Bolt preload from tightening torque
Preload and stress in a bolt or stud for a known wrench torque, and their share of the yield strength.
F = T / (K · d)σ = F / A_sk_y = σ / σ_yThe accuracy is that of T = K · F · d: with an unknown thread condition and lubrication the actual preload may differ by up to ±30 %. During tightening the bolt is also twisted, so the equivalent stress exceeds the axial one: VDI 2230 limits it to 90 % of the yield strength during tightening, which corresponds to an axial stress of about 70–80 %.
Source: Shigley's Mechanical Engineering Design — torque and preload; ISO 898-1 and ASME B1.1 — tensile stress area
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Per Shigley: plain black steel 0.30; zinc-plated 0.20; lubricated 0.18; cadmium-plated 0.16; with anti-seize compound 0.12. Condition not known: 0.20.
Coarse pitch: M12 1.75; M16 2; M20 2.5; M24 3; M30 3.5; M36 4 mm. Inch threads: pitch = 25.4 / threads per inch (8UN: 3.175 mm).
ISO 898-1: class 5.6 300 MPa; 8.8 640 (d ≤ 16 mm) and 660 MPa (d > 16 mm); 10.9 940; 12.9 1 100. ASTM A193 B7 studs (d ≤ 64 mm): 725 MPa.
Unit converter for this formulaTorque · Length · Pressure · Force and load · Fraction and percent
- N·m1
- kN·m0.001
- kgf·m0.101972
- lbf·ft0.737562
- lbf·in8.85075
- σ — Stress in the threaded section–
- k_y — Share of the yield strength–
More in Strength and bolting
Hoop and longitudinal stresses in the cylindrical shell of a vessel or pipe under internal pressure, the required wall thickness and the allowable pressure per GOST 34233.2 with the weld joint efficiency and allowances.
Tightening torque for a required preload — as a share of the bolt's yield strength — through the nut factor K, which covers the friction in the thread and under the nut.
Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.