Synthesis of a Correcting Equation for 3 Point Bending Test Data

Abstract A frequent requirement of a Mechanics of Deformable Bodies course is for students to complete an experiment using a compression/tension test fixture incorporating a 3-point flexure fixture. The prominent goals of such an assignment are to understand the basic concepts of load/deflection relationships for pure bending situations, to calculate and correlate theoretical analysis with experimental results, and to use computer software to plot and analyze data. Once completed, students should be able to compare theoretical and experimental modulus of elasticity values. The student should then be able to not only determine the type of material used in the 3-point bending test but also discuss any discrepancies between theoretical and experimental values. During the preparation of lab materials for such an experiment, it was noticed that the data collected from the instrument produced incorrect modulus of elasticity values for all specimens. Extension values suggested that there was more deflection occurring in the test specimen than predicted resulting in modulus of elasticity values lower than expected. In fact, the modulus of elasticity values could be so low that a student could not correctly determine the material type of the specimen being analyzed. In order to correct the extension data, a system deflection analysis was initiated. First, internal displacements occurring within the 3-point flexure fixture members were determined by calculating the deflections produced during experimental loading. Next, the remaining sources of internal displacements within the system were investigated with the results being fitted to a curve. A correction equation with support separation distance, applied load, and specimen weight as independent variables was generated by summing all the internal displacements found. The original extension data could then be adjusted by subtracting this correction displacement. The resulting correction equation was validated using specimens with a known modulus of elasticity. Successful completion of this project allows students to appropriately correct the 3-point bending extension data collected during an experiment and more accurately calculate an unknown specimen's modulus of elasticity.