Why Does a Beam Bend Only About the Centroidal Axis?

[chandran]

in beam bending the resistance of a cross section is measure by
moment of inertia about centroidal why. How do we know that the bends
only about the centroidal axis . Any detailed discussion on this?

 

[jasc15]

Looking at the cross section of the beam in bending, you should be able to understand that some portion of the beam is in tension, and some portion is in compression. So is follows from logic that there must be a point in between that experiences no stress, called the centroidal axis. Maybe that is not rigorous enough explanation and I am sure someone around here can elaborate.