Answer
Standard wave spring formulas assume a slender beam where curvature effects are negligible. However, for springs where the ratio of mean diameter $D_m$ to radial wall $b$ is less than 10, a curvature correction factor $K$ must be applied. Using a modified Wahl factor approach for flat wire, $K = \frac{4C-1}{4C-4} + \frac{0.615}{C}$ where $C = D_m/b$. The corrected stress $\sigma_c$ becomes $\sigma_c = K \cdot \frac{3 \pi P D_m}{4 b t^2 N^2}$. This correction accounts for the non-linear distribution of fiber stress across the radial cross-section, where the inner diameter experiences significantly higher compressive stress than the outer diameter experiences in tension, leading to potential premature yielding if only nominal stress is considered.
