How to identify if the section of the specified beam will crack or not

This construction video tutorial provides detailed guidelines on the process to know if the beam section will crack or not?

To figure out this, you have to measure the cracking moment and then compare the cracking moment with the internal moment resulting from external load.

In this video, a cantilever beam is utilized with modulus of elasticity of material = E = 2x104 KN/cm2 and the maximum bending stress (f) = 75 KN/cm2

The length of the beam is 3 meter. The cross section of beam is given as the depth (d) = 20 cm and breath = 10 cm.

The solution is given as follows :-
To find out cracking moment, use the following formula :-

Bending Equation = M/I = f/y = E/R
Here, M denotes maximum bending moment that can be taken as cracking moment.
Now, only select 2 pairs of equation out of 3 pairs, i.e.

M/I = f/y
Now, multiply I with both sides, i.e.
I x M/I = f/y x I
We get, M = f/y x I
Here, I is an unknown factor.

To calculate value of I, apply the following formula :-
I = bd3/12 = 10(203)/12 = 6666.67 cm4
Therefore, M = 75/10 x 6666.67 = 50000 KN.cm (the value of y is taken as the value half the depth)

To get the complete process, watch the following video.