Warping Transmission in 3-D Beam Element Including Secondary Torsional Moment Deformation Effect

Abstract eng:
In this paper a 3-D beam element including shear and secondary torsional moment deformation effects is formulated with general warping and bimoment transmission capabilities. The beam’s cross section is an arbitrarily shaped doubly symmetric constant one, while its shape is assumed to remain undistorted. Shear deformation (due to shear forces) is taken into account employing shear correction factors determined through an energy approach. Secondary torsional moment deformation effects are modelled by introducing the primary angle of twist per unit length as an additional degree of freedom at each end node of the element and employing a torsional shear correction factor. An exact 14x14 stiffness matrix and the corresponding nodal load vector are formulated based on the solution of the global equilibrium differential equations of the beam. At joints connecting space members, all kinds of warping and bimoment transmission (not involving cross sectional distortion) are modelled, including free warping, full or partial warping restraint, full warping and bimoment continuity, complete direct and inverse warping transmission and general warping and bimoment transmission between intersecting members. A computer program is developed in a mathematical package permitting symbolic algebraic manipulations. Numerical results of great practical interest are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method.

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