Load combinations
Takes the unfactored effect of each load (an axial force, a shear, a moment, a reaction, any number) through the ASCE 7-22 Chapter 2 combinations and gives the value of each combination and the largest and smallest result. Use it where a member calculation is done by hand or in another program, or to see which combination governs. Each effect keeps your units; the type does no conversion, so it has no units switch.
The design calculations carry their own combinations for D, L, Lr, S, R, W and E (loads.py). This type adds flood, ice, tornado, fluid, earth pressure, self-straining effects, and seismic combinations with ρ, Ev and Ω0. Copy the results into a calculation as values: nothing links the two.
Inputs of the combinations #
- Load effects: up to four named effects, and a row per load type with its effect and sign: D, L, Lr, S, R, W, WT (tornado), E (entered as QE, the effect of the horizontal seismic forces), Di, Wi, Fa, F, H, T. Rows of one type add up.
- Design method: LRFD (2.3) or ASD (2.4). 2.1 says an element is designed by one or the other.
- Seismic: the redundancy factor ρ (12.3.4); whether Ev = 0.2 SDS D applies, on by default (12.4.2.2 excepts SDC B and some foundation checks, and it is your call that an exception holds); SDS; and whether to add the overstrength combinations with Ω0 (Table 12.2-1) where the standard requires them.
- Code options: the factor 0.5 on L (2.3.1 and 2.3.6 exception 1), off by default because it depends on the occupancy; the flood zone (2.3.2, 2.4.2); whether H is permanent; and the factor on T, which 2.3.4 leaves to you at no less than 1.0 and 2.4.4 at no less than 0.75.
Checks performed #
| Result | Basis |
|---|---|
| Basic LRFD | 2.3.1: 1a to 5a; (Lr or S or R) and (L or 0.5W) written out one by one; W or WT |
| Basic ASD | 2.4.1: 1a to 7a, the same way |
| Flood | 2.3.2 (4b, 5b), 2.4.2 (5b, 6b, 7b), by zone, used when Fa is entered |
| Ice | 2.3.3 (2b, 4c, 4d, 5c), 2.4.3 (1b, 2b, 3b, 7c), used when Di is entered |
| Seismic | 2.3.6 (6, 7), 2.4.5 (8, 9, 10) with Eh = ρ QE (12.4.2.1), Ev (12.4.2.2), and Emh = Ω0 QE (12.4.3) as separate combinations |
| F | The factor of D in 1a to 4a, 6, 7 (LRFD) and 1a to 6a, 8, 9, 10 (ASD) |
| H | 1.6 (LRFD) or 1.0 (ASD) where it has the sign of the rest of the combination; otherwise 0.9 or 0.6 if permanent, 0 if not |
| T | The entered factor in every combination |
| Largest and smallest | W, WT, E and Wi in both directions. A variable load that helps is left out, for "effects of one or more loads not acting": D and F stay |
The type is a calculation of numbers: it reads Calculated, and it has no drawing, as the unit converter does.
Limitations #
- Extraordinary events (2.5), the alternative for water in soil (2.3.7) and the capacity limit on Emh (12.4.3.1: enter a lower effect yourself) are not covered, nor exceptions 2 and 3 of 2.3.1, those of 2.4.1, or the 0.9D of 2.4.5 exception 2. The allowable stress increase of 2.4.5 belongs to the member check.
- The effects add linearly. Where the analysis is not linear (second-order effects), combine the loads in the analysis itself.
- A row is one effect at one location. Two effects from one combination must be read together from its rows, not from the largest and smallest values, which can come from different combinations.
- ρ, Ω0 and the seismic design category are your inputs.
- The H factor follows the sign against the rest of that combination, for each effect on its own. "Principal load effect" is a judgment in the code: where it reads differently for your case, check that combination by hand.
- T is added to every combination with one factor; 2.4.4 lets you lower it where its peak is unlikely to coincide, not per combination here.
Verification examples #
Verification status: 53 values compared in 13 examples (3 published, 10 hand calculations from the cited equations): 52 within tolerance, 1 recorded deviations. Code basis: the provisions it uses were read in the target edition.
The combinations are the code's own text, so most of the checks are hand calculations of each combination group. Few published examples apply these on their own. Three do use them:
| Example | Source | Values |
|---|---|---|
| Beam moment | AISC Design Examples v16.0, F.1-1A, pp. F-3 to F-4 | 266 kip-ft (LRFD), 184 kip-ft (ASD) |
| Shear wall axial force, with Ev | FEMA P-2192-V1 Table 4-8, p. 151 | 10,015 kips, 6,460 kips; and −378 kips, a documented deviation |
| Collector at ASD | FEMA P-2192-V1 Section 7.4, pp. 267 to 272 | 13,350 lb |
In FEMA's table only results are printed: D and L were worked back from its first two rows, so those rows confirm that step and not the program. With them and QE = 3,385 kips from the text, the program gets 10,011 and 6,462 kips for rows 3 and 4. Row 5 prints −378 kips where the same inputs give −308 kips: rows 4 and 5 differ by 2 QE, and their printed difference is 6,838 kips, not 6,770. The program keeps its own value.
Hand calculations cover the LRFD and ASD basic groups, overstrength, both flood zones, ice, F, H adding and resisting, loads not acting, the 0.5 factor on L and T. The test file also checks that the combination set equals the one in loads.py for every mix of D, L, Lr, S, R, W and E tried.