Size a round-wire cylindrical helical extension spring per GB/T 1239. Same rate formula as compression, plus initial tension F0 and Wahl shear-stress correction. Formula: k = Gd⁴/(8D³n); F = k·δ + F0; τ = K·8FD/(πd³).
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k = Gd⁴/(8D³n) — identical stiffness formula to compression springs.
F0 = πd³τ0/(8D) from the closing force between coils; τ0 ~ 0.2–0.3 of tensile strength.
F = k·δ + F0 — deflection must first overcome the initial tension.
τ = K·8FD/(πd³) at the inner coil, with K = (4C−1)/(4C−4)+0.615/C.
End hooks carry bending — check separately against allowable bending stress.
G ≈ 78500–79000 MPa for spring steel; reduce for stainless.
Wire d, mean D, active coils n.
G and initial stress τ0 (0 if none).
Working extension δ and allowable [τ].
Rate, initial tension, load, stress, pass/fail.