Abstract 1. Introduction


2. Calculating Stresses in
a Solid Body In the typical problemsolving 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. 
An external link to the authors' feedback.


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


Figure 2. Stress Transformation Equations. 
4. Explaining the Purpose of
Stress Transformations to Students
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:

5. The Amazing Stress Camera
Animation 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 clickanddrag 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:
An interactive demo (~136 KB) of the Amazing Stress Camera Animation. 

Figure 3. A screenshot of The Amazing Stress Camera, showing the keyboard controls instructions, the doubleheaded arrow for the clickanddrag movement of the camera, the icon next to the doubleheaded 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 inplane 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 ydirection 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 Students were asked to use a Likert scale to rate their disagreementagreement with each statement on a scale of 110. They were also requested to offer an openended 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:
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 

^{1} p < .05 
Table 1. Subject Ratings as a Function of Learning Mode 
6.3 Qualitative Analysis 

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


2. Students found the lectures motivating, due to clarity, interest, and instructor enthusiasm.
3. Students saw a clear relationship between lecture and quizzes/tests/grades.
4. Lectures emphasized why stress transformations were important, and included "real world" applications


2. The software was viewed by some as redundant with the class.
3. Students generally viewed the software as effective overall
4. The software was particularly effective for helping with visualization of concepts.


2. Include more "real world" applications


7. Conclusions 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 
9. Appendix 
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