Automatic Load Combination Generator: Eurocode EN 1990 and DK NA Implementation

The greenStruct automatic load combination generator implements Table A.1.8 from EN 1990 and Table A1.2(B+C) from the Danish National Annex (DK NA), producing complete, code-compliant load combinations for foundation design.

Author: Daniel Fester Henningsen
Published: February 5, 2026
Featured image: Automatic Load Combination Generator: Eurocode EN 1990 and DK NA Implementation

Introduction

Manual generation of load combinations according to Eurocode EN 1990 is a tedious and error-prone task. For even a simple structure with 3-4 load cases, engineers must create 15-20 unique combinations considering multiple limit states, variable load arrangements, combination factors ($\psi_0$, $\psi_1$, $\psi_2$), and reliability differentiation factors.

The greenStruct automatic load combination generator implements Table A.1.8 from EN 1990 and Table A1.2(B+C) from the Danish National Annex (DK NA), producing complete, code-compliant load combinations for foundation design. The tool handles both structural resistance and geotechnical design scenarios, with intelligent duplicate avoidance when reliability factors equal 1.0.

Getting Started with the Generator

The load combination generator offers two modes: Default (manual combinations) and Auto-generated (automatic Eurocode combinations). When Auto-generated mode is selected, users specify which limit states to generate—ULS (Ultimate Limit State) and/or SLS (Serviceability Limit State)—and the tool creates all required combinations.

Screenshot showing Default/Auto-generated toggle button
Figure 1: Mode selection toggle between Default and Auto-generated combinations

EN 1990: Generic Implementation

The generator implements Table A.1.8 from EN 1990, which defines partial factors for verification cases VC1 through VC4. These cover structural resistance (STR), static equilibrium (EQU), and geotechnical design (GEO).

Structural Resistance Combinations (VC1/VC2)

For each variable action designated as leading, three combination types are generated according to expressions 6.10, 6.10a, and 6.10b:

Expression Description $\gamma_G$ (unfav) $\gamma_{Q,\text{lead}}$ $\gamma_{Q,\text{acc}}$
6.10 Leading variable dominant $1.35 \cdot k_F$ $1.5 \cdot k_F$ $1.5 \cdot k_F \cdot \psi_0$
6.10a All variable actions with $\psi_0$ $1.35 \cdot k_F$ $1.5 \cdot k_F \cdot \psi_0$
6.10b Reduced permanent, $\xi = 0.85$ $\xi \cdot 1.35 \cdot k_F$ $1.5 \cdot k_F$ $1.5 \cdot k_F \cdot \psi_0$

Where $k_F$ is the reliability differentiation factor (default = 1.0 for consequence class CC2). Favorable permanent actions use $\gamma_{G,\text{inf}} = 1.0$. The reduction factor $\xi = 0.85$ applies only to expression 6.10b.

Geotechnical Design Combinations (VC3/VC4)

These combinations verify soil-structure interaction and are always generated in foundation design applications:

Case Application $\gamma_G$ $\gamma_Q$
VC3 Geotechnical with unfavorable variable actions 1.0 1.3 (lead)
$1.3 \cdot \psi_0$ (acc)
VC4 Geotechnical with favorable variable actions 1.0 1.0 (all)
Note: VC3 generates one combination per variable action (as leading). VC4 generates a single combination with all factors at 1.0. Both are essential for foundation bearing capacity verification against soil failure.

EN 1990 DK NA: Danish National Annex

Table A1.2(B+C) from the Danish National Annex provides modified partial factors specific to Danish practice. The generator implements intelligent combination logic that adapts based on the reliability differentiation factor $K_{FI}$.

Smart Duplicate Avoidance

When $K_{FI} = 1.0$, combinations 1-2 (with $K_{FI}$ factors) would be mathematically identical to combinations 3-4 (standard factors). For example:

  • Combo 1: $\gamma_{G,\text{sup}} = 1.2 \times 1.0 = 1.2$ (identical to Combo 3)
  • Combo 2: $\gamma_Q = 1.5 \times 1.0 = 1.5$ (identical to Combo 4)

To avoid this redundancy, the generator selects combinations based on $K_{FI}$ value:

When $K_{FI} \neq 1.0$: Generate Combos 1, 2, and 5 (with $K_{FI}$-adjusted factors)
When $K_{FI} = 1.0$: Generate Combos 3, 4, and 5 (standard factors)

Combination 5 (geotechnical) is always generated regardless of $K_{FI}$, as it uses $\gamma = 1.0$ for all actions.

DK NA Partial Factors (Table A1.2)

Combo Expr. $\gamma_{G,\text{sup}}$ $\gamma_{G,\text{inf}}$ $\gamma_Q$ (leading) $\gamma_Q$ (acc) Generated
1 6.10a $1.2 \cdot K_{FI}$ 1.0 0 0 $K_{FI} \neq 1$
2 6.10b $1.0 \cdot K_{FI}$ 0.9 $1.5 \cdot K_{FI}$ $1.5 \cdot \psi_0 \cdot K_{FI}$ $K_{FI} \neq 1$
3 6.10a 1.2 1.0 0 0 $K_{FI} = 1$
4 6.10b 1.0 0.9 1.5 $1.5 \cdot \psi_0$ $K_{FI} = 1$
5 6.10a 1.0 1.0 0 0 Always

The rightmost column indicates when each combination is generated. Combination 5 (highlighted) is the geotechnical combination and is always produced for foundation design.

Serviceability Limit State (SLS) Combinations

The characteristic combination (Expression 6.14b) is generated for SLS verification of deflections, cracking, and vibrations. All actions use $\gamma = 1.0$, with combination factors applied:

  • Permanent actions: $\gamma_G = 1.0$ (characteristic value)
  • Leading variable action: $\gamma_Q = 1.0$ (full characteristic value)
  • Accompanying variable actions: $\gamma_Q = \psi_0$ (reduced value)

One SLS combination is generated for each variable action designated as leading. If only permanent actions are present, a single combination with all $\gamma = 1.0$ is generated, as deflection and crack checks remain necessary.

Combination Factors ($\psi_0$, $\psi_1$, $\psi_2$)

The $\psi$ factors reduce variable actions when they act simultaneously. The DK NA specifies different values from generic EN 1990:

Load Category EN 1990 ($\psi_0$) DK NA ($\psi_0$)
Category A: Residential 0.7 0.5
Category B: Office 0.7 0.6
Category E: Storage 1.0 0.8
Snow (standard) 0.5 0.3
Wind (standard) 0.6 0.3

The DK NA uses more conservative (lower) $\psi_0$ values, reducing the influence of accompanying variable actions. The generator automatically applies the correct factors based on the selected National Annex.

Configuring Partial Factors

After selecting Auto-generated mode, configure which limit states to generate (ULS and/or SLS) and set the partial factors. The generator provides input fields for all partial factors, allowing customization for specific projects. Default values comply with standard Eurocode requirements (consequence class CC2):

Screenshot showing ULS/SLS checkboxes and partial factors: γG,sup = 1.35, γG,inf = 1, ξ = 0.85, γQ = 1.5, KFI = 1
Figure 2: Load system configuration showing limit state selection and partial factors (DK NA notation with $K_{FI}$)

For projects with different consequence classes, adjust $K_{FI}/k_F$:

  • CC1 (low consequences): $K_{FI} = 0.9$
  • CC2 (normal consequences): $K_{FI} = 1.0$ (default)
  • CC3 (high consequences): $K_{FI} = 1.1$

All factors update immediately when modified, and the generator automatically recalculates all combinations when the "Regenerate" button is clicked.

Practical Workflow

The following workflow demonstrates the complete process from configuring the generator to obtaining final design loads for foundation calculations. Partial factors should already be configured as described in the previous section.

Step 1: Define Load Cases

Enter characteristic loads in the load cases table. For each load case, specify:

  • Name and load type (Permanent, Imposed, Snow, Wind, Temperature)
  • Load values: $F_z$ (vertical), $F_x$, $F_y$ (horizontal), $M_x$, $M_y$ (moments)
  • Subcategory (for imposed loads: A-H corresponding to building use)
  • Favorable checkbox (for loads that reduce design actions)
Screenshot showing table with Formar (permanent), Favorable (permanent), Formar - Nyttelast (imposed), and Load 3
Figure 3: Load cases input table with characteristic values and categories

Step 2: Review Generated Combinations

After clicking "Regenerate", the tool creates all required combinations based on the selected standard and limit states. Each combination displays:

  • Combination name and expression (e.g., "SLS - Char", "ULS - DK Combo 4 (6.10b)")
  • Limit state (LS) and duration classification
  • Partial factors for each load case (marked with yellow "Auto" badges)

The Auto badges indicate auto-generated factors. Clicking any factor allows manual override, which the tool preserves during regeneration.

Screenshot showing generated combinations with Auto badges on factors
Figure 4: Auto-generated load combinations with partial factors (DK NA example showing DK Combo naming)

Step 3: Final Design Loads

The load combinations results table displays the final design loads calculated as $F_d = \gamma \cdot F_k$ for each combination. These design loads are directly used in foundation bearing capacity, stability, and settlement calculations.

Screenshot showing design loads Fz,d, Fx,d, Fy,d, Mx,d, My,d for each combination
Figure 5: Final design loads for all combinations, ready for foundation analysis (results from DK NA combinations)

Technical Implementation Notes

Foundation-Specific Design

This generator is specialized for foundation design in greenStruct. All load cases represent structural actions from the building superstructure. Soil actions (earth pressure, water pressure, base friction) are calculated separately within the foundation analysis modules.

Geotechnical combinations (VC3/VC4 or DK Combo 5) are always generated because they define how structural loads should be factored when verifying bearing capacity and soil stability, even though soil resistances themselves are not part of the load combination input.

Reliability Differentiation ($k_F$ / $K_{FI}$)

Both standards allow consequence class adjustment via reliability factors. The smart duplicate avoidance ensures efficient output: when $k_F = 1.0$, only one set of combinations is generated rather than producing mathematically identical pairs.

Conclusion

The greenStruct automatic load combination generator eliminates manual combination creation while ensuring full compliance with Eurocode EN 1990 (generic or Danish National Annex). By implementing Tables A.1.8 and A1.2 with intelligent duplicate avoidance, category-specific $\psi$ factors, and reliability differentiation, the tool produces complete, verified load combinations for foundation design.

Engineers can focus on structural analysis and optimization rather than verifying partial factors, confident that their designs are based on correct, code-compliant load combinations.

References

  • EN 1990:2002+A1:2005 – Eurocode: Basis of structural design
  • EN 1990 DK NA:2013 – Danish National Annex to Eurocode
  • EN 1990:2002 Table A.1.8 – Partial factors for verification cases VC1-VC4
  • EN 1990 DK NA Table A1.2(B+C) – Design values for STR/GEO (sets B and C)