Singularity functions revisited: Clarifications and extensions for construction of shear–moment diagrams in beams

This paper provides clarification and extension of singularity functions for the construction of shear–moment diagrams in beams and the subsequent determination of beam deflections. The mathematical formulation for impulse, polynomial, and general-form singularity functions and their integral properties is reviewed, clarified, and provided graphically in tabular form. Several examples of various complexity are presented to assist the student at evaluating the constants of integration and properly interpreting the values of shear force and bending moment in the limit of approach to points of discontinuity. The main emphasis of the paper is to demonstrate the applicability of the singularity function method for any specified distributed load function.