rob 3 ey Gn the precast T beam Calculade the des Shrenarty w

rob. 3 ey Gn the precast \"T \"beam Calculade the des Shrenarty weght cmerete Veihy and assump hms you make. .orma u en 12m

Solution

Given grade of concrete = 3000 psi

Grade of rebar=60 ksi

efective depth of beam = d=21.5\"

Area of rebar provided = 3-#11=3*1.56=4.68 in²

Let the depth of compression zone be a

0.85*3000*24*a=0.9*60000*4.68

a=4.13\"

But thiclkness of flange is 3\"(<4.13\")

Therefore, let the compression zone be of depth b below bottom of flange

0.85*3000*24*3 + 0.85*3000*12*b=0.9*60000*4.68

b=2.26\"

Let us determine the location of centroid of compression force

Let the distance from top of flange at which resultant compression force acts be c

c=[(24*3*1.5)+(12*2.26*4.13)]/[(24*3)+(12*2.26)] = 2.22 in

lever arm length = 21.5-2.22=19.28\"

Moment capapcity = 0.9*60*4.68*19.28/12=406 kip-ft

Moment capapcity with resistance factor = 0.75*406=304.5 kip-ft