Bolting
Bolt tensile stress area from diameter and thread pitch (ISO 898-1)
- where
- pitch diameter (mm)
- nominal bolt diameter (mm)
- thread pitch (mm)
- minor diameter for stress area, d₁ − H/6 (mm)
- tensile stress area (mm²)
Explain this equation
Calculates the tensile stress area of a metric bolt, the area used for bolt tension, preload and torque. Use it when you have a bolt size and pitch but no table to hand.
d is the nominal diameter and p is the thread pitch, the distance from one thread crest to the next. d₂ is the pitch diameter, where thread and gap are equally wide. d₃ is a diameter slightly below the root of the thread. A_s is the effective area that carries tension.
A threaded bolt breaks across the threads, not the plain shank, so its strength depends on a reduced area. Tests showed the effective area matches a circle whose diameter is the average of d₂ and d₃; the constants come from the shape of the 60° ISO thread.
Sense check: M20 coarse thread (2.5 mm pitch) gives about 245 mm², M24 gives about 353 mm². That is about three quarters of the plain shank area.
Watch out: structural bolts are coarse thread. Entering a fine pitch gives a larger area than the bolt actually has.
Tensile stress area of a metric thread, the area used for bolt tension, preload and torque calculations.
Enter your values to see the result.
Good to know
ISO 898-1 defines As from the mean of the pitch diameter d2 and d3, where d3 = d1 − H/6 and H = 0.866025p is the fundamental triangle height (ISO 724). This gives d2 = d − 0.649519p and d3 = d − 1.226869p. Results round to the familiar table values: M12 84.3, M16 157, M20 245, M24 353, M30 561 mm².
Common mistake
Using the shank area πd²/4, which is about 25% higher than the stress area for M20, or using a fine-pitch value for a coarse-thread structural bolt.
Limits
ISO metric 60° threads. Structural bolts to BS EN 14399 and BS EN 15048 are coarse pitch.
Sources
- BS EN ISO 898-1:2013 Mechanical properties of fasteners made of carbon steel and alloy steel – Bolts, screws and studs (stress area As = π/4 × ((d2 + d3)/2)², d3 = d1 − H/6; fub 800 N/mm² for 8.8, 1000 N/mm² for 10.9)
- ISO 724 ISO general-purpose metric screw threads – Basic dimensions (H = 0.866025p, d2 = d − 0.649519p, d1 = d − 1.082532p)
- Bossard technical data F.040: ISO 898-1 stress area As,nom = π/4 × ((d2 + d3)/2)²; M12 84.3, M16 157, M20 245, M24 353, M30 561 mm²
- BS EN 14399-1 and -3/-4 High-strength structural bolting assemblies for preloading (systems HR and HV, property classes 8.8 and 10.9, k-class declared on the certificate)
- BS EN 15048-1 Non-preloaded structural bolting assemblies – General requirements
Results are calculations from the published methods and figures shown, and depend on the data you enter. Always work to the engineer’s drawings and bending schedules, BS 8666, BS EN 1992, BS EN 1090-2, BS 5531/the BCSA National Structural Steelwork Specification and manufacturers’ data. Lifting must be planned under LOLER by a competent person.