The Beam Bends without Twisting.
It is assumed that the cross-section of the beam is symmetric about the plane of bending (x-y plane in this case) and will undergo symmetric bending (where no twisting of the beam occurs during the bending process). If the beam is not symmetric about this plane, then the beam will twist during bending and the situation will no longer be one-dimensional and must be approached as an unsymmetric bending problem (where the beam twists while bending) in order to obtain a correct solution.