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Calculating of cracking moment for hollow rectangular 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 shape is symmetrical. therefore neutral axis located at the center of rectangular X=33.75cm

moment of inertia=(45*67.5^3)/12-(15*22.5^3)/12=1,139,062.5cm^4=0.01139m^4

Mc=fy*I/y=3670*0.01139/.3375=123.63kn.m




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