In three-dimensional space, the deflection curve of a simple beam of linear elasticity when a load acts perpendicular to the beam axis and in a non-unidirectional manner is a spatial curve. A smooth spatial deflection curve has continuous curvature and torsion, and the curvature is an elastic strain proportional to the bending moment. Similarly, if a deflection curve with curvature is twisted and has torsion, the torsion is also an elastic strain, and the component of the bi-moment (the couple formed by the bending moment vector) causes bending-torsional deformation. This paper will clarify this.
