Pursuing The Perfect Statically Indeterminate Bar: Model Versus Experiment

Engineers and technologists often now function in a professional environment where analytical modeling and simulation must serve the role previously filled by prototyping and experimentation. An inherent difficulty in the development of both conceptual and analytical models is recognizing the limitations on the applicability of the model to a given component or system. These limitations come from numerous sources, including simplification for ease of calculation, idealized dimensions, and neglecting the effects of manufacturing processes. A primary goal of basic mechanics courses is to teach students how to develop appropriate engineering models which will allow them to reasonably approximate “real-life” results. In a typical first laboratory-based strength of materials course, students conduct established experiments to verify simple engineering models, but may not consider the constraints imposed on the test specimen in order to obtain experimental results which match theoretically predicted values. In particular, manufacturing factors are frequently overlooked. A laboratory exercise based on the statically indeterminate bar of multiple, equal length, adjacent materials subject to tensile axial loading was designed to help clarify the importance of recognizing the constraints of a theoretical model. This application was selected due to the difficulty many students have in correctly using the theory, as well as its sensitivity to deviations from the conditions assumed when developing the model. According to the conceptual model included in various textbooks, each material will experience equal strain, even though internal forces generally differ. A collection of bar specimens was produced to show some of the factors that can affect the validity of the application of the theory, including force balance; method of joining; tolerances; and strain gage mounting. The following paper describes the exercise and the significance of overlooking various engineering constraints as demonstrated through simple strain measurements. The experiment was originally intended as a review laboratory session for an elective upper division course in experimental strength of materials, but is also appropriate in an introductory mechanics/strength of materials course, with some simplification. Introduction The statically indeterminate bar which is subjected to axial loading with one degree of indeterminacy, such as that shown in Figure 1, is commonly an early topic in a first course in mechanics/strength of materials. Study of this topic affords students the opportunity to integrate the fundamental concepts of stress and strain, and to recognize more fully the effect of material stiffness on load-carrying capability. The necessary inclusion of material effects for determination of internal loads differs significantly from their previous mechanics coursework, so many students struggle with this initial encounter with interdependent variables. In order to aid the student as s/he strives to master this new idea, the typical elementary mechanics or