Torsion of Nonprismatic Beams of Open Section

A general methodology is outlined for the closed-form solution of the basic differential equation of torsion for any straight, nonprismatic, open section beam configuration. Six specific cases of single span, variable-sectioned beams under torsional loading were examined by this exact procedure. The algebraic and design chart formulations of these solutions are described. These results are particularly useful for analysis of coverplated bridge and building members. A numerical technique, employing the finite differences method, is developed as a versatile and expedient alternative to peforming a closed-form examination. The basic interior mesh equation and the modified mesh patterns near the boundaries (pinned and fixed) are included. The finite differences results are compared with the closed-form theory, and are shown to be very accurate and reliable. Model testing of partially cover-plated wide-flange beams provided very reasonable correlation with the non-prismatic, closed-form solutions for various cases of boundary conditions.