Problem 3 Calculate the design moment capacity AL of the bea

Problem 3 Calculate the design moment capacity (AL) of the beams below. All beams contain Gr 60 steel and are 25 ft long. Assume the steel fits in the section in a single row as shown. 5 3 #9 Bars 2 #8 Bars = 12 ksi 2 #8 Bars 3 #9 Bars

Solution

1) Width of beam=12 in

effective depth of beam=20 in

Area of steel provided=2*0.79=1.58 in²

Grade of concrete=4 ksi

Grade of steel=60 ksi

Let depth of compression zone be a

0.85*12*4*a=0.9*1.58*60

a=2.09 in

lever arm length = 20-(2.09/2)=18.95 in=1.58 ft

moment capacity = 0.75*0.9*1.58*60*1.58=101 kip-ft

2)Width of beam=12 in

effective depth of beam=20 in

Area of steel provided=2*0.79=1.58 in²

Grade of concrete=12 ksi

Grade of steel=60 ksi

Let depth of compression zone be a

0.85*12*12*a=0.9*1.58*60

a=0.697 in

lever arm length = 20-(0.697/2)=19.65 in=1.64 ft

moment capacity = 0.75*0.9*1.58*60*1.64=104.8 kip-ft

3)Width of beam=12 in

effective depth of beam=20 in

Area of steel provided=3*1=3 in²

Grade of concrete=4 ksi

Grade of steel=60 ksi

Let depth of compression zone be a

0.85*12*4*a=0.9*3*60

a=3.97 in

lever arm length = 20-(3.97/2)=18 in=1.5 ft

moment capacity = 0.75*0.9*3*60*1.5=182.25 kip-ft

4)Width of beam=12 in

effective depth of beam=30 in

Area of steel provided=3*1=3 in²

Grade of concrete=4 ksi

Grade of steel=60 ksi

Let depth of compression zone be a

0.85*12*4*a=0.9*3*60

a=3.97 in

lever arm length = 30-(3.97/2)=28 in=2.33 ft

moment capacity = 0.75*0.9*3*60*2.33=283.6 kip-ft