ComputerBased Instructional Media for Mechanics of Materials
Timothy A. Philpot, Nancy Hubing, Ralph E. Flori,
Richard H. Hall, David B. Oglesby, Vikas Yellamraju,
University of MissouriRolla
Computerbased instructional materials offer great potential for engineering education. Using readily available development software, sophisticated graphics and animations can be created to present engineering topics in ways that are not possible within the confines of the traditional textbook and lecture format. This paper presents examples of instructional media developed for the Mechanics of Materials course. These examples include lecture supplements, animated example problems, interactive example problems, interactive instructional learning tools, and games. Using animations, graphics, and interactivity, the instructional media is designed to engage and stimulate students, to effectively explain and illustrate course topics, and to build student problemsolving skills.
For a many years, engineering educators have sensed that computerbased media could offer new ways to improve instruction for students. Much of the initial software developed for engineering courses could be characterized as providing advanced analytical tools that enable students to perform calculations more sophisticated than those possible with pen and paper. This type of computer application provides students with the means to explore problems beyond the scope of the typical textbook; however, these tools in themselves do not offer instruction.
In recent years, the computer has been used to facilitate the distribution of course materials. For example, many professors now make course notes and old exams available to their students via the Internet. By eliminating barriers of time and distance, this improved distribution mechanism makes it easier for professors to provide reference materials and examples to their students. Much of the material delivered in this manner, however, is no different from that which could be photocopied and handed out in the classroom.
The computer offers some unique capabilities that can be harnessed to provide new types of instructional material. With threedimensional (3d) modeling and rendering software, it is possible to create photorealistic images of various components and to easily show these components from various viewpoints. Animation software allows objects or processes to be shown in motion. By combining these two capabilities, a fuller description of a physical object can be presented to the student. Better images can facilitate the mental visualization that is so necessary to understanding and solving engineering problems.
Animation also offers a medium for a new generation of computerbased learning tools. The traditional instructional device – example problems – can be greatly enhanced through animation to emphasize and illustrate desired problem solving thought processes in a more memorable and engaging way. Animation can also be used to create interactive tools and games that focus on specific skills students need to become proficient problemsolvers. These computerbased tools can provide not only the correct solution but also a detailed visual and verbal explanation of the process needed to arrive at the solution.
The new generation of instruction media stands on the foundation of previous work. Through animation, analytical tools can now be developed that not only perform calculations but also explain how those calculations should be performed. Internet delivery makes the new instructional media freely and widely available. A challenge that must be addressed in the successful use of this medium, however, is overcoming the students’ tendency toward passively receiving the instruction. To be effective, software must use the capability of the computer to engage and stimulate students, both visually and through interaction and feedback.
This paper presents examples of instructional media developed for the Mechanics of Materials course required in many engineering programs. These examples have been developed with the intent of adapting the advantages of the computer in novel ways that offer the potential for improved instruction. Following background information on the Mechanics of Materials course, examples of computer media that are used primarily as lecture supplements are presented. An animated example problem and several interactive example problems are discussed. A learning tool that teaches the process of constructing Mohr’s circle for plane stress, and an example of a game that is useful in preparing foundational comprehension are presented. Early student reaction and course performance is discussed, and conclusions are presented.
The Mechanics of Materials course is one of the core courses for students in civil, mechanical, aerospace, metallurgical, ceramic, geotechnical, and architectural engineering programs. The course is also included in architecture, engineering mechanics, engineering physics, engineering management, and engineering technology curricula. The course is typically taken during the sophomore or junior years after students complete their general mathematics and science preparation. The Mechanics of Materials course introduces students to the principles involved in designing typical components found in machines and structures such as drive shafts; floor beams, pressure tanks, and bolted connections. The course explores various common structural components, teaching students how to analyze the effects of forces and loads on the internal stresses and deformations in the components.
While many of the structures, components, and machines studied in the Mechanics of Materials course are threedimensional objects, students are generally taught about these objects through static, twodimensional illustrations in textbooks and on the classroom board. One of the initial challenges faced in this course is conveying a visual understanding of various physical objects to our students. Only when this foundation is in place can we proceed to establish an understanding of the relevant theory and to develop the problemsolving skills needed to become proficient in specific topic areas.
One of the first topics in the Mechanics of Materials course is the concept of shear stress. A common illustration of shear stress is a bolted connection. To understand this connection, the student must visualize the surfaces upon which shear stress acts. Figure 1 shows a sequence of illustrations for a double shear bolted connection. The first frame shows the basic configuration, as it might be shown on the chalkboard or in the textbook. In the classroom, the professor might typically draw a side view and a top view of the connection after the bolts break. With 3d animation, however, the action of breaking the connection can be set in motion to illustrate the bolt failure surfaces on the front side and then rotated to reveal the additional bolt failure surfaces on the backside of the connection, as illustrated in the frames of Figure 1. Seeing the object as a threedimensional solid in motion makes it very clear to the student exactly where the stress acts in the connection.
Figure 1.
Using 3d rendering and animation to illustrate a double shear connection.

An animation that portrays a biaxial stress state is shown in Figure 2. In Figure 2a, a cube of material is subjected to a normal stress s in the x direction. The strains in the longitudinal and transverse directions due to s_{x} are then animated (Figure 2b). Next, a normal stress in the y direction is then applied to the cube (Figure 2c), and the additional strains due to s_{y} are animated (Figure 2d). By seeing the cube deformation in continuous motion, the student forms a vivid mental image of the interactions of the two normal stresses on a material.
Figure 2.
Illustrating deformations

Figure 3 presents an animation that explains a statically indeterminate torsion member. Using 3d rendering, the torsion member and the applied torque are shown initially in perspective (Figure 3a). The freebody diagram (FBD) required for analysis is shown in Figure 3b. To convey the twisting action that occurs along the member, a grid is superimposed on the two shaft elements (Figure 3c) and deformed as the torque is applied (Figure 3d). The angles of twist that are produced in each shaft are then highlighted (Figures 3e and 3f). This type of structure is particularly difficult to draw clearly in the classroom since it involves a cylindrical threedimensional object. Through animation, the behavior of this torsion structure becomes much more understandable for the student.
Figure 3.
Animation explaining a statically indeterminate torsion member.

Figures 4 and 5 are from an example problem illustrating shear flow in a builtup beam shape consisting of a wideflange steel beam and two channel shapes. The overall crosssection geometry is shown in Figure 4. The camera then flies in to focus on the bolts required to attach the channel shapes to the wideflange shape (Figure 5), and specifically, on the bolt spacing dimension that is to be calculated. Many students are unfamiliar with this type of beam construction, and consequently, they often have difficulty understanding exactly which spacing is to be determined. For this type of problem, 3d rendering is especially useful in describing and defining the problem to be solved. Once the configuration of the builtup beam is clearly understood, the student can better understand the purpose of the calculations.
A portion of an interactive example problem involving the transverse shear stress developed in a teeshaped beam is shown in Figure 6. The animated movie defines the problem and describes the calculation of the section properties needed to compute the shear stress in the beam. The student is then presented with a crosssectional view and a side view of the tee beam including nine preidentified vertical locations (labeled a through i in the figure). When the student clicks on a location:
1. the proper area needed for the calculation of the first moment of area Q is highlighted in an animated fashion,
2. the corresponding equation needed to calculate Q is presented,
3. the transverse shear stress formula with values for the specific location is presented, and
4. the shear stress magnitude is plotted.
After clicking on each location, the plotted points are connected to reveal the complete shear stress distribution over the depth of the tee shape. This movie is particularly helpful in demonstrating the calculation procedure for Q, a topic that is quite often difficult for students to master.
Figure 6.
Interactive example problem

Portions of a movie on beam deflections by the integration method are shown in Figure 7. After the problem to be solved is defined, the movie presents the student with four possible freebody diagrams that could be used to develop the moment equation for the beam (Figure 7a). Two of the freebody diagrams are incorrect. If the student selects an incorrect FBD, the movie explains why that FBD is incorrect. The solution process is slightly different for the two correct freebody diagrams, and thus, depending upon which choice the student makes, the movie branches to the appropriate process. As the movie proceeds, the student must select the boundary conditions needed to complete the solution. Given four possibilities, the student is told to select the two correct boundary conditions. If an incorrect boundary condition is selected, the movie explains the reason why that boundary condition will not work for the given beam configuration (Figure 7b). The movie will not proceed until the student has clicked on the two correct boundary conditions (Figure 7c). The movie concludes by revealing the correct solution and animating the beam deflection (Figure 7d).
Figure 7.
Interactive example problem for beam deflections by integration method.

A feature called Concept Checkpoints is illustrated in Figure 8. An example problem illustrating the concept of shear flow is shown in Figure 8a. The animated movie goes on to explain the calculation procedure for this type of problem. After the example problem has been fully presented, the movie proceeds to the Concept Checkpoints feature (Figure 8b). Concept Checkpoints are a series of short answer questions that test the student’s understanding of the concepts discussed in the preceding example problem. In general, the Concept Checkpoints include a set of four to ten truefalse or multiple choice questions. As the student responds to each question, the movie indicates whether the student was correct or incorrect. After completing the question set, the student is presented with a summary page indicating the number of questions correctly answered (Figure 8c). The student may elect to repeat the question set to improve his or her score. The summary page may also be printed, making it possible for a professor to collect the pages as verification that the student has actually viewed and studied the example problem.
Figure 8.
Example problem that includes

The Concept Checkpoint feature is included in a number of animated example problems. The intent of this feature is to draw the student’s attention to specific concepts or skills that the student should glean from an example problem. Since the student can repeat the question set, it is hoped that the student will not be intimidated by the quizzing format. Rather, it is hoped that the student will take note of the questions that he or she answered incorrectly and then review the example problem. While it is human nature to casually browse through a presentation, the Concept Checkpoints feature can help to engage the student in the example problem in a deeper way.
Figure 9 shows a comprehensive learning tool for the construction of Mohr’s circle for plane stress. The student enters values for normal and shear stresses in the x and y directions and a value for q (if desired) and clicks the enter button. The correct Mohr’s circle for the data is drawn to scale along with stress elements showing the input data and the desired results.
Figure 9.
Interactive Mohr's Circle learning tool.

The unique aspect of this tool, however, is found in the how to menu in the upper right hand corner. From this menu, the student can select any aspect of Mohr’s circle construction, and the software tool will present up to a dozen detailed instructions along with the corresponding animation. For example, if the student doesn’t understand how to use Mohr’s circle to compute the stresses acting on the plane defined by the angle q, he or she can click on the menu item “compute s_{n} and t_{nt}” to receive detailed stepbystep instructions for this calculation (Figure 10).
Figure 10.
Typical explanation for an aspect of Mohr's Circle analysis.

Several games have been developed for the Mechanics of Materials course. An example of this type of application is a game entitled The Centroids Game – Learning the Ropes (Figure 11). In the Statics course, a prerequisite for the Mechanics of Materials course, students learn how to compute the centroid of a crosssectional area. Many students, however, are not as proficient at this skill as they need to be to apply it as required for Mechanics of Materials problems. To help students improve their proficiency in centroid calculations, The Centroids Game was developed. This game is constructed in six levels, termed rounds, designed to lead the student from recognition of a proper calculation to the ability to correctly perform the calculation.
Figure 11.
Game designed to build student proficiency in centroid calculations.

In round 1 (Figure 11a), the student is presented with a series of shapes comprised of rectangles. A target centroidal axis is superimposed on each shape in an incorrect location. The student is asked to decide whether the true centroidal location is above or below this axis. The purpose of this round is to try to develop a student’s intuitive understanding of centroids. We want students to develop a sense of where the centroid should be located before they begin the calculation, rather than performing a calculation and blindly accepting whatever number they obtain. For each question in the round, students receive immediate feedback whether they answer correctly or incorrectly, and points are awarded for correct answers. After responding to all shapes in round 1, students are shown a scorecard that indicates the points scored and the possible points in the round. At this juncture, a student may elect to repeat round 1 to improve their score. If they do repeat the round, the game randomly shuffles the target centroidal axes so that the student sees a slightly different problem. The student may elect to repeat the round as many times as they wish before moving on to round 2.
For round 2, a centroid calculation presented in a tabular format is shown for a shape (Figure 11b). One of the terms in the calculation table is purposefully made incorrect, and the student is asked to identify the incorrect term. The student receives full points if they identify the incorrect term on the first attempt, but the available points are successively reduced for each unsuccessful attempt. A student could opt to randomly guess, but the odds of gaining full points for each question are not favorable. After completing round 2, the scoreboard is again shown and the student is given the chance to repeat the round. The student may repeat only the most recent round; therefore, a student could not opt to repeat round 1 at this point. As in round 1, the round 2 questions are randomly shuffled if the student does elect to repeat the round so that students will generally encounter a slightly different problem each time they repeat the round.
For round 3, a centroid calculation is presented in a tabular format; however, one area term and one distance term are left blank (Figure 11c). In round 4, all of the distance terms are omitted (Figure 11d), and in round 5, all of the terms are left blank (Figure 11e). In each of these rounds, the student receives points for each correct term that they enter. The points awarded increases with each round. The game provides feedback immediately after the student submits his or her answers. At the close of each round, the student is allowed to repeat the round with the problems randomly shuffled for each attempt.
In the final round, the student is presented with a single dimensioned shape but no other information. The student is asked to compute the correct centroid for the shape (Figure 11f). After submitting his or her answer, the student is shown the correct calculation. The possible points for this last question are set very high so that the student cannot get a good score for the entire game unless they successfully answer the round 6 question.
In the Mechanics of Materials course, students were assigned to individually play the Centroids Game and turn in their scorecard showing that they had scored 90 percent or better on the game. They were free to play the game as many times as they wished until they obtained the minimum score.
Initial student reaction to these computerbased learning tools has generally been strong, both pro and con. Particularly in the first semester of use, a number of students seemed opposed to using the computer in any fashion. It was noted that many students would not voluntarily use the computer supplements at first, but once they were required to use the tools in some fashion, they began to realize some of the benefits of the software. At the other extreme, a number of students commented that the computerbased instructional material communicated to them in ways that traditional teaching methods had failed to accomplish. Several students who had failed the Mechanics of Materials course on one or more previous attempts were strongly favorable. Typical student comments included:
§ “Using the software outside of class with notes really helped for understanding the material.”
§ “Computer pictures sometimes give a better understanding of the material.”
§ “Keep improving the computer work. The computer helps to visualize and keep going over material outside of class.”
§ “Visual aids are great help.”
§ “The computer learning aids are very helpful!”
§ “Computer programs and Internet sites were beneficial – really helped to understand the material.”
A number of learning experiments have been conducted to assess the effectiveness of these computerbased instructional modules. Since the Mechanics of Materials course depends heavily on the use of example problems, an inclass experiment was conducted comparing animated example problems (such as those illustrated herein) with those delivered by a lecturer and by a static web page [1, 2]. Students who viewed the animated example problems did not perform quite as well as those who viewed the lecturer, but they performed better than students who used the static web pages. The 50minute limitation of the experiment and other factors, however, suggest that these findings should not be extrapolated to predict student performance over an entire semester. A similar experiment was conducted with a group of stresstransformation modules that featured interactivity rather than examples [3]. Student performance measured after working with these modules was very good. The most positive improvement in student performance, however, was found when the lecture material was delivered in a game format [4]. Students who played a topicrelated computerdelivered game performed much better than those who did not.
This paper has presented examples of instructional media developed for the Mechanics of Materials course. Use of the computer as a medium for instruction provides many capabilities that cannot be readily duplicated within the traditional lecture format. The motion and deformation of common engineering objects can be realistically depicted in both space and time dimensions with animation. Sophisticated graphics including photorealistic, rendered, threedimensional solids can greatly improve visual communication. Concepts that are difficult for the student to visualize based solely on static, twodimensional images become much more understandable when computer graphics are combined with animation techniques. Desired mental processes such as problemsolving methodology are demonstrated and reinforced through animation, repetition, and games. Altogether, computerbased materials can provide fundamental instruction in ways that are not possible within the limitations of traditional textbook and lecture formats. The medium is relatively new, and further work is needed to develop new approaches that utilize the capabilities of the computer for instruction and to effectively integrate these alternative and supplementary instructional tools into the overall teaching and learning effort.
This work was supported in part by a grant from the United States Department of Education Fund for the Improvement of PostSecondary Education (FIPSE #P116B000100).
1. Philpot, T.A., Hall, R.H., Flori, R.E., Hubing, N., Oglesby, D.B., and Yellamraju, V. “Is There A Better Way to Present an Example Problem?” American Society for Engineering Education Annual Conference & Exposition 2003, Nashville, TN, June 2225, 2003, (2003).
2. Hall, R.H., Philpot, T.A., Flori, R.E., Yellamraju, V., and Subramanian, P. “A Comparison of Different Formats for Presenting Example Problems in Basic Engineering WebBased Learning Modules.” Proceedings of the 2003 AACE EdMedia 2003 World Conference on Educational Multimedia, Hypermedia & Telecommunications, Honolulu, Hawaii, June 2328, 2003, 10111014, (2003).
3. Philpot, T.A., Hubing, N., Flori, R.E., Hall, R.H., Oglesby, D.B., and Yellamraju, V. “Animated Instructional Media for Stress Transformations in a Mechanics of Materials Course,” Computer Applications in Engineering Education, John Wiley and Sons, Inc. 11(1), 4052, (2003).
4. Philpot, T.A., Hubing, N., Hall, R.H., Flori, R.E., Oglesby, D.B., and Yellamraju, V. “Games as Teaching Tools in Engineering Mechanics Courses,” American Society for Engineering Education Annual Conference & Exposition 2003, Nashville, Tennessee, June 2225, 2003, (2003).
Effective software begins with an understanding of specific difficulties that students encounter in learning the subject material and a mental picture of new ways to explain these topics in a visual manner. Once the mental picture is in place, the process of transforming it into animated instructional software can begin. The animations presented in this paper were developed with Macromedia Flash 5 software. Interactive features and computations are written in ActionScript, Macromedia Flash’s internal coding language. Threedimensional renderings were developed with Electric Rain Swift 3D software. Developing instructional animations is a timeconsuming process. A basic animated example problem requires 2040 manhours to develop. For movies that feature interactivity and complex graphics, much more development time is required.
Materials presented in this paper are available via the Internet at:
http://web.umr.edu/~bestmech/preview_mechmatl.html
Timothy A. Philpot is an Assistant Professor in the Basic Engineering Department and a Research Associate for the Instructional Software Development Center at the University of Missouri–Rolla. Dr. Philpot received a Ph.D. degree from Purdue University in 1992, an M.Engr. Degree from Cornell University in 1980, and a B.S. from the University of Kentucky in 1979, all in Civil Engineering. Dr. Philpot teaches Mechanics of Materials and is the project director of the U.S. Department of Education grant that supported this work. Dr. Philpot is the author of MDSolids – Educational Software for Mechanics of Materials.
Dr. Hubing is an Associate Professor in the Basic Engineering Department at the University of Missouri–Rolla. Prior to joining the BE department in August 2000, she was on the faculty of the Electrical and Computer Engineering Department at UMR from 1989 to 1999, and taught high school physics in 199900. She completed her Ph.D. in ECE at N.C. State University in 1989. Dr. Hubing enjoys research involving educational methods and technology in the classroom.
Dr. Ralph E. Flori was educated as a petroleum engineer at the University of Missouri–Rolla (Ph.D. 1987). Now an Associate Professor in the Basic Engineering Department at UMR, he teaches Dynamics, Statics, Mechanics of Materials, and a freshman engineering design course. He has earned thirteen awards for outstanding teaching and faculty excellence. Dr. Flori is a Research Associate for the Instructional Software Development Center at UMR and is actively involved in developing educational software for teaching engineering mechanics courses. Dr. Flori is the author of the educational software BEST Dynamics.
Richard H. Hall, Associate Professor of Information Science and Technology at the University of Missouri–Rolla. He received his B.S. degree in Psychology from the University of North Texas, and Ph.D. degree in Experimental Psychology from Texas Christian University. He is the director of the UMR Media Design and Assessment Laboratory, and his research focuses on Web Design and Usability Assessment.
David B. Oglesby is a Professor of Basic Engineering and a Research Associate for the Instructional Software Development Center at the University of Missouri–Rolla. Dr. Oglesby received a B. S. degree in Civil Engineering from the Virginia Military Institute in 1963, and M. S. and D. Sc. degrees in Applied Mechanics from the University of Virginia in 1965 and 1969, respectively. He is actively involved in developing software for teaching Statics. Dr. Oglesby is the author of the educational software BEST Statics.
Vikas Yellamraju is a Software Support Analyst at the University of Missouri–Rolla. He received a M.S. in Industrial Engineering from the University of Oklahoma in 2001 and a B.Tech. in Mechanical Engineering from Nagarjuna University, India in 1995. His present work involves research on multimedia and online learning technology for engineering applications. He is responsible for designing, developing, supervising, and implementing online education tools.