---
title: "Factors affecting endurance limit of shafts"
subject: "Machine Design I"
chapter: 5
key: "semester_6/machine_design_i:endurance-limit-modifying-factors"
source: https://www.bctengineer.com/q/semester_6/machine_design_i/endurance-limit-modifying-factors
site: BCT Engineering
---

# Factors affecting endurance limit of shafts

Machine Design I · Chapter 5: Design of shafts

- Asked in: year not given, 5 marks
- Video: [Marin Factors for ENDURANCE LIMITS in Just Over 10 Minutes!](https://www.youtube.com/watch?v=kZwl9Jysk64) — Less Boring Lectures
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/machine_design_i/endurance-limit-modifying-factors
- Whole chapter: https://www.bctengineer.com/md/semester_6/machine_design_i/chapter-5

## Question

Explain the factors that modify the endurance limit of a rotating shaft. Write the Marin equation and describe how each factor is accounted for.

## Short answer

Corrected endurance limit Se = ka kb kc kd ke kf Se' where Se' ≈0.5 Sut. Surface factor ka reduces for rough finish; size factor kb decreases with diameter; load factor kc is1 (bending),0.85 (axial),0.59 (torsion); temperature factor kd; reliability factor ke; miscellaneous kf. Fatigue stress concentration factor Kf =1+q(Kt-1).

## Answer

The endurance limit $S_e'$ found from a standard rotating-beam test on a small polished specimen is much higher than the endurance limit of an actual shaft. The actual value is obtained using the **Marin equation**:

$$
S_e = k_a\, k_b\, k_c\, k_d\, k_e\, k_f\, S_e'
$$

where, for steels, $S_e' \approx 0.5\,S_{ut}$ (for $S_{ut} \le 1400$ MPa, with an upper limit of 700 MPa).

#### Modifying factors

| Factor | Name | Effect |
|---|---|---|
| $k_a$ | Surface factor | Rough surfaces (machined, hot rolled, forged) start cracks more easily than a polished one, so $k_a < 1$. It decreases as $S_{ut}$ increases, for example $k_a = 4.51 S_{ut}^{-0.265}$ for machined steel. |
| $k_b$ | Size factor | Larger shafts have more highly stressed volume and a flatter stress gradient, so a larger diameter gives lower strength. For $2.79 \le d \le 51$ mm, $k_b = 1.24 d^{-0.107}$; $k_b = 1$ for axial load. |
| $k_c$ | Load factor | 1 for bending, 0.85 for axial and 0.59 for torsion (when the tests were for bending). |
| $k_d$ | Temperature factor | Strength falls at high temperature; $k_d = 1$ at room temperature. |
| $k_e$ | Reliability factor | 0.897 for 90 %, 0.868 for 95 %, 0.814 for 99 %, 0.753 for 99.9 %. |
| $k_f$ | Miscellaneous factor | Corrosion, plating, residual stress, and other effects. |

#### Stress concentration

Notches such as keyways, shoulders and grooves are included by the fatigue stress concentration factor $K_f = 1 + q(K_t - 1)$, where $q$ is the notch sensitivity. The nominal alternating stress is multiplied by $K_f$ (or the endurance limit is divided by it).

These corrected values are used in the Soderberg or Goodman equations when designing shafts for fatigue.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The Marin equation for the shaft endurance limit is
   A. Se = Se'/(ka kb kc)
   B. Se = Se' + ka + kb + kc
   C. Se = ka kb kc kd ke kf Se'
   D. Se = 0.5 Sut only
   Answer: C. The specimen limit is multiplied by the modifying factors. (Key point: Marin equation)

2. How does shaft size affect strength?
   A. Larger diameter gives higher strength
   B. Size has no effect
   C. kb is 1 for all bending
   D. Larger diameter gives lower endurance strength (kb decreases)
   Answer: D. A larger stressed volume and flatter gradient reduce strength. (Key point: Size factor)

3. The load factor kc for torsion (bending test basis) is
   A. 0.59
   B. 1
   C. 0.85
   D. 0.897
   Answer: A. 1 for bending, 0.85 axial, 0.59 torsion. (Key point: Load factor)

4. How is a keyway accounted for in fatigue?
   A. By multiplying Se' by 1.5
   B. Using Kf = 1 + q(Kt - 1) applied to the alternating stress
   C. By using Kt directly regardless of notch sensitivity
   D. It is ignored
   Answer: B. q is the notch sensitivity. (Key point: Stress concentration)

## Related in Machine Design I

- [ASME code equation for shaft diameter](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Aasme-code-shaft-diameter-derivation) — Machine Design I, chapter 5
- [Goodman and Soderberg lines for shafts](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Agoodman-soderberg-diagram) — Machine Design I, chapter 5
- [AGMA bending stress equation and its factors](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Aagma-factors-stress-concentration-geometry) — Machine Design I, chapter 9
- [Soderberg design with reversed bending and steady torque](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Asoderberg-bending-torsion-shaft) — Machine Design I, chapter 5
- [Bending stress and safety factor of a spur pinion](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Aagma-bending-stress-safety-factor) — Machine Design I, chapter 9
- [Lewis equation for beam strength of a gear tooth](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Alewis-beam-strength-derivation) — Machine Design I, chapter 9

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