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

Ing-Chang Jong

Download Paper | Permalink

Conference: 2012 ASEE Annual Conference & Exposition
Location: San Antonio, Texas
Publication Date: June 10, 2012
Start Date: June 10, 2012
End Date: June 13, 2012
ISSN: 2153-5965
Conference Session: Statics and Strength of Materials
Tagged Division: Mechanics
Page Count: 18
Page Numbers: 25.1247.1 - 25.1247.18
DOI: 10.18260/1-2--22004
Permanent URL: https://peer.asee.org/22004
Download Count: 2364

Paper Authors

biography

Ing-Chang Jong University of Arkansas

visit author page

Ing-Chang Jong is a professor of mechanical engineering at the University of Arkansas. He received a B.S.C.E. in 1961 from the National Taiwan University, a M.S.C.E. 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 Bruce G. Rogers coauthored the textbook Engineering Mechanics: Statics and Dynamics, Oxford University Press (1991). Jong was Chair of the Mechanics Division, ASEE, 1996-1997, and received the Archie Higdon Distinguished Educator Award in 2009. His research interests are in mechanics and engineering education.

visit author page

Download Paper | Permalink

Abstract

Teaching Deflections of Beams: Advantages of Method of Model Formulas versus Those of Conjugate Beam MethodAbstractIn the method of model formulas (MoMF), four equations are derived and used as modelformulas. These formulas can account for the beam’s flexural rigidity, applied concentratedloads, linearly distributed loads, and the boundary or support conditions. No explicit integrationis needed in using the model formulas in this method, and it is not prone to generate inordinatenumbers of simultaneous equations in solving beam problems even if any of the followingconditions 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 be applied to solve most problems involving beam reactions and deflectionsencountered in the teaching and learning of Mechanics of Materials.The conjugate beam method (CBM) is actually a natural extension of the moment-area theorems.It is an elegant, efficient, and powerful method published by Westergaard some nine decadesago. Elementary presentation of this method did appear in early textbooks in mechanics of materials.For reasons unknown, this method is missing in most such current textbooks. The pedagogy of theconjugate beam method lies in teaching and applying the ten guiding rules in this method.The MoMF is a new method for solving statically indeterminate reactions and deflections ofelastic beams. Since its publication in the IJEE in 2009, many instructors of Mechanics ofMaterials have expressed considerable interest in teaching this method to enrich students’ set ofskills in determining beam reactions and deflections. Additionally, they are interested in seeingcomparative advantages of this method versus those of the long-established CBM. This paper isaimed at providing comparisons of the MoMF versus the CBM regarding their (a) pedagogy andmethodology, (b) effectiveness in solving problems of deflections of beams and staticallyindeterminate reactions at supports via several head-to-head contrasting solutions of the sameproblems, and (c) steps for use to effectively introduce and teach either the MoMF or the CBMto students.The paper contains several examples. Each of them is first solved with the MoMF then solvedwith the CBM. Assessment of the effectiveness of these methods to help students understandbeam deflections and reactions is included.

Citation
Format

Jong, I. (2012, June), Teaching Deflections of Beams: Advantages of Method of Model Formulas versus Those of Conjugate Beam Method Paper presented at 2012 ASEE Annual Conference & Exposition, San Antonio, Texas. 10.18260/1-2--22004

TY  - CPAPER
AB  -          Teaching Deflections of Beams: Advantages of Method of Model              Formulas versus Those of Conjugate Beam MethodAbstractIn the method of model formulas (MoMF), four equations are derived and used as modelformulas. These formulas can account for the beam’s flexural rigidity, applied concentratedloads, linearly distributed loads, and the boundary or support conditions. No explicit integrationis needed in using the model formulas in this method, and it is not prone to generate inordinatenumbers of simultaneous equations in solving beam problems even if any of the followingconditions 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 be applied to solve most problems involving beam reactions and deflectionsencountered in the teaching and learning of Mechanics of Materials.The conjugate beam method (CBM) is actually a natural extension of the moment-area theorems.It is an elegant, efficient, and powerful method published by Westergaard some nine decadesago. Elementary presentation of this method did appear in early textbooks in mechanics of materials.For reasons unknown, this method is missing in most such current textbooks. The pedagogy of theconjugate beam method lies in teaching and applying the ten guiding rules in this method.The MoMF is a new method for solving statically indeterminate reactions and deflections ofelastic beams. Since its publication in the IJEE in 2009, many instructors of Mechanics ofMaterials have expressed considerable interest in teaching this method to enrich students’ set ofskills in determining beam reactions and deflections. Additionally, they are interested in seeingcomparative advantages of this method versus those of the long-established CBM. This paper isaimed at providing comparisons of the MoMF versus the CBM regarding their (a) pedagogy andmethodology, (b) effectiveness in solving problems of deflections of beams and staticallyindeterminate reactions at supports via several head-to-head contrasting solutions of the sameproblems, and (c) steps for use to effectively introduce and teach either the MoMF or the CBMto students.The paper contains several examples. Each of them is first solved with the MoMF then solvedwith the CBM. Assessment of the effectiveness of these methods to help students understandbeam deflections and reactions is included.
AU  - Ing-Chang Jong
CY  - San Antonio, Texas
DA  - 2012/06/10
PB  - ASEE Conferences
TI  - Teaching Deflections of Beams: Advantages of Method of Model Formulas versus Those of Conjugate Beam Method
UR  - https://peer.asee.org/22004
DO  - 10.18260/1-2--22004
ER  -