Effective Teaching of Determining Beam Deflections Using Moment-Area Theorems: Avoiding a Pitfall

Several established methods for determining deflections of beams may be found in textbooks on mechanics of materials.The method using moment-area theorems is preferred by many engineers because it has the inherent advantage of graphical visualization in solving problems.This method employs two moment-area theorems, which are derived by integrating well-behaved functions in domains along beams.Unfortunately, most textbooks do not provide explicit warning that one cannot apply any moment-area theorem directly to the entire beam when the beam under loading has a discontinuity in its slope, such as that in a hinge-connected beam.This is a pitfall for unsuspecting beginners, who often reach erroneous results and are puzzled by them.This paper contributes definitive concepts and detailed explanations to expel ambiguities often encountered by students in applying the method to solve problems.The examples illustrate steps for use in effective teaching of the method and help beginners avoid tumbling into pitfalls.It is aimed at contributing to the better teaching and learning of mechanics of materials.