Authoritative Data Source and Methodology
Authoritative Data Source: EN 1993-1-8:2005 “Eurocode 3 – Design of steel structures – Part 1-8: Design of joints”. Official copy: EN 1993-1-8:2005 (PDF). All calculations strictly follow the clauses and parameters given for non-preloaded bearing bolts.
Important: Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formula Explained
Glossary of Variables
| Symbol / Field | Meaning | Units |
|---|---|---|
| d | Bolt diameter | mm |
| As | Shank area, π·d²/4 | mm² |
| At | Tensile stress area (≈0.78·As for ISO coarse threads) | mm² |
| fub | Bolt ultimate tensile strength per property class | MPa (N/mm²) |
| αv | Shear factor for non-preloaded bearing bolts (commonly 0.6) | – |
| γM2 | Partial safety factor for bolt resistance | – |
| Fv,Rd | Design shear resistance (per plane, per bolt) | kN |
| Ft,Rd | Design tension resistance (per bolt) | kN |
| VEd, TEd | Total factored shear and tension on the connection | kN |
| n | Number of bolts in the connection | – |
| n_v | Number of shear planes per bolt (1 single, 2 double shear) | – |
How it Works: A Step-by-Step Example
Suppose you have 4 bolts of class 8.8 with diameter d = 20 mm, double shear (n_v = 2), threads not in the shear plane (use As), αv = 0.6 and γM2 = 1.25.
- Areas: As = π·20²/4 = 314.16 mm²; At ≈ 0.78·As = 245.04 mm².
- Shear per plane per bolt: Fv,Rd = αv·fub·A/γM2 = 0.6·800·314.16/1.25 = 120, or 120,? Wait compute precisely: 0.6×800×314.16/1.25 = (480×314.16)/1.25 = 150,796.8/1.25 = 120,637.44 N = 120.64 kN.
- Per-bolt shear in double shear: 2 × 120.64 = 241.28 kN.
- Tension per bolt: Ft,Rd = 0.9·fub·At/γM2 = 0.9·800·245.04/1.25 = 141,? Calculation: 720×245.04/1.25 = 176,428.8/1.25 = 141,143.04 N = 141.14 kN.
- Total connection shear resistance: n·n_v·Fv,Rd(per plane) = 4·2·120.64 = 965.12 kN.
- Total connection tension resistance: n·Ft,Rd = 4·141.14 = 564.56 kN.
If you check against loads VEd = 300 kN and TEd = 200 kN, the per-bolt demands are VEd/n = 75 kN and TEd/n = 50 kN. The combined utilization is sqrt[(50/141.14)² + (75/241.28)²] ≈ sqrt(0.125 + 0.096) ≈ 0.46 < 1.0 → OK.
Frequently Asked Questions (FAQ)
Does this tool cover slip-resistant (preloaded) connections?
No. It covers non-preloaded bearing bolts per EN 1993-1-8 §3.6. Slip-resistant checks require additional parameters (k_s, slip factor μ, preloading force), which are beyond this version.
Can I change the shear factor αv?
Yes. The default is 0.6 for non-preloaded bolts as commonly adopted. Adjust αv if your National Annex or project specification requires otherwise.
Why is At approximated as 0.78·As?
For ISO metric coarse threads, the tensile stress area is approximately 0.78 of the shank area. If you require exact At values, consult ISO tables for the specific thread pitch.
Are eccentric and prying effects considered?
No. The “Check against loads” mode assumes uniform distribution without prying or secondary effects. Use bolt group analysis or finite element methods when eccentricities are present.
What about plate bearing, tear-out, and block shear?
Those are essential verifications per EN 1993-1-8 and plate detailing rules. This tool focuses on bolt resistances. Future versions will add bearing checks with end/pitch distances and hole sizes.
Which units are used?
Input MPa and mm; outputs are in kN. Internally, 1 MPa × 1 mm² = 1 N, then divided by 1000 for kN.
Formula (LaTeX) + variables + units
','
A_s = \frac{\pi d^2}{4} \qquad A_t \approx 0.78\,A_s
F_{v,Rd} = \frac{\alpha_v\, f_{ub}\, A}{\gamma_{M2}}
F_{t,Rd} = \frac{0.9 \, f_{ub} \, A_t}{\gamma_{M2}}
F_{v,Rd}^{(conn)} = n \, n_v \, F_{v,Rd}^{(per\;plane)} \qquad F_{t,Rd}^{(conn)} = n \, F_{t,Rd}^{(per\;bolt)}
\left(\frac{F_{t,Ed}^{(per\;bolt)}}{F_{t,Rd}^{(per\;bolt)}}\right)^2 + \left(\frac{F_{v,Ed}^{(per\;bolt)}}{F_{v,Rd}^{(per\;bolt)}}\right)^2 \le 1.0
$ A_s = \frac{\pi d^2}{4} \qquad A_t \approx 0.78\,A_s $ $ F_{v,Rd} = \frac{\alpha_v\, f_{ub}\, A}{\gamma_{M2}} $ where A = As (threads not in shear) or A = At (threads in shear). $ F_{t,Rd} = \frac{0.9 \, f_{ub} \, A_t}{\gamma_{M2}} $ For a connection with n bolts and n_v shear planes per bolt: $ F_{v,Rd}^{(conn)} = n \, n_v \, F_{v,Rd}^{(per\;plane)} \qquad F_{t,Rd}^{(conn)} = n \, F_{t,Rd}^{(per\;bolt)} $ Combined (non-preloaded bearing bolts – conservative approximation): $ \left(\frac{F_{t,Ed}^{(per\;bolt)}}{F_{t,Rd}^{(per\;bolt)}}\right)^2 + \left(\frac{F_{v,Ed}^{(per\;bolt)}}{F_{v,Rd}^{(per\;bolt)}}\right)^2 \le 1.0 $
- No variables provided in audit spec.
- Engineering — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/engineering - EN 1993-1-8:2005 (PDF) — phd.eng.br · Accessed 2026-01-19
https://www.phd.eng.br/wp-content/uploads/2015/12/en.1993.1.8.2005-1.pdf
Last code update: 2026-01-19
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