Shaft Sizing (Strength & Stiffness) Calculator

Shaft Sizing (Strength & Stiffness) Calculator

Shaft Sizing (Strength & Stiffness)

CE Style

Loading, Material, Limits

Steel ≈ 79–82 GPa (11.5–12 Mpsi)
Use > 1 if keyways/shoulders exist
deg/m (SI) or deg/ft (Imp)

Geometry Inputs

If set, tool also evaluates τ and θ for this d
kg/m³ (SI) or lb/in³ (Imp)

Sizing Results

Strength: τ = Kt · T·c / J → solid dmin = [16 KtT / (π τallow,eff)]1/3.
Stiffness: θ = T·L / (J·G) → solid dmin = [32 T L /(π G θlim)]1/4. Hollow uses J = π(Dₒ⁴ − Dᵢ⁴)/32 and c = Dₒ/2 with numeric search (small step).

Section & Check (at Sized Geometry)

Evaluation at Existing Geometry (optional)

How to Use the Shaft Sizing (Strength & Stiffness) Calculator

Size a solid or hollow round shaft from torque, shear limit, and twist limits. The tool reports minimum diameter / outer diameter / thickness, shows which criterion governs, and summarizes section properties, stress, twist, and mass.

1) Choose Units & Shaft Type

  • Units: SI (mm, N·m, MPa, GPa) or Imperial (in, lbf·in, psi, Mpsi).
  • Type: Solid (solve d), Hollow (solve Do) with given Di, or Hollow (solve t) with given Do.
Presets provide quick examples to verify behavior.

2) Enter Load, Material, and Limits

  • T: applied torque (match units to the dropdown).
  • L: free span over which twist is considered.
  • G (shear modulus): steel ≈ 79–82 GPa (11.5–12 Mpsi), aluminum ≈ 26 GPa.
  • Kt: stress concentration factor > 1 for keyways/shoulders.
  • τallow and optional FS for strength; θlim and/or twist/length for stiffness.
Core relations: τ = Kₜ·T·c/J, θ = T·L/(J·G).

3) Geometry Inputs

  • Solid: leave “Existing d” blank to compute dmin; enter a value to evaluate stress/twist of that size.
  • Hollow (solve Do): provide Di and a small search step (mm or in).
  • Hollow (solve t): provide Do, minimum tmin, and a step.
  • (Optional) ρ (density) to estimate mass from area × length.

4) Run & Read the Results

  • Sizing Results: dmin / Do,min / tmin from strength and from stiffness, plus the governing value.
  • Section & Check: area, J, c, τmax at T, total twist, and twist per length at the sized geometry. Mass shown if ρ is set.
  • Units and conversions are automatic based on your selections.

5) Existing Geometry Check (Optional)

  • Enter a known d (solid) to see τmax, θ, and safety factors vs your limits.
  • Use this to validate current designs or to compare against the sized result.

Quick Checklist

  • Correct unit system chosen
  • Appropriate shaft type selected
  • Torque, span L, material G entered
  • Realistic τallow and Kt set (keyways/steps)
  • Twist limits reflect service needs (deg total or per length)
  • Search step (hollow) small enough for resolution
  • Governing criterion understood (strength vs stiffness)
  • Safety factor applied where needed
FAQ & Tips

What values should I use for τallow?
Use a conservative shear allowables table for your alloy/temper and temperature. Apply a safety factor if in doubt.

How do I pick Kt?
Kt ≈ 1 for plain shafts. Increase for keyways, shoulders, sharp fillets, or other discontinuities; consult charts or FEA for critical parts.

The tool says “governing = stiffness”. Why?
Long, slender shafts often meet stress limits but exceed twist limits. Reduce L, increase diameter, or choose a hollow section with larger Do/thickness.

Search step for hollow options?
Use a small step (e.g., 0.1 mm or 0.005 in) for a fine result; larger steps run faster but reduce resolution.

Copy-Paste Mini Workflow

1) Pick Units and Shaft Type
2) Enter T, L, G, Kt
3) Set τ_allow (+ optional FS), and/or twist limits (θ or per length)
4) Enter geometry inputs (d or Dᵢ / Dₒ as required)
5) Read d_min / Dₒ_min / t_min and see which criterion governs
6) Review τ_max, θ, twist/length, J, and mass at the sized geometry