A support bar for a machine component is suspended to soften applied loads.

During operation, the load on each spring varies from $180$ to $220$ lb $.$ The

position of the rod is to move no more than $0\mathrm{.}500$ in as the load varies. Design

a compression spring for this application. Several million cycles of load

application are expected. Use ASTM A$229$ steel wire with shear modulus

found in Table $18-4$ and design stress found in Figure $18-10.$ Spring length at

the lowest load is $3\mathrm{.}00$ in $.$ Try solid length $2\mathrm{.}50$ in first. Select a Gage no$.$ from

Table $18-2$ and specify: $(15\text{'}$ in total$)$

wire diameter, mean diameter, spring index, Wahl factor

OD$,$ID$,$ free length

solid length and corresponding force

total number of coils

determine actual design stress

determine the maximum shear stress at the operating load and at the solid

length condition

Hint: refer to Equation $(18-10)$ on page $675$ in the textbook for an estimate of

starting wire diameter. Use Equation $(18-11)$ to estimate number of coils.

Please do out the actual calcs.