Operational Method for Continuous Beams

The operational method, similar to the theory of electricity, can be available for continuous systems in applied mechanics of solids. Two kinds of continuous beams are treated: Continuous beams with rigid supports, and continuous beams with elastic supports. According to the operational method, simultaneous equations are no longer necessary even for a large number of spans. The entire procedure of analysis is developed in matrix algebra, in which the necessary physical quantities, the boundary conditions, and the connection conditions between two consecutive spans are all expressible in terms of corresponding matrices. Thus, the solution can be obtained by formal operations, multiplications, and at times additions, among these matrices. The present analysis will demonstrate more efficiency in computations than shown in previous fundamental systems. Similar developments can be made for the case of distributed loads and for continuous systems other than those cited herein.