylinder $\backslash ($ t $\backslash$geq $120\backslash$times O D $\backslash )$

$\backslash (\backslash$mathrm$\{$OD$\}=\backslash )$ Outside Diameter.

$6.$ A simply supported laminated steel spring carries a central load. The spring has a span of $0\mathrm{.}85$ m supports a load of $7\mathrm{.}5$ kN $.$ The spring's central deflection should not exceed $50$ mm and the bending stress is limited to $\backslash (450\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$mm$\}2\backslash ).$ Thickness of spring plates is available in multiples of $1$ mm with a $4$ mm width. Determine for the spring, stitable values of width, thickness, and number of plates, also calculate the radius to which the plates should be formed. Assume that width $\backslash (=12\backslash$times $\backslash )$ thickness $\backslash ($ E$=200\backslash$mathrm$\{$GPa$\}\backslash ).$