A Design Approach to Teaching Truss Bridge Mechanics in a Statics Course

A Design Approach to Teaching Truss Bridge Mechanics in a Statics Course Alyssa DeSimone1 1 Department of Civil and Environmental Engineering, George Washington University Abstract Introductory statics or mechanics courses traditionally have limited design experiences for students. For example, students typically learn to analyze the support reactions and the internal forces in a truss but lack practical experience in understanding what makes a truss stronger or weaker, how to optimize its design for given parameters (e.g., load, dimensions), or the realworld considerations engineers face when designing a truss. To address this gap, a truss design project was developed, allowing students to compare the internal forces in similarly dimensioned Pratt and Warren trusses under identical loading conditions. After selecting the more suitable truss based on their analysis, students reanalyzed the internal forces after increasing the truss’s height. They then compared the results of the shorter and taller trusses to determine which design was best suited for the given loads. Student feedback, measured using a five-point Likert scale, showed strong agreement that the project reinforced classroom concepts (4.75 ± 0.47). Additionally, students found the project made learning about trusses more engaging (4.15 ± 0.96) and improved their understanding of truss analysis and design (4.30 ± 0.80). Students also evaluated their confidence in truss analysis and design before and after completing the project. On average, confidence in their ability to draw free-body diagrams for truss analysis increased by 31%, confidence in analyzing a truss increased by 42%, and confidence in making design decisions that optimize cost and performance increased by 63%. These results underscore the value of design-based learning in early mechanics courses, demonstrating its ability to enhance conceptual understanding, engagement, and student confidence in real-world engineering applications. Introduction Static mechanics courses typically emphasize theory applied to well-defined textbook problems. While this approach provides students with a solid foundation in core mechanics principles, it can limit their ability to contextualize these concepts within practical engineering scenarios. As a result, students may struggle to see the relevance of what they are learning beyond the classroom, which can dampen engagement and curiosity. Project-based learning (PBL), or design-based learning, offers a valuable complement to traditional lecture-based instruction by allowing students to engage with the material in an active and applied manner. By working through open-ended design problems, students are encouraged to synthesize theoretical knowledge and make decisions based on real-world constraints. Many studies have shown the pedagogical benefits of PBL [1], [3], [4]. Despite these benefits, incorporating design experiences into early mechanics courses can be challenging in terms of the time commitment required in class and for grading the project. In this paper, I present an easy-to-adopt design-based learning project for a statics course that focuses on truss design. The project guides students through the analysis and comparison of different truss designs, helping them develop an intuition for structural behavior while reinforcing fundamental statics concepts. The project prompt and instructions are included in the appendix of this paper. Statics is a foundational engineering course. The main concepts covered in a statics course involve determining resultant force systems and studying the external and internal loads of bodies at rest or in a state of equilibrium. A typical statics student is in their sophomore year and planning on pursuing civil, mechanical, aerospace, biomedical engineering, or others. Statics is often one of the first technical engineering courses a student will encounter in their curriculum and as such, students in this course do not yet have experience in engineering design. The project outlined in this paper provides students an early opportunity to engage in engineering design, highlights the relevance of engineering and ideally, sparks student interest in the field. Truss Project Design Description In this project, students were asked to envision themselves as the lead structural engineer tasked with designing a new truss bridge for their community. The objective of this project was for students to design the most cost-effective solution that met the prescribed needs of their town. To do that, they must assess and compare several different truss designs, before making their final recommendation. Students were told to assume each member of the truss is equally sized and made from a uniform material. Each student was given unique values for the vertical load (P), the width of each truss panel (a), and the height of their truss (h), in order to ensure that each student was responsible for their own work. Given these conditions, students were tasked with analyzing a Pratt truss (Figure 1) and a Warren truss (Figure 2). In addition to determining the force in each member of both trusses, students were also asked to report the maximum member force in each truss (the absolute value of the largest member force in their truss) and the linear feet of material required to construct each bridge. From the results of their analyses, students chose which design was the most costeffective considering both strength and weight of the bridge. Figure 3. Pratt Truss Design Figure 4. Warren Truss Design The designs presented in Figure 5 and 6, were conceived such that students (assuming their analysis was correct), would have determined that the maximum member forces in both the Pratt and Warren truss are equal, meaning that the trusses have the same “strength”. On the other hand, the Pratt truss required less linear feet of material, so it requires less “weight”. This was meant to lead students to the conclusion that the Pratt truss had a higher strength to weight ratio and is therefore the most cost-effective option. The Pratt truss has more vertically orientated members than the Warren truss, so it is more efficiently able to resist the vertical load, P. Once an overall bridge design had been chosen (Pratt or Warren), students were instructed to add seven feet of height to their chosen bridge design and re-analyze their truss bridge (with the height now set at h+7). The increased bridge height will result in a reduced maximum member force, therefore increasing the bridge’s “strength”, but increased member lengths, increasing the bridge’s “weight”. Students were then asked to consider this design compared to their original and make their final design recommendation. Recall that students were assigned varying heights for their bridges. If their given bridge height was relatively small, the 7-foot increase in height led to a dramatic decrease in the maximum member force when compared to the increase in linear feet of material required for the bridge. Conversely, if their given bridge height was already relatively high, the reduction in maximum member force would be small compared to the additional linear feet of material required to construct the bridge. The results from this analysis served as an excellent introduction to covering moment of inertia in this course, which is often a very abstract concept to students at this stage. Grading A prohibitive factor in including this type of design experience in an introductory course (which typically have larger enrollments) is the time requirement for grading. For this reason, special consideration was given to grading in both the conception and execution of this project. The standard designs of the trusses given to the students to analyze allowed for the development of a simple code that could easily check the solution to all students’ work (given the differences in loading and dimensions). In addition, students were asked to limit their discussion when comparing truss designs to one paragraph each. Therefore, each student’s project report was only two paragraphs of writing, plus an introduction. Time Commitment in Class Another prohibitive factor in including a design-based project in an introductory course is the time commitment required in class. Often, a wide range of material and topics are required to be covered in these courses, making a reduction in class time a real sacrifice to both the students and the professor. Because this project did not include a physical building and testing component, there was minimal class time used for this project. Specifically, there was a 15minute block of time to introduce and explain the project and a final 15-window to debrief the project after the students had completed their analysis and reports, leading to a total 30 minutes of class time reserved for this project. Results and Discussion Student feedback on the project was positive. Students were asked to anonymously complete both a pre-activity and post-activity survey. The pre-activity survey asked students to rate their confidence in their ability to complete the steps associated with successfully analyzing a truss. The post-activity survey again asked students to rate their confidence in those same abilities and asked some additional questions related to the activity. Total enrollment in the course was 69 students, 65 students completed the pre-activity survey, and 57 students completed the postactivity survey. A five-point Likert scale (1 = strongly disagree, 5 = strongly agree) used in the post-activity survey, showed that students strongly agreed that the project reinforced classroom concepts (4.75 ± 0.47). Additionally, students found the project made learning about trusses more engaging (4.15 ± 0.96) and improved their understanding of truss analysis and design (4.30 ± 0.80). In both the pre-survey and post-project survey, students were asked to rate their confidence in their ability to perform various tasks related to truss analysis using a five-point Likert scale (1 = not confident, 5 = very confident). The pre-activity survey was given to the students after truss analysis had been covered in the lecture and students were actively working on a homework assignment related to the topic. It was not entirely possible to separate improved confidence from the truss project specifically as compared to improved confidence through typical teaching methods such as lecture and homework. The post-activity was disseminated to students the day the project was due, and before the design project debrief, which may have resulted in additional confidence gains. The survey feedback relating to student confidence in performing tasks related to truss design is presented in Table 1. On average, students rated their confidence in their ability to draw freebody diagrams necessary for truss analysis before the project at 3.5/5, and after the project at 4.6/5, representing a 31% increase. Students rated confidence in their ability to determine truss member forces at 3.1/5 before the project and after the project at 4.4/5, representing a 42% increase. Finally, students rated confidence in their ability to make truss design decisions that optimize cost and performance at 2.4/5 before the project, and at 3.9/5 after the project, representing a 63% increase. The low initial confidence that students reported in the ability to make truss design decisions illustrates the necessity of including this type of project in a statics course. It offers an opportunity for students to engage in the course content is a way that is not covered by traditional teaching methods. Therefore, it saw the largest increase in student confidence after the project was completed. Table 2. Impact of Truss Design Project on Student Confidence Across Key Learning Objectives Learning Objective Pre-Activity Average (out of 5) Post-Activity Average (out of 5) Percent Increase in Confidence (1) Confidence in the ability to draw FBDs necessary to truss analysis 3.5 4.6 31% (2) Confidence in the ability to analyze a truss (determine member forces) 3.1 4.4 42% (3) Confidence in the ability to make truss design decisions that optimize cost and performance 2.4 3.9 63% Additionally, in course evaluations that were administered at the end of the semester, students were asked to select the teaching methods that enhanced their learning in this course. Of the 59 respondents, 69% of students indicated that the project enhanced their learning in this course. While students reported a positive impact on learning, this project is not without its limitations. There were certain aspects of truss design that had to be simplified to accommodate student understanding and ability at this stage in their engineering curriculum. For example, it was stated that all truss members would be sized equally, meaning that that the overall truss would be designed to its most critical member to simplify considerations for cost-effectiveness. This is not realistic. Additionally, students were not told to give special considerations for compression members subjected to buckling, which would result in larger member sizes than a tension member subjected to the same axial load. A final drawback to this project is the lack of hands-on experience building and testing truss bridges. One student noted on their post-activity survey that they would have found the project more engaging if a physical component was added. Unfortunately, the large class enrollment would have made this time consuming and impractical for this particular course, but the author recommends the projects outlined in these studies [2], [5] to any instructor interested in including a hands-on truss design project in their course. Summary and Conclusion A possible area of improvement would be adding a horizontal load to the bridge in addition to the vertical load, which would better demonstrate the advantages of the Warren truss. Different horizontal and vertical loads would be assigned to students, such that some students would find the Warren truss to be more efficient, and some would see that the Pratt truss is more efficient. This would cause the loading on the truss to no longer be symmetric and increase the workload for students. This could be addressed by turning some aspects of this project into a group activity. Additionally, the complexity and accuracy of this project could be improved by having students size the members once they calculate internal member forces, similar to the project outlined in this study [2]. Students would be provided with a table that compiles the tensile and compressive capacities of different size truss members, allowing the cost-effective considerations in this project to be more realistic. Overall, this project successfully implemented a design-based learning approach to teaching truss analysis in an introductory mechanics course, connecting theoretical concepts and practical engineering decision-making. Survey results indicated that the project had a positive impact on student confidence, particularly in areas like making design decisions, which are not typically emphasized in traditional statics coursework. While the project simplified some aspects of realworld design, the activity helped students engage more deeply with the material, offered a practical context for applying the concepts learned in class, and resulted in improved educational outcomes. References [1] S. A. Kumar, S. Sasikala, and K. Kavitha, “Towards Enhancing Engineering Education through Innovative Practices in Teaching Learning,” vol. 8, no. 2, 2018. [2] R. Marlor, “A Design Project for a Mechanics & Statics Course,” in 2011 ASEE Annual Conference & Exposition Proceedings, Vancouver, BC: ASEE Conferences, Jun. 2011, p. 22.36.1-22.36.10. doi: 10.18260/1-2--17318. [3] S. Palmer and W. Hall, “An evaluation of a project-based learning initiative in engineering education,” Eur. J. Eng. Educ., vol. 36, no. 4, pp. 357–365, Aug. 2011, doi: 10.1080/03043797.2011.593095. [4] S. Freeman et al., “Active learning increases student performance in science, engineering, and mathematics,” Proc. Natl. Acad. Sci., vol. 111, no. 23, pp. 8410–8415, Jun. 2014, doi: 10.1073/pnas.1319030111. [5] Y. Song, “Integrating a Design Project to Bridge Experiment for Statics learning in General Engineering Education,” in 2024 ASEE Annual Conference & Exposition Proceedings, Portland, Oregon: ASEE Conferences, Jun. 2024, p. 47641. doi: 10.18260/1-2--47641. Appendix Truss Bridge Design Project Complete the anonymous pre-design project survey here: XXX For this project, imagine you are the lead structural engineer on a project to design a truss bridge in your town. To develop the most cost-effective solution for the community, you intend to assess and compare several different truss bridge designs. Assume each bridge is simply supported (i.e., a roller support on one end and a pin support on the other end) and that each member of truss is equally sized and made from a uniform material. Submission Notes: • All calculations should be complete, detailed, and clearly labeled and include a FBD for each joint or section of the truss analyzed. Another engineer at your design firm should be able to easily review your work and check for mistakes. Task 1: Determine the force in each member of the Pratt truss and state if the members are in tension or compression. Refer to the last page of this project outline for specific details of your bridge (width, height, and load). Task 2: Determine the force in each member of the Warren truss and state if the members are in tension or compression. Refer to the last page of this project outline for specific details of your bridge (width, height and load). Task 3: Compare the Pratt and Warren truss designs. Which design better meets the needs of your community and why (from an engineering perspective)? Consider the strength and weight of both bridges. Task 4: Once you have decided to move forward with either the Pratt bridge or the Warren bridge, add 7 feet to the height of your chosen bridge design. Determine the force in each member of the truss (now that the height increased by 7 ft) and state if the members are in tension or compression. Task 5: Compare your original bridge design with that of the design with an increased height. Which design better meets the needs of your community and why (from an engineering perspective)? Consider the strength and weight of both bridges. Truss Designs Pratt Truss: Warren Truss: Report Outline: 1. Cover Page 2. Introduction • Brief description of the project • Clearly outline your truss bridge parameters (a, h, P) 3. Report on Pratt truss • Include the figure provided of the Pratt Truss labeled with member forces and dimensions. • Table of member forces that includes columns for member name (AB, BD, etc.), member length, and member force. • Then, report on the overall material in linear feet needed to construct the bridge and the absolute value of maximum member force in the bridge. 4. Report on Warren truss • Include the figure provided of the Warren Truss labeled with member forces and dimensions. • Table of member forces that includes columns for member name (AB, BD, etc.), member length, and member force. • Then, report on the overall material in linear feet needed to construct the bridge and the absolute value of maximum member force in the bridge. 5. Comparison of Pratt and Warren truss designs • This does not need to be longer than a paragraph. 6. Report on Truss Design with increased height • Include the figure provided of the whichever truss you analyzed labeled with member forces and dimensions. • Table of member forces that includes columns for member name (AB, BD, etc.), member length, and member force. • Then, report on the overall material in linear feet needed to construct the bridge and the absolute value of maximum member force in the bridge. 7. Comparison of original truss design and the increased height truss design • This does not need to be longer than a paragraph. 8. Appendix containing complete, detailed and labeled calculations for each truss design (these can be handwritten). Rubric: Points Requirement 1 Neatly formatted cover page that includes necessary information 4 Introduction that briefly describes the project and clearly shows the bridge parameters for the design. 10 Report on Pratt Bridge Design. Includes a figure of the bridge with truss member forces and dimensions. Includes a table that complies the member name, length, and force. Includes the total material in linear feet needed to construct the bridge and maximum member force. 10 Report on Warren Bridge Design. Includes a figure of the bridge with truss member forces and dimensions. Includes a table that complies the member name, length, and force. Includes the total material in linear feet needed to construct the bridge and maximum member force. 10 The Pratt and Warren truss design are thoughtfully analyzed and compared using engineering insights.