Thin-walled Beam Bending Quartic Deplanation Analytical Function for Improved Experiment Matching

Abstract

Ensuring the accuracy of an analytical solution is important in modeling real engineering structures. For determining the stress-deformation condition of a thin-walled beam structure in bending, inadequately, the simple beam formula can only provide uniform average stress-deformation distribution at specific cross-sectional elevations. The recently developed analytical solution for determining stress-deformation conditions with consideration of the shear lag effect of a prismatic thin-walled box beam subjected to transverse load causing bending using classical quadratic deplanation function did not provide an accurate but rather a good estimate when compared with finite element analysis results. In this paper, the objective of the study was to see if the accuracy can be improved. The same Vlasov’s method was used. The method was developed using Calculus of Variations based on a Stress-form stationary condition complementary energy which included the shear lag effect. All calculations were computerized using the software MAPLE 18 which assisted in getting quick results (especially for preliminary design studies) for various geometries, material properties, and loading conditions. Several deplanation functions were introduced. Two variants of the quadratic functions, i.e. x 2 y 3 and x 2 y, and the quartic functions, i.e. x 4 y 3 and x4 y were used to find the best match against empirical data and FEA (finite element analysis) results. The finding was that the quartic variant of the deplanation functions provided improved matching with experimental data as well as FEA results. Noteworthy to point out that the characteristic of the functions with quartic-x or x4 of having almost flat variation in the center part enhances matching with the experimental data. Moreover, the characteristic of the function with cubic-y or y3 of having steeper slopes enhances matching with the FEM results at the edge.