Bolt and joint
- Target preload
- Thread pitch
- Metric thread half angle
- Nominal bolt diameter (M12)
- Thread friction coefficient
- Collar friction coefficient
- Washer face outer diameter
- Tensile stress area of M12 (ISO 898-1)
Mechanical · sample calcsheet · 3 pages
Bolt tightening and preload
The wrench torque that develops a target preload in a metric bolt, split into its thread and collar (under-head friction) parts, with the bolt stress checked against the proof strength. Power-screw method as in Shigley's Mechanical Engineering Design.
What this calculation covers
Thread geometry
- Proof strength, property class 8.8
- Pitch (mean thread) diameter
- Thread lead angle
Tightening torque
- Torque carried by the thread
- Mean collar (washer face) diameter
- Torque lost to collar friction
- Equivalent nut factor K
- Wrench torque to apply
Bolt stress at preload
- Preload stress in the bolt
- Share of proof strength used
- Preload within 90% of proof
How friction moves the answer
Most of the wrench torque is spent on friction, so the assumed coefficients dominate. The same calculation as a function of a single shared coefficient:
- Wrench torque for friction μ on thread and collar
- Dry, unlubricated (μ = 0.15)
- Lightly oiled (μ = 0.10)
Results summary
- Reaching a 40 kN preload in this dry M12 joint takes about 94 N·m at the wrench (K ≈ 0.20), stressing the bolt to about 82% of its 8.8 proof strength. Oiling the threads drops the needed torque by nearly a third — tightening to 94 N·m when oiled would overload the bolt.
Try changing…
- Set both friction coefficients to 0.10 — the wrench torque falls to about 66 N·m for the same preload.
- Raise the preload to 48 kN — stress passes 90% of proof and the check fails.
- Use an M16 bolt (d, p, A_t from its table row) — torque rises with diameter even at the same preload.