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Goodman & Gerber Fatigue Mean Stress Correction Calculator

In structural machine design, cyclic stress often occurs with a non-zero mean stress (e.g. rotating shafts under static torque, pre-tensioned bolts).

Cyclic fluctuating stress half-range (Smax - Smin)/2.

Steady static mean stress (Smax + Smin)/2.

Fully reversed endurance limit accounting for Marin surface/size factors.

Material ultimate static tensile strength.

Calculated Result
1.50

Goodman Safety Factor (n)

Gerber Safety Factor (Parabolic)

1.89

Equivalent Reversed Stress (S_eq)

180.0 MPa

Fatigue Life Prediction

Infinite Life (>10⁶ cycles)

Calculation Breakdown

  1. Goodman Criterion: S_a/S_e + S_m/S_ut = 1/nn = 1.50
  2. Gerber Parabola: S_a/S_e + (S_m/S_ut)² = 1/nn = 1.89
  3. Reversed Equivalent: S_eq = S_a / (1 - S_m/S_ut)180.0 MPa

What Is the Goodman & Gerber Fatigue Mean Stress Correction Calculator?

Mean stress correction diagrams (Haigh diagram) plot allowable alternating stress against steady mean stress.

The Goodman relation provides a safe, conservative linear design envelope, while the Gerber relation fits ductile metal experimental data more closely.

How Does the Goodman & Gerber Fatigue Mean Stress Correction Calculator Work?

Calculates linear Goodman factor of safety n_Goodman.

Calculates parabolic Gerber factor of safety n_Gerber.

Computes equivalent fully reversed stress amplitude S_eq.

Verifies whether the component is expected to achieve infinite life (> 10^6 cycles).

Goodman & Gerber Fatigue Mean Stress Correction Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

\text{Goodman: } \frac{S_a}{S_e} + \frac{S_m}{S_{ut}} = \frac{1}{n}, \quad \text{Gerber: } \frac{S_a}{S_e} + \left(\frac{S_m}{S_{ut}}\right)^2 = \frac{1}{n}

Linear Goodman and parabolic Gerber mean stress correction fatigue boundaries.

How to Use the Goodman & Gerber Fatigue Mean Stress Correction Calculator

  1. Enter alternating stress amplitude and static mean stress in MPa.
  2. Enter material endurance limit Se and ultimate tensile strength Sut.

Step-by-Step Example Calculation

Power Transmission Shaft Cyclic Loading

Input Values:

alternatingStressAmpMpa:150
meanStressMpa:100
enduranceLimitSeMpa:300
ultimateTensileStrengthSutMpa:600
Worked Steps: Evaluating rotating shaft bending fatigue under steady axial tensile pre-load.

Understanding Your Result

A safety factor n >= 1.0 predicts infinite cyclic life without fatigue failure.

Goodman is more conservative than Gerber; engineering codes (ASME, AGMA) recommend Goodman for safe design.

Factors That Affect the Result

  • Tensile vs Compressive mean stress: Compressive mean stress (Sm < 0) retards crack opening, significantly raising fatigue thresholds.
  • Surface finish: Rough machining lowers endurance limit Se, scaling down the entire Haigh envelope.

When Should You Use This Calculator?

  • Designing crankshafts, connecting rods, bolted joints, and railway axles subjected to cyclic vibration with static preload.
  • Failure analysis of fatigue fractures.

Assumptions & Limitations

  • Assumes high-cycle fatigue (HCF, N > 10^4 cycles) where stresses remain below yield.
  • Peak stress (Sm + Sa) must also be checked against yield strength Sy to prevent static yielding.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard Shigley machine design textbook and ASME fatigue methodology.

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