TABLE OF CONTENTS An essential part of the computer-based stiffness method of analysis and also of the moment distribution method are the slope deflection relationships for beam elements. In these, the shear forces and moments at the ends of a beam element are related to the end displacements and rotations. In addition these relationships provide a method of solution for the determination of end moments in statically indeterminate beams and frames; this method is known as the slope deflection method.
Consider the beam, AB, shown in Fig. 16.32. The beam has flexural rigidity EI and is subjected to moments, M AB and M BA, and shear forces, S AB and S BA, at its ends. The shear forces and moments produce displacements ? A and ? B and rotations ? A and ? B as shown. Here we are concerned with moments at the ends of a beam. The usual sagging/hogging sign convention is therefore insufficient to describe these moments since a clockwise moment at the left-hand end of a beam coupled with an anticlockwise moment at the right-hand end would induce a positive bending moment at all sections of the beam. We shall therefore adopt a sign convention such that the moment at a point is positive when it is applied in a clockwise sense and negative when in an anticlockwise sense; thus in Fig. 16.32 both moments M AB and M BA are positive. We shall see in...
