Answer
When the groove material is sufficiently hard, the failure mode shifts to the shearing of the ring itself. The thrust load capacity based on ring shear $P_r$ is calculated as $P_r = \frac{D \cdot t \cdot π τ_{ult}}{S}$, where $t$ is the ring thickness and $τ_{ult}$ is the ultimate shear strength of the material (typically $τ_{ult} \approx 0.6 \cdot σ_{uts}$). For a spiral ring made of SAE 1070 carbon steel with a tensile strength of $200$ ksi, the shear strength would be approximately $120$ ksi. It is vital to note that spiral rings are often multi-turn; however, the shear calculation usually focuses on the thickness of a single turn unless the turns are perfectly synchronized in load sharing. For Smalley-style 2-turn rings, the effective $t$ is the sum of the turn thicknesses.
