Elastic Stress Analysis of General Prismatic Beams: Final Report

Report No: 81-R26

Published in 1980

About the report:

This 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.

Disclaimer Statement:The contents of this report reflect the views of the author(s), who is responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the Virginia Department of Transportation, the Commonwealth Transportation Board, or the Federal Highway Administration. This report does not constitute a standard, specification, or regulation. Any inclusion of manufacturer names, trade names, or trademarks is for identification purposes only and is not to be considered an endorsement.


  • Steven Del Leftwich, Furman W. Barton, Ph.D.

Last updated: January 22, 2024

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