Helical Spring

Compression & extension share the rate k = G·d⁴/(8·D³·Nₐ) with Wahl-corrected shear stress; extension springs must first overcome their initial tension. Torsion springs use bending: angular rate E·d⁴/(10.8·D·Nₐ) and inner-fibre stress. Units: mm, N, MPa.

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Wire, ends and stability

Spring wire is drawn, so its strength depends on how thin it is: S_ut = A/d^m (Shigley Table 10–4), and E and G move with diameter too. The ends decide how many coils are dead, how short it closes and how long it must be free (Table 10–1), and a long spring buckles like a column (Table 10–2).