$3.$ A helical compression spring is to be designed for static service. The spring is made of A$313$ stainless $($an austenitic variety$),$ with a wire diameter of $0\mathrm{.}3$ in$.$ Determine the required mean coil diameter D for each of the following situations: a$)$ Free$-$standing, no set removal, with a design factor ns $=1\mathrm{.}2,$ a fractional overrun of $0\mathrm{.}15,$ and a maximum force Fmax $=300$ lbf$.$ Use conservative estimates for Ssy$.$ b$)$ Free$-$standing, set removed, with a design factor ns $=1\mathrm{.}2,$ a fractional overrun of $0\mathrm{.}15,$ and a maximum force Fmax $=300$ lbf$.$ Use conservative estimates for Ssy$.$ c$)$ Laterally supported with a $0\mathrm{.}75$ in$.$ diameter rod, with an allowable clearance of $0\mathrm{.}2$ in$.$ d$)$ Installed in a $2$ in$.$ diameter hole, with an allowable clearance of $0\mathrm{.}15$ in$.$