EC3 bolted connection calculator
Calculate the resistance of a structural steel bolt to DIN EN 1993-1-8, Table 3.4: shear resistance F_v,Rd, bearing resistance F_b,Rd and tension resistance F_t,Rd. Choose bolt size and grade, enter the connected part, plate thickness and end/edge distances – the calculator returns all checks with a traffic-light assessment, live with every input.
Bolted connection calculator (EC3)
Model: single-bolt check to DIN EN 1993-1-8, Table 3.4 (shear, bearing, tension, interaction). No block tearing, no net/gross member cross-section, no slip-resistant connection (category C). Design tool, not a submittable structural verification.
Results
Calculating …
Formulas and fundamentals
The basis is the design of bolted connections to DIN EN 1993-1-8, Table 3.4 with the partial factor γ_M2 = 1.25. The shear resistance per shear plane is F_v,Rd = α_v·f_ub·A/γ_M2 with the shear coefficient α_v = 0.6 for grades 4.6, 5.6 and 8.8 and α_v = 0.5 for 10.9. The area A is the stress area A_s when the shear plane passes through the threaded portion, otherwise the shank area π·d²/4. Multiple shear planes add up (n·F_v,Rd).
The bearing resistance is F_b,Rd = k_1·α_b·f_u·d·t/γ_M2 with the ultimate strength f_u of the connected part, the bolt diameter d and the governing (smallest) plate thickness t. The coefficient in the load direction is α_b = min(α_d; f_ub/f_u; 1.0), where α_d = e_1/(3·d_0) for end bolts and α_d = p_1/(3·d_0) − 0.25 for inner bolts. Perpendicular to the load, k_1 = min(2.8·e_2/d_0 − 1.7; 2.5) for edge bolts and k_1 = min(1.4·p_2/d_0 − 1.7; 2.5) for inner bolts.
The tension resistance is F_t,Rd = k_2·f_ub·A_s/γ_M2 with k_2 = 0.9. If shear and tension act simultaneously, the interaction F_v,Ed/F_v,Rd + F_t,Ed/(1.4·F_t,Rd) ≤ 1.0 must also be verified. The connection is governed by the smallest resistance; often this is the bearing of thin plates, not the shear of the bolt.
Worked example
An M16 bolt of grade 8.8 (f_ub = 800 N/mm², A_s = 157 mm²) connects S235 plates (f_u = 360 N/mm²) with a governing thickness t = 10 mm. The shear plane is in the thread, there is one shear plane, as an end/edge bolt with k_1 = 2.5 and α_b = 1.0.
Shear: F_v,Rd = 0.6·800·157/1.25 = 60.3 kN. Tension: F_t,Rd = 0.9·800·157/1.25 = 90.4 kN. Bearing: F_b,Rd = 2.5·1.0·360·16·10/1.25 = 115.2 kN.
Here shear governs at 60.3 kN. With thinner plates or smaller edge distances, however, bearing can drop below shear and govern the connection – which is why the calculator checks each failure mode separately.
Frequently asked questions
When is the stress area A_s used and when the shank area?
If the shear plane lies in the threaded portion of the bolt, the stress area A_s governs. If it passes through the unthreaded shank, the full shank area π·d²/4 may be used. The calculator offers both cases via a switch; A_s is the conservative default.
Why is bearing often governing rather than shear?
The bearing resistance F_b,Rd = k_1·α_b·f_u·d·t/γ_M2 depends linearly on the plate thickness t and on the end/edge distances. For thin plates or tight distances (small α_b or k_1) it falls below the bolt shear resistance. Then the plate, not the bolt, governs the connection.
How do end and edge distances enter k_1 and α_b?
In the load direction the end distance e_1 (or spacing p_1) sets α_d = e_1/(3·d_0) and thus α_b. Perpendicular to the load, e_2 (or p_2) sets k_1 = 2.8·e_2/d_0 − 1.7, capped at 2.5. Large distances give the full values α_b = 1.0 and k_1 = 2.5; small distances reduce the resistance.
Which checks are covered and which are not?
The calculator performs the single-bolt checks shear, bearing, tension and shear-tension interaction to Table 3.4. Not included are block tearing, the net and gross cross-section of the member, punching shear and slip-resistant connections (category C). These must be checked separately.
Which partial factor γ_M2 applies?
For the resistance of bolts, bearing and the net cross-section, EC3 and the German National Annex use γ_M2 = 1.25. The value is preset in the calculator but can be adjusted if a different National Annex governs.