Bolting
Bolt tensile stress area, tension and shear resistance, and preload (BS EN 1993-1-8)
- where
- tensile stress area (mm²)
- nominal bolt diameter (mm)
- thread pitch (mm)
- design tension resistance (kN)
- ultimate tensile strength of the bolt (N/mm²)
- partial factor
- design shear resistance per shear plane (kN)
- shear factor
- preload for preloaded bolts (kN)
Explain this equation
Works out the tensile stress area of a metric bolt and its design resistance in tension and shear, plus the preload for preloaded bolts, using BS EN 1993-1-8.
A thread is weaker than the plain shank. The stress area uses an effective diameter, d less 0.9382 times the pitch, roughly the average of the pitch and minor diameters. Tension resistance is 0.9 of the bolt's ultimate strength over that area, divided by the safety factor γ_M2. Shear through the thread uses α_v instead of 0.9. Preload is 70% of the ultimate strength times the stress area. Dividing by 1000 turns newtons into kN.
Resistance is strength times area times a factor, with a safety factor on top.
Sense check: an M20 8.8 bolt has about 245 mm², about 141 kN design tension and 94 kN design shear per plane through the threads, and a preload of about 137 kN.
Watch out: also check bearing and punching shear in the plates. These are bolt resistances only.
Tensile stress area of a metric bolt from its size and pitch, with the Eurocode design resistances in tension and in shear (threads in the shear plane) and the standard preload.
Enter your values to see the result.
Good to know
The stress area uses the ISO 898-1 definition (mean of pitch and minor diameters, which reduces to d − 0.9382p). Grade 8.8 bolts have fub = 800 N/mm², 10.9 have 1000. Resistances use BS EN 1993-1-8 Table 3.4 with γM2 = 1.25 (UK National Annex). If the shear plane passes through the plain shank, use the shank area πd²/4 and αv = 0.6 instead. Fp,C = 0.7 fub As is the design preload for slip-resistant joints; only 8.8 and 10.9 assemblies may be preloaded, using the tightening method in BS EN 1090-2.
Common mistake
Using the shank area for a bolt whose threads are in the shear plane, which overstates shear capacity by about a third. Also forgetting to check bearing on the plate, which often governs for thin material.
Limits
Single bolt resistances only. Does not check bearing, punching shear, combined shear and tension, prying, or long-joint and packing reductions. Coarse-thread metric bolts.
Sources
- BS EN 1993-1-8 Eurocode 3: Design of joints (Table 3.4: Ft,Rd = k2 fub As/γM2, Fv,Rd = αv fub A/γM2; clause 3.9: Fp,C = 0.7 fub As)
- ISO 898-1:2013 Mechanical properties of fasteners – Bolts, screws and studs (stress area As = π/4 × ((d2 + d3)/2)²; grade 8.8 fub = 800 MPa)
- Eurocode Applied: Table of design properties for metric bolts (As per ISO 898-1; d0 = d + EN 1090-2 Table 11 clearance; M12 d0 13, M16 18, M20 22, M24 26 mm)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the welding procedure specification (WPS), BS EN ISO 15614/9606, BS EN 1090, BS EN 1993 and manufacturers’ data. Structural welds need qualified welders and engineered designs.