Derive the correction factor for the spring rate when accounting for the 'radial wall' (b) to 'thickness' (t) ratio in narrow-geometry springs.

In standard wave spring formulas, the ratio $b/t$ is assumed to be large enough for beam theory to apply. When $b/t < 8$, the spring behaves less like a simple beam and more like a curved plate. A correction factor $C_f = \frac{1}{1 - \nu^2}$, where $\nu$ is Poisson's ratio, is sometimes applied to the Modulus of Elasticity $E_{eff} = \frac{E}{1 - \nu^2}$ to account for the transverse constraint. For stainless steel ($\nu \approx 0.3$), this increases the theoretical stiffness by approximately 10%. Furthermore, for very narrow radial walls, the risk of 'twisting' or lateral-torsional buckling increases, requiring the use of a stabilization factor in the design calculations.