Live load reduction
The reduced uniform live load on one member by ASCE/SEI 7-22 4.7, with the roof live load reduction of 4.8: the live load element factor KLL, the tributary area of the floors the member supports, Eq. 4.7-1 with its 0.50 / 0.40 limits, heavy live loads, garages, assembly areas and one-way slabs, and the roof by Eq. 4.8-1 (R1, R2) or as an occupiable roof. It is an analysis: the result reads Calculated. The reduced loads are service loads for a member calculation.
Inputs of the live load reduction #
- Live load element factor KLL: a row of Table 4.7-1 (interior and exterior columns 4, edge columns with cantilever slabs 3, corner columns with cantilever slabs 2, edge beams without cantilever slabs and interior beams 2, all other members 1), or a calculated KLL (the table footnote permits it; Commentary C4.7.1 defines KLL as the influence area over the tributary area).
- Tributary area per floor and floors supported: AT is the area per floor times the floors (C4.7.1: areas of a member supporting more than one floor are summed). Enter 0 floors for a member that carries only the roof.
- Unreduced live load Lo (Table 4.3-1) and the use: reducible, assembly area (4.7.5, not reduced), passenger vehicle garage (4.7.4) or a use Table 4.3-1 marks as not reducible. Live loads over 100 psf are treated by 4.7.3 automatically.
- Reduce the floor live load: 4.7.1 permits the reduction; it is your choice. One-way slab limits AT to the span times 1.5 times the span (4.7.6); a one-way slab carries one floor.
- Roof: an ordinary flat, pitched or curved roof, awning or canopy (4.8.2: Lr = Lo R1 R2, with the reduction on or off), a fabric awning or canopy on a skeleton structure (outside 4.8.2, not reduced), an occupiable roof (4.8.3: a floor-type live load reduced by 4.7, with its use) or a roof for other special purposes (loads approved by the authority having jurisdiction, not reduced). The roof slope F is in inches of rise per foot; for an arch or dome, enter the rise-to-span ratio (F = 32 × rise / span).
Checks performed #
| Check | Basis |
|---|---|
| Reduced live load | L = Lo (0.25 + 15/√(KLL AT)) where KLL AT ≥ 400 ft² (Eq. 4.7-1, 4.7.2) |
| Lower limit | L ≥ 0.50 Lo for one floor, 0.40 Lo for two or more (4.7.2); heavy live loads 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 slab | AT ≤ 1.5 ℓ² (4.7.6) |
| Roof live load | Lr = Lo R1 R2, 12 ≤ Lr ≤ 20 psf; R1 = 1, 1.2 − 0.001 At, 0.6; R2 = 1, 1.2 − 0.05 F, 0.6 (Eq. 4.8-1, 4.8.2) |
| Occupiable roof | Reduced by 4.7 with the roof counted as one more floor of the member and its area added to AT (4.8.3 with C4.8.3 and C4.7.1: our reading) |
| Loads on the member | L × n × A and Lr × At (service loads) |
The drawings show the tributary plan (the areas as squares of the same area) and a schematic stack of the levels the member supports with their unreduced and reduced loads.
Limitations #
- One member and one live load per floor. Members carrying floors of different loads or areas: use the load chasedown.
- Pattern (partial) loading of 4.3.3, concentrated loads, the load combinations and the member design are the member calculation's.
- The occupiable roof as an extra floor of the member is our reading of 4.8.3 with the Commentary.
- No auto-design: nothing is sized.
Verification examples #
Verification status: 38 values compared in 23 examples (16 published, 7 hand calculations from the cited equations): 38 within tolerance, 0 recorded deviations. Code basis: the provisions it uses were read in the target edition.
AISC Design Examples v16.0, Part III, designs a building to ASCE/SEI 7-22; its beams, girders and columns reduce the live load by 4.7 and the roof live load by 4.8.2. All values agree within the printed digits.
| Example | What it checks | Published | ILX Calcs |
|---|---|---|---|
| III-26, III-31 | Interior beams, AT 450 and 300 ft² | 60.0, 69.0 psf | same |
| III-40 | Edge girder with a calculated KLL = 1.98, AT 690 ft² | 52.5 psf | same |
| III-43 | Interior girder, AT 1,130 ft² | 45.2 psf | same |
| III-50 to III-53 | Columns over three floors (KLL = 4) and the roof | L 33.2, 51.1, 40.2, 35.2 psf, 32.0 psf (0.40 Lo over 30.3); R1 0.6, 0.882, 0.658; Lr 12.0, 20.0, 17.6, 13.2 psf | same |
Hand calculations (closed form, no published example on disk): heavy live load over two floors (120 psf) and one floor (not reduced), a garage over three floors (0.8 Lo), an assembly area, a one-way slab with AT capped at 600 ft², an arch roof (F = 8, R1 = R2 = 0.8, Lr = 12.8 psf) and an occupiable roof counted as a floor; Table 4.7-1 values.