Bolt Preload⚠ unverified
Mechanical / Joints · Compute the recommended bolt preload
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| Fi | Fi | N | 1.0 | Nominal preload value (unused in the recommended-preload form) |
| At | At | m**2 | 1.0 | Tensile-stress area of the bolt |
| sigma_p | σp | Pa | 1.0 | Proof strength of the bolt material |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Fi | N | Recommended preload, in newtons (N) |
The science & history
Understanding the Parameters
-
Tensile-stress area $A_t$ — the effective load-bearing area of the threaded section (between pitch and minor diameter), from Bolt Tensile Stress Area. Preload scales directly with it.
-
Proof strength $\sigma_p$ — the stress a bolt can carry with no measurable permanent set (~90 % of yield); the property grade (e.g. 8.8, 10.9, Grade 5/8) defines it. It caps how much preload the bolt can safely hold.
-
The 0.75 factor — for reused fasteners, preload is set to 75 % of proof load: high enough for good clamping and fatigue resistance, low enough to leave margin for the added external load $C F_e$ without yielding. For permanent connections the factor is raised to 0.90.
-
Proof load $A_t\sigma_p$ — the reference the preload is a fraction of; see Bolt Proof Load.
Derivation (Approaching a Proof)
The bolt's usable tensile capacity is its proof load, $F_p = A_t\,\sigma_p$ — the largest tension it can carry without permanent deformation. Preload must sit below this, with enough headroom that the peak bolt tension (preload plus the external-load increment $C F_e$) still stays under proof:
$$F_i + C F_e \le A_t\,\sigma_p.$$
Design practice fixes the preload fraction rather than solving this per joint. Choosing 75 % of proof for reusable joints,
$$F_i = 0.75\,F_p = 0.75\,A_t\,\sigma_p,$$
leaves a nominal 25 % of proof load as margin for the external-load increment and scatter in the tightening method. Permanent joints, tightened once, use $F_i = 0.90\,A_t\sigma_p$.
Dimensional check. $F_i = 0.75\,A_t\,\sigma_p = \text{m}^2\cdot\text{Pa} = \text{m}^2\cdot(\text{N}/\text{m}^2) = \text{N}$ — a force, as required.
History and Development
Preloading transformed bolted joints from loosenable fasteners into fatigue-resistant structural elements. The 0.75 / 0.90 of proof load rule is the Shigley/industry codification of decades of experience: enough preload to keep the joint from separating and to minimise the bolt's cyclic stress, without exhausting the bolt's static margin. Achieving the target in practice — via torque (Bolt Torque from Preload), turn-of-nut, or bolt-stretch measurement — is a whole discipline, because torque control alone scatters preload by $\pm 25\%$ through friction variation.
Related Concepts: Bolt Proof Load, Bolt Tensile Stress Area, Bolt Torque from Preload, Joint Stiffness Ratio, Bolt Load External, Bolt Fatigue Factor
Notes: $0.75\times$ proof load for reused bolts, $0.90\times$ for permanent. Input $F_i$ is unused (placeholder). Proof load $= A_t\sigma_p$; $\sigma_p \approx 0.9\,S_y$. Torque control scatters actual preload ±25%.