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Connection Design: worked example
A bolted beam-to-column shear connection checked bolt by bolt and plate by plate.
EN 1993-1-8:2005 — Eurocode 3: Design of steel structures — Part 1-8: Design of joints · SI units · Calculator v1.1
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Inputs
| Connection category | Bolted shear |
| Member section | IPE300 |
| Member grade | S355 |
| Sub-type | double angle |
| Bolts | 3 × M20, Class/grade Class 8.8 |
| Pitch / e1 / e2 | 70 / 40 / 40 mm |
| Plate | S275, 10 mm thick |
| Threads excluded from shear plane | No |
| Applied shear | 150 kN |
Design checks All checks pass
| Check | Required | Provided | Utilisation | Result |
|---|---|---|---|---|
| Bolt shear | 150.0 kN | 564.5 kN | 26.6% | PASS |
| Bolt bearing | 150.0 kN | 263.3 kN | 57.0% | PASS |
| Block shear | 75.0 kN/angle | 248.3 kN/angle | 30.2% | PASS |
| Plate/angle capacity | 75.0 kN/angle | 349.3 kN/angle | 21.5% | PASS |
Calculation steps
Bolt shear (2 steps)
EN1993-1-8 Table 3.4
Bolt shear resistance per shear plane
Fv,Rd = αv·fub·A/γM2
αv=0.60, fub=800 MPa, A=245 mm² (As, threaded)
Fv,Rd = 94.1 kN/plane
—
Bolt-group shear capacity
ΣVRd = n·nplanes·Fv,Rd
n=3, nplanes=2 (double shear)
ΣVRd = 564.5 kN vs VEd = 150.0 kN
Bolt bearing (3 steps)
EN1993-1-8 Table 3.4
Bolt bearing resistance (governing bolt)
Fb,Rd = k1·αb·fu·d·t/γM2
k1=2.50, αb=0.61, fu=510 MPa, d=20 mm, t=7.1 mm
Fb,Rd = 87.8 kN
—
Governing ply
Plate/angle t=10.0 mm → 104.2 kN; member web tw=7.1 mm → 87.8 kN
Governs: member web
—
Bolt-group bearing capacity
ΣFb,Rd = n·Fb,Rd(governing ply)
n=3
ΣFb,Rd = 263.3 kN vs VEd = 150.0 kN
Block shear (per angle) (2 steps)
EN1993-1-8 §3.10.2 Eq. 3.9
Block shear (unsymmetric — one tension face, one shear face)
Veff,2,Rd = 0.5·fu·Ant/γM2 + fy·Anv/(√3·γM0)
Ant=290 mm², Anv=1250 mm², fu=430 MPa, fy=275 MPa
Veff,2,Rd = 248.3 kN
—
Two angles share the applied shear equally
Vperelement = VEd/2
150.0/2
Vperelement = 75.0 kN vs Veff,Rd = 248.3 kN
Plate/angle capacity (per angle) (2 steps)
—
Bolt-line depth
Lp = e1(top) + (n−1)·p + e1(bottom)
Lp = 40 + 2×70 + 40
Lp = 220 mm
EC3 §6.2.6(2)
Plate/angle gross shear yielding
Vpl,Rd = Av·(fy/√3)/γM0
Av=2200 mm², fy=275 MPa
Vpl,Rd = 349.3 kN
Design basis and assumptions
- National Annex: none applied as a whole — the EN recommended values are used, except where noted below. There is no National Annex selector; check the values against the annex for your project.
- γM0 = 1.0 and γM2 = 1.25 (EN 1993-1-8 Table 2.1 recommended values) for bolts, welds and net sections.
- Covers exactly three connection types — bolted shear, bolted moment, welded — not a hybrid bolted-and-welded configuration.
- Applied loads (shear, moment, eccentric load) are inputs from your own analysis or load combination — this tool doesn’t derive them from a larger structural model.
- Bolted moment: row tensions come from an elastic (linear) distribution about the centre of the compression flange — a conservative simplification of the EN 1993-1-8 §6.2.7.2 plastic distribution. Every tension row is checked as its own equivalent T-stub, and every contiguous group of rows between the flanges as a group; the beam web in tension is checked for the same rows and groups (§6.2.6.8).
- Bolted moment scope: the column side (flange and web in tension, compression and shear), the beam flange/web in compression, bolt bearing on the end plate and joint stiffness/rotation capacity are not checked — an overall PASS covers only the listed checks.
- Welded connections use the basic (direction-independent) weld-strength method, not the directional-strength-increase method.
- End-plate effective lengths follow EN 1993-1-8 Table 6.6 by bolt-row location (extension row uses mx/ex as a separate T-stub). m is derived from the gauge, web and weld (Fig. 6.8), not entered. The Figure 6.11 α factor is entered by you from the chart (4.45–8; 4.45 is the conservative lower bound). Tension-zone bolts are assumed fully used in tension when checking their shear. AISC mode applies the same T-stub with φ = 0.90 — not the AISC Design Guide 4/16 yield-line method.
- Verified against hand calculations, published code tables and textbook examples. For real projects, have a licensed engineer review the results.
Example values for illustration only. Results are checked against a published validation suite; for real projects, have a licensed engineer review the results.