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

\(k=\dfrac {\ Gd^{4}}{44.9n_{w}r^{3}}\)

\( v_{(F)}=\dfrac {\ 44.9Fn_{w}r^{3}} {Gd^{4}} \)

\( v_{max}=\dfrac {\ 44.9n_{w}r^{2}σ} {4.8Gd} \)

\(σ_{(F)}=\dfrac {\ 4.8Fr} {d^{3}} \)