Load Combinations — EN 1990 Eurocode

EN 1990 ULS and SLS load combinations. Fundamental, accidental, and seismic combinations with partial factors gamma_G and gamma_Q for Eurocode design. Educational use only.

This page documents the scope, inputs, outputs, and approach of the EN 1990 Load Combinations tool on steelcalculator.app. The interactive tool runs in your browser; this documentation ensures the page is useful even without JavaScript.

What this tool is for

Generating ULS and SLS load combinations per EN 1990 (Eurocode Basis of Structural Design).
Applying partial factors gamma_G (permanent), gamma_Q (variable) and psi factors (psi_0, psi_1, psi_2) for combination, frequent, and quasi-permanent values.
Identifying the governing combination for a given set of characteristic actions.

What this tool is not for

It does not determine characteristic action values (those come from EN 1991 parts).
It does not handle National Annex variations for all countries (partial factors may differ by country).
It does not produce combination-specific load paths or member forces.

Key concepts this page covers

fundamental ULS combination (EN 1990 Eq. 6.10, 6.10a/b)
accidental and seismic design situations
SLS characteristic, frequent, and quasi-permanent combinations
psi factors for combination of variable actions

Inputs and outputs

Typical inputs: characteristic permanent actions Gk, variable actions Qk (imposed, wind, snow), accidental action Ad, seismic action AEd, and the consequence class.

Typical outputs: all applicable ULS and SLS combinations with computed factored values, the governing combination, and clear identification of the leading variable action.

Computation approach

The tool applies EN 1990 expression 6.10 (or the alternative 6.10a/6.10b twin expressions where permitted by the National Annex). Permanent actions are factored by gamma_G = 1.35 (unfavourable) or 1.0 (favourable). Variable actions are factored by gamma_Q = 1.5, with companion variable actions reduced by psi_0. The tool iterates through each variable action as the leading action to find the most onerous combination.

Frequently Asked Questions

What is the difference between Eq. 6.10 and Eq. 6.10a/6.10b? EN 1990 Eq. 6.10 is the single expression: gamma_G Gk + gamma_Q Qk,1 + gamma_Q psi_0 Qk,i. Equations 6.10a and 6.10b are an alternative pair: 6.10a uses a reduced permanent factor (xi gamma_G) with full variable, while 6.10b uses the full permanent factor with psi_0 on the leading variable. Using the twin expressions can give more economical results, but requires checking both. Which option is allowed depends on the National Annex.

What are the psi factors and how are they used? Psi factors reduce variable actions for combination (psi_0), frequent (psi_1), and quasi-permanent (psi_2) values. Psi_0 is used at ULS to account for the low probability of two variable actions reaching their peaks simultaneously. Psi_1 represents the value exceeded for a small fraction of the reference period (used in SLS frequent combination). Psi_2 represents the long-term average value (used in SLS quasi-permanent combination and in accidental/seismic design situations).

How does EN 1990 differ from ASCE 7 load combinations? The most significant conceptual difference is EN 1990's explicit use of psi factors to distinguish leading and accompanying variable actions, while ASCE 7 uses fixed load factors per combination type. EN 1990 also provides separate partial factors for favourable and unfavourable permanent actions, whereas ASCE 7 uses a single factor (1.2 or 0.9) depending on the combination. The reliability targets differ: Eurocode calibrates to a 50-year reference period with beta = 3.8 for CC2, while ASCE 7 uses a different calibration basis.

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice, a design service, or a substitute for an independent review by a qualified structural engineer. Any calculations, outputs, examples, and workflows discussed here are simplified descriptions intended to support understanding and preliminary estimation.

All real-world structural design depends on project-specific factors (loads, combinations, stability, detailing, fabrication, erection, tolerances, site conditions, and the governing standard and project specification). You are responsible for verifying inputs, validating results with an independent method, checking constructability and code compliance, and obtaining professional sign-off where required.

The site operator provides the content "as is" and "as available" without warranties of any kind. To the maximum extent permitted by law, the operator disclaims liability for any loss or damage arising from the use of, or reliance on, this page or any linked tools.