Question

A rectangular steel-reinforced concrete beam supports a uniformly distributed load of 875 lb/ft (including the beam weight) for a span of 24 ft. The breadth of the beam is 12 in. Concrete with a specified compressive of 3000 lb/sqin and grade 60 steel for tensile and web reinforcement are specified. Four longitudinal tensile bars are to be used. If required, No. 3 stirrups will be used.

1. Determine the minimum effective depth of the beam section (Round to the nearest inch increment).
2. Specify the gauge number of the longitudinal tensile reinforcement.
3. Determine whether web reinforcement is required.

Answer 1

fc=3000 psi fy=60000 psi Span L = 24 ft b=12" Loading Assume givenload is factored wu = 875 lb/ft =0.875 kips/ft

0.875k/ft 24 ft

Maximum moment in the center of span wu* 12 Mu 8 0.875* 242 Mu = = 63 K - ft 8 Mu Murequired o as 0.9 for tension controlled memeber 63 Mnrequired = 70k - ft 0.9 = 840 k - in Assume a rebar ratio of fc Thumb rule fy 3 = 0.009 60 P = 0.18* P = 0.18*

a)

bd2 * Required section property Murequired 1.7fc fy p(1.7fc-p* fy) 840 1.7* 3 60 0.009(1.7*3-0.009*60) = 1739.76 in for b= 12" d (1739.76 12 = 12.04"

b)

Required Area of rebar As =p*b*d = 0.009*12*12.04 = 1.300 in? for four longitudinal tensile bars 1.3 Area of each bar = 0.325 in? 4 Nearest available bar with area >0.325 in? is # 6 bars choose #6 bars with area = 0.44 in? Bar size, no = 6

c)

0.875k/ft R R 24 ft B

0.875*24 Support reaction RA = RB = 10.5 kips 2 for a section a distance of x from left support Shear force is given by Vx=RA-WU* x = 10.5-0.875*x ---(1) Critical section is located at a distance of d from support 12.04 vd = 10.5-0.875* = 10.62 kips 12 Factored shear force Vu=10.62 kips =

Shear resistance of Concrete The ACI 318 provide formula for computing shear resistance offered by concrete Vc=2*2*b*d* fc where 1 = 1 for normal weght concrete Vc=2*1*12*12.04 * 3000 = 15826.99 lb = 15.826 kips strength reduction factor for shear design is Ø = 0.75 Vc =0.75*15.286 =11.87 kips Vu<ØVc load <Capacity Hence no web reinforcement is required Concrete will carry shear force acting