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Enriching Students’ Study Of Beam Reactions And Deflections: From Singularity Functions To Method Of Model Formulas

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2010 Annual Conference & Exposition


Louisville, Kentucky

Publication Date

June 20, 2010

Start Date

June 20, 2010

End Date

June 23, 2010



Conference Session

Teaching Mechanics of Materials & General Mechanics

Tagged Division


Page Count


Page Numbers

15.520.1 - 15.520.14

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Paper Authors


Ing-Chang Jong University of Arkansas

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Ing-Chang Jong serves as Professor of Mechanical Engineering at the University of Arkansas. He received a BSCE in 1961 from the National Taiwan University, an MSCE in 1963 from South Dakota School of Mines and Technology, and a Ph.D. in Theoretical and Applied Mechanics in 1965 from Northwestern University. He and Dr. Bruce G. Rogers coauthored the textbook Engineering Mechanics: Statics and Dynamics, Oxford University Press (1991). Professor Jong was Chair of the Mechanics Division, ASEE, 1996-97, and received the Archie Higdon Distinguished Educator Award in 2009. His research interests are in mechanics and engineering education.

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Enriching Students’ Study of Beam Reactions and Deflections: From Singularity Functions to Method of Model Formulas


Since publication of the method of model formulas in a recent issue of the IJEE,1 there has been considerable interest in knowing a good approach to teaching this method to enrich students’ study and set of skills in determining statically indeterminate reactions and deflections of elastic beams. This paper is aimed at sharing with mechanics educators an approach that can be used to effectively introduce and teach such a method. 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. Besides enhancing the learning experience of upper class engineering students, this method can benefit practicing engineers. In particular, this method may readily serve as an independent and effective means to quickly check or assess the solutions obtained using other 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 deflection of beams under a variety of loads. Traditional methods that are used in determining statically indeterminate reac- tions and deflections of elastic beams include: 2 - 1 2 method of integration (with or without the use of singularity functions), method of superposition, method using moment-area theorems, method using Castigliano’s theorem, method of conjugate beam, and method of segments.

The method of model formulas1 is a newly propounded method. Beginning with a general preset model loading on a beam, a set of four model formulas are established for use in this 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, who 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

Jong, I. (2010, June), Enriching Students’ Study Of Beam Reactions And Deflections: From Singularity Functions To Method Of Model Formulas Paper presented at 2010 Annual Conference & Exposition, Louisville, Kentucky.

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