Teaching Virtual Work without the Abstract Concepts

Barry T. Rosson

Download Paper | Permalink

Conference: 2016 ASEE Annual Conference & Exposition
Location: New Orleans, Louisiana
Publication Date: June 26, 2016
Start Date: June 26, 2016
End Date: June 29, 2016
ISBN: 978-0-692-68565-5
ISSN: 2153-5965
Conference Session: Teaching & Learning Statics and Mechanics of Materials
Tagged Division: Mechanics
Page Count: 20
DOI: 10.18260/p.26056
Permanent URL: https://peer.asee.org/26056
Download Count: 554

Paper Authors

biography

Barry T. Rosson P.E. Florida Atlantic University

visit author page

Dr. Barry Rosson is a Professor of Structural Engineering at Florida Atlantic University. Prior to joining FAU, he was a professor at the University of Nebraska for 16 years. His areas of research interest are in nonlinear structural mechanics, numerical methods, structural dynamics and steel structures. He has received numerous campus and college-wide teaching and service awards. At the national level of the American Society of Civil Engineers, he has served as the Chair of the society-wide Committee on Professional Practice, President of the Architectural Engineering Institute, and Associate Editor of the Journal of Structural Engineering. He is a Fellow of both ASCE and AEI and is a Registered Professional Engineer. Prior to working as a professor, he was a consulting engineer at Ellisor and Tanner, Inc. in Dallas, Texas.

visit author page

Download Paper | Permalink

Abstract

The principle of virtual work has been known since it was first introduced by John Bernoulli in 1717 and ever since then it has been widely used in a variety of applications in mechanics. However despite this fact, it is rarely taught in Mechanics of Materials courses. Although most students have usually had one or more Physics courses where work and energy principles were routinely discussed, instruction of this subject is often delayed for inclusion in upper-division courses because it is considered to be too advanced and difficult to understand. This is an understandable reaction from students considering that in most textbooks the subject is introduced with an imaginary force on an arbitrary shape to produce internal virtual loads that somehow mysteriously ride along real displacements. Whereas there is nothing technically wrong with this description, students have a difficult time comprehending these abstract concepts. With a description such as this, which is so very different from anything the students have ever seen before, they find it difficult to anchor these concepts to any previously acquired skill or knowledge of mechanics.

With a way of teaching the principle of virtual work as a straightforward and logical extension of real external work and strain energy principles, students find the subject to be much less mysterious and learn why the method works, instead of just how to use it. The focus of this paper is to provide a way of teaching the subject that does not rely on using an imaginary force from the start. Instead, the principle is presented using real forces that are applied to a real structure using two force-time functions and two load application sequences. The principle is explained by carefully presenting the total external work and total strain energy equations beginning first with two real forces P and Q applied to a simple truss. The force Q is applied at the location and in the direction of the desired displacement. The first loading sequence has the full magnitude of P applied before the full magnitude of Q is applied, and the second loading sequence has the full magnitude of P applied after the full magnitude of Q is applied. The total external work and total strain energy produced over the full duration of both loading sequences provides the necessary equations to develop a single expression for the displacement at the location of Q that is due entirely to the force P. From this basis of understanding, one additional force S is then applied to the truss to discuss its influence on the displacement expression. This leads to a general understanding of the influence any number of additional forces has on the displacement expression, and that the effect of the force Q remains unchanged as these forces are applied. It then becomes evident that the desired displacement due to all the applied forces except Q can be determined directly from this expression. Because of this unique condition, the force Q does not actually need to be one of the forces from the actual loading condition of the truss. It can exist solely as a convenience to find the displacement at Q due to the all the other applied forces. Since the force Q has this property, it can be placed anywhere on the truss where a displacement is desired, and it can have any magnitude. Students then readily understand that the magnitude is set to one for the sake of convenience with the calculations, and it is referred to as a virtual force because it does not need to be part of the actual loading condition of the structure. The special case where the desired displacement happens to correspond with the location and direction of a single load in a multi-force system, discussion is provided on how to include this load in the displacement expression.

Citation
Format

Rosson, B. T. (2016, June), Teaching Virtual Work without the Abstract Concepts Paper presented at 2016 ASEE Annual Conference & Exposition, New Orleans, Louisiana. 10.18260/p.26056

TY - CPAPER
AB - The principle of virtual work has been known since it was first introduced by John Bernoulli in 1717 and ever since then it has been widely used in a variety of applications in mechanics. However despite this fact, it is rarely taught in Mechanics of Materials courses. Although most students have usually had one or more Physics courses where work and energy principles were routinely discussed, instruction of this subject is often delayed for inclusion in upper-division courses because it is considered to be too advanced and difficult to understand. This is an understandable reaction from students considering that in most textbooks the subject is introduced with an imaginary force on an arbitrary shape to produce internal virtual loads that somehow mysteriously ride along real displacements. Whereas there is nothing technically wrong with this description, students have a difficult time comprehending these abstract concepts. With a description such as this, which is so very different from anything the students have ever seen before, they find it difficult to anchor these concepts to any previously acquired skill or knowledge of mechanics.

With a way of teaching the principle of virtual work as a straightforward and logical extension of real external work and strain energy principles, students find the subject to be much less mysterious and learn why the method works, instead of just how to use it. The focus of this paper is to provide a way of teaching the subject that does not rely on using an imaginary force from the start. Instead, the principle is presented using real forces that are applied to a real structure using two force-time functions and two load application sequences. The principle is explained by carefully presenting the total external work and total strain energy equations beginning first with two real forces P and Q applied to a simple truss. The force Q is applied at the location and in the direction of the desired displacement. The first loading sequence has the full magnitude of P applied before the full magnitude of Q is applied, and the second loading sequence has the full magnitude of P applied after the full magnitude of Q is applied. The total external work and total strain energy produced over the full duration of both loading sequences provides the necessary equations to develop a single expression for the displacement at the location of Q that is due entirely to the force P. From this basis of understanding, one additional force S is then applied to the truss to discuss its influence on the displacement expression. This leads to a general understanding of the influence any number of additional forces has on the displacement expression, and that the effect of the force Q remains unchanged as these forces are applied. It then becomes evident that the desired displacement due to all the applied forces except Q can be determined directly from this expression. Because of this unique condition, the force Q does not actually need to be one of the forces from the actual loading condition of the truss. It can exist solely as a convenience to find the displacement at Q due to the all the other applied forces. Since the force Q has this property, it can be placed anywhere on the truss where a displacement is desired, and it can have any magnitude. Students then readily understand that the magnitude is set to one for the sake of convenience with the calculations, and it is referred to as a virtual force because it does not need to be part of the actual loading condition of the structure. The special case where the desired displacement happens to correspond with the location and direction of a single load in a multi-force system, discussion is provided on how to include this load in the displacement expression.

AU - Barry T. Rosson P.E.
CY - New Orleans, Louisiana
DA - 2016/06/26
PB - ASEE Conferences
TI - Teaching Virtual Work without the Abstract Concepts
UR - https://peer.asee.org/26056
DO - 10.18260/p.26056
ER -