Bolt Fatigue Endurance⚠ unverified
Mechanical / Fasteners · Compute the modified endurance limit for a bolt
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| Se_prime | Seprime | Pa | 1.0 | Unmodified (rotating-beam) endurance limit |
| ka | ka | — | 1.0 | Surface-condition modification factor |
| kb | kb | — | 1.0 | Size modification factor |
| kc | kc | — | 1.0 | Loading modification factor |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Se | Pa | Modified endurance limit, in pascals (Pa) |
The science & history
Understanding the Parameters
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Baseline endurance limit $S_e'$ — the endurance limit from an idealised polished rotating-beam specimen, roughly $S_e' \approx 0.5\,S_{ut}$ for steels below ~1400 MPa. It is the ceiling the factors reduce; every real-world imperfection can only lower it.
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Surface factor $k_a$ — accounts for surface finish, the usual fatigue crack origin. Rolled and machined threads, forging skin, and corrosion all reduce it below 1. Thread-rolling after heat treatment is a key improvement: it leaves a smooth, work-hardened, compressively-stressed surface, markedly raising fatigue life.
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Size factor $k_b$ — larger diameters have more highly-stressed material and a higher probability of a critical flaw, so $k_b < 1$ for bigger bolts.
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Loading factor $k_c$ — corrects for load type; axial loading (as in a bolt) gives $k_c \approx 0.85$, lower than pure bending, because the whole section is uniformly stressed.
Registry note: the full Marin equation has additional factors — temperature $k_d$, reliability $k_e$, and a miscellaneous $k_f$ (which for bolts carries the crucial thread fatigue stress-concentration effect). This calculator includes only $k_a k_b k_c$; apply the others (and the thread $K_f$) separately for a complete assessment. See Fatigue Endurance Limit.
Derivation (Approaching a Proof)
The endurance limit is not derived from first principles but built up multiplicatively from a baseline by the Marin factors. The logic: an idealised specimen has endurance limit $S_e'$; each real-world departure (surface, size, loading, temperature, reliability, stress concentration) independently degrades fatigue strength, so their effects compound as a product:
$$S_e = k_a k_b k_c (k_d k_e k_f)\, S_e'.$$
The multiplicative form encodes the assumption that these mechanisms act independently — a rough surface degrades fatigue by the same fraction regardless of size, and vice versa. Each factor is a fitted correlation (e.g. $k_a = a\,S_{ut}^{\,b}$ with tabulated $a,b$ per finish). For bolts, the single most important factor is the thread-root fatigue stress concentration (carried in $k_f$ as $1/K_f$), which is why rolled threads and generous fillets matter so much. This page evaluates the $k_a k_b k_c$ portion.
Dimensional check. The $k$ factors are dimensionless, so $[S_e] = [S_e'] = \text{Pa}$. ✓
History and Development
The Marin factor method is due to Joseph Marin (1960s) and is the standard fatigue-design approach in Shigley's Mechanical Engineering Design. Applied to bolts, it is combined with the Goodman or Gerber mean-stress criterion (Goodman Line) — because a preloaded bolt always has a high mean stress — to set the safe alternating stress. Junker's work on preload and vibration underlies the companion insight that high preload plus a compliant bolt minimises the alternating stress the bolt actually sees.
Related Concepts: Fatigue Endurance Limit, Bolt Fatigue Factor, Goodman Line, Bolt Shank Stiffness, Bolt Proof Load
Notes: Only $k_a k_b k_c$ of the full Marin product; apply $k_d$ (temperature), $k_e$ (reliability), and the thread stress-concentration $K_f$ separately. Use with a Goodman/Gerber mean-stress criterion, since preloaded bolts carry high mean stress.