A helical compression spring is fabricated from ASTM A229 oil-quench-tempered cold-drawn steel wire having a diameter d = 0.9 mm, a modulus of rigidity G = 80 GPa, and a modulus of elasticity E = 200 GPa. The spring has 14.5 active coils with a mean diameter D = 10 mm. The ends are squared-and-ground. The spring is supported between flat parallel surfaces (fixed ends). Required:
a. Determine the spring rate.
b. Determine the minimum hole diameter for the spring to operate in.
c. Determine the total number of coils needed.
d. Determine the solid length.
e. Determine a static factor of safety based on the yielding of the spring if it is compressed to its solid length.