Midpoint difference method for analysing beam structures

The midpoint difference method is organized for analyzing beam structures by approximating the solution of the differential equation of the elastic deflection curve. The method requires the generation and solution of a system of simultaneous, algebraic equations which yield the deflection, slope, bending moment and shear at specified points along the span of the beam. The method is rather simple and well suited for programming on the digital computer.

All of the basic equations necessary for developing an analysis of a beam structure are established and the application of the method is given in the paper. Some general comments are made about the development of a computer program and about the solution of the system of simultaneous equations peculiar to this method of analysis.