Closed-form moment solution for continuous beams and bridge structures

Moment distribution continues to be a valuable structural analysis tool for spot-checking member-end-moments of continuous beams and frame structures from computer results. Prior to the widespread use of mainframe and, later, personal computers in the 1980s and 1990s, moment distribution provided a simple hand method for practicing civil engineers to analyze and design statically indeterminate structures, since its public introduction in the early 1930s by Hardy Cross, directly leading to new types of designs and construction. The chief benefits of this method of analysis over the other available methods are that (1) member-end-moments are found directly from the applied loads without first determining various displacement components, (2) no simultaneous equations need to be formed and solved, (3) it is easy to remember and apply, (4) an approximate solution can be obtained at any stage in the analysis and (5) a remarkable variety of statically indeterminate structures can be solved by hand. While the development and introduction of moment distribution represents a great advancement in the history of structural engineering, the distribution process can be tedious, especially if only a few final member-end-moments of a multi-redundant structure are desired. Additionally, when results are wanted to a greater accuracy, the number of distribution cycles required and the number of significant figures that must be carried through the process make it a daunting procedure. In this paper, a new method is presented that gives exact member-end-moments for continuous beams and bridge structures, without the need to distribute moments back and forth as in moment distribution or to set up and solve simultaneous equations, as with the stiffness method. It is anticipated that the primary application of the proposed method will be to spot-check computer results.