Date of Graduation


Document Type


Degree Name

Bachelor of Science in Mechanical Engineering

Degree Level



Mechanical Engineering


Jong, Ing-Chang

Committee Member/Reader

Springer, William T.


The purpose of this paper is to investigate the slopes and deflections of a beam with two steps (i.e. a beam with a change of cross section) by use of a global formula. In order to understand the derivation and use of this formula, a brief review of singularity functions is provided. The global formula simplifies the solution method for stepped beams (eliminating the need for dividing the beam into segments and solving multiple simultaneous equations). It has been found that, when loaded on the first beam segment, the global formula allows for quick calculations of slope and deflection of a stepped beam at any location on the beam. For most cases, the global formula will yield good approximate solutions for loads applied past the first segment. Five sample problems are solved to demonstrate the use of the global formula.