I am reading about pure bending from Beer Johnston's mechanics of materials. There, a prismatic member with a plane of symmetry was subjected to equal and opposite couples M and M' acting in that plane. It was said about this member that since the bending moment M is same in any cross section, the member will bend uniformly. I could not understand this.
Is it because that stress will be same on each cross section and therefore since same stresses cause same deformation, it will bend uniformly?