Question

3. A composite beam consists of a concrete slab that has an effective width be 72-in and a thickness t 7-in. Compressive strength of concrete is 4 ksi. The slabis connected to a A992 steel beam (W36x160) with an adequate number of steel studs to produce a fully composite beam. Determine the nominal moment strength of this beam.

Please refer AISC 15th edition

Answer 1

effective width of beam = 72 in

thickness of slab= 7 in

grade of concrete = 4 ksi

Beam section = W36x160

Area of beam = 47 in²

depth of beam = 36 in

beam yield strength = 50 ksi

maximum tension that can be taken by beam = 50*47=2350 kips

maximum compression that can be taken by concrete = 0.85*4*72*7=1713.6 kips

Since compression is greater than tension,for full composite action there will be some part of steel in tension

Let area of steel in compression be A_c and that in tension be A_t

1713.6+50*A_c = 50*A_t = 50*(47-A_c)=2350-50A_c

A_c = 6.364 in²

A_t = 47-6.364=40.636 in²

width of flange of W36x160 = 12 in

thickness of flange in compression = 6.364/12=0.53 in

compression force in steel = 50*6.364=318.2 kips

Total compression force = 1713.6+318.2=2031.8 kips

approximate location of resultant tension force from top of steel = 36/2=18 in

lever arm length between compression in concrete and tension in steel = (7/2)+18=21.5 in

lever arm length between compression in steel and tension in steel = 18-0.53/2=17.735 in

nominal moment strength = 1713.6*21.5/12 + 318.2*17.735/12 = 3540 kip-ft