Question

Fixed load bending moment MD = 130 kN·m, live load bending moment ML = 140 kNNm
Rectangular short beams with width b = 400 mm and depth h = 600 mm are designed as follows:
Determine design suitability. Assume the coating thickness is 40 mm.(f ck = 27 MPa, f y = 300 MPa , tensile reinforcement 6-D22, shear reinforcement D10)

Answer 1

Solution:- the values given in the question are as follows:

dead load bending moment(MD)=130 kN-m

live load bending moment(ML)=140 kN-m

width of beam(b)=400 mm

total depth of beam(h)=600 mm

effective cover=40 mm

effective depth(d)=560 mm

characteristic strength of concrete(fck)=27 MPa , or 27 N/mm^2   

yield strength of concrete(fy)=300 MPa , or 300 N/mm^2

tensile reinforcement=6D22

diameter of shear reinforcement=10 mm

Checking design suitability:-

total moment on beam(M)=dead load moment+live load moment

total moment on beam(M)=130+140

total moment on beam(M)=170 kN-m

Calculating moment of resistance of the beam-

moment of resistance(Mr)=0.85*fc*b*a*(d-a/2) , [Eq-1]

where, a=As*fy/(0.85*fc*b)

area of steel(As)=number of bars*area of single bar

area of steel(As)=6*(3.14/4)*22^2

area of steel(As)=2279.64 mm^2

a=(2279.64*300)/(0.85*27*400)

a=74.498 74.5 mm

values put in above equation-(1) and calculate moment of resistance

moment of resistance(Mr)=0.85*27*400*74.5*(560-74.5/2)

moment of resistance(Mr)=357513952.5 N-mm

moment of resistance(Mr)=357.5139 kN-m

moment of resistance(Mr) total moment on beam(M)

moment of resistance is much greater than the total moment on beam , so the design of beam is sufficient(suitable) and good.

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