HAVE YOU EVER WANTED TO LIVE IN A TREEHOUSE? Your “Aunt Ada” is looking for just that. With a plot of land in the Pocono Mountains, she is looking to build a treehouse so elaborate that it needs an artificially engineered tree trunk to meet safety requirements. As a generous aunt, she has outsourced these engineering considerations to her favorite relative studying finite element analysis — you. Armed with limited information and their mechanical engineering knowledge, student teams determine the most valuable considerations for designing Aunt Ada’s artificial treehouse and the trunk material to support it. Students start by brainstorming with very minimal guidance. Outside of class, the teams have less than a week to compose a list of considerations to present to their classmates. I roll dice to first select a team and then a student to elaborate on a potentially important design consideration. Another team/ student is randomly selected to comment on the consideration presented and provide some new ones. This continues for the duration of the class session. Students discuss topics such as how much a house weighs. One student referenced a thread where various contractors quoted total disposal weight for different sized houses. Eventually, consensus was established for an estimate of 200 lb/ft 2 . Giving Aunt Ada an appropriate amount of space is a hefty task. Throughout the project, the students realize they need to debate the relative importance of appeasing the customer’s desired aesthetics, maintaining appropriate levels of safety, staying within a budget, and the impact on the surrounding environment. There are clear tradeoffs at work; the design constraints and the project’s goals are competing. As a result, student teams are forced to consider their customer more closely. Over the next few weeks, each team creates a design proposal for Aunt Ada. Individual proposals are diverse, with different aesthetic considerations. Seemingly simple specifications like the total height of the artificial tree trunk must be considered in light of the customer’s desires. For instance, students learn that Aunt Ada wants to view fireworks launched from a campground about 10 miles away. To my pleasant surprise, many student teams thought about Aunt Ada’s view. They researched the average tree height in the Poconos, which influenced their design. A particularly industrious team turned up a plot of detonation height and distance for various grade fireworks and used it to justify their proposed design height. When Aunt Ada wants an internal elevator, students realize that a hollow trunk is necessary. With information on total height of the tree trunk and the desired radius at three different heights, students uniquely fit parabolic equations for the inner and outer radius as functions of height, or x. From submitted designs, Aunt Ada selects proposal elements and combines them with ideas of her own. Then she generates custom design guidelines for each team. However, she doesn’t provide engineering specifications; her requests are vague. For example, she expresses interest in a more natural look, suggesting a circular cross-section with a quadratically varying radius. She notes, “There are other ways to achieve that look, so I’m open to suggestions.” Student teams optimize the cross-section of the tree trunk to minimize required material while ensuring safety. They assume that all structures connected to the tree trunk manifest loading along a vertical line. After discretizing the structure into finite elements, the students construct the element stiffness matrix using: , where A, E, and L are the element’s area, Young’s modulus, and length, respectively. The area of an element is the average of the area computed for the two nodes at the end of each element. These element stiffness matrices are assembled into a global stiffness matrix ( K G ) that reflects the connectivity of the system. Once the elements are mapped together, the equations ’ve been teaching strength of materials at Lehigh University for six years. One of the most important parts of the course is how finite element methods can be used to understand complex one-dimensional loading scenarios and two-dimensional trusses. After attending KEEN’s Integrating Curriculum with Entrepreneurial Mindset (ICE) workshop, I was inspired to make a radical change in the way I approach teaching finite element analysis. I realized that I wanted to present this powerful method of stress analysis in a way that reflected its use in many commercial sectors. I altered the first course project, which spans about one-third of the semester, to include elements of the 3C’s. Now the project revolves around writing a computational analysis tool — a computer algorithm — to analyze a fairly complex one-dimensional loading scenario and optimize an associated structure. Woven throughout the experience is an entrepreneurially minded learning framework that has ignited student excitement for the project. By Edmund Webb III Associate Professor of Mechanical Engineering Lehigh University 5 4

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