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Calcimator

Shaft Design Calculator

Design a shaft for combined bending and torsional loads using the von Mises failure criterion. Calculates minimum diameter and stresses.

Inputs

in·lb
in·lb
psi

Results

Minimum Shaft Diameter

1.44 in

Von Mises Stress

18,000 psi

Shear Stress (τ)8,542 psi
Bending Stress (σ)10,251 psi
Allowable Stress18,000 psi
How to Use This Calculator
  1. Enter the Applied Torque (T) in in·lb from power transmission — use T = 63,025 × HP / RPM if starting from motor horsepower.
  2. Enter the Bending Moment (M) in in·lb from transverse loads such as gear separating forces, belt tension, or overhanging weight.
  3. Enter the material Yield Strength (Sy) in psi: 1018 steel ≈ 36,000 psi, 4140 steel ≈ 60,000 psi.
  4. Set the Safety Factor: 2.0 for well-defined static loads, 2.5–3.0 for fatigue or shock loading.
  5. Read the Minimum Shaft Diameter in inches and round up to the next standard size for keyway compatibility.
  6. Review the Von Mises Stress versus the Allowable Stress to confirm the design margin is adequate.

How the result changes with Yield Strength (Sy)

Yield Strength (Sy)Minimum Shaft DiameterVon Mises Stress
39,0001.4 in19,500 psi
111,5000.99 in55,750 psi
198,5000.82 in99,250 psi
271,0000.73 in135,500 psi

What each input means

Applied Torque (T)
Torsional load on the shaft from power transmission. T = 63,025 × HP / RPM.
Bending Moment (M)
Maximum bending moment from transverse loads such as gear forces, belt tension, or weight.
Yield Strength (Sy)
Yield strength of the shaft material. 1018 steel ≈ 36,000 psi; 4140 steel ≈ 60,000 psi; stainless 304 ≈ 31,000 psi.
Safety Factor
Design safety factor. Typical: 2.0 for static loads, 2.5-3.0 for fatigue or shock loads.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Applied Torque (T) = 5000, Bending Moment (M) = 3000, Yield Strength (Sy) = 36000, Safety Factor = 2 = 4 input(s) provided
  2. Calculate Minimum Shaft Diameter
    Minimum Shaft Diameter
    1.439 = 1.439
  3. Calculate Von Mises Stress
    Von Mises Stress
    18000 = 18000
  4. Calculate Shear Stress
    Shear Stress
    8542 = 8542
  5. Calculate Bending Stress
    Bending Stress
    10251 = 10251

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