Load takeoff
Gravity loads on a beam or a column from area loads over its tributary area, with the live load reduction of ASCE/SEI 7-22 Section 4.7 and the roof live load reduction of Section 4.8. The results are service loads by load type, ready to enter in a member calculation (which applies the load combinations).
Inputs of the load takeoff #
- Member: a beam (span, tributary width, whether it supports a floor or the roof, and an optional self-weight added to D) or a column (tributary area per floor, the number of floors it carries, and the roof with its own tributary area).
- Area loads: one row per component, on the floor or on the roof, with its load type: D (dead), L (live, Table 4.3-1), Lr (roof live), S (snow, Chapter 7) and R (rain, Chapter 8).
- Live load reduction: the reduction is permitted, not required, so it is a choice. KLL is selected from Table 4.7-1. The occupancy selects the assembly rule (4.7.5, not reduced) or the passenger vehicle garage rule (4.7.4). Live loads above 100 psf follow 4.7.3 automatically. One-way slab limits AT to 1.5 times the span squared (4.7.6).
- Roof live load reduction: on or off, with the roof slope F in inches of rise per foot (4.8.2 R2).
Checks performed #
| Check | Basis |
|---|---|
| Loads by type | Line load w = q × tributary width (beam) or point load P = q × area × floors (column), each load type separately |
| Live load reduction | L = Lo (0.25 + 15/√(KLL AT)) (Eq. 4.7-1) where KLL AT ≥ 400 ft², not less than 0.50 Lo (one floor) or 0.40 Lo (two or more floors) (4.7.2); Lo > 100 psf and garages: not reduced for one floor, at most 20 % for two or more (4.7.3, 4.7.4); assembly: not reduced (4.7.5); one-way slabs: AT ≤ 1.5 ℓ² (4.7.6) |
| Roof live load reduction | Lr = Lo R1 R2 (Eq. 4.8-1 with R1 and R2 of 4.8.2), 12 psf ≤ Lr ≤ 20 psf, for ordinary roofs with Lo ≤ 20 psf (4.8.2) |
For a beam the key results also list the simple-span end reactions of each load type.
The drawings (on screen, in the report and as a PDF / DXF sheet) show the tributary plan to scale: for a beam the span and the tributary strip (drawn centred on the beam; the calculation uses its width) with the tributary area, and the beam with its service line loads by load type on a simple span; for a column the tributary area per floor and of the roof, each drawn as a square of the same area around the column symbol. The sheet notes list the area loads and the reductions used. The member size, its supports and the framing are not part of the calculation.
Limitations #
- One tributary area for all the floors a column carries (the same plan on every floor) and one for the roof.
- Concentrated live loads (4.4), partition loads (4.3.2) and impact loads are entered as area loads or left to the member calculation; snow drifts and unbalanced snow come from a snow calculation.
- Roof live loads above 20 psf are not reduced by Eq. 4.8-1 (it is for ordinary roofs, 4.8.2). An occupiable roof (4.8.3 permits the 4.7 reduction) is entered as L on the roof and is carried unreduced.
- KLL comes from Table 4.7-1; a calculated KLL (permitted by the table footnote) cannot be entered.
- The loads are service values; the load combinations are applied in the member calculation.
Verification examples #
Checked against ASCE/SEI 7-22 (PDF pp. 78 to 79): Eq. 4.7-1, the 0.50 Lo / 0.40 Lo limits, 4.7.3 to 4.7.6, Eq. 4.8-1 with R1 and R2 of 4.8.2, and Table 4.7-1. The seven KLL values of Table 4.7-1 are golden values (T4.7-1, p. 78). Published worked takeoffs: the AISC Design Examples v16.0 building (Part III, to ASCE/SEI 7-22; floor D 75 psf, L 80 psf, roof D 20 psf, Lr 20 psf, snow 24.6 psf):
| Example | What it checks | Published | ILX Calcs |
|---|---|---|---|
| AISC-III-B45 | 45 ft interior beam at 10 ft (pp. III-25 to III-26) | KLL 2, L 60.0 psf, wD 0.750 kip/ft, wL 0.600 kip/ft | same |
| AISC-III-B30 | 30 ft interior beam at 10 ft (p. III-31) | L 69.0 psf, wL 0.690 kip/ft | same |
| AISC-III-G30 | 30 ft interior girder (p. III-43) | L 45.2 psf (AT rounded to 1,130 ft²) | 45.3 psf (AT 1,125 ft²) |
| AISC-III-C2C | Interior column, 3 floors + roof, 1,125 ft² (pp. III-52 to III-55) | L 32.0 psf (0.40 Lo), Lr 12.0 psf, PD 276, PL 108, PS 27.7, PLr 13.5 kips | same |
| AISC-III-C2A, -C1A, -C1B, -C1C | Exterior and corner columns (pp. III-49 to III-55) | L 33.2 / 40.2 / 51.1 / 35.2 psf, R1 0.882 / 0.658, Lr 12.0 / 17.6 / 20.0 / 13.2 psf, PL 68.7 / 35.7 / 19.0 / 54.9 kips, PS and PLr | same within 1 % |
The example's edge girder uses a KLL calculated from the influence area (1.98, Table 4.7-1 footnote); the program offers the tabulated KLL only, so that case is not compared. The arithmetic is also checked by hand calculations in closed form:
| Example | What it checks | Hand calculation | ILX Calcs |
|---|---|---|---|
| LT-1 | Interior beam, 30 ft × 10 ft, KLL = 2 | L = 43.12 psf, wD = 0.500 kip/ft, wL = 0.431 kip/ft | same |
| LT-2 | Interior column, 3 floors × 900 ft² and the roof | PD = 234 kips, L = 0.40 Lo = 20 psf, PL = 54 kips, Lr = 12 psf, PLr = 10.8 kips | same |
| LT-3 | Roof beam, At = 400 ft², F = 6 | R1 = 0.8, R2 = 0.9, Lr = 14.4 psf | same |
| LT-4 | Storage column, Lo = 125 psf, two floors | L = 0.8 Lo = 100 psf, PL = 80 kips | same |
| T4.7-1 | KLL of the seven elements of Table 4.7-1 | 4, 4, 3, 2, 2, 2, 1 | same |