Helical spring with square cross section

Determine mechanical properties of a helical spring with wire thickness d, radius r, shear modulus G and nw as number of active windings. Calculate also deflection v and tension σ as a function of force F.

The shear modulus can be calculated using Young's Modulus and Poisson's ratio of a material.

\( G=\dfrac {E}{2(1+ν)}\)

F d D m r n w = 5

\(k=\dfrac {\ Gd^{4}}{5.61 n_{w}D_{m} ^{3}}\)

\( v_{(F)}=\dfrac {\ 5.61 Fn_{w}D_{m} ^{3}} {Gd^{4}} \)

\( v_{max}=\dfrac {\ 5.61 n_{w} D_{m} ^{2}τ} {2.4Gd} \)

\(τ_{(F)}=\dfrac {\ 2.4FD_{m}} {d^{3}} \)