The fastest way to understand load combinations is to run one column through all of them and watch which wins. This worked example takes a column carrying 519 kN dead, 270 kN live and 30 kN roof, applies the ASCE 7 gravity combinations and the Eurocode 6.10 combination, and finds the governing factored reaction. StructLoads does this automatically, but seeing the arithmetic makes the result legible.
The starting loads
A load takedown gives the service loads at the base of the column: 519 kN dead, 270 kN live and 30 kN roof. These are the unfactored structural loads, the real expected values. Combinations turn them into factored design loads, the basis of limit state design, where the factored demand must stay below the factored capacity.
The ASCE 7 gravity combinations
Apply each ASCE 7 strength combination and take the largest.
| Combination | Calculation | Result |
|---|---|---|
| 1.4 D | 1.4 x 519 | 727 kN |
| 1.2 D + 1.6 L + 0.5 Lr | 623 + 432 + 15 | 1070 kN |
| 1.2 D + 1.6 Lr + 1.0 L | 623 + 48 + 270 | 941 kN |
The live-leading combination governs at 1070 kN, because live load carries the largest factor and there is plenty of it here. That 1070 kN is the factored axial load that sizes the column and its footing. The factors themselves are not round-number guesses: they trace back to Ellingwood, Galambos, MacGregor and Cornell’s probability-based load criterion study for ANSI A58, which calibrated the dead and live factors against statistical load and resistance models so members reach a consistent target reliability.
The Eurocode 6.10 combination
For comparison, Eurocode 6.10 with the roof as the accompanying variable and a combination factor of 0.5 on it gives 1.35 times 519 plus 1.5 times 270 plus 1.5 times 0.5 times 30, which is 701 plus 405 plus 23, or about 1129 kN. The two codes land within about 5 percent, with Eurocode slightly higher because its dead factor of 1.35 exceeds the ASCE 1.2. The full side-by-side is in Eurocode vs ASCE 7 load combinations.
Why the live-leading case wins here
The result depends on the dead-to-live ratio. With 270 kN of live load, the 1.6 factor adds 432 kN, which easily pushes the live-leading case above the 727 kN dead-only case. If the live load were much smaller, say 60 kN, the live-leading case would give 623 plus 96 plus 15, or 734 kN, barely above 727, and a little less live would let the dead-only case govern. This is why you check every case rather than assume, the point of the governing load combination.
Service stays separate
These factored numbers size the member for strength. Deflection and other serviceability checks use the unfactored service loads, 519 plus 270 plus 30, which is 819 kN, with their own lighter combinations. The same loads therefore produce a 1070 kN strength number and an 819 kN service number, for two different questions, as set out in factored loads vs service loads.
Key takeaways: a worked load combination
Run the service loads through every combination and take the largest: here ASCE live-leading governs at 1070 kN, Eurocode 6.10 gives 1129 kN, and the dead-only case at 727 kN does not control. The governing factored value sizes the member; service loads handle serviceability separately. StructLoads computes all combinations and names the governing one as a preliminary figure a qualified engineer confirms.
Quick answers
How do you work through load combinations with numbers?
Take the service loads, dead, live and roof, then multiply each by the factors in every relevant combination and add them. For 519 kN dead, 270 kN live and 30 kN roof, the ASCE live-leading case is 1.2 times 519 plus 1.6 times 270 plus 0.5 times 30, which is 1070 kN. Repeat for every combination and the largest result governs.
What is the governing factored load in the example?
About 1070 kN under ASCE 7, from the live-leading combination 1.2 times dead plus 1.6 times live plus 0.5 times roof. The dead-only case, 1.4 times 519, gives 727 kN, which is smaller, so it does not govern. Under Eurocode 6.10 the same loads give about 1129 kN. The governing value is the one that sizes the member.
Why do ASCE and Eurocode give different numbers?
Because the factors differ. ASCE 7 uses 1.2 on dead and 1.6 on live; Eurocode uses 1.35 on permanent and 1.5 on the leading variable with combination factors on the rest. For the same loads the two land within a few percent, with Eurocode slightly higher here because its dead factor is larger. You apply one code consistently.
When do these gravity combinations not cover the design?
They do not cover it when wind, seismic, uplift or load reversal act, which bring in further combinations, some that subtract load. They also do not cover serviceability, which uses separate, lighter combinations. The gravity combinations here size members for vertical strength; a full design adds the lateral and serviceability cases, confirmed by a qualified engineer.