Teaching Deflections of Beams: Comparison of Advantages of Method of Model Formulas versus Method of Superposition

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Abstract Teaching Deflections of Beams: Comparison of Advantages of Method of Model Formulas versus Method of SuperpositionAbstractThe method of model formulas (MoMF) is a new method for solving statically indeterminatereactions and deflections of elastic beams. Since its publication in the IJEE in 2009, manyinstructors of Mechanics of Materials have considerable interest in teaching this method toenrich students’ set of skills in determining beam reactions and deflections. Additionally, theyare interested in seeing comparative advantages of this method versus the traditional method ofsuperposition (MoS). This paper is aimed at providing comparisons of the MoMF versus theMoS regarding their (a) pedagogy and methodology, (b) effectiveness in solving problems ofdeflections of beams via several head-to-head contrasting solutions of same problems, and (c)steps for use to effectively introduce and teach either the MoMF or the MoS to students.In the MoMF, four equations are derived and used as model formulas. These formulas canaccount for the beam its flexural rigidity, applied concentrated loads, linearly distributed loads,and the boundary or support conditions. No explicit integration is needed in using the modelformulas in this method, and it is not prone to generate inordinate numbers of simultaneousequations in solving beam problems even if any of the following conditions exists:● The beam carries multiple concentrated loads (forces or moments).● The beam has one or more simple supports not at its ends.● The beam has linearly distributed loads not starting at its left end.● The beam has linearly distributed loads not ending at its right end.The MoMF can effectively be applied to solve most problems involving beam reactions anddeflections encountered in the teaching and learning of Mechanics of Materials.The paper contains several examples. Each of them is first solved with the MoMF then solvedwith the MoS. Although solutions obtained by the MoMF are often more direct than the MoS, aone-page excerpt containing the four model formulas must be made available to those who usethe MoMF. Nevertheless, one may remember that a table of formulas for slope and deflection ofselected beams having a variety of supports and loading is also needed by persons who use theMoS. In this regard, the MoMF is on a par with the MoS. Readers of this paper will have anopportunity to form an opinion if the new MoMF is a competitive alternative to the traditionalMoS.

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