Teaching Quantitative Error Estimates for Engineering Approximations: Application to Torsion in Thin-Walled Sections

摘要

While engineering approximations are at the heart of engineering education and practice, students are rarely equipped with quantitative estimates of the errors associated with such approximations. Typically the curriculum includes only a qualitative discussion of the character of the errors involved and the assumptions made in using the studied approximate formulas or equations. Yet, as an engineer, the graduate student would often have to make decisions that depend on the level of accuracy of these approximations, e.g., a decision on the necessity to perform a costly computational analysis vs. relying on a standard approximate formula. The goal of this paper is to point to the need for in-class discussion on quantitative error estimates, as part of the engineering curriculum. As a case in point, the torsion of elastic rods with thin-walled cross sections is considered. Quantitative error estimates are provided for the standard formulas for the torsional stress and rigidity. A preliminary investigation is performed, involving 3rd-year students at the Department of Aerospace Engineering, Technion, at the end of a Structural Analysis course. This preliminary study shows that without having been exposed in class to quantitative error estimates, intuition leads most of the students to making the wrong practical decisions in some situations, which might have a negative impact on their future work as engineers. This study thus points to the educational benefit in teaching the subject of quantitative error estimates for engineering approximations during undergraduate studies. In the case of a 3rd year Structural Analysis course, the material associated with the subject would require about half an hour of frontal teaching, but can also be offered to the students as an enrichment in writing for self-study.