Not As Bad As It Seems: Teaching Probability And Statistics In Civil Engineering

Most engineering students dread the day they take probability and statistics. This paper documents a project-based, learn-by-doing approach that provides the vehicle for teaching the analytical skills of probability and statistics. Through this project, students also engage in the engineering design and construction process doing so with realistic engineering constraints. This approach also provides opportunities for discussions related to societal, environmental, and ethical issues. All of this is geared towards the sophomore level and thus allows for realistic design early in the curriculum at the same time it reinforces prior knowledge and introduces new technical content. The Problem Probability and statistics are perhaps one of the most commonly found yet least understood topics in most engineering programs. Sure, a large number of students successfully pass their probability and statistics courses. Some even are successful at applying the course information to subsequent courses and eventually in their professional work. But ask the typical engineer “on the street” to interpret the outcome of the 2001 Major League Baseball World Series. The Arizona Diamondbacks won the contest with a “thrilling and dramatic” bottom-of-the-ninth rally. Little could have been more dramatic except unless there had been two outs instead of one. When informally surveyed, most students in a sophomorelevel probability and statistics course found this to be “one of the best world series ever.” When prompted to explain why the Diamondbacks won, few thought critically about the application of variability and uncertainty; even fewer paused to consider basic probabilistic models to shed light on the outcome, perhaps even in a Bayesian manner. Instead, interpretations and explanations of the outcome tended to focus on a team or player being “the better one that day.” Most even thought the Diamondbacks would have been clearly the dominant team had they won in four straight games instead of seven. Explanations tended to include everything but the notions of variability and uncertainty, especially if the respondent was a fan of the winner. In Bloom’s taxonomy 1 parlance, students were performing at best on the application level when synthesis and evaluation levels would have been preferable. When students were prompted with similar engineering-based scenarios, there were responses were much the same. That is, there was a clear ceiling in the students’ mastery of the course material that did not extend beyond the application level. P ge 949.2 Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition Copyright © 2004, American Society for Engineering Education The Approach With the goals of moving student performance to the higher levels on Bloom’s taxonomy including the valuation level, a hands-on, learn-by-doing, bridge design project was selected. This project replaced many of the traditional textbook problems, even those that used engineering data. The bridge building project documented in Designing and Building FileFolder Bridges 2 was modified for a sophomore-level applied probability and statistics course for civil engineering students during the fall semester of the 2001-2002 academic year when the author was teaching at Valparaiso University. Learning Objectives By the end of the project, students were expected to be able to: • Conduct experiments, collect and analyze data to develop empirically-based design models for structural members. • Design a model truss bridge to meet a set of design requirements. • Construct a model truss bridge, consistent with their set of plans and specifications. • Analyze and Assess the performance of their model truss bridge. • Explain how construction quality affects the performance of a structure. • Explain the difference between system and component reliability and the implication for design. • Discuss hazard and risk and implications for protecting public safety and welfare. Project Description Student teams of three each designed, constructed, tested, and assessed a 1/40 scale truss bridge made of manila folder material. Strength data on tubes and bars made of file-folder material was limited, so students conducted their own physical experimentation and developed their own models representing structural member strength. Geometric criteria were provided as well as probabilistic load criteria. Figure 1 shows one bridge being subjected to the probabilistically simulated load, which for this case was 5 kg. Figure 1: A successful bridge resisting the probabilistic design load. P ge 949.3 Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition Copyright © 2004, American Society for Engineering Education As shown in the table below, the project was divided into eight components. Project Component Title Description A Member Preparation Manufacture of Specimens for Strength Testing B Member Testing Strength testing of tubes and bars C Data Analysis Statistical analysis of strength data and development of empirical strength models. D Bridge Analysis System analysis of the strength capacity of the 6-bay Pratt Truss of Learning Activity One 2 . E.1 Preliminary Design Preliminary selection of truss configuration. E.2 Preliminary Design Preliminary selection of member sizes and gusset plates. F Final Design Submission of design drawings and documents. G Load Testing In-service load testing of bridge. H Analysis and Assessment Analysis and assessment of bridge performance. Design Criteria The project criteria generally followed that of Ressler 2 of a 60-cm span and 11 cm road-width with the following exclusions and exceptions: • Each bridge was designed for a random sampling of two simultaneous extreme truck loads, the maximum total mass of which was 6 kg. This was termed a “design level load.”