Second-order torsional warping theory considering the secondary torsion-moment deformation-effect

Abstract

In this paper, the influence of the variable axial force and of the Secondary Torsion-Moment Deformation-Effect (STMDE) on the deformations of beams due to torsional warping is investigated. The investigation is based on the second-order torsional warping theory of doubly symmetric beams with thin-walled open or closed cross-sections. The effect of the axial force on the torsional stiffness of thinwalled beams is considered according to the second-order torsional warping theory. The solutions of the underlying differential equations are used for setting up the relations, needed for application of the transfer matrix method. They are derived, considering both static and dynamic action. This enables stablishing the local

Effect of Non-Uniform Torsion on Elastostatics of a Frame of Hollow Rectangular Cross-Section

“…Higher eigenforms of the hollow cross-section are characterized by a pronounced crosssectional distortion that reduces the torsional stiffness of the cross section over that which is calculated in the sense of Thin Tube Theory (TTT). But as shown in [7,13], the results of an elastostatic analysis of the thin-walled straight beams with our warping beam finite element agree well with the ones obtained with the solid finite elements [7,13].…”

“…From this point of view, the consideration of the Saint Venant torsion theory could be assumed as satisfactorily for the displacement calculation in the solved example. However, as shown in [3], [7], [12], [13] and also in the following investigations, the warping torsion effect and the STDME influence the stress state significantly and therefore could not be neglected.…”

Second-Order Torsional Warping Modal Analysis of Thin-Walled Beams

“…The solution functions are calculated numerically by means of the algorithm published in [27]. In addition, by the approach described in [34], the transfer matrix method relation …”

“…is obtained, where ( ) x Z is the "static vector", Z i is the static vector at the starting point i and ( ) xi F x is the transfer matrix [34]. By neglecting the secondary torsion-moment deformation-effect and setting the warping constant equal to zero, equation (6) degenerates to the relation for Saint-Venant torsion, including the influence of the variable axial force, resulting in a geometric stiffness.…”

“…The numerical investigation includes torsional modal analyses of thin-walled beams under usual boundary conditions. Results of elastostatic analysis are presented in [34].…”