Question

4. A W12x50 beam acts compositely with a 4.5-inch concrete slab. The effective slab width is 70 inches. Shoring is not used. Applied bending moments are as follows: from the beam, Mbeam = 14 ft-kips; from the weight of slab, Msiab-78 ft-kips; and from the live load, M1-150 ft kips. Steel is A992, the compressive strength of concrete at 28 days is 4ksi. Determine whether the flexural strength of this beam is adequate. Assume full composite action and assume that the formwork provides lateral support of the W12x50 before curing of the concrete. Use LRFD.

Answer 1

Given beam is W12x50

Area of steel =14.7 in²

effective width of concrete = 70 inches

thickness of slab = 4.5 in

maximum tension in steel = 50*14.7=735 kips

maximum compression in concrete = 0.85*4*70*4.5=1071 kips

compression is greater than tension

let depth of compression zone in concrete be a

0.85*a*70*4=735

a=3 in

depth of beam =d= 12.19 in

lever arm length = d/2 + 4.5-(a/2) = 12.19/2 + 4.5 -(3/2) = 9.1 in = 0.76 ft

design moment strength of composite beam = 0.9*735*0.76=502.74 kip-ft

Design moment demand = 1.2*(14+78)+1.6*150=350.4 kip-ft

design moment is less than composite beam strength.

Therefore, section is adequate