EN 1990 (Eurocode 0) — Load Combination Generator

The EN 1990 (Eurocode 0) Load Combination Generator was developed by Civil Engineer Utku Çiçek. The tool automatically creates ULS (Ultimate Limit State) and SLS (Serviceability Limit State) load combinations in accordance with BS EN 1990:2023. It delivers fast, reliable and code-compliant results for façade engineering, fenestration and general structural design.

With this online tool you can quickly obtain combinations for dead load (G), wind load (W), snow load (S), imposed loads (Q) and seismic action (A_e) per Eurocode. Engineering verification of the results is mandatory for safe design. For detailed support, please contact your façade consultant.

Loads

Results — ULS

Results — SLS

Program Logic (BS EN 1990:2023 — STR)

1. Input Collection
   • Checkboxes for G (Dead), W_p (Wind — pressure), W_s (Wind — suction), S (Snow), Q (Imposed A–H), A_e (Seismic), A_d (Accidental).
   • Select Q Category (A–H) and Snow Region (FI/IS/NO/SE, >1000 m, ≤1000 m).
   • Select Consequence Class and include k_F (CC3=1.10, CC2=1.00, CC1=0.90).
   • Verification Case (VC)
     • VC1 — STR (Structural resistance)
       When? Resistance of members/assemblies is checked.
       Examples: Beams, columns, frames, steel/aluminium members; façade mullions/transoms; anchors and fixings.
     • VC2a / VC2b — EQU (Equilibrium)
       When? Global equilibrium (overturning, uplift, sliding) governs.
       Difference: VC2a (upper) amplifies permanent loads; VC2b (lower) takes G as 1.0. Check both; adopt the more adverse.
     • VC3 — GEO
       When? Shallow foundations or gravity walls where soil–structure interaction governs (per EN 1997).
       Examples: Strip/raft/footings, gabion or gravity walls; machine bases, tower footings.
     • VC4 — GEO (Embedded/Deep)
       When? Embedded retaining/anchored systems and transversely loaded piles (EN 1997).
       Examples: Diaphragm/sheet-pile walls, anchored shoring, quay walls, laterally loaded piles.
     SLS combinations are independent of VC (8.29–8.32 unchanged).
2. Preparation of Factors
   • ψ (Table A.1.7): depends on Q category; for W approx. 0.6/0.2/0.0; for S depends on region (FI/IS/NO/SE and >1000 m: 0.7/0.5/0.2; ≤1000 m: 0.5/0.2/0.0).
   • γ (Table A.1.8) — depends on VC:
     • VC1 (STR): γ_G=1.35·k_F, γ_Q=1.50·k_F.
     • VC2a (EQU–upper): γ_G=1.35·k_F, γ_Q=1.50·k_F.
     • VC2b (EQU–lower): γ_G=1.00, γ_Q=1.50·k_F (use the more adverse of upper/lower).
     • VC3 (GEO): γ_G=1.00, γ_Q=1.30. (For soil effects, γ_E≈1.35 informative.)
     • VC4 (GEO): γ_G=1.00, γ_Q,red≈1.11 (=1.50/1.35). (Table note: “G_k is not factored”.)
   • ξ (8.13–8.14 “lower”): default ξ=0.85; the tool enforces ξ·γ_G ≥ 1.0.
   • SLS factors do not depend on VC (8.29–8.32 constant).
3. Building the Set of Variable Actions
   • Each selected variable action is created as an item with symbol, γ_Q (per VC) and relevant ψ values.
   • W_p and W_s are separate (pressure/suction scenarios listed separately).
   • Q is labelled like Q_A, Q_B, …
4. Generating ULS Combinations
   (8.12) Fundamental — create a row with each selected variable as leading.

   Combination 1 — ULS (8.12): γG·G + γQ·Q_lead + Σ(γQ·ψ0·Q_accompanying)

   (8.13) Upper / Lower — two separate rows; adopt the more adverse.

   2A — ULS (8.13 upper): γG·G + γQ·ψ0·Q_lead + Σ(γQ·ψ0·Q_acc)

   2B — ULS (8.13 lower): ξ·γG·G + γQ·Q_lead + Σ(γQ·ψ0·Q_acc)

   (8.14) Upper / Lower

   3A — ULS (8.14 upper): γG·G

   3B — ULS (8.14 lower): ξ·γG·G + γQ·Q_lead + Σ(γQ·ψ0·Q_acc)

   (8.15) Accidental ULS — γ not applied (permanent loads 1.0·G)

   — ULS (8.15): 1.0·G + A_d + (ψ1 or ψ2)·Q_lead + Σ(ψ2·Q_acc)

   (8.16) Seismic ULS

   4 — ULS (8.16): 1.0·G + A_Ed,ULS + Σ(ψ2·Q)

   For each leading action (e.g., W_p, W_s, S, Q_A), the tool writes separate rows for 8.12/8.13/8.14/8.15 as applicable.

5. Generating SLS Combinations
   (8.29) Characteristic

   1 — SLS (8.29): 1.0·G + 1.0·Q_lead + Σ(ψ0·Q_acc)

   (8.30) Frequent

   2 — SLS (8.30): 1.0·G + ψ1·Q_lead + Σ(ψ2·Q_acc)

   (8.31) Quasi-permanent

   3 — SLS (8.31): 1.0·G + Σ(ψ2·Q)

   (8.32) Seismic SLS

   4 — SLS (8.32): 1.0·G + A_Ed,SLS + Σ(ψ2·Q)

   No SLS combination is defined for Accidental; SLS tables remain the same.

6. Printing / UI
   • Each combination is printed as a row.
   • Symbols: W_p=wind pressure, W_s=wind suction, Q_A…Q_H=use categories, S=snow.
7. Buttons
   • Calculate: Read selections → prepare γ/ψ per VC → produce ULS/SLS combinations → update result tables.
   • Example: Loads a typical set (e.g., G + W_s) and shows results.
   • Clear: Resets all selections and result tables.
8. Notes
   • k_F is derived from CC and applied to γ in VC1/VC2; in VC3/VC4 table values are used without k_F.
   • For 8.13/8.14 “lower”, enforce ξ·γ_G ≥ 1.0.
   • A_d (8.15): γ not applied; combine as 1.0·G + A_d + ψ. For seismic (8.16/8.32), print A_Ed.