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ASME DE-Goodman

Shafts & Power Transmission

Shaft diameter is the minimum diameter of a shaft to safely transmit a given torque. Use the formula d = ∛(16T / (π × τ)) where T = applied torque, τ = allowable shear stress per ASME B106.1M.

Shaft Diameter Calculator

Calculate the minimum required shaft diameter for combined torsion and bending loads using the ASME DE-Goodman fatigue criterion. Includes both static yielding and fatigue failure analysis.

Workspace Mode:

Unsaved Configuration

Calculated Sizing outputs

Required Outer Diameter (Do)

34.410mm

Inner Diameter is not applicable to Solid Shaft profiles.

Design Allowable Stress

25MPa

Calculation Summary

Input Parameters

Shaft Profile Type	Solid Shaft
Calculation Source	Applied Torque
Torsional Moment	200N·m
Bending Moment (M)	0N·m
Allowable Shear Limit (τ_allow)	50MPa
Factor of Safety (FOS)	2

Calculated Results

Required Outer Diameter (Do)	34.410mm KEY
Allowable Design Stress	25.00MPa

Safety Notes

Omitting bending moments: Pulleys, belts, and gear radial forces create bending that must be included.

Neglecting fatigue on rotating shafts: Rotating shafts experience fully reversed bending cycles requiring lower allowable stresses.

Keyway correction — ASME B106.1M requires 25% reduction in allowable stress when keyways are present.

Mathematical Models & Equations

Torsional Shaft Sizing Equations (Solid Shaft)

Design Shear Stress (τ_design) = Allowable Shear Stress (τ_allow) / Factor of Safety (FOS)
Outer Diameter (D_o) = [ (16 * T) / (π * τ_design) ]^(1/3)

Verification Calculation Log

1Torque (T) is directly specified by the user:
- •Torque (T) = 200.00 N·m
2Calculate Design Shear Stress (τ_design) based on Factor of Safety (FOS):
- •Formula: τ_design = τ_allow / FOS
- •Inputs: τ_allow = 50 MPa, FOS = 2
- •Design Shear Stress (τ_design) = 50 / 2 = 25.00 MPa
3Size Solid Shaft Outer Diameter (D_o) under pure torsion:
- •Formula: D_o = [ (16 * T) / (π * τ_design) ]^(1/3)
- •Convert τ_design to Pascals (N/m²): τ_design = 25.00 MPa = 2.500e+7 Pa
- •D_o (meters) = [ (16 * 200.00) / (π * 2.500e+7) ]^(1/3) = 0.03441016055312399 m
- •Convert to mm: D_o = 0.034410 * 1000 = 34.41 mm

Design Tips

Engineering Application Notes

Design Tips: - Place pulleys and gears close to bearings to minimize bending moments and deflection. - Use generous shoulder fillet radii where gears or bearings seat to reduce stress concentration. - Hollow shafts offer high torque-to-weight ratio for weight-critical applications; material near the center carries little torsional load. - Allowable shear is typically 30% of yield strength (Sy) or 18% of ultimate tensile strength (Su), whichever is lower per ASME B106.1M. - Apply 25% reduction to allowable stress when keyways are present per ASME B106.1M.

Common Mistakes

Common Mistake: Omitting Bending MomentsBelieving the shaft only undergoes torsion neglects radial forces from pulleys, belts, and gear mesh. Always check combined loading when transverse loads exist.

Common Mistake: Neglecting Fatigue on Rotating ShaftsRotating shafts experience fully reversed bending stress every revolution. Fatigue allowable stresses are significantly lower than static yield limits. Use ASME combined loading formula for fatigue design.

Common Mistake: Keyway Correction NeglectPer ASME B106.1M, keyways cut through the outermost fibers where bending and torsional stresses peak. Reduce allowable shear stress by 25% when keyways are present.

Frequently Asked Questions

What is the difference between a shaft and an axle?

A shaft transmits torque and power between rotating machine elements like gears and pulleys. An axle primarily supports rotating components or wheels without transmitting significant torque.

How do you calculate shaft diameter from power and speed?

First convert power and speed to torque using T = (Power × 60) / (2 × π × RPM) for metric, or T = (HP × 63025) / RPM for imperial. Then apply the ASME torsion formula d = [16T / (π × τ_allow)]^(1/3).

What is ASME B106.1M and why does it matter?

ASME B106.1M is the standard for designing transmission shafts. It defines allowable shear stress limits (30% of yield or 18% of ultimate, whichever is lower) and the combined loading formula.

When should you use a hollow shaft instead of a solid one?

Hollow shafts are preferred when weight reduction is critical. Material near the center carries very little torsional load, so removing it reduces weight without significantly reducing torque capacity.

What factor of safety should I use for shaft design?

For well-defined loads with reliable material data, FOS of 1.5 to 2.0 is typical. For uncertain or shock loads, FOS of 2.5 to 3.0 or higher may be needed.

How do stress concentrations affect shaft fatigue life?

Stress concentrations at keyways, shoulders, and grooves create local stress peaks that can be 1.5 to 3 times the nominal stress. Under cyclic loading, these become fatigue crack initiation points.

What material properties matter most for shaft design?

The two most critical properties are yield strength (Sy) and ultimate tensile strength (Su). For fatigue-critical shafts, the endurance limit (Se) is also important.

What is the difference between pure torsion and combined loading?

Pure torsion assumes the shaft only carries torque. Combined loading accounts for both bending moment and torque using the ASME formula. In real applications, shafts almost always experience both.

Why does keyway presence reduce allowable shaft stress by 25%?

Keyways create sharp internal corners and cut through the shaft's outermost fibers where stresses are highest. This geometric disruption acts as a stress concentrator.

When should shaft deflection be checked instead of stress limits?

For long shafts or shafts supporting precision gears. Excessive deflection at gear seats causes misalignment, noise, and premature wear.

Domain of Validity

Valid for solid circular shafts of steel and other metals under combined bending and torsion. Assumes ductile material behavior. Not valid for hollow shafts, composite materials, or non-circular cross-sections.

Worked Example

M = 500 N.m, T = 300 N.m, Sy = 400 MPa, N_sf = 2: d = [(16 x 2 / (pi x 400e6)) x sqrt(500^2 + 300^2)]^(1/3) = 28.4 mm. Round up to 30 mm standard shaft.

Verification

ASME B106.1M and ASME DE-Goodman criteria verified. Last verified: August 2026.

Accuracy and Uncertainty

Results accurate to plus/minus 3% for standard loading. Fatigue life predictions have plus/minus 50% uncertainty due to surface finish and loading variability.

Shaft Design Reference & Combined Loading Tools

Explore comprehensive shafting design guides, stress formulas, and motor power relations:

Shaft Design BasicsFatigue, keyways & ASME sizing guide ASME Shaft Sizing FormulaCombined bending and torsion equations Torsional Shear StressSolid and hollow shaft torsion derivation Combined Bending & TorsionInteractive ASME DE-Goodman calculator

Frequently Asked Questions

What is the ASME shaft diameter formula?

The ASME B106.1M formula for combined bending and torsion is: d = [(16 x N_sf / (pi x Sy)) x sqrt(M^2 + T^2)]^(1/3), where N_sf = safety factor, Sy = yield strength, M = bending moment, T = torque.

What safety factor should I use?

For well-defined loads with reliable material data, FOS of 1.5 to 2.0 is typical. For uncertain or shock loads, FOS of 2.5 to 3.0 or higher may be needed. ASME B106.1M implicitly builds in a safety margin through its allowable stress limits.

How do stress concentrations affect shaft fatigue life?

Stress concentrations at keyways, shoulders, and grooves create local stress peaks that can be 1.5 to 3 times the nominal stress. Under cyclic loading, these hotspots become fatigue crack initiation points. ASME B106.1M requires a 25% reduction in allowable stress when keyways are present.

What material properties matter most for shaft design?

The two most critical properties are yield strength (Sy) and ultimate tensile strength (Su). For fatigue-critical shafts, the endurance limit (Se) is also important. Common materials: AISI 1045, AISI 4140, AISI 4340.

What is the difference between pure torsion and combined loading?

Pure torsion: d = [16T / (pi x tau_allow)]^(1/3). Combined loading: d = [(16 x N_sf / (pi x Sy)) x sqrt(M^2 + T^2)]^(1/3). Combined loading always produces a larger required diameter.

Calculated Sizing outputs

Required Outer Diameter (Do)

34.410mm

Inner Diameter is not applicable to Solid Shaft profiles.

Design Allowable Stress

25MPa

Calculation Summary

Input Parameters

Shaft Profile Type	Solid Shaft
Calculation Source	Applied Torque
Torsional Moment	200N·m
Bending Moment (M)	0N·m
Allowable Shear Limit (τ_allow)	50MPa
Factor of Safety (FOS)	2

Calculated Results

Required Outer Diameter (Do)	34.410mm KEY
Allowable Design Stress	25.00MPa

Safety Notes

Omitting bending moments: Pulleys, belts, and gear radial forces create bending that must be included.

Neglecting fatigue on rotating shafts: Rotating shafts experience fully reversed bending cycles requiring lower allowable stresses.

Keyway correction — ASME B106.1M requires 25% reduction in allowable stress when keyways are present.

Mathematical Models & Equations

Torsional Shaft Sizing Equations (Solid Shaft)

Design Shear Stress (τ_design) = Allowable Shear Stress (τ_allow) / Factor of Safety (FOS)
Outer Diameter (D_o) = [ (16 * T) / (π * τ_design) ]^(1/3)

Verification Calculation Log

1Torque (T) is directly specified by the user:
- •Torque (T) = 200.00 N·m
2Calculate Design Shear Stress (τ_design) based on Factor of Safety (FOS):
- •Formula: τ_design = τ_allow / FOS
- •Inputs: τ_allow = 50 MPa, FOS = 2
- •Design Shear Stress (τ_design) = 50 / 2 = 25.00 MPa
3Size Solid Shaft Outer Diameter (D_o) under pure torsion:
- •Formula: D_o = [ (16 * T) / (π * τ_design) ]^(1/3)
- •Convert τ_design to Pascals (N/m²): τ_design = 25.00 MPa = 2.500e+7 Pa
- •D_o (meters) = [ (16 * 200.00) / (π * 2.500e+7) ]^(1/3) = 0.03441016055312399 m
- •Convert to mm: D_o = 0.034410 * 1000 = 34.41 mm

Design Tips

Engineering Application Notes

Common Mistakes

Related Calculators

Shaft Combined Bending & Torsion

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Shaft Torsional Deflection & Stress

shafts

Engineering Unit Converter

unit conversion

Material Weight Calculator

materials

Applicable Standards

ISO 281 Bearing Life Calculation: L10 Life & Dynamic Load Rating

ISO CODE

ASME B106.1M Transmission Shafting Sizing

ASME CODE

ANSI/AGMA 2001-D04 Gear Rating: Bending & Pitting Resistance

ANSI CODE

Related Formulas

Beam Bending Stress Formula (Flexure Equation σ = My/I)

Strength of Materials

Torsional Shear Stress in Shafts

Strength of Materials

ASME Shaft Sizing Formula (ASME B106.1M)

Machine Design

Torque, Speed & Power Relation (P = Tω = 2πNT/60)

Mechanics

Frequently Asked Questions

What is the difference between a shaft and an axle?

A shaft transmits torque and power between rotating machine elements like gears and pulleys. An axle primarily supports rotating components or wheels without transmitting significant torque.

How do you calculate shaft diameter from power and speed?

What is ASME B106.1M and why does it matter?

ASME B106.1M is the standard for designing transmission shafts. It defines allowable shear stress limits (30% of yield or 18% of ultimate, whichever is lower) and the combined loading formula.

When should you use a hollow shaft instead of a solid one?

What factor of safety should I use for shaft design?

For well-defined loads with reliable material data, FOS of 1.5 to 2.0 is typical. For uncertain or shock loads, FOS of 2.5 to 3.0 or higher may be needed.

How do stress concentrations affect shaft fatigue life?

Stress concentrations at keyways, shoulders, and grooves create local stress peaks that can be 1.5 to 3 times the nominal stress. Under cyclic loading, these become fatigue crack initiation points.

What material properties matter most for shaft design?

The two most critical properties are yield strength (Sy) and ultimate tensile strength (Su). For fatigue-critical shafts, the endurance limit (Se) is also important.

What is the difference between pure torsion and combined loading?

Pure torsion assumes the shaft only carries torque. Combined loading accounts for both bending moment and torque using the ASME formula. In real applications, shafts almost always experience both.

Why does keyway presence reduce allowable shaft stress by 25%?

Keyways create sharp internal corners and cut through the shaft's outermost fibers where stresses are highest. This geometric disruption acts as a stress concentrator.

When should shaft deflection be checked instead of stress limits?

For long shafts or shafts supporting precision gears. Excessive deflection at gear seats causes misalignment, noise, and premature wear.

Required Outer Diameter (Do):	34.4102 mm
ASME Design Allowable Stress:	25.00 MPa
Applied Torsional Torque (T):	200.00 N·m
Applied Bending Moment (M):	Not applied (pure torsion)
Pure Torsion Diameter:	N/A
ASME Combined Loading Diameter:	N/A
Governing Mode:	Pure Torsion

Required Outer Diameter (Do):	34.4102 mm
ASME Design Allowable Stress:	25.00 MPa
Applied Torsional Torque (T):	200.00 N·m
Applied Bending Moment (M):	Not applied (pure torsion)
Pure Torsion Diameter:	N/A
ASME Combined Loading Diameter:	N/A
Governing Mode:	Pure Torsion

Shaft Diameter Calculator