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; fe 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

-300 469 -008 ACI CODE GIVEN DATA:- bxh = 300 x 800 mm, Md= 500 kNm, MI= 400 kNm, d'=65mm f'c=28 Mpa, fy=420 Mpa , Mu=1.2 x Md+ 1.6 x MI= 1.2 x 500 +1.6 x 400 =1240 kNm Mn= Mu/0.9 = 1240 /0.9 = 1377.8 kNm d= 800 - 50 clear cover-10 stirrups-30-30/2 =695 mm pmax if singly reinforced = 0.0181 As1 = 0.0181 x 300 x 695 = 3774 sqmm Mu1/phi x bx d^2 =6.388 MPa Mu1 = 6.388 x 0.9 x 300 x 69542/10^6 =925.7 kNm Mn1 Mu1/0.9 = 925.7 / 0.9 = 1028.6 KNM <Mn = 1377.8 kNm Hence Doubly Reinforced Required. Mn2 = Mn - Mn1 = 1377.8 - 1028.6 = 349.2 kNm Checking to See if compression Steel yields a= 3774 x 420/(0.85 x 28 x 300 ) = 222 mm c= 222 /0.85 = 261.18 mm E's = ( 261.18 - 65 ) x 0.003/ 261.18=0.0022 > 420 / 200000 = 0.00210 Hence compression steel yields A's reqd = Mn21/f (d-d') = 349.2 x 10^6/{420 x( 695-65 )} = 1320 sqmmm (Use 3 - 26mm dia =1592 sqmm) = As = As1 + As2 = 3774 + 1320 = 5094 sqmm ( Use 8 - 30 mm dia = 5652 sqmm in 2 layers )