The Amazing Stress Camera: An Interactive Discovery Experience
Timothy A. Philpot, University of Missouri - Rolla
Richard H. Hall, University of Missouri - Rolla

Abstract
Stress transformation is one of the most important foundational concepts in engineering design. However, the nature of stress transformation is hard for students to understand since it is an abstract, mathematical concept that is not easily visualized. The Amazing Stress Camera is an interactive software animation that helps students discover the meaning of stress transformation through an analogy with a familiar everyday object: a simple camera.

1. Introduction 
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 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.

2. Calculating Stresses in a Solid Body 
One of the key concepts taught in the Mechanics of Materials course concerns the nature of stress in a solid body. Internal forces in a body produce stresses that tend to elongate or contract the material and stresses that tend to warp or skew the material. Students in the Mechanics of Materials course learn how to calculate stresses that arise in a variety of structural and mechanical components.

An external link to the authors' feedback: http://www.douglas.bc.ca/ossification/files/feedback.html

In the typical problem-solving process, internal forces are initially considered individually. For example, consider a simple component such as the pipe with a bend as shown in Figure 1. Two forces, P and W, act on the end of the pipe. The force P pulls on the component, causing elongation at points A and B. The force P also causes the pipe to bend about the vertical y axis. The force W causes the pipe to twist about its longitudinal axis (the x axis). The force W also causes the component to bend, but, in this instance, the bending occurs about the horizontal z axis. Each of these effects produces stress in the pipe component. Furthermore, the stresses that are produced in the pipe depend on which point we choose to examine. The stresses produced at point A by loads P and W are different from the stresses produced at point B.

To complicate matters further, the individual stresses produced at either point A or point B by the two loads are calculated in the x, y, and z directions. The combined effect of all stresses acting at a point will produce stresses in the pipe material that act simultaneously in all directions, and, in general, the largest stresses will not occur in the x, y, or z directions. Consequently, the engineer must be able to consider all possible combinations of stress acting in any direction. To properly design the pipe component, the Mechanics of Materials student must (1) be able to compute each of the stresses acting at any point of interest, and (2) from this set of stresses in the x, y, and z directions, compute the most critical stresses acting at any possible orientation.

Figure 1. Typical component considered in the Mechanics of Materials Course.

3. Stress Transformations 
To assess the combined effect of stresses on a solid body, stress transformation relationships are used. Based on the necessity of satisfying equilibrium conditions, a set of equations can be derived that expresses the variation of two types of stress, normal stress and shear stress, for any orientation with respect to the original xyz coordinate system (Figure 2). Although an abstract mathematical concept, stress transformations are an important tool necessary to design components such as beams and pipes that are safe and reliable.

Figure 2. Stress Transformation Equations.

4. Explaining the Purpose of Stress Transformations to Students
In dealing with solid bodies made from materials such as steel or concrete, it is impossible to show students actual stresses in components and very difficult to physically demonstrate the effect of stress combinations. Furthermore, it is difficult to visualize and difficult for a professor to adequately describe or depict on the classroom board. The notion of a stress transformation is a mathematical concept; consequently, there is little in a student's educational or everyday background that can be drawn upon as a model for the behavior. This situation poses particular difficulties for two types of learners: visual learners and global learners.

• Visual learners get more information from visual images (pictures, graphs, illustrations, sketches, etc.) than from verbal material (written and spoken words and mathematical formulas).
• As a general definition, one could say that sequential learners acquire understanding of material in small, connected chunks while global learners take in information in seemingly unconnected fragments and achieve understanding in large quantum jumps. Whereas sequential learners can solve problems with an incomplete understanding of the material and in the absence of a sense of the big picture, global learners generally are poor problem-solvers until they grasp the overall context of a topic.

When stress transformations are taught in the Mechanics of Materials course, therefore, it is not uncommon to find that most students fall into two performance groups:

1. Students who can produce the correct numerical results but have no sense of how these results relate to real physical objects, and
2. Students who struggle to apply the transformation equations because they have no sense of the purpose or meaning of stress transformations.

5. The Amazing Stress Camera Animation
The Amazing Stress Camera, developed to guide students toward self-discovery of the meaning of stress transformations, is an interactive computer animation that uses the analogy of a photographic camera to convey the idea that stresses at a single point in a solid body vary depending upon the orientation with which we view the point.

To establish the context in which an engineer might be required to consider a combination of stresses, The Amazing Stress Camera begins by showing and briefly discussing a simple system of pipes that could be found in any manufacturing or process plant. The story continues by introducing "a new instrument that will let us look into the microscopic structure of the pipe material ... the amazing stress camera." The camera is brought to eye level so that the student can look through the viewfinder at the pipe. The camera zooms in on a single point and a "calibration" measurement is made. This calibration reading determines the stresses that act in the x and y directions at a point on the pipe. Next, the user is instructed on how to use the camera to make stress readings and asked to try out the click-and-drag movement of the camera using the computer mouse. (Figure 3)

The Amazing Stress Camera animation presented in this paper and additional instructional media are available via the Internet at: http://web.umr.edu/~bestmech/preview_mechmatl.html

An interactive demo (~136 KB) of the Amazing Stress Camera Animation. Flash Player required.

Figure 3. A screen-shot of The Amazing Stress Camera, showing the keyboard controls instructions, the double-headed arrow for the click-and-drag movement of the camera, the icon next to the double-headed arrow for capturing the data, the blue arrows, and the red arrows.

After being introduced to the context, the premise, and the operation of the camera, students begin Virtual Experiment One. Students are asked to rotate the camera to find the largest blue arrow. In The Amazing Stress Camera, blue arrows correspond to a specific type of internal stress: tension normal stresses. Once students have found the largest blue arrow, they are instructed to click on an icon to "snap the picture." Students then manipulate the camera, changing the viewing orientation, until the largest blue arrow is found and the reading is captured. If students fail to find the correct orientation, they are sent back to repeat the measurement. Once they have correctly identified the orientation that contains the largest blue arrow, the significance of their measurement is explained. The largest blue arrow is called a principal stress, and principal stresses are important values that must be determined in order to successfully design the pipe system.

Next, students proceed to Virtual Experiment Two. In this experiment, the largest value for the red arrows is to be determined. In The Amazing Stress Camera, red arrows correspond to shear stresses. As before, students manipulate the camera orientation until the largest red arrow value is found and recorded. Once they have correctly identified the orientation that contains the largest red arrow, the significance of this measurement is explained. The largest red arrow is called the maximum in-plane shear stress, another important value that must be considered in the pipe system design.

Following these two virtual experiments, students are presented with general conclusions to be drawn from The Amazing Stress Camera . Advancing to the final scene in the animation, which is a page suitable for printing, students can enter their names on this page and print it for submission as a part of a homework assignment.

Because practically everyone has taken pictures with a camera, students are afforded a familiar analogy for rotated reference axes (i.e., changing viewing orientation). As students rotate the camera, they are exposed to the notion that stresses at a point in a solid body depend upon orientation. Although the stresses are initially known only in the x and y directions, various combinations of stress occur at other orientations, and these other stress combinations may be larger than the initial x- and y-direction stresses. Through the familiar act of taking pictures with a camera, students can discover how stresses vary as the viewpoint is rotated. From these readings, the purpose and importance of stress transformation equations are demonstrated. The Amazing Stress Camera, thus, prepares the conceptual foundation for the topic, enabling the professor to teach the details of stress transformations to students who more clearly understand the larger purpose of the topic.

6. Evaluation of The Amazing Stress Camera Animation
6.1 Method
During the portion of the course that covered stress transformation equations, students in two sections of Mechanics of Materials were required to complete an assignment that used The Amazing Stress Camera animation. Following this portion of the course, these students completed a thirteen-question questionnaire. The questionnaire consisted of four sets of three questions and a final open-ended question. Each of the three-question sets included a question that related to: a) the class textbook, b) the class lectures, and c) The Amazing Stress Camera animation.

Students were asked to use a Likert scale to rate their disagreement-agreement with each statement on a scale of 1-10. They were also requested to offer an open-ended explanation of their response. The four sets of questions addressed learning, motivation, and application (two questions). More specifically, the four sets of questions were stated as:

• "I learned a great deal of information about stress transformations from the ..." (learning)
• "I found the ... coverage of stress transformations to be very motivational." (motivation)
• "The ... helped me to understand why we do stress transformations." (why)
• "The ... helped me to see how stress transformations might be necessary in "real world" situations." (real world)

Each of the four sets of questions consisted of three questions in which the "..." was replaced by class text, class lectures, or amazing stress camera multimedia module. The thirteenth question asked students to "Please list below any other comments you can provide that would aid in the improvement in the 'amazing stress camera' multimedia module."

6.2 Quantitative Analysis
Students' mean responses were compared for each teaching method (text vs. lecture vs. module) for each of the four types of questions (learning, motivation, why, and real world). The means are displayed in Table 1. The statistical significance of these four sets of comparisons was assessed using four one-way repeated measures Analyses of Variance, followed by a set of Tukey's Post Hoc comparisons. All comparisons were statistically significant. In each case, (1) students rated the lecture as significantly more positive than the modules on each question, and (2) students rated the animation module significantly higher than the textbook.

¹ p < .05
² All Tukey's Post-Hoc Mean Comparisons Significant
Table 1. Subject Ratings as a Function of Learning Mode

6.3 Qualitative Analysis
A classification framework was developed based on an initial reading of students' comments for all questions. The comments were grouped into four broad categories: a) textbook, b) lecture, c) The Amazing Stress Camera animation, and d) suggestions for improvement of the multimedia module. Within each of these categories, several themes emerged. The categories and themes are demarcated below, with representative comments listed.

6.3.1 Textbook Category
1. Students found the textbook's presentation confusing.

• I found the book confusing; examples were not useful
• The book was difficult to follow and the examples were even harder to follow
• The book goes into very lengthy derivations. By the time I read through it all I am just confused.
• Book is confusing; too many equations and derivations; too many symbols, easy to get lost.
• The text ... provided a base of confusion mainly.

2. The confusing nature of the textbook was demotivating

• It confused me more than motivated me.
• The books confusion was discouraging
• The book is a snoozer, and not always all that clear.
• Got lost, got confused, got pissed!
• I did not care for the textbook; it was dry and unmotivational.

3. There was a disconnect, in the form of redundancy or even inconsistency, between the class in general (especially the grading) and the textbook

• ... most (text) examples don't help with homework
• There are a few examples in the text, but I couldn't always apply them to the homework.
• I had trouble understanding the text; much of it seemed to contradict what was being lectured about.
• Much of the time equations in the book are not equal to the ones used in class. It's really hard to read I think also.
• Textbook = useless.

6.3.2 Lecture Category
1. Students found the instructor to be a very effective lecturer. More specifically, they reported that he focused on important points and presented them clearly.

• Tim really hit key points in the lecture as well as showing methods and steps in the problem solving.
• Lectures are concise and clear.
• Did a great job explaining and emphasizing key points.
• Dr. Philpot "cut through the crap" in the book to tell us what we wanted to know about stress transformations.
• Dr. Philpot took the time to explain things in a clear consistent manner

2. Students found the lectures motivating, due to clarity, interest, and instructor enthusiasm.

• My instructor did a great job of making the info easier and more enjoyable!
• Dr. Philpot really enjoys this stuff.
• ... He was so motivated it just rolls over to you.
• The professor knew what he was talking about and made the class much more enjoyable
• The clear presentation and answering of questions is the difference. Just working on problems (such as homework) can get discouraging. The lecture helps clear up any questions and helps reduce the frustration of not getting the problems right.

3. Students saw a clear relationship between lecture and quizzes/tests/grades.

• Every thing covered in class was helpful in the tests, just the right amount of info
• In class many examples were worked and when combined with the online stuff proved quite useful
• I used notes from class to do all homework and learned the most from class.

4. Lectures emphasized why stress transformations were important, and included "real world" applications

• Basic concepts, as well as at least one example, were always covered. It always allowed for a bigger picture view ...
• Lectures with real examples helped me understand this topic.
• Examples in lecture helped me to see why we use stress transformations
• In class we went over why. It was great to know the purpose.
• His examples put what we're doing in perspective.

6.3.3 Amazing Stress Camera Category
1. The multimedia was viewed as a potentially effective complement to the lectures.

• This helped reinforce the ideas presented in the lecture and strengthen understanding
• The camera was more helpful in strengthening and supporting what was learned in class.
• It was helpful in conjunction with lecture and homework to better understand
• I already knew most of it, but it was nice to interact and see the camera "work."
• The "camera" helped to solidify what was taught in class.

2. The software was viewed by some as redundant with the class.

• I did learn a couple of things from this, but learned most in class.
• It was just a review basically.
• Probably just reinforced concepts.
• Very well done software, but I already knew all of the stuff by the time I used it.
• The module did a good job, I just had already learned it in class.

3. Students generally viewed the software as effective overall

• I found it easy to use and informative.
• Fun and user-friendly
• easy to use, good graphics, not overly long
• ... the "ASC" is a really neat way to teach the material.
• It helped explain some confusing points to stress transformations.

4. The software was particularly effective for helping with visualization of concepts.

• I really learned how the stresses change with your viewing angle. From the lecture I was under the impression that you changed the element or something
• It was useful to help illustrate principal stresses and max shear, put a picture with words.
• It helped me visualize it in a way that no other could.
• It was a good visual tool to see stress transformation.
• The lecture did it (showed real world applications) for me but this gave me a visual example

6.3.4 Suggestions for Improving Amazing Stress Camera
1. Add more interactivity

• Make the students explain the concepts before it lets you finish
• Do a connection with computing stress transformation, so you can apply what you see
• Make it more interactive
• More interaction with program ...
• ... Maybe a game that would go over a lot of examples and guess where the highest stress would be.

2. Include more "real world" applications

• Provide a couple more examples of application type scenarios.
• Give pictures or examples of real world applications for amazing stress camera.
• More stuff about real world things.
• Showing that materials fail in the direction of the principal stresses would make it very clear why being able to find the stress transformations is helpful.

7. Conclusions
The quantitative findings indicate that students found the lectures to be significantly more effective than the multimedia module, while, in turn, they found the module to be significantly more effective than the textbook. The qualitative results support and further elucidate the quantitative findings. In short, this instructor did a very effective job of lecturing, and students found the text to be very ineffective. While students viewed the multimedia module as generally effective, particularly for aiding in the visualization of abstract concepts, the module ratings did not reach the highly positive ratings that students gave for lectures.

As an initial evaluation of The Amazing Stress Camera animation, these results are quite positive. It's important to note that students were exposed to lecture and the text throughout the semester, while the module only constituted a small portion of the class. Moreover, the module was being compared to a lecturer whom students found highly effective. The fact that the module was judged as significantly more effective than the textbook is strong support for the module's effectiveness, given students' long history of experience with textbooks. In addition, the module appears to have been particularly effective for aiding students in visualizing concepts, which was its main purpose. Further, the module was viewed as an effective adjunct to the lecture, which was also the purpose. The qualitative results also provide two useful directions for further improvement of the modules: increase interactivity and add more "real life" applications and examples.

8. Acknowledgement
This work was supported in part by a grant from the United States Department of Education Fund for the Improvement of Post-Secondary Education (FIPSE #P116B000100).

9. Appendix
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. Three-dimensional renderings were developed with Electric Rain Swift 3D software.

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