A helical compression spring has N_a active coils, mean coil diameter D, wire diameter d, and shear modulus G. The spring stiffness (spring rate) k is:

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Mechanical Engineering QUESTION #2470

Question 1

A helical compression spring has \(N_a\) active coils, mean coil diameter \(D\), wire diameter \(d\), and shear modulus \(G\). The spring stiffness (spring rate) \(k\) is:

\(k = \frac{Gd^4}{8D^3 N_a}\)✔️
\(k = \frac{Gd^3}{8D^4 N_a}\)
\(k = \frac{8FD^3 N_a}{Gd^4}\)
\(k = \frac{Gd^4}{8D^3}\)

Correct Answer Explanation

The spring rate: \(k=F/\delta=Gd^4/(8D^3N_a)\). Note that \(k \propto d^4\) (strong wire diameter dependence) and \(k \propto 1/N_a\) (more coils = softer spring).

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