What $is$ the spring constant?

Consider a helical steel spring of shear modulus $G$ . Let the thickness of the wire be $2r$ and the coil radius be $R$ .

Let the number of turns of the wire be $n = 8$ .

Estimate the force constant (in S.I. units) of the spring.

Details and Assumptions :

• $r = 1\text{ mm}$ .

• $R = 6 \text{ cm}$ .

• $G_{shear} = 78\text{ GPa}$ .

• Assume small enough pitch.

• Determine axial force constant considering shear forces only.