Shaft Design Calculator

This calculator solves directly for the SMALLEST diameter that keeps combined bending-and-torsion stress at or below the allowable limit, so by construction the resulting Von Mises Stress lands right at Allowable Stress (aside from rounding) at the computed Minimum Shaft Diameter. That means there is no built-in safety margin remaining at that exact size -- standard practice is to round up to the next available stock diameter rather than machining to the calculated minimum precisely.

Allowable Stress is Yield Strength divided by Safety Factor, so a higher-strength material (higher Yield Strength) directly raises the allowable stress the shaft is sized against. Since the required diameter shrinks as allowable stress rises, switching to a stronger alloy at the same Safety Factor lets you use a smaller-diameter shaft for the same combined torque and bending load.

Safety Factor divides directly into Allowable Stress (Yield Strength divided by Safety Factor), so a higher safety factor lowers the stress the shaft is allowed to reach, which in turn requires a larger cross-section -- and therefore a larger Minimum Shaft Diameter -- to keep actual stress at or below that lower allowable value for the same torque and bending moment.

A shaft carrying both Applied Torque and Bending Moment experiences shear stress from torsion and normal stress from bending simultaneously at the same surface point, and these combine in a way that a single-load formula doesn't capture. The von Mises (distortion-energy) criterion combines both effects into one equivalent stress, which is the standard approach in mechanical design references for sizing ductile shafts under combined loading.