Asee peer logo

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

Download Paper |

Conference

2010 Annual Conference & Exposition

Location

Louisville, Kentucky

Publication Date

June 20, 2010

Start Date

June 20, 2010

End Date

June 23, 2010

ISSN

2153-5965

Conference Session

Teaching Mechanics of Materials & General Mechanics

Tagged Division

Mechanics

Page Count

14

Page Numbers

15.520.1 - 15.520.14

Permanent URL

https://peer.asee.org/15690

Download Count

396

Request a correction

Paper Authors

biography

Ing-Chang Jong University of Arkansas

visit author page

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.

visit author page

Download Paper |

Abstract
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

Abstract

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. https://peer.asee.org/15690

ASEE holds the copyright on this document. It may be read by the public free of charge. Authors may archive their work on personal websites or in institutional repositories with the following citation: © 2010 American Society for Engineering Education. Other scholars may excerpt or quote from these materials with the same citation. When excerpting or quoting from Conference Proceedings, authors should, in addition to noting the ASEE copyright, list all the original authors and their institutions and name the host city of the conference. - Last updated April 1, 2015