Question

A reinforced concrete beam with dimensions (300 mm * 800 mm) subjected to a service dead load moment (MD= 500 kN.m) and a service live load moment (ML = 400 kN.m). Design the section as a double reinforced section (the dimensions can't be increased). Place the compression reinforcement at 65 mm from the compression face. Compressive strength of concrete; fc = 28 MPa, yielding stress of reinforcement; fy= 420 MPa. Assume 30 mm to be used in the tension (two layers), 26 mm to be used in the compression (one layer), stirrups of 10 mm.

Answer 1

Given wiath (b)=300mm Total depth (h)=800mm Dead loa a moment (MD] =500KN-m Live loaa moment (ML) = 400KN-m fcl=28 Mpa fy = 420Mpa Tension reinforcement = 30mm compression reinforcement = 826mm Stirrups =10mm おこ65 mm Step Is calculation of tactorea moment ana Ultimate moment (Mu) Weknow that Factorea moment (M) = 104 M₂ + 1 -6 ML = .4*500 +1-6X400) = 1340KN-m Effective depth (d) = 6-81 cover- (800-10-45-30 Assume cover zusmm i.d = 730mm ultimate moment (Mu) = 0.1567cbd2 -6-156X28X300X7302-) = 698.31 KN-m since, (M> Mu) the compression reinforcement is requiredo

Step II : - calculation of compression reinforcement Diameter of compression reinforcement = 26mm We know that Where dloos istJ0025-kloog) K'=0.158 = 73060-st Jouzs-0.156/09) - 566.24 ZE 566•24 mm z = - 363.89mm ous M-Mu x = (d-z 730-566-24 bous, As = 0.878fyldad') = (1340- 698 31)x106 0087X420(730-65) As' 2640.79 mm² Number of bars=(2640.79) = 4097 X262) 25 provide 5H26 (AS = 2653 mm2) as Compression reinforcemento Step III - Calculation of tension reinforcement Diameter of tension reinforcement =30mm Weknow that Mu As 0.87fy Z 698.31 X106 0087 x 420 X 566624

As = 3375.04 mm Number of bars 3375.0 - 4077 AX302 5 Provide 5H30 bars (As = 3532.5 mm2) as tension reinforcement. -300mm 65mmad 5426 Hlolinkt 43omm 800mm 5 H30 70mm fig: - Reinforcement detailing