Determining Deflections of Hinge-Connected Beams Using Singularity Functions: Right and Wrong Ways

When the method of double integration is used to determine deflections, as well as statically indeterminate reactions at supports, of a beam in Mechanics of Materials, one has the option of using singularity functions to account for all loads on the entire beam in formulating the solution.This option is an effective way and a right way to solve the problem if the beam is a single piece of elastic body.However, this option becomes a wrong way to do it if one fails to heed the existence of discontinuity in the slope of the beam under loading.Beginners tend to have a misconception that singularity functions are a powerful mathematical tool, which can allow one to blaze the loads on the entire beam without the need to divide it into segments.It is pointed out in this paper that hinge-connected beams are a pitfall for unsuspecting beginners.The paper reviews the sign conventions for beams and definitions of singularity functions, and it includes illustrations of both right and wrong ways in solving a problem involving a hinge-connected beam.It is aimed at contributing to the better teaching and learning of mechanics of materials.