Stiffnesses for Pin Connectors

All applicable studies model the spring used for a pin connector as linear elastic. You can estimate the axial and rotational stiffness values based on the actual pin geometry:

Axial stiffness Rotational stiffness
You can use the linear stiffness of a rod with constant diameter in tension.

K = AE/L

A is the cross sectional area of the spring

E is the elastic modulus of the spring

L is the free length of the spring without any deflection

You can use the linear stiffness of rod with constant diameter in torsion.

K = JG/L

J is the polar moment of inertia = 2I

I is the moment of inertia = (Πr4)/4

r is the radius of the coil

G is the modulus of rigidity = E/(2(1+ν))

E is the elastic modulus of the spring

ν is the Poisson's ratio

L is the free length of the spring without any deflection