Load Combinations (ASCE/SEI 7-22)
Combines the load effects on one member (an axial force, a shear or a reaction) into the factored demands of ASCE/SEI 7-22 [1]: every basic combination for strength design (LRFD, §2.3.1 combinations 1a to 5a and the seismic combinations 6 and 7 of §2.3.6) and for allowable stress design (ASD, §2.4.1 combinations 1a to 7a and the seismic combinations 8 to 10 of §2.4.5). It picks the governing case and the minimum, for an uplift check. Engineers use it to find the design force for a column, footing or connection.
How the combinations work
Each combination sums factored effects, for example LRFD 2a:
U = 1.2D + 1.6L + (0.5Lr or 0.3S or 0.5R)
D is dead load, L live load, Lr roof live load, S snow, R rain, W wind, Eh horizontal seismic and Ev vertical seismic. Each “or” takes the largest term. The 7-22 ground snow loads are strength-level, so S carries 1.0 in combination 3a, 0.3 or 0.15 as a companion load, and 0.7 or 0.1 in ASD. Where S is a companion load it may be the flat or the sloped roof snow load.
The seismic load effect is split as in §12.4.2:
Eh = ρQE Ev = 0.2SDSD
QE is the effect of the horizontal seismic forces, ρ the redundancy factor and SDS the design short-period spectral acceleration. Enter Eh with ρ applied.
The factor on L in combinations 3a, 4a and 6 may be 0.5 where the unreduced live load Lo is 100 psf (4.78 kN/m²) or less, except in garages and places of public assembly (§2.3.1 and §2.3.6, Exception 1).
Limits and common mistakes
- Enter effects, not loads: the force each load case produces in the member, all in one unit.
- For uplift, enter W or Eh as negative in the direction that lifts the member. A negative minimum demand means net uplift.
- Tornado (WT), flood, ice, self-straining, fluid and earth-pressure loads, and the overstrength combinations with Emh, are not included.
Worked example
An interior steel column in a two-story office (Lo under 100 psf) carries the effects below. Find its LRFD and ASD design forces.
- Enter Dead load effect (D) 210, Live load effect (L) 135, Roof live load effect (Lr, kN) 18, Snow load effect 40 and Rain load effect (R) 0.
- Enter Wind load effect 65 and Horizontal seismic load effect 50.
- Choose Vertical Seismic Load Effect Ev Ev = 0.2·SDS·D and enter SDS 0.6.
- Choose Factor on L 0.5 — other occupancies.
- Press Solve. The Solution shows Ev = 25.2 kN, each combination, and:
→ Governing LRFD combination: 2a. 1.2D + 1.6L + (0.5Lr or 0.3S or 0.5R)
→ Max factored demand (LRFD): 480 kN
→ Min factored demand (LRFD, uplift check): 213.8 kN
→ Governing ASD combination: 6a. D + 0.75L + 0.75(0.6W) + 0.75(Lr or 0.7S or R)
→ Max service demand (ASD): 361.5 kN
→ Min service demand (ASD, uplift check): 143.36 kN
Check LRFD 2a by hand: 1.2 × 210 + 1.6 × 135 + 0.3 × 40 = 252 + 216 + 12 = 480 kN. The LRFD to ASD ratio, 480/361.5 = 1.33, is typical. Both minimums stay positive, so the column never goes into tension.