The building section associated with the floor plan in Figur

The building section associated with the floor plan in Figure P2.4 is shown in Figure P2.8 Assume a live load of 60 Ib/ft2 on all three floors. Calculate the axial forces produced by the live load in column C2 in the third and first stories. Consider any live load reduction if permitted by the ASCE standard Figure P2.4: 6@6.67. = 40% C4 B2 G1 B3 B4 2@10.= 20 C2 G4 G3 G2 B1 5@8. = 40 C3 C1 40 20 Figure P2.8: C3 C1 40 20 Building Section

Solution

tributary length of column C2= (40/2)+(20/2)=30\'

tributary widtrh of column C2=(40/2)+(20/2)=30\'

tributary area of column C2 at each storey = 30*630=900 sq ft

K_LL = 4

for 3rd storey column:

live load reduction = 60*[0.25+15/sqrt(4*900)]=30 psf

axial load on column = 30*900=27000 lb=27 kips

for 1st storey column:

tributary area = 3*900=2700 sq ft

live load reduction = 60*[0.25+15/sqrt(4*2700)]=23.66 psf

Per ASCE 7-10, live load should not be less tyhan 0.4L for members supporting 2 or more floors

Therefore, live load to be considered = 0.4*60=24 psf

Axial load due to live load = 24*2700=64800 lb=64.8 kips

Therefore, Axial load in third storey column = 27 kips and axial load in 1st storey column = 64.8 kips