Free Tool · EN 1993-1-8 §3.5 & §3.6

Bolted Connection Calculator

Figure out if a bolt can take the load — in seconds. Enter your bolt size, grade, plate details, and shear force. Get shear resistance, bearing resistance, and the utilisation ratio, all backed by EN 1993-1-8. No sign-up, no PDF download — just the numbers an engineer needs.

§3.6 Shear §3.5 Bearing γM2=1.25 M12–M30 4.6 · 8.8 · 10.9

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Results EN 1993-1-8

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Formulas

The Math Behind It

Shear resistance (EN 1993-1-8 §3.6):

Fv,Rd = (0.6 × fub × A) / γM2

γM2 = 1.25  ·  A = shear area (shank or thread)

M20 8.8: Fv,Rd = (0.6 × 800 × 314) / 1.25 = 120.6 kN

Bearing resistance (EN 1993-1-8 §3.5):

Fb,Rd = (k1 × αb × fu × d × t) / γM2

αb = e1/3d0 (end bolt)  |  p1/3d0 − 1/4 (inner bolt)

k1 = 1.0 when e2 ≥ 1.5d0, else 0.6e2/d0

Combined shear + tension (EN 1993-1-8 §3.6):

(VEd / Fv,Rd) + (Ft,Ed / Ft,Rd) ≤ 1.0

Ft,Rd = (0.9 × fub × A) / γM2

Verification — Worked Example

M20 8.8, Single Shear, t = 15 mm

Input

Bolt: M20 8.8  ·  Single shear  ·  S355 plate (fu = 510 MPa, t = 15 mm)
e1 = 40 mm  ·  e2 = 35 mm  ·  p1 = 60 mm  ·  VEd = 100 kN

Shear resistance Fv,Rd

Fv,Rd = (0.6 × 800 × 314) / 1.25 = 150,720 / 1.25 = 120.6 kN

Bearing resistance Fb,Rd

d0 = 22 mm  ·  p1/d0 = 60/22 = 2.73 > 1.5 (inner bolt)

αb = 60/(3×22) − 1/4 = 0.909 − 0.250 = 0.659

k1 = 0.6 × 35/22 = 0.955

Fb,Rd = (0.955 × 0.659 × 510 × 20 × 15) / 1.25 = 77.0 kN

Result

Bearing (77.0 kN) < Shear (120.6 kN) → Bearing governs.

Utilisation = 100 / 77.0 = 129.9% — FAILS.

If VEd = 100 kN, F_v,Rd = 120.6 kN, utilisation = 100/120.6 = 82.9% — PASS.

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Deep Dives

Docs
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How to prepare a PDF for FrameAI — good drawings, bad drawings, what we extract.
Example
Bolted Moment Connection
Full worked project: beam-to-column moment plate, EN 1993-1-8 §6.2, with DXF export.
Docs
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Full list of every EN 1993 and EN 1992 check FrameAI supports — with worked examples.

FAQ

Common Questions

How to calculate bolt shear resistance EN 1993 ▾
Use F_v,Rd = (0.6 × f_ub × A) / γ_M2 from EN 1993-1-8 §3.6. Where f_ub is the bolt ultimate tensile strength, A is the shear area (gross shank when the shear plane passes through the shank, or thread shear area when through the threads), and γ_M2 = 1.25. For M20 8.8 bolts in single shear: F_v,Rd = (0.6 × 800 × 314) / 1.25 = 120.6 kN per bolt.
What is the bearing resistance formula in Eurocode 3 ▾
F_b,Rd = (k_1 × α_b × f_u × d × t) / γ_M2 from EN 1993-1-8 §3.5. k_1 depends on the edge distance e_2 (1.0 when e_2 ≥ 1.5d_0, otherwise 0.6e_2/d_0). α_b depends on end distance (e_1/3d_0 for end bolts, p_1/3d_0 − 1/4 for inner bolts). f_u is the plate ultimate strength, d is nominal bolt diameter, t is plate thickness, γ_M2 = 1.25.
Single shear vs double shear bolted connection ▾
Single shear has one shear plane — the applied load tries to cut the bolt across one section. Double shear has two — the load is carried by two parallel planes, approximately doubling the design resistance. In double shear, both plies must be checked independently and the lower bearing capacity of the two connected plies governs the group design.
Bearing vs shear — which one governs? ▾
Shear resistance is a property of the bolt material and diameter. Bearing resistance is a property of the connected plate — its thickness, ultimate strength, and the spacing of the bolt group. In practice, bearing governs for thin plates (t < 10 mm) and for plates with high f_u (e.g. S690). Shear governs for thick plates with generous end/pitch distances. FrameAI checks both and flags the governing mode.
What is the minimum ply thickness for high-strength bolts? ▾
EN 1993-1-8 Table 3.3 requires t ≥ 0.33d for grades 8.8 and 10.9, and t ≥ 0.25d for grade 4.6. For an M20 10.9 bolt the minimum is 6.6 mm; for M20 4.6 it is 5 mm. Thinner plates risk thread shear-out in the connected material and premature bearing failure.
How to include tension in a bolt group calculation ▾
When a connection carries both shear V_Ed and tension F_t,Ed (e.g. moment end plates), EN 1993-1-8 §3.6 interaction applies: (V_Ed / F_v,Rd) + (F_t,Ed / F_t,Rd) ≤ 1.0. F_t,Rd = (0.9 × f_ub × A_s) / γ_M2. This is a linear interaction — no reduction in shear capacity is needed for tension up to F_t,Rd.
Which Eurocode clauses apply to bolted shear connections? ▾
EN 1993-1-8 §3.5 (bearing resistance), §3.6 (shear resistance), §3.7 (block tearing), §3.9 (bolt groups), and Table 3.4 (design resistance formulas). Design values of f_ub are taken from the relevant product standard (EN 14399 for preloaded HSFG bolts, EN 15048 for structural non-preloaded bolts). γ_M2 = 1.25 applies throughout.
M20 8.8 bolt shear capacity — why 120.6 kN? ▾
M20 grade 8.8 bolt: f_ub = 800 MPa, gross shank area A_s = 314 mm². F_v,Rd = (0.6 × 800 × 314) / 1.25 = 150,720 / 1.25 = 120,576 N = 120.6 kN. Using thread shear area (245 mm²) gives 94.1 kN — always use the shank area unless the shear plane is specifically through the threaded portion.

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