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cracking moment calculation example for inverted T beam

determine the cracking moment for the beam shown in figure 1.
knowing that fc'=27.5 Mpa, and fr=0.7√fc'= 3.67 Mpa=3670kn/m2









Figure 1

the first step is to calculate the neutral axis location

X=moment of area for each part/area of composite section
=((15*45*7.5)+(50*15*40))/(45*15+50*15)=24.56 cm
Figure 2

moment of inertia using parallel axis theorem
I=Is+Ad^2
I=(45*15^3)/12+45*15*(17.06^2)+(15*50^3)/12+15*50*15.44^2
=544,155.88cm^4=0.00544m^4
the cracking moment will be calculated at the extreme fiber of the tension zone. 
the extreme fiber of tension zone located at 24.56 cm from the neutral axis, y=24.56cm
Mcr=fr*I/y
=3670*0.00544/0.2456
=54.616kn.m



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