Load Combinations

Factored load combinations — IS / ASCE / Eurocode

Pick a code and the loads present; get the factored combinations with absent-load terms dropped.

Only combinations whose loads are present are listed (a companion imposed load L drops to zero where the code combination still applies). W and E act in both directions (±).

IS 456 (LSD — collapse) — 1 combination
  1. 11.5(D+L)

Reference only. IS 456 Table 18 collapse & serviceability combinations (EL in place of WL), IS 800, ASCE 7-16 §2.3.1/§2.4.1 (roof, snow, rain and vertical Ev omitted) and EN 1990 Eq 6.10 / 6.12b with ψ0 = 0.7 (imposed, cat. A/B), ψ0 = 0.6 (wind), ψ2 = 0.3 (imposed, cat. A/B) — national annexes using Eq 6.10a/b are not covered. Notional loads and thermal cases are not included. Confirm against the governing code, then size members in Section Design.

How the Load Combination Generator works

Every analysis starts with a list of factored load combinations for the governing code. This generator holds the combination sets for IS 456 (limit state of collapse and of serviceability), IS 800 (limit state design), ASCE 7-16 (LRFD and ASD) and Eurocode EN 1990 ULS. You pick a code and tick the loads that act on the structure: dead (D), live (L), wind (W) and seismic (E).

Any combination that needs a load you have not ticked is removed. The exception is a combination where live load is only a companion: if there is no imposed load it still applies with L = 0, so 1.5(D+L) becomes 1.5D rather than disappearing. Wind and seismic always act in both directions, so they are written with ±. Duplicate lines are removed and the list can be copied in one click.

When seismic load is ticked you can expand E into the 100 % + 30 % orthogonal pair of IS 1893 Part 1:2016 Cl 6.3.2.2 / 6.3.4.1. Each seismic combination is then written twice, once as (Ex ± 0.3Ey) and once as (0.3Ex ± Ey).

The tool writes out the combinations only. It does not take load values or calculate design forces; you apply the factors to your own load cases in the analysis.

IS 456 collapse, gravity
1.5(D + L)
IS 456 collapse, lateral alone
1.5(D ± W) or 1.5(D ± E)
IS 456 collapse, gravity + lateral
1.2(D + L ± W) or 1.2(D + L ± E)
IS 456 collapse, dead load favourable
0.9D ± 1.5W or 0.9D ± 1.5E
IS 456 serviceability
1.0(D + L), 1.0(D ± W), 1.0D + 0.8(L ± W), and the same with E
Orthogonal seismic pair
E → (Ex ± 0.3Ey) and (0.3Ex ± Ey)

Follows: IS 456:2000 Table 18 · IS 800 (limit state design) · IS 1893 Part 1:2016 Cl 6.3.2.2 and Cl 6.3.4.1 · ASCE 7-16 §2.3.1 and §2.4.1 · EN 1990 Eq 6.10 and Eq 6.12b

Worked example: IS 456 collapse combinations for a building with seismic load and no wind

Given

  • Code: IS 456 (limit state of collapse)
  • Loads present: dead (D), live (L) and seismic (E); wind (W) not ticked
  • Orthogonal 100 % + 30 % option: first off, then on

Steps

  1. The IS 456 collapse set has seven combinations: 1.5(D+L), 1.5(D±W), 1.5(D±E), 1.2(D+L±W), 1.2(D+L±E), 0.9D ± 1.5W and 0.9D ± 1.5E.
  2. Wind is not present, so the three combinations containing W are removed: 1.5(D±W), 1.2(D+L±W) and 0.9D ± 1.5W.
  3. Four combinations remain: 1.5(D+L), 1.5(D±E), 1.2(D+L±E) and 0.9D ± 1.5E.
  4. With the orthogonal option on, each of the three seismic combinations is written twice, for example 1.5(D±(Ex ± 0.3Ey)) and 1.5(D±(0.3Ex ± Ey)). 1.5(D+L) has no E and stays as one line.

Result: 4 combinations without the orthogonal rule; 7 combinations (1 gravity + 3 × 2 seismic) with it.

Enter the same values in the calculator above to check each step.

Frequently asked questions

What are the load combinations as per IS 456 for limit state of collapse?

IS 456 Table 18 gives 1.5(DL + LL), 1.5(DL ± WL), 1.2(DL + LL ± WL) and 0.9DL ± 1.5WL, with earthquake load EL substituted for WL in the same combinations. That makes seven lines when both wind and seismic are present: 1.5(D+L), 1.5(D±W), 1.5(D±E), 1.2(D+L±W), 1.2(D+L±E), 0.9D ± 1.5W and 0.9D ± 1.5E.

What is the 100 % + 30 % rule for seismic load in IS 1893?

IS 1893 Part 1:2016 Cl 6.3.2.2 requires the full design earthquake in one horizontal direction to be combined with 30 % of it in the perpendicular direction, and the other way round. The generator writes this as (Ex ± 0.3Ey) and (0.3Ex ± Ey), so each seismic combination becomes two lines.

What are the serviceability load combinations in IS 456?

For the limit state of serviceability the tool lists 1.0(D+L), 1.0(D±W), 1.0D + 0.8(L±W), 1.0(D±E) and 1.0D + 0.8(L±E). With dead, live and wind ticked it returns three lines: 1.0(D+L), 1.0(D±W) and 1.0D + 0.8(L±W).

Why does 1.5(D+L) become 1.5D when there is no live load?

In that combination live load is a companion to dead load, so the combination still has to be checked with L = 0. The generator keeps it as 1.5D instead of dropping it. Combinations that cannot exist without live load, such as 1.2(D+L±W), are dropped when L is not ticked, because 1.5(D±W) already covers that case.

Which loads and cases does the load combination generator not cover?

It handles dead, live, wind and seismic only. Roof live, snow, rain and vertical earthquake Ev are left out of the ASCE 7 sets, notional and thermal loads are not included, and Eurocode national annexes that use Eq 6.10a/b are not covered. It also does not calculate load values or member forces.

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