MEN $3020-$ Materials Science

Homework $3$

Professor Gallagher

Assigned: $9/10/24$

Due: $\frac{9}{17}\frac{?}{24}$

currently designed with a low$-$alloy steel, as a width $t=60mm$ and a depth $h=5mm.$ However,

if possible, it is desirable to replace this steel with another material to reduce the weight of the

component. To avoid redesigning other related parts, the $t$ dimension should not be changed, but

$h$ can be varied, as long as it does not exceed $12$ mm $.$ The spring stiffness must be $k=\frac{P}{v}=50$

$k\frac{n}{m}.$ Also, the spring hits a limit to its motion at $v_{\text{m}\text{a}\text{x}}=30mm,$ at which point the stress should

not be so large that the safety factor against material failure is less than $x=1\mathrm{.}4.$

a$)$ First, considering only the $k=50k\frac{N}{m}$ requirement, determine which materials in Table

$3\mathrm{.}13$ would provide a lighter weight component.

b$)$ Next, for each material, calculate the $h$ necessary to meet the $k=50k\frac{N}{m}$ requirement,

and also the safety factor relative to ${}_c$ at $v_{\text{m}\text{a}\text{x}}=30mm.$ Eliminate any materials that do not

meet $h12mm$ and $x1\mathrm{.}4.$

c$)$ Finally, compare the alloy steel design with the use of each of the remaining candidates,

considering cost and any other factors that you believe to be important.