Text, animations help students master statics
ith a wide grin, Professor **Mike Plesha** proudly holds up a thick softcover textbook. Inside, the wide margins, neatly formatted text and myriad figures evoke the idea of engaging, understandable information. Together, design and content fill an important role: helping students master statics, the study and analysis of structural equilibrium.

Set officially to publish via McGraw-Hill in early 2009,* Engineering Mechanics: Statics* (and its companion,* Engineering Mechanics: Dynamics*) is the result of an eight-year collaboration among Plesha and co-authors Gary Gray and Francesco Costanzo of the Penn State University Department of Engineering Science and Mechanics.

Statics is a required course for nearly two-thirds of the UW-Madison engineering undergraduate student body. In addition to presenting real-life design challenges, the new statics text lays out straightforward problem-solving approaches that include modeling, idealizations, governing equations, computations and discussion of the results.

For Plesha, however, the textbook is only the first step in his unique approach to teaching this difficult-to-master subject. With funding through the College of Engineering 2010 initiative, Plesha and PhD student Jonathan Fleischmann are developing animations of free-body diagram construction—and other difficult concepts—that enable statics students to visualize the phenomena they study. “This course is a course in which the math isn’t challenging,” says Plesha. “It’s the visualization—taking a real-life problem and replacing it with a mathematical idealization. That’s where they struggle.”

Students draw free-body diagrams to help them analyze the forces acting on a free body: a structure removed from its environment. Vectors in their drawings show the direction and magnitude of forces, such as contact, friction, weight due to gravity and others, that act on the structure. Based on their free-body diagrams, students then write, solve and interpret the results of equations that govern the structure’s equilibrium. “The ability to draw free-body diagrams—this is something that they’ll do in a good number of their courses after this,” says Plesha. “It’s an essential skill, and if they don’t develop that skill, it’ll adversely affect them in a lot of coursework to follow—and in their professional practice.”

Some free-body diagrams are relatively straightforward; others create more confusion, says Plesha. The animations, which last about a minute, demonstrate the process for drawing a free-body diagram and help students ensure they don’t miss—or misinterpret—forces.

One recently animated structure has a pin at one point, a roller at another point, and includes a pulley and cable. Because it includes multiple components, says Plesha, this is the kind of problem that’s difficult for students. Fleishmann’s animation begins by taking a cut that separates the structure from its environment; next, arrows glide into place to indicate the appropriate forces. Then, the roller goes away and the force-vectors for it appear. Next, the cable is cut and the pulley drifts away, while arrows move in to show the forces at those locations.

Also in the works are animations that demonstrate force reactions for various structure supports, behavior of springs, mechanisms in truss structures, and others.

Sophomore Chris Holland, a current statics student who intends to major in chemical engineering, calls the animations incredibly helpful, particularly as the structures he studies become increasingly more complex. “They allow for a much simpler visualization of the problem you are looking at,” he says.

While the animations are important to students’ understanding of free-body diagrams, they also are key instructional tools, says Plesha. “This subject will be taught in increasingly larger courses, without blackboard and chalk,” he says. “It’ll be whiteboard and a place to plug in a computer. Effective lecture materials are kind of a challenge—and also an opportunity—because there are some things that are hard for students to visualize and hard for instructors to convey.”

So far, Plesha and Fleishmann mainly have used Adobe Illustrator and Apple QuickTime Pro, but hope to use Mathematica and Working Model in future animations. The two aim to develop 20 animations that instructors can incorporate into statics courses in technology-rich classrooms and lecture halls. Plesha also envisions an additional benefit to students. “Longer range, I would like to see the animations be a resource for students on a class website that they can consult independently of the lectures,” he says.

Already, aspiring chemical engineer Holland appreciates the value of having the animations at his fingertips. His message to Plesha: “Keep using them and developing them. They will be of incredible use in statics and dynamics classes in the future.”