Bolt resistances to Eurocode 3

EN 1993-1-8 gives the design resistance of a single bolt in a bearing-type connection with three formulas and one partial factor, γ_M2 = 1.25 (recommended value, confirmed by most National Annexes). The values below are computed from them for the common structural sizes and classes; for the bearing resistance, which depends on the plate and the bolt spacing, and for slip-resistant connections, use the Bolts tool in Steel Profiles.

Formulas

• Shear per shear plane: F_v,Rd = α_v f_ub A / γ_M2. With the threads in the shear plane A is the tensile stress area A_s and α_v = 0.6 for classes 4.6, 5.6 and 8.8, 0.5 for class 10.9. With the shank in the shear plane A is the gross area and α_v = 0.6 for every class.
• Tension: F_t,Rd = k₂ f_ub A_s / γ_M2, with k₂ = 0.9 (0.63 for countersunk bolts).
• Combined shear and tension: F_v,Ed / F_v,Rd + F_t,Ed / (1.4 F_t,Rd) ≤ 1.0.
• Preload (classes 8.8 and 10.9 only, EN 14399 assemblies): F_p,C = 0.7 f_ub A_s. The slip resistance per bolt is then F_s,Rd = k_s n μ F_p,C / γ_M3 with γ_M3 = 1.25 at ultimate (1.1 at serviceability), μ = 0.5 for class A surfaces down to 0.2 for class D.

f_ub is 800 MPa for class 8.8 and 1,000 MPa for class 10.9 (400 and 500 MPa for 4.6 and 5.6). The bolt must also be checked for bearing on the plate: F_b,Rd = k₁ α_b f_u d t / γ_M2, which usually governs with thin plates or small end distances.

Design resistances per bolt

Threads in the shear plane, one shear plane, kN. Hole diameter d₀ is the normal round hole of EN 1090-2 (d + 1 mm up to M14, d + 2 mm from M16 to M24, d + 3 mm from M27).

With the shank in the shear plane the shear resistance rises to 0.6 f_ub A / γ_M2 on the gross area: 120.6 kN for an M20 8.8 and 150.8 kN for an M20 10.9. Note that a 10.9 bolt gains little in shear through the threads over an 8.8 (α_v drops to 0.5) but 25 % in tension and preload.

Reading the table

• A double shear connection (bolt through three plates) has two shear planes: multiply F_v,Rd by 2.
• The resistances are design values: compare them with factored actions (F_Ed), not with working loads.
• Minimum spacing and edge distances of Table 3.3: end distance e₁ ≥ 1.2 d₀, edge distance e₂ ≥ 1.2 d₀, pitch p₁ ≥ 2.2 d₀, gauge p₂ ≥ 2.4 d₀. The usual detailing values are 1.5 d₀ for edges and 3 d₀ for pitch, which also gives the full bearing factor α_b.
• Oversize and slotted holes reduce the slip resistance (k_s = 0.85 to 0.63) and need a hardened washer.
• National Annexes may change γ_M2 and γ_M3: check the one that applies to the project.

In the app

The Bolts tool of Steel Profiles lists M8 to M64 with the ISO 4014 head, ISO 4032 nut and ISO 7089 washer dimensions, the EN 14399 HV dimensions for M12 to M36 and the EN 1090-2 hole clearances, and computes shear, tension, punching shear, bearing (with your plate grade, thickness and end distance) and slip resistance for every class and surface. The imperial side covers 1/2" to 1 1/2" A307, A325 and A490 bolts to AISC 360 Tables J3.1 to J3.4 in LRFD and ASD. Results are design aids and must be verified by a qualified engineer.