Formula
As = π/4 · (d − 0.9382·P)² Proof load Fp = Sp · As Target preload F = (percentage/100) · Fp Tightening torque T = K · F · d
d is the nominal diameter (mm), P the pitch (mm) and Sp the proof stress for the property class. T = K·F·d lumps thread and bearing-face friction into a single torque coefficient K. It is the form most widely used in design practice.
Proof stress by property class
| Class | Sp (MPa) | Note |
|---|---|---|
| 4.6 | 225 | General structural |
| 5.6 | 280 | |
| 8.8 | 580 / 600 | M16 and below / above M16 |
| 10.9 | 830 | |
| 12.9 | 970 | Common for socket head cap screws |
Automated tests check that the tensile stress area matches the ISO 898-1 table values (M10 58.0 mm², M12 84.3 mm², M20 245 mm² and others) to within 0.6 %.
Worked example
M10, class 8.8, dry (K 0.20), 75 % of proof load:
- As = π/4 × (10 − 0.9382 × 1.5)² ≈ 58.0 mm²
- Proof load = 580 × 58.0 ≈ 33.6 kN, target preload ≈ 25.2 kN
- Torque = 0.20 × 25,225 N × 0.010 m ≈ 50.5 N·m (about 5.1 kgf·m)
With oil on the threads (K 0.15) the same preload needs only about 37.8 N·m. Tightening an oiled bolt to the dry torque can overload it.
Limitations
- When preload is controlled by torque, friction scatter makes the actual preload vary by roughly ±25 %. For critical joints, follow the manufacturer's recommended torque or measure preload directly.
- These values do not apply directly to fine threads, stainless steel bolts or internal threads in soft materials such as aluminium.
- Joints with their own rules, such as high-strength friction-grip bolts, must follow the tightening method in that standard.
References
- ISO 898-1, Mechanical properties of fasteners made of carbon steel and alloy steel (proof stress, tensile stress area)
- ISO 261 / ISO 724, ISO general purpose metric screw threads (pitch, basic dimensions)
- Budynas & Nisbett, Shigley's Mechanical Engineering Design, bolt torque T = K·F·d and the torque coefficient