Automatic combinations

Generating EN 1990 and ASCE 7 combinations, understanding the equations behind them, and reading the generated set critically.

Loads & combinations 5 min read

Elementarium generates load combinations from the design standard and your load groups. The generator is a convenience, not an authority: it applies the rules to the cases and groups you defined, and if those are wrong the combinations will be wrong in a way that looks extremely tidy.

Two standards ship, and a project may hold combinations from both (a Eurocode project can still carry an ASCE combination for comparison):

Standard	Rules generated
EN 1990	ULS 6.10, or the 6.10a / 6.10b pair; SLS characteristic, frequent and quasi-permanent
ASCE 7	LRFD §2.3.1 (combinations 1–7); ASD §2.4.1 (1–10); and the ASD service-level set CC.1–CC.4

A new combination starts on the standard of the project's national code family; you can change it per combination.

The Eurocode equations

For persistent and transient design situations, EN 1990 gives the ultimate limit state combination in equation 6.10:

j \sum γ_{G, j} G_{k, j} + γ_{Q, 1} Q_{k, 1} + i > 1 \sum γ_{Q, i} ψ_{0, i} Q_{k, i} (6.10)

and the alternative pair 6.10a / 6.10b, which many national annexes prefer because it is less conservative:

j \sum γ_{G, j} G_{k, j} + γ_{Q, 1} ψ_{0, 1} Q_{k, 1} + i > 1 \sum γ_{Q, i} ψ_{0, i} Q_{k, i} j \sum ξ_{j} γ_{G, j} G_{k, j} + γ_{Q, 1} Q_{k, 1} + i > 1 \sum γ_{Q, i} ψ_{0, i} Q_{k, i} (6.10 a) (6.10 b)

Each variable action takes a turn as the leading action $Q_{k, 1}$ , with the others accompanying at their $ψ_{0}$ values. That is why the number of combinations grows quickly: one per equation, per leading action, per arrangement.

From load cases to an envelope. Each wind combination is generated once per direction; the favourable-permanent set is the one that governs uplift. Factors are EN 1990 recommended values before any national annex.

Partial factors

Every factor the generator uses is an editable field on the combination, not a constant compiled into the app. The defaults are EN 1990's recommended values; where your national annex departs from them, change the field and say so in the report.

The Load Combinations dialog with the ULS combination selected: Limit state ULS, Usage Design, Evaluation Code · Pro, Standard EN 1990, Rule 6.10, parameters γG,sup 1.35, γG,inf 1.0, γQ 1.50, a toggle for favourable permanent actions, and a footer reading 41 generated combinations — The load combinations dialog for the steel hall’s ULS combination: limit state, usage and evaluation, then Code generation with the standard (EN 1990 or ASCE 7), the rule (6.10 or 6.10a/b), the editable γG,sup, γG,inf and γQ fields, and the switch that also generates every combination with the permanent actions favourable. The 6.10 rule resolves to 41 permutations here.

Factor	Default	Applies to
$γ_{G, s u p}$	1.35	Permanent actions, unfavourable (Table A1.2(B))
$γ_{G, in f}$	1.00	Permanent actions that relieve
$γ_{Q}$	1.50	Variable actions, unfavourable
$ξ$	0.85	Reduction on permanent actions in 6.10b

The ASCE 7 rules work the same way: 1.4D, 1.2D, 0.9D, 1.6L, 1.6Lr, 1.0W, 1.0E and the companion live factor are all fields, so the §2.3.1 exception permitting 0.5 for light live loads is a value you set, not a branch you have to work around.

The ψ factors, by category:

Action	$ψ_{0}$	$ψ_{1}$	$ψ_{2}$
Imposed, domestic and office (A, B)	0.7	0.5	0.3
Imposed, congregation and shopping (C, D)	0.7	0.7	0.6
Imposed, storage (E)	1.0	0.9	0.8
Snow, ≤ 1000 m altitude	0.5	0.2	0
Wind	0.6	0.2	0

Serviceability

EN 1990 has three SLS rules, used for different things. All three are generated:

Combination	Form	Typical use
Characteristic	$G + Q_{k, 1} + \sum ψ_{0, i} Q_{k, i}$	Irreversible effects, cracking checks
Frequent	$G + ψ_{1, 1} Q_{k, 1} + \sum ψ_{2, i} Q_{k, i}$	Reversible effects, vibration comfort
Quasi-permanent	$G + \sum ψ_{2, i} Q_{k, i}$	Long-term deflection, creep

Deflection limits are usually checked under the characteristic or quasi-permanent combination depending on what is being protected. The code clause tells you which, and using the wrong one is a common review comment.

Favourable and unfavourable

A permanent action that relieves the effect being checked is factored at $γ_{G, in f}$ , not $γ_{G, s u p}$ . The generator produces both variants (there is a switch for it, on by default), because a set without them is silently wrong wherever self-weight relieves the effect — uplift on a purlin, a hogging moment, tension in a hold-down — and taking it at 1.35 would be unsafe.

These are STR/GEO combinations. Static equilibrium of the structure as a whole — overturning, sliding, lifting off its supports — is the EQU set, with $γ_{G, s u p} = 1.10$ and $γ_{G, in f} = 0.90$ (Table A1.2(A)). The generator does not produce it; build those combinations by hand.

Every generated set also contains a permanent-only combination: the sum with no variable action leading at all.

Reading the generated set critically

Generation is not verification. Before you use the set:

Count it. Does the number look plausible for the number of variable actions and arrangements? Two variable actions and no arrangements should give a handful, not ninety.
Open the governing one. After solving, look at which combination governs and read its factors. They should be the ones you would have written by hand.
Check for the missing case. Exclusive groups that were not marked exclusive produce combinations with wind from two directions at once: obvious once you look, invisible if you do not.
Regenerate after adding a case. A combination set does not update itself when you add a load case later.

Manual combinations

You can always write a combination by hand: pick the cases and type the factors. Use this for anything the generator does not cover (construction stages, a bespoke accidental situation, a client-specified check) and label it clearly so a reviewer can see it was deliberate.

Load cases for building the inputs, and Envelopes for getting the governing result out of a large set without reading every one.

Something wrong or unclear on this page? Tell us, and it gets corrected.

The Eurocode equations

Partial factors

Serviceability

Favourable and unfavourable

Reading the generated set critically

Manual combinations

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