A helical tension spring is made of 1.2 mm wire having a yield strengths of 1280 MPa (tension) and 740 MPa (torsion). The spring has an OD of 12 mm, 36 active coils and hook ends. The mean radii at the ends is 5.4 mm for bending and 3 mm for torsion. The spring is pre-stressed to 75 MPa during winding, which keeps it closed solid until an external load of sufficient magnitude is applied. When wound, the distance between the hook ends is 70 mm.
a. What is the spring pre-load?
b. What load would cause yielding?
c. What is the spring rate?
d. What is the distance between the hook ends if the spring is extended until the stress just reaches the yield strength?