Load Combination Calculator — NBR 8681 · ASCE 7 · EN 1990

Structures are never checked under a single load. Dead weight, live (imposed) load, wind and earthquake all act together, but not at their peak values at the same instant — so every design code multiplies each nominal (characteristic) action by a partial safety factor γ and reduces the accompanying actions by a combination factor ψ, then adds the parcels into a set of design load combinations. The member is verified against the worst of them.

A load combination calculator takes your nominal actions — G (permanent/dead), Q (variable/live/imposed), W (wind) and E (seismic) — and expands the full family of combinations the code requires, for both limit states:

• ULS — Ultimate Limit State (ELU, strength): the factored combination that sizes the section against yielding, buckling and rupture.
• SLS — Serviceability Limit State (ELS): the near-service combination that checks deflection, vibration and cracking.

What makes this tool different from every other free calculator is that it runs three codes at once — Brazilian NBR 8681, American ASCE 7-16/22 and European EN 1990 (Eurocode) — and lays their combinations side by side, with each parcel's γ·ψ factor shown in colour and the governing case flagged. You immediately see that the same three loads produce a design action that can differ by 15–20% between codes, and exactly which parcel drives the difference. That is invaluable for international projects, for students comparing normative philosophies, and for anyone auditing a combination by hand.

1. Enter the nominal actions. Type the characteristic value of the permanent load G, the variable load Q, the wind load W and, if relevant, the seismic load E. They can be any single consistent quantity — an axial force, a reaction, a moment or a line load — the combination is a linear form, so the factors apply the same way. Leave E = 0 for a non-seismic structure and the seismic rows stay hidden.
2. Pick the occupancy. The ψ (combination) factors for the serviceability combinations depend on use: residential, office/retail or storage/library. This drives the NBR 8681 and EN 1990 SLS ladder automatically (the ULS ψ come fixed from the engine; ASCE 7 uses fixed factors throughout).
3. The ULS combinations are generated by the CalcSteel engine. The three ultimate columns are produced by the same production combination engine that drives the CalcSteel 3D editor — generateCombinations mapped to NBR 8800, AISC 360 and EC3 (EN 1993) — so the γ and ψ factors are the authoritative values the full solver uses, not a hand-typed table.
4. Read the results — no button. The KPI strip shows each code's governing ULS, the bar chart breaks that governing combination into its G / Q / W / E parcels so you see why the codes diverge, and the code-spread badge reports the percentage gap. Below, the full ULS + SLS matrix is listed per code with the governing row highlighted in green and reversal/uplift cases marked.
5. Export. Download CSV — free writes every combination for all three codes — the clause reference, the per-load factors and the factored value — into a spreadsheet-ready file, with no watermark and no login.

Tip: the SI ⇄ imperial toggle above converts the loads and every result (kN ↔ kip); the factors are dimensionless, so the combinations are identical in either system.

The philosophy is shared — factor the loads, combine, take the envelope — but the numbers differ. These are the general/recommended values this calculator uses.

NBR 8681:2003 (Brazil) — normal ULS combination

Fd = Σ γg·Gk + γq·( Q1k + Σ ψ0j·Qjk ), with γg = 1.4 (unfavourable) / 1.0 (favourable) and γq = 1.4 for variable actions, wind included. The leading variable is taken in full; the others enter at ψ0. (NBR 8800 later refines these to γq = 1.5 for live and 1.4 for wind — this tool uses the NBR 8681 general γq = 1.4; switch codes if you need the steel-specific set.)

ASCE 7-16/22 (USA) — strength design (LRFD), §2.3.1

Fixed combination factors, no ψ:

Since ASCE 7-16, wind and seismic are strength-level loads, so the wind factor is 1.0 (it was 1.6 in ASCE 7-05, when W was a service-level load). The ASD service set (§2.4) — D, D+L, D+0.6W, D+0.75L+0.45W, 0.6D+0.6W … — is shown in the SLS column.

EN 1990 (Eurocode) — persistent/transient ULS, §6.4.3.2

Two options. Equation 6.10: Σ γG·Gk + γQ,1·Qk,1 + Σ γQ,i·ψ0,i·Qk,i. Or the more economical pair, whichever governs:

• 6.10a Σ γG·Gk + γQ,1·ψ0,1·Qk,1 + Σ γQ,i·ψ0,i·Qk,i
• 6.10b Σ ξ·γG·Gk + γQ,1·Qk,1 + Σ γQ,i·ψ0,i·Qk,i

with γG = 1.35 / 1.0, γQ = 1.5 and ξ = 0.85. The 6.10a/b pair reduces the permanent action in 6.10b, which is why it usually gives a lighter design than 6.10.

This calculator generates the Eurocode column from the CalcSteel engine's EN 1993 combination set — the single-equation 6.10 family (full γG with the leading variable in full and companions at ψ0, plus the wind-uplift reversal). The 6.10a/b economical pair above is shown for reference; for a design governed by it, run the member in the 3D editor, which evaluates whichever of 6.10a/6.10b controls.

ψ combination factors (imposed / wind), as used here:

Use the ULS (ELU) combination — the one with the γ factors above — for every strength check: bending, shear, axial, buckling, connection design. It is the largest of the factored combinations, and it is what the green Governs row reports.

Use the SLS (ELS) combination — factors near 1.0 — for serviceability: deflection limits (L/250, L/360…), vibration and crack width. Each code offers a ladder of service combinations of decreasing severity:

• Characteristic / rare (G + Q + ψ0·W in EN; G + Q + ψ1·W in NBR) — irreversible SLS, e.g. permanent deflection or cracking of brittle finishes.
• Frequent (G + ψ1·Q + ψ2·W) — reversible effects that occur often, e.g. felt vibration.
• Quasi-permanent (G + ψ2·Q) — long-term effects such as creep and the deflection that finishes actually "see" over the structure's life.

ASCE 7 does not use a ψ-graded serviceability state — deflection is normally checked under the unfactored service loads (D, D+L) or the ASD combinations; this tool lists the ASD set (§2.4) in the SLS column so you still have a comparable service envelope, but treat it as ASCE's service load set rather than a Eurocode-style ψ ladder.

Feed the three codes the same loads and the governing ULS action can differ by 15–20%. There are two structural reasons, both visible in the bar chart:

1. Different permanent-load treatment. NBR uses γg = 1.4 on the dead load; EN 1990 uses 1.35, and in 6.10b even reduces it to ξ·1.35 = 1.1475; ASCE splits it into 1.4D-alone and 1.2D-with-companions. When dead load dominates, the code with the higher γg (NBR) governs.
2. Different leading-variable factor. NBR γq = 1.4 and ASCE 1.6L versus EN γQ = 1.5 — so when live load dominates, ASCE's 1.6 can push its combination above the others, or its lower dead factor can pull it below. The winner depends on the G : Q : W ratio, which is exactly why a side-by-side generator beats memorising one code's rules.

The code-spread badge quantifies the gap as (max − min) / min of the governing ULS, and the KPI strip highlights the governing code. For the reference set (G = 30, Q = 20, W = 15, office) the engine yields NBR 82.6, ASCE 71.0 and EN 84.0 — EN 1990 governs and ASCE is lightest, an 18.3% spread. This is not academic: on a cross-border project (a Brazilian client, a European fabricator, a US reviewer) the same steel member can pass one code and fail another, and the difference is entirely in these factors — not in the analysis.

• Nominal in, factored out. You supply characteristic (nominal, unfactored) actions; the tool applies the code γ and ψ. If your loads are already factored, do not enter them here.
• Linear combination. A combination is a weighted sum of the individual load effects, so it applies directly to any single response quantity (a reaction, an axial force, a moment). For load effects that are non-linear in the loads (P-Δ, large-displacement, some cable/tension structures) combine the loads first and re-analyse — do not superpose effects.
• One leading variable at a time. The generator cycles each variable action as the leading one (live-leading, wind-leading) so the true envelope is captured; you take the worst row.
• Reversal / uplift cases (0.9D + 1.0W, 1.0G + 1.5W…) are included and marked — they matter for wind uplift and overturning even though they are not the maximum when all loads act downward.
• Seismic is shown in the accidental/seismic design situation for each code (ASCE 1.2D+1.0E+L and 0.9D+1.0E; EN 1998 G+E+ψ2·Q). Brazilian seismic detailing is governed by NBR 15421; the NBR seismic row is presented in the accidental-combination form for comparison — confirm the coefficients against NBR 15421 for a real seismic project.
• National Annexes can change the EN recommended γ and ψ values (and NBR 8800 refines the NBR γq). The values here are the code-recommended/general set; always confirm against the annex in force for your jurisdiction. For the full member verification with these combinations, open the model in the CalcSteel 3D editor.