What is the ASME distortion energy method for shaft sizing?

The ASME DE (distortion energy) method uses the von Mises criterion to combine bending and torsion: d^3 = (16/pi*Ss_allow) * sqrt((Km*M)^2 + (Kt*T)^2) * 2, where Km and Kt are shock/fatigue factors. This gives d = (32*sqrt((Km*M)^2 + (Kt*T)^2) / (pi * Ss_allow))^(1/3).

What is the stiffness criterion for shaft sizing?

The stiffness (rigidity) criterion limits the angle of twist to a specified rate, commonly 0.5 to 1.0 degrees per metre. From theta/L = T/(GJ), the required J >= T*L_ref/(G*theta_allow), which gives d_min = (32*T*L_ref / (pi*G*theta_allow_rad))^(1/4) for a solid shaft.

Which criterion usually governs shaft diameter?

For short, heavily loaded shafts, strength (torsional or combined bending-torsion) usually governs. For long, lightly loaded shafts, stiffness (twist limit) may govern. The calculator evaluates all criteria simultaneously and highlights the one requiring the largest diameter.

Shaft Sizing Calculator – Minimum Diameter for Strength & Stiffness | CalcEngines

Mechanical Engineering Tools · CalcEngines

Shaft Sizing Calculator

Find the minimum shaft diameter required to satisfy torsional strength, bending strength, combined loading (DE / ASME), and angular stiffness limits simultaneously.

Torsion criterion Bending criterion Combined (DE) Stiffness criterion 11 materials SI & Imperial

Shaft Cross-Section

Quick Presets

Applied Loads

Torque T

Applied torsional moment

Bending Moment M

Peak bending moment (optional)

Shaft Length L

Used for stiffness criterion

Shock & Fatigue Factors (ASME DE Method)

K_m – Bending factor 1.0 smooth · 1.5–2.0 shock

K_t – Torsion factor 1.0 smooth · 1.5 moderate

Safety Factor S_f Applied to all criteria

Twist Limit θ_lim

°/m

0.5°–1.0°/m typical

Material Properties

Material Sy = 250 MPa · Su = 400 MPa · G = 80 GPa

Yield Strength S_y

MPa

τ_y = 0.577 × S_y (von Mises)

Shear Modulus G

GPa

For stiffness criterion

Imperial

Minimum Required Diameter

Enter torque, material, and safety factor above, then click Calculate.

All Criteria Comparison

Criterion	Formula	Min Diameter	Utilisation	Status
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Stresses at Governing Diameter

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Section Properties at Governing Diameter

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Design & Material Summary

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Shock / fatigue factors (K_m, K_t) reference: Stationary shaft (no rotation) = 1.0 · Light shock 1.5 · Medium shock 2.0 · Heavy shock 3.0. Increase for stress concentrations (keyways, shoulders, holes).

Design Formulae

Criterion	Formula for d_min (solid shaft)	Notes
Torsion only	d = (16T / πτ_allow)^1/3	τ_allow = S_y / (2 · S_f) – von Mises
Bending only	d = (32M / πσ_allow)^1/3	σ_allow = S_y / S_f
Combined DE (von Mises)	d = (16 / πτ_allow × 2√((K_mM)² + (K_tT)²))^1/3	ASME distortion energy method
Stiffness (twist limit)	d = (32TL / πGθ_allow)^1/4	θ_allow in rad/m; L in metres
Hollow shaft factor	d_o = d_solid / (1 − k⁴)^{1/3 or 1/4}	k = d_i/d_o; strength or stiffness respectively

Governing criterion = the one requiring the largest diameter. Always round up to the nearest standard size in practice.

Common Questions

How is minimum shaft diameter calculated for torsion? +

From the torsion formula τ = 16T/(πd³), rearranging for solid shaft gives d = (16T / (πτ_allow))^1/3. The allowable shear stress is typically S_y/(2·S_f) using the von Mises criterion. For a hollow shaft with bore ratio k = d_i/d_o, divide the solid result by (1 − k⁴)^1/3.

What is the ASME distortion energy (DE) method? +

The DE method combines bending and torsion using the von Mises criterion: d = (16/(πτ_allow) × 2√((K_mM)² + (K_tT)²))^1/3. K_m and K_t are combined fatigue/shock factors for bending and torsion respectively. This is the most commonly used method for rotating shafts under combined loading.

When does the stiffness criterion govern? +

The stiffness criterion governs when the shaft is long relative to its load, typically in precision machinery or long drive shafts. The required diameter from stiffness is d = (32TL / (πGθ_lim))^1/4. Since this scales with L^1/4, doubling the shaft length only increases required diameter by about 19%.

What safety factor should I use for shaft design? +

For static loading: S_f = 1.5–2.0. For repeated loading (fatigue): S_f = 2.0–3.0, higher if stress concentrations are present (keyways, grooves, shoulders). AGMA and ASME recommend factors specific to application type. For preliminary design, S_f = 2.0 is a reasonable starting point.

Why is a hollow shaft more efficient than a solid shaft? +

Torsional stress is zero at the shaft centreline and maximum at the surface, so material near the centre contributes little to torsional resistance. Removing it with a bore (hollow shaft) gives a higher strength-to-weight ratio. With k = 0.6, a hollow shaft retains ~87% torsional strength at ~64% mass compared to a solid shaft of the same outer diameter. The calculator shows both solid and hollow required diameters for comparison.