Eurocode 0 (EN 1990) – Basis of Structural Design Helper

Build Eurocode 0 ultimate and serviceability load combinations, apply partial factors and check design values step‑by‑step.

Eurocode 0 Load Combination Calculator

RC2: residential, office, standard bridges.

Recommended EN 1990 value (may vary by National Annex).

Recommended EN 1990 value for ULS.

Actions (loads)

Type Name Characteristic value
(Fk) 		ψ0 ψ1 ψ2 Leading? Remove

This helper follows the general format of EN 1990 load combinations. Always verify factors and ψ-values against the relevant National Annex and material Eurocodes.

How this Eurocode 0 helper works

Eurocode 0 (EN 1990) defines the basis of structural design for all other Eurocodes (EN 1991–EN 1999). It introduces reliability concepts, partial factors and load combination rules for ultimate and serviceability limit states.

This tool does not replace the standard, but it helps you assemble design combinations quickly and consistently for preliminary design and teaching.

1. Choose design situation and limit state

  • Persistent / transient: normal long-term use or temporary conditions (e.g. construction).
  • Accidental: rare events such as impact, explosion or fire.

Then select the limit state:

  • ULS – safety against collapse or loss of equilibrium.
  • SLS characteristic – rare serviceability checks (e.g. crack width).
  • SLS frequent – frequent service conditions (e.g. deflection under live load).
  • SLS quasi-permanent – long-term effects (e.g. creep, settlement).

2. Reliability class and partial factors

EN 1990 groups structures into reliability classes (RC1–RC3) based on the consequences of failure. National Annexes may link these to consequence classes and adjust partial factors accordingly.

  • RC1: low consequence (e.g. small agricultural buildings).
  • RC2: normal consequence (residential, offices, standard bridges).
  • RC3: high consequence (large public buildings, critical infrastructure).

The calculator pre-fills recommended γG and γQ values for ULS persistent/transient situations (e.g. γG = 1.35, γQ = 1.50 for RC2), but you can override them to match your National Annex.

3. Define actions and ψ-factors

Add each action (load) with:

  • Type: permanent (G), variable (Q) or accidental (A).
  • Name: e.g. self-weight, imposed load, wind, snow.
  • Characteristic value Fk: in any consistent unit (kN, kNm, etc.).
  • ψ-factors: ψ0, ψ1, ψ2 from EN 1990 / EN 1991 tables.
  • Leading variable action: mark the main variable action for the combination.

4. Combination formulas used

The helper uses simplified forms of the EN 1990 combination rules:

ULS – Fundamental combination (persistent / transient)

\( E_d = \gamma_G \sum G_k + \gamma_Q \left[ Q_{k,1} + \sum_{i>1} \psi_{0,i} Q_{k,i} \right] \)

SLS – Characteristic combination

\( E_{d,\text{char}} = \sum G_k + Q_{k,1} + \sum_{i>1} \psi_{0,i} Q_{k,i} \)

SLS – Frequent combination

\( E_{d,\text{freq}} = \sum G_k + \psi_{1,1} Q_{k,1} + \sum_{i>1} \psi_{2,i} Q_{k,i} \)

SLS – Quasi-permanent combination

\( E_{d,\text{qp}} = \sum G_k + \sum \psi_{2,i} Q_{k,i} \)

For accidental design situations, the tool treats the accidental action as leading and applies γG to permanent actions and ψ-factors to accompanying variable actions, following the general EN 1990 format.

Key concepts from Eurocode 0

Limit states

  • Ultimate Limit States (ULS): loss of equilibrium, collapse, fatigue failure, etc.
  • Serviceability Limit States (SLS): unacceptable deflections, cracking, vibrations, damage to finishes.

Design values and partial factors

EN 1990 uses the partial factor method to achieve a target reliability level. Design values are obtained by multiplying characteristic values by partial factors:

\( F_d = \gamma_F \cdot F_k \)

\( R_d = \dfrac{R_k}{\gamma_M} \)

where γF is the partial factor for actions and γM for material properties. The inequality to be satisfied at ULS is:

\( E_d \leq R_d \)

National Annexes

Eurocode 0 provides recommended values, but each country publishes a National Annex that may modify partial factors, ψ-factors, reliability classes and combination rules. Always check the National Annex applicable to your project.

Worked example

Consider a simply supported beam with:

  • Permanent action Gk = 20 kN/m (self-weight + finishes).
  • Variable action Qk,1 = 10 kN/m (imposed load, leading).
  • Additional variable action Qk,2 = 5 kN/m (snow), ψ0,2 = 0.5.

For ULS, persistent situation, RC2, using γG = 1.35, γQ = 1.50:

\( E_d = 1.35 \cdot 20 + 1.50 \left[ 10 + 0.5 \cdot 5 \right] = 27.0 + 1.50 \cdot 12.5 = 27.0 + 18.75 = 45.75 \,\text{kN/m} \)

Enter these values in the calculator, mark the imposed load as leading, and you should obtain the same design action effect.

Limitations and good practice

  • This tool focuses on global combination rules, not on member or section design.
  • It does not include material partial factors γM or resistance checks.
  • Always cross-check with EN 1990, the relevant EN 1991 parts and material Eurocodes (EN 1992–EN 1999).
  • Use it for pre-design, teaching and quick checks, not as the sole basis for final design.

FAQ

Is this calculator valid for all Eurocode countries?

The combination formats follow EN 1990, but partial factors and ψ-values may differ between National Annexes. Adjust the factors in the inputs to match your country’s requirements.

Can I mix units?

No. All actions must be in consistent units (e.g. all in kN or all in kNm). The calculator treats them as dimensionless numbers and outputs Ed in the same unit.

Where do I find ψ-factors?

ψ-factors for variable actions are given in EN 1990 Annex A and in the relevant EN 1991 parts (e.g. imposed loads on buildings, wind, snow). National Annexes may modify them.