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

Ing-Chang Jong; William T. Springer

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Conference: 2011 ASEE Annual Conference & Exposition
Location: Vancouver, BC
Publication Date: June 26, 2011
Start Date: June 26, 2011
End Date: June 29, 2011
ISSN: 2153-5965
Conference Session: Teaching Mechanics
Tagged Division: Mechanics
Page Count: 16
Page Numbers: 22.1380.1 - 22.1380.16
DOI: 10.18260/1-2--18871
Permanent URL: https://peer.asee.org/18871
Download Count: 7886

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Paper Authors

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Ing-Chang Jong University of Arkansas

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Ing-Chang Jong is a 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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William T. Springer University of Arkansas

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William T. Springer is 21st Century Chair in Mechanical Engineering and Associate Professor at the University of Arkansas. He received his BSME in 1974 from the University of Texas at Arlington, his MSME in 1979 from the University of Texas at Arlington, and his Ph.D. in Mechanical Engineering in 1982 from the University of Texas at Arlington. Dr. Springer is active in ASME where he received the Dedicated Service Award in 2006, was elected to Fellow Grade in 2008, and was awarded the S. Y. Zamrik Pressure Vessels and Piping Medal in 2011.

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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.

Citation
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Jong, I., & Springer, W. T. (2011, June), Teaching Deflections of Beams: Comparison of Advantages of Method of Model Formulas versus Method of Superposition Paper presented at 2011 ASEE Annual Conference & Exposition, Vancouver, BC. 10.18260/1-2--18871

TY  - CPAPER
AB  -            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.
AU  - Ing-Chang Jong
AU  - William T. Springer
CY  - Vancouver, BC
DA  - 2011/06/26
PB  - ASEE Conferences
TI  - Teaching Deflections of Beams: Comparison of Advantages of Method of Model Formulas versus Method of Superposition
UR  - https://peer.asee.org/18871
DO  - 10.18260/1-2--18871
ER  -