Elastic stress analysis of general prismatic beams : final report.

7497222PDFTech ReportVHTRC 81-R26VirginiaVirginia Transportation Research CouncilLeftwich, Steven DelBarton, F. WVirginia Highway & Transportation Research CouncilUS Transportation CollectionThis study developed a numerical methodology for the elastic stress analysis of general prismatic beams. The objective was to accurately determine stresses and displacements on a cross section of a beam where the stress resultants are prescribed. Applied loads may include axial force, bending moment, uniform (constant) torsion, constant (transverse) shear, and the rates of change of twisting moment, axial force, and wear. By assuming that the stresses and strains in a beam vary as a quadratic function of the longitudinal coordinate, the formulation expressed in terms of displacement functions was reduced from a three-dimensional analysis to a two-dimensional one. Numerical solutions were obtained using the finite element method of analysis. Numerical results were compared with exact and approximate solutions for selected cross sections. Several representative beams having cross sections commonly used in bridges were used to demonstrate the applicability of the method