1 Determine the moment capacity of a simply support 20 ft x

1. Determine the moment capacity of a simply support 20 ft x 40 ft slab (supported on the long side) Assume the slab is 4 inch thick, and has a 1.5 inch clear cover with #4 rebar space 12\" on center. Use fy-60,000 psi and fc 4000 psi.

Solution

thickness of slab = 4 in

clear cover=1.5\"

bar size=#4

diameter of #4=0.5 in

effective depth=4-1.5-0.25=2.25 in

let us consider unit width of slab

b=12 inches

d=2.25 inches

area of stel provided = 0.2 in²

let depth of compression be a

0.85*4000*12*a=0.9*60000*0.2

a=0.26 in

lever arm=2.25-(0.26/2)=2.18 in=0.176 ft

moment capacity = 0.9*60*0.2*0.176=1.9 kip-ft

total width of sab=40 ft

total moment capacity=40*1.9=76.2 kip-ft