Drawing No. EH–ME–011 // Mechanical Engineering
Shaft Design Calculator
Reviewed August 2026
Size and check solid or hollow rotating shafts under combined bending and torsion, with elastic-yield and twist screening.
Calculation workflow
Inputs are converted internally to SI, the engineering model is solved, and results are converted back to the selected unit system.
Design inputs
Design and check results
Cross-section and stress screening
Worked example
15 kW at 900 rpm gives about 159 N·m torque. A simultaneous 800 N·m bending moment dominates this example.
T = P/ω ≈ 159 N·m.
The calculator combines factored bending stress and torsional shear using von Mises stress.
The calculated requirement is a minimum elastic-yield size; choose a practical diameter and verify fatigue and local features.
Background
A rotating shaft commonly experiences simultaneous bending and torsion.
σb = 32M / [πD³(1-k⁴)] ; τ = 16T / [πD³(1-k⁴)]
For a solid shaft k = 0. The selected service factors multiply nominal M and T for the strength check.
σvm = √(σb² + 3τ²)
The required diameter is solved by setting σvm equal to yield strength divided by the target safety factor.
θ = TL / JG
Twist uses the actual operating torque, not the strength service factor. Local torsional flexibility at couplings, splines and keys is not included.
Frequently asked questions
Practical questions about assumptions, limits and interpretation.
The sizing calculation uses the distortion-energy or von Mises criterion for combined bending normal stress and torsional shear stress.
Kb and Kt are user-entered multipliers applied to the nominal bending moment and torque for screening transient or service effects. They are not substitutes for a detailed fatigue load spectrum or standard-specific factors.
No. Rotating shafts often fail by fatigue, especially at shoulders, keyways and fillets. This page is an elastic-yield and torsional-stiffness screening tool.
No. Select a practical standard size above the calculated requirement and then check fatigue, stress concentrations, critical speed, bearings, keys/splines, tolerances and manufacturing details.