Generate ULS, accidental and seismic load combinations to EN 1990 (Eurocode - Basis of structural design), with the partial safety factors and ψ combination coefficients applied automatically.
Free online calculator with step-by-step working and one-click Excel (.xlsx) and PDF export.
This tool builds the full set of Eurocode load combinations to EN 1990 from the actions you define. It generates the ultimate limit state combinations by expression 6.10, or the 6.10a/6.10b pair where your National Annex uses them, and the three serviceability combinations - characteristic, frequent and quasi-permanent - taking each variable action in turn as the leading one.
The output is the complete enumerated set with each factor shown, not a single governing number, because which combination governs depends on what you are checking: the case that maximises the column axial load is rarely the case that maximises the overturning moment or the deflection.
6.10 versus 6.10a and 6.10b
EN 1990 offers two routes to the ULS combination. Expression 6.10 is the simple one: full partial factors on everything, with the non-leading variable actions reduced by their psi_0 factors. The alternative is the more/less favourable pair 6.10a and 6.10b, where 6.10a reduces every variable action by psi_0 while 6.10b instead reduces the permanent action by the factor xi, typically 0.85. You take the worse of the two.
The pair always gives a lower - that is, less conservative - governing value than 6.10 alone, which is why many National Annexes adopt it. The saving is real but modest, usually in the range of 5 to 10 per cent, and it comes at the cost of roughly doubling the number of combinations to enumerate. Which route applies is a National Annex decision, not a designer preference.
Worked example - one permanent and two variable actions
Take a permanent action G = 100 kN, an imposed floor load Q = 60 kN (category B, so psi_0 = 0.7, psi_1 = 0.5, psi_2 = 0.3) and a wind action W = 40 kN (psi_0 = 0.6). With gamma_G = 1.35, gamma_Q = 1.5 and xi = 0.85:
Two things to take from this. First, the leading action matters: taking imposed as leading gives 261.0 kN against 258.0 kN for wind leading, so both must be enumerated and the worse taken - you cannot guess which one governs, and with more variable actions the number of permutations grows quickly.
Second, 6.10b governs over 6.10a here (240.8 against 234.0). That is the usual outcome when the permanent action is not dominant. Where dead load dominates, 6.10a can govern instead, which is exactly why the code requires both to be checked rather than just the one that looks worse.
The three serviceability combinations
SLS uses no partial factors on the actions - the load is taken at its characteristic value - but the variable actions are reduced by a different psi factor depending on how long the effect needs to be sustained. On the same actions:
Characteristic (irreversible effects)
G + Q + psi_0 W = 184.0 kN
Frequent (reversible effects)
G + psi_1 Q = 130.0 kN
Quasi-permanent (long-term, creep)
G + psi_2 Q = 118.0 kN
Use the characteristic combination for effects that cause permanent damage, such as cracking a brittle finish; the frequent combination for reversible effects such as comfort and vibration; and the quasi-permanent combination for long-term effects - concrete creep deflection and crack width are both checked at quasi-permanent, which is why that combination appears in EN 1992 rather than EN 1990 alone.
Formula reference
ULS 6.10
∑γG,jGk,j+γQ,1Qk,1+∑i>1γQ,iψ0,iQk,i
ULS 6.10a
∑γG,jGk,j+γQ,1ψ0,1Qk,1+∑i>1γQ,iψ0,iQk,i
ULS 6.10b
∑ξjγG,jGk,j+γQ,1Qk,1+∑i>1γQ,iψ0,iQk,i
SLS characteristic
∑Gk,j+Qk,1+∑i>1ψ0,iQk,i
SLS frequent
∑Gk,j+ψ1,1Qk,1+∑i>1ψ2,iQk,i
SLS quasi-permanent
∑Gk,j+∑i≥1ψ2,iQk,i
Accidental
∑Gk,j+Ad+ψ1,1Qk,1+∑i>1ψ2,iQk,i
Assumptions and limits
The recommended values gamma_G = 1.35, gamma_Q = 1.5 and xi = 0.85 are used unless you change them. These are National Annex parameters and several countries modify them, as they do the choice between 6.10 and the 6.10a/6.10b pair - check your Annex before relying on the defaults.
The combinations generated are for STR and GEO persistent and transient design situations. EQU (static equilibrium, for overturning and uplift) uses a different set of factors with an unfavourable and a favourable permanent action treated separately, and accidental and seismic situations use their own expressions. A permanent action that can act favourably - self-weight resisting uplift - must be entered at its favourable factor, which the tool cannot infer for you.
The psi factors depend on the category of the variable action, and the tool applies the EN 1990 Table A1.1 values. Storage areas, traffic loads and snow above 1000 m all have their own values that differ from the ordinary imposed-floor case used in the example above.
FAQ
Whichever your National Annex specifies - it is a national choice, not a designer preference. If both are permitted, the 6.10a/6.10b pair gives a lower governing value, typically 5 to 10 per cent, at the cost of roughly twice as many combinations to check.
Each in turn - that is the point. You cannot know in advance which gives the worst effect, so every variable action must be taken as leading once, with the others reduced by psi_0. The tool enumerates all of them.
They represent how much of a variable action is likely to be acting at the same time as something else. psi_0 is the combination value used when the action is not leading at ULS, psi_1 the frequent value, psi_2 the quasi-permanent value. They decrease in that order, and psi_2 is the fraction considered permanently present.
It depends on the effect. Instantaneous deflection under full service load uses the characteristic combination; comfort and reversible effects use the frequent one; long-term deflection including creep uses quasi-permanent. Concrete crack width is also checked at quasi-permanent.
No. A permanent action that reduces the effect being checked - self-weight resisting overturning or uplift - is taken at gamma_G,inf, normally 1.0, not 1.35. Applying the unfavourable factor to a stabilising load is unsafe, and the tool cannot detect which case you are in.
The generator covers STR and GEO persistent and transient situations plus the three SLS combinations. EQU uses a different factor set, and accidental and seismic situations have their own expressions - check EN 1990 Table A1.2 directly for those.
