What is the difference between ULS STR/GEO and ULS EQU combinations?

ULS STR/GEO combinations (STR = structural resistance, GEO = geotechnical) are used to verify strength and stability of members and foundations. They typically use partial factors γG = 1.35 for permanent actions and γQ = 1.5 for variable actions (recommended values). ULS EQU combinations are used for equilibrium of the structure as a rigid body (e.g. overturning, sliding) and usually apply γG = 0.9 or 1.1 and γQ = 1.5, depending on whether permanent actions are stabilising or destabilising.

How are ψ0, ψ1 and ψ2 factors used in Eurocode load combinations?

The ψ-factors reduce variable actions when they are not the leading action or when checking serviceability. ψ0 is used for accompanying variable actions in ULS combinations, ψ1 for frequent SLS combinations and ψ2 for quasi-permanent SLS combinations. Their values depend on the action type (e.g. imposed load, wind, snow) and are given in EN 1990 Annex A and the relevant parts of EN 1991, often modified by National Annexes.

Can I use this calculator with National Annex values?

Yes. The calculator exposes all key parameters (partial factors γG, γQ, γP, γA and ψ0, ψ1, ψ2 factors) so you can override the default recommended EN 1990 values with those from your National Annex. Always check your National Annex and project specifications before final design.

Does this tool replace a full structural analysis?

No. This tool helps you generate and understand Eurocode load combinations and quickly evaluate design actions, but it does not perform structural analysis or member design. You must still use appropriate structural analysis software or hand calculations and apply the relevant material Eurocodes (EN 1992–EN 1999) for final design and verification.

Eurocode Load Combinations Calculator (EN 1990)

Generate ultimate and serviceability Eurocode load combinations (EN 1990) for permanent, variable, wind, snow and accidental actions. Fully configurable partial and combination factors.

1. Define characteristic actions

Enter characteristic values in consistent units (e.g. kN, kN/m, kN/m²). The calculator works on scalar values and does not check sign conventions.

Permanent action G_k (e.g. self-weight)

Prestress P_k (optional)

Leading variable action Q_k,1 (e.g. imposed load)

Variable action Q_k,2 (e.g. wind)

Variable action Q_k,3 (e.g. snow)

Accidental action A_d (design value)

2. Factors (EN 1990 recommended values – editable)

Partial factors γ

γ_G (perm., ULS STR/GEO) γ_Q (var., ULS STR/GEO) γ_P (prestress) γ_A (accidental)

ULS EQU factors

γ_G,stb (stabilising) γ_G,dst (destabilising) γ_Q,EQU

Combination factors ψ

Typical values (office building):

ψ_0,2 (wind) ψ_0,3 (snow) ψ_1,1 (imposed, frequent) ψ_2,1 (imposed, quasi-perm.)

3. Select design situation

Current: ULS STR/GEO (fundamental)

4. Generated load combinations

Each row shows the combination expression and the resulting design action E_d for the given input actions.

#	Type	Expression	E_d
No combinations yet. Enter actions and click “Generate combinations”.

Eurocode load combinations – overview

Eurocode load combinations are defined in EN 1990: Eurocode – Basis of structural design. They combine permanent actions (G), prestressing (P), variable actions (Q), accidental actions (A) and seismic actions (E) using partial factors γ and combination factors ψ.

Ultimate limit state (ULS) – fundamental (STR/GEO)

For persistent and transient design situations, the basic combination for STR/GEO is:

$$E_d = \gamma_G \cdot G_k + \gamma_P \cdot P_k + \gamma_Q \cdot Q_{k,1} + \sum_{i>1} \gamma_Q \cdot \psi_{0,i} \cdot Q_{k,i}$$

where $Q_{k,1}$ is the leading variable action and $Q_{k,i}$ are accompanying variable actions reduced by the ψ₀ factors.

Ultimate limit state (ULS) – EQU (equilibrium)

EQU combinations check loss of equilibrium of the structure as a rigid body (e.g. overturning, sliding). Permanent actions are split into stabilising and destabilising parts with different γ-factors:

$$E_d = \gamma_{G,stb} \cdot G_{k,stb} + \gamma_{G,dst} \cdot G_{k,dst} + \gamma_Q \cdot Q_{k,1} + \sum_{i>1} \gamma_Q \cdot \psi_{0,i} \cdot Q_{k,i}$$

Accidental limit state

For accidental design situations, the accidental action A_d is combined with the quasi-permanent value of variable actions:

$$E_d = G_k + P_k + A_d + \sum_i \psi_{2,i} \cdot Q_{k,i}$$

Serviceability limit states (SLS)

EN 1990 defines three main SLS combinations:

Characteristic: full leading variable action, others with ψ₀
Frequent: leading variable action with ψ₁, others with ψ₂
Quasi-permanent: all variable actions with ψ₂

Characteristic:

$$E_{d,\,char} = G_k + P_k + Q_{k,1} + \sum_{i>1} \psi_{0,i} \cdot Q_{k,i}$$

Frequent:

$$E_{d,\,freq} = G_k + P_k + \psi_{1,1} \cdot Q_{k,1} + \sum_{i>1} \psi_{2,i} \cdot Q_{k,i}$$

Quasi-permanent:

$$E_{d,\,qp} = G_k + P_k + \sum_i \psi_{2,i} \cdot Q_{k,i}$$

How this calculator works

You enter characteristic actions G_k, P_k, Q_k,1, Q_k,2, Q_k,3 and A_d.
You choose the design situation (ULS STR/GEO, ULS EQU, Accidental, SLS).
The tool applies the selected γ and ψ factors and generates a set of combinations, treating each variable action in turn as the leading action where relevant.
For each combination it shows the symbolic expression and the numerical value of E_d.

Typical ψ-factor values (illustrative)

Values depend on the action type and National Annex. As an example (office building):

Action	ψ₀	ψ₁	ψ₂
Imposed load (category B)	0.7	0.5	0.3
Wind	0.6	0.2	0.0
Snow	0.7	0.5	0.2

Always check the relevant parts of EN 1991 and your National Annex for project-specific values.

Limitations and good practice

This tool does not distinguish between favourable and unfavourable actions; you must apply correct signs and engineering judgement.
National Annexes may modify γ and ψ values and even combination formats – always verify against your local code.
Use the results as input to structural analysis software or hand calculations; they are not a substitute for full design to EN 1992–EN 1999.

Frequently asked questions

Which Eurocode standard defines load combinations?

Load combinations are defined in EN 1990: Eurocode – Basis of structural design. EN 1990 is used together with EN 1991 (actions on structures) and the material Eurocodes (EN 1992–EN 1999).

How many combinations should I check?

In principle, each relevant variable action should be taken in turn as the leading action, with the others as accompanying actions. In practice, engineers often focus on a small set of governing combinations (e.g. imposed + wind, imposed + snow) based on experience and structural behaviour.

Can I include more than three variable actions?

This simplified tool exposes three variable actions. For more complex situations (e.g. multiple imposed load categories, temperature, crane loads), you can group similar actions or run the calculator multiple times with different groupings.

Does the calculator handle seismic combinations?

No. Seismic combinations with action E are defined in EN 1998 (Eurocode 8) and are not covered here. Use dedicated seismic design tools and follow EN 1998 and your National Annex.