EngineerBenchSizing a solid shaft for bending and torsion
A solid round shaft under bending and torque develops both normal and shear stress. This tool combines those stresses using a von Mises equivalent stress and compares it with the entered allowance. It can find a minimum diameter for that model or check a diameter you already have.
Use loads at the section being checked
The bending moment is not the same as a transverse force; it depends on loads and support positions. Enter the moment and torque at the critical section, along with the chosen stress multipliers. Check more than one section if the shaft diameter or loading changes along its length.
Static stress is not a complete shaft design
Keyways, shoulders, fatigue, deflection, bearings, and critical speed can govern a real shaft. The entered multipliers do not automatically account for all of those effects. Treat the diameter as a static stress screening result, then check the remaining design requirements.
Reading diameter sensitivity
For a solid round shaft, bending and torsional stress both vary inversely with diameter cubed in the stated formulas. Increasing diameter by ten percent reduces those nominal stresses to about 75 percent of their original values when moments remain unchanged. This is a stress comparison, not a general statement that every shaft failure mode improves by the same amount.
Determine the bending moment at the section from the complete arrangement of forces and supports. A belt load, overhung gear, or coupling can introduce bending even when the main purpose of the shaft is transmitting torque. Stress multipliers should represent the selected design basis and features rather than being treated as arbitrary safety knobs. In a rotating shaft, a fixed-direction transverse load can produce cyclic material stress, so a static equivalent-stress check may not govern life. After selecting a candidate diameter, check deflection, bearing alignment, shoulders, keyways, and dynamic behavior. The minimum diameter result is not automatically a standard stock size or a final machining dimension.
Formula
σ = 32M/(πd³); τ = 16T/(πd³); von Mises = √(σ² + 3τ²).