TABLE OF CONTENTS Examples 16.15 and 16.16 show that the greater the complexity of a structure, the greater the number of unknowns and therefore the greater the number of simultaneous equations requiring solution; hand methods of analysis then become extremely tedious if not impracticable so that alternatives are desirable. One obvious alternative is to employ computer-based techniques but another, quite powerful hand method is an iterative procedure known as the moment distribution method. The method was derived by Professor Hardy Cross and presented in a paper to the ASCE in 1932.
Consider the three-span continuous beam shown in Fig. 16.37(a). The beam carries loads that, as we have previously seen, will cause rotations, ? A, ? B, ? C and ? D at the supports as shown in Fig. 16.37(b). In Fig. 16.37(b), ? A and ? C are positive (corresponding to positive moments) and ? B and ? D are negative.
Suppose that the beam is clamped at the supports before the loads are applied, thereby preventing these rotations. Each span then becomes a fixed beam with moments at each end, i.e. FEMs. Using the same notation as in the slope deflection method these moments are M F AB, M F BA, M F BC, M F CB, M F CD and M F DC. If we now release the beam at the support B, say,...
