Four Point Bending: A New Look

Four point bending (FPB) is a cornerstone element of the beam flexure portion of a sophomorelevel mechanics of materials course. The FPB lecture has traditionally developed the theory from free body diagram through beam deflection, with related homework problems providing analytical practice. Similarly, the FPB laboratory, which has been essentially unchanged for nearly two decades, has provided students an opportunity to experimentally and analytically verify and validate beam flexure theory. Although excellent correlation between theoretical and experimental results was frequently obtained, hardware requirements have limited the accuracy and amount of data that collected within a standard 110-minute laboratory session. Recent FPB laboratory upgrades utilizing data acquisition (DAQ) hardware and software have enabled the students to test a much larger sample of beams in roughly the same timeframe with increased repeatability. The DAQ upgrade has facilitated increased understanding of flexural theory, introduced modern experimental methods in both lecture and laboratory, given students a more robust data set upon which to base their analyses, and enhanced student experiences with technical report writing. This paper includes an overview of FPB theory, analysis techniques, and traditional laboratory procedures, and details the success of the FPB DAQ upgrade, operation, and outputs. Introduction: Beam flexure represents one of the three most common loading categories for mechanical systems. As such, it is on the syllabi of nearly all sophomore-level mechanics of materials courses, including the mechanical engineering technology course under consideration here. Within the lecture setting, FPB theory is developed from free-body diagram through beam deflection. Theory is reinforced by analytical practice solving related homework problems. The corresponding FPB laboratory has afforded students the opportunity to experimentally and analytically verify and validate beam flexure theory. Excellent correlation between theoretical and experimental results is often obtained. However, the person-centered, primarily analog method used for acquiring, recording, and analyzing the data is cumbersome and frustrating for the students. The accuracy and amount of data that can be collected within a standard 110-minute laboratory session has been limited, as has the extent of the analysis that seems reasonable to require. To address student dissatisfaction with the FPB laboratory, a revision was deemed desirable. The implemented revision was designed to accommodate faculty concerns that the students have a laboratory experience that mirrors the industrial laboratory and obtain additional practice manipulating experimental data. Thus, the FPB laboratory has recently been upgraded through the inclusion of automated data acquisition (DAQ) hardware and software. This upgrade has P ge 774.1 Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright ” 2002, American Society for Engineering Education facilitated increased understanding of flexural theory, introduced modern experimental methods in both lecture and laboratory, given students a more robust data set upon which to base their analyses, and enhanced student experiences with technical report writing. The following paragraphs provide an overview of FPB theory, analysis techniques, the basic laboratory procedure, and details of the upgraded FPB experiment. Theoretical Basis for the FPB Experiment: Following the testing conventions specified in ASTM D6272-00 transverse vertical loads are applied to horizontal beams such that a constant bending moment results between the two inner load locations. Figure 1 shows the corresponding loading diagrams, from free-body to bending moment. Figure 1: Example of Free Body, Instantaneous Load, Distributed Load, Shear, and Moment diagrams for the laboratory experiment on four point bending. Stress-strain relationships are utilized to develop the theoretical parametric relationship between strain, e, bending moment, M, tensile modulus, E, width, b and height, h. The relationship between these parameters is depicted below in equation 1 below: