One of several displacement methods for analyzing statically indeterminate structures that
resist loads by bending involves use of slope-deflection equations. This method is convenient for analysis of continuous beams and rigid frames in which axial force effects may be neglected. It is not intended for analysis of trusses.
Use of these equations for each member in a structure plus equations for equilibrium at the member connections is adequate for determination of member displacements. These displacements can then be substituted into the equations to determine the end moments.
As an example, the beam in Fig. 3.75a will be analyzed by employing the slope-deflection
equations [Eqs. (3.135a and b)]. From Fig. 3.76, the fixed-end moments in span AB are
The fixed-end moments in BC are