Teaching Deflections of Beams: Advantages of Method of Model Formulas versus Those of Conjugate Beam Method

The method of model formulas is a recently published method. It employs a general model loading diagram and derived four key equations as model formulas. These formulas can account for the beam’s flexural rigidity, applied concentrated loads, linearly distributed loads, and the boundary or support conditions. No explicit integration is needed in using the model formulas in this method. This method can be applied to solve most problems involving beam reactions and deflections encountered in the teaching and learning of mechanics of materials. On the other hand, the conjugate beam method is a natural extension of the moment-area theorems. It is an elegant, efficient, and powerful method propounded by Westergaard in 1921. Elementary presentation of this method did appear in some early textbooks of mechanics of materials. For reasons unknown, this method is currently missing in most such textbooks. This paper is aimed at providing comparisons of the method of model formulas versus the conjugate beam method regarding their (a) pedagogy and methodology, (b) effectiveness in solving problems of deflections of beams and statically indeterminate reactions at supports via several head-to-head contrasting solutions of the same problems, and (c) ways to effectively introduce and teach either of these methods to students.