Teaching Deflections of Beams: Advantages of Method of Model Formulas versus Method of Integration

The method of model formulas is a new method for solving statically indeterminate reactions and deflections of elastic beams. Since its publication in a recent issue of the IJEE, 1 many instructors of Mechanics of Materials have considerable interest in knowing an effective way for teaching this method to enrich students’ study and their set of skills in determining beam reactions and deflections. Moreover, people are interested in seeing demonstrations showing any advantage of this method over the traditional methods. This paper is aimed at (a) providing comparisons of this new method versus the traditional method of integration via several head-to-head contrasting solutions of same problems, and (b) proposing a set of steps for use to effectively introduce and teach this new method to students. It is a considered opinion that the method of model formulas be taught to students after having taught them one or more of the traditional methods. I. Introduction Beams are longitudinal members subjected to transverse loads. Students usually first learn the design of beams for strength. Then they learn the determination of deflections of beams under a variety of loads. Traditional methods used in determining statically indeterminate reactions and deflections of elastic beams include: 2-12 method of integration (with or without use of singularity functions), method of superposition, method using moment-area theorems, method of conjugate beam, method using Castigliano’s theorem, and method of segments. The method of model formulas 1 is a newly propounded method. Beginning with an elastic beam under a preset general loading, a set of four model formulas are derived and established for use in this new method. These formulas are expressed in terms of the following: (a) flexural rigidity of the beam; (b) slopes, deflections, shear forces, and bending moments at both ends of the beam; (c) typical applied loads (concentrated force, concentrated moment, linearly distributed force, and uniformly distributed moment) somewhere on the beam. For starters, one must know that a working proficiency in the rudiments of singularity functions is a prerequisite to using the method of model formulas. To benefit a wider readership, which may have different specialties in mechanics, and to avoid or minimize any possible misunderstanding, this paper includes summaries of the rudiments of singularity functions and the sign conventions for beams. Readers, who are familiar with these topics, may skip the summaries. An excerpt from the method of model formulas is needed and shown in Fig. 1, courtesy of IJEE. 1