### Calculating of cracking moment for 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

• first step is to calculate the neutral axis
• $\dpi{120}&space;\large&space;neutral&space;axis=\frac{moment-of-area}{area-of-T&space;beam{\color{Green}&space;}}&space;{\color{Green}&space;}$

$\dpi{120}&space;\large&space;neutral&space;axis=\frac{75*10*5+15*50*35}{75*10+50*15}$
neutral axis=20cm from the top (reference axis shown in figure 2
Figure 2

$\dpi{120}&space;\large&space;parallel-axis-theorem=Ic+A.{d^{2}}$

$\dpi{120}&space;\large&space;parallel-axis-theorem=\frac{75*10^{3}}{12}+75*10*15^{2}+\frac{15*50^{3}}{12}+50*15*15^{2}$

I=500,000cm4=0.005m4

cracking moment calculated at extreme tension fiber.
tension fiber located at 40 cm from the neutral axis=0.4

$\dpi{120}&space;\large&space;Mcr=\frac{fy*I}{y}$
$\dpi{120}&space;\large&space;Mcr=\frac{3670*0.005}{0.4}$