2 A riat roof is subject to the following uniformly distribu

2. A riat roof is subject to the following uniformly distributed loads: a dead load of 21 psf (pounds per square foot of roof surface), a roof live load of 12 psf, a snow load of 13.5 psf, and a wind load of 22 psf upward. (Although the wind itself is in a horizontal direction, the force that it exerts on this roof is upward. It will be upward regardless of wind direction. The dead, live and snow loads are gravity loads and act downward.) a. If load and resistance factor design is used, compute the factored load (required strength) in pounds per square foot. Which AISC load combination controls?

Solution

given dead load=D=21 psf

Roof Live = Lr=12 psf

Snow Load =S= 13.5 psf

Wind load=W=22 psf(upwards)

The LRFD load combinations per ASCE 7-10 nare as shown below:

1)1.4D

Load = 1.4*21=29.4 psf

2)a)1.2D+1.6L+0.5Lr

Load = (1.2*21)+(1.6*0)+(0.5*12)=31.2 psf

b)1.2D+1.6L+0.5S

Load =  (1.2*21)+(1.6*0)+(0.5*13.5)=31.95 psf

3)a)1.2D+1.6Lr+0.5W

load = (1.2*21)+(1.6*12)+(0.5*-22)=33.4 psf

b)1.2D+1.6S+0.5W

load = (1.2*21)+(1.6*13.5)+(0.5*-22)=35.8 psf

4)a)1.2D+W+L+0.5Lr

load = (1.2*21)+(-22)+0+(0.5*12)=9.2 psf

b)1.2D+W+L+0.5S

load = (1.2*21)+(-22)+0+(0.5*13.5)=9.95 psf

Therefore governing load combination is load combination number 3(b) and the load is 35.8 psf

Note: you have mentioned that answer should be 46.8 psf which is achieved in load combination 3(b) if wind load is not considered,i.e., 1.2D+1.6S=46.8 psf. Howvere, since there is wind load component also in the combination, we cannot choose to ignore that. Therefore, the correct answer is 35.8 psf and not 46.8 psf