Live Load Reduction

Roof live load calculations in ASCE 7-10 Section 4.8.2:
The roof live load is calculated using Equation 4.8-1:
Lr = Lo R1 R2 
Where:
Lr = Reduced roof live load per square foot of horizontal projection (psf)
Lo = Unreduced roof live load per square foot of horizontal projection (psf) 
R1 = Reduction factor for tributary area
R2 = Reduction factor for roof slope
The unreduced roof live load (Lo) is specified in ASCE 7-10 Table 4-1 based on the roof occupancy/use. 
The reduction factor R1 accounts for tributary area and is calculated per ASCE 7-10 Table 4-2. Larger tributary areas allow for some statistical live load reduction.
The reduction factor R2 accounts for roof slope and is calculated per ASCE 7-10 Table 4-3. Steeper sloped roofs allow for some live load reduction.
So in summary, the unreduced live load Lo is reduced by factors R1 and R2 to determine the design roof live load Lr used for structural design. This accounts for the effect of tributary area and roof slope on expected live load.

Floor live load calculation in ASCE 7-10 Section 4.7.2:

The floor live load is calculated using Equation 4.7-1:

L = Lo R

Where:

L = Reduced live load per square foot of area supported by the member (psf) Lo = Unreduced live load per square foot of area (psf) R = Reduction factor

The unreduced live load (Lo) is specified in ASCE 7-10 Table 4-1 based on the occupancy/use of the area.

The reduction factor (R) accounts for one or more of the following:

• Tributary area (Ta) per ASCE 7-10 Section 4.7.2 and Table 4-1
• Multi-story loading reduction
• Concentrated loads and areas without reductions

The tributary area reduction factor Ta allows for a reduction in live load for larger tributary areas, as the maximum live load over a large area is unlikely. Ta is calculated per ASCE 7-10 Table 4-1.

The multi-story reduction factor allows for additional live load reduction for members supporting 2 or more floors.

Concentrated loads and areas specified without reductions in ASCE 7-10 Table 4-1 are not permitted to have their loads reduced.

So in summary, the unreduced live load is reduced by the factor R to determine the design live load L used in structural member design. This accounts for tributary area, multi-story reductions, and unreduced loads.