Mechanical Systems $2$

For each material below, find $S_{ut}$ and $S_y.$ Then indicate which of the materials shown below would you choose to obtain:

a$.$ maximum stiffness $($find $E$ for each material$),$

b$.$ maximum modulus of resilience $($find by equation$),$

c$.$ maximum modulus of toughness $($find by equation$).$

What is the common treatment on aluminum to prevent oxidation? What other metals can also be treated with this method? What options are available with this method? What other methods can be used on aluminum to prevent oxidation?

A $2\mathrm{.}5$ m long square bar is needed to support a mass of $500$ kg $.$ A desired factor of safety of $3$ means that the applied tensile stress is one third the yield strength of the material selected. Assume the approximate cost per kg for bar stock is given in the table below for several materials that are being considered. Select one of the materials for each of the following additional design goals:

a$)$ Find the side length of the bar for each material and choose the material giving the smallest side length.

b$)$ Find the mass of each bar and choose the material giving the lightest bar.

c$)$ Find the cost of each bar and choose the material giving the cheapest bar.

d$)$ Find the axial extension of each bar and choose the material giving the bar with the smallest axial extension.

A useful formula: Extension $=\frac{PL}{AE}$;

$\backslash$table$[[$Material$,$Sy $($MPa$),$Cost $($$$/$kg$)],[7075$ Aluminum,$503,14\mathrm{.}25],[4140$ Steel,$655,11\mathrm{.}50],[$A$-36$ Steel,$248,7\mathrm{.}00],[$Grade $5$ Titanium,$758,157\mathrm{.}60]]$