ABSTRACT
This chapter considers problems of beam bending and beam-column analysis using one-dimensional idealization. In the case of one-dimensional column deformation, it deals only with plane deformations. To satisfy the physical condition of continuity of such structures, it was necessary to satisfy interelement compatibility at least with respect to nodal displacement. It was therefore possible to fulfill the physical and mathematical requirements of the problem by using only first-order approximation. In contrast to the plane deformations, for realistic approximation of the physical conditions in the case of bending, it is necessary to satisfy interelement compatibility with respect to both the displacements and slopes, that is, first derivative of displacement. For generating a stable structural element for beam bending, one needs to eliminate rigid-body degrees of freedom. For the beam element, such degrees of freedom are those relevant to the conditions of displacement and rotations at one of the nodes. This leads to an element like a built-in beam or cantilever.
