Problem 2 A cantilever reinforced concrete beam carries 25 k

Problem 2 A cantilever reinforced concrete beam carries 2.5 kips/ft live load and 2.0 kips/ft dead load and a point live load 6 kips. The cross section of the beam is shown below. The width and overall depth of the beam cross section are 20 in. and 38 in., respectively. The center of the longitudinal bars is 2.5 in. below the top face of the beam cross section. a) Calculate the design moment M. b) Check the adequacy of the section if five No. 8 bars are used as longitudinal reinforcement. . c) What will be the design moment strength (Mn) if 5 No.9 bars are used? Solve the problem using kmethod only . Use f 4000 psi and f-60,000 psi. . Consider own weight of the beam (addition to externally applied dead load given above). P-6 kips wz-2.5 kips/ft wp-2.0 kips/ft 38 in. 5#8 bars 15 ft 20 in.

Solution

consider the unit weight of concrete = 150 lb/ft³

self weight = 150*3.167*1.66=0.788 kip/ft

total dead weight= 2+0.788 =2.788 kip/ft

total UDL = 2.778 +2.5 =5.278 KIP/FT

bending moment at fixed end = 5.278*15²/2 +6*15 = 683.775 kips-ft

b)

let lever arm Z= 0.75*h = 0.75*38=28.5 in

area of each #8 bar A= 0.79 in²

strength of reinforcement = f_y*n*A*Z = 60*5*0.79*28.5 =6754.5 kips-in = 6754.5/12 =562.875 kips-ft < 683.775 kips-ft

hence reinforcement is not adequate.

c)

Area of #9 bar is 1 in²

desigm moment = 60*5*1*28.5 = 8550 kips-in = 712.5 kips-ft > 683.775 kips-ft

hence this reinforcement is adequate.