Algorithm of correcting bimoments in calculations of thin-walled bar systems

Structural mechanics

An algorithm developed for enhancing the accuracy of the calculation of frames formed by thin-walled open-section bars is presented. The existing bar models for analysis of frame systems consisting of open-section bars subjected to restrained torsion require improvement. Some authors have shown that the traditional premise of a balance of bimoments at the junction of such bars may be violated in many cases. The methodology described in this article is formulated on the condition that the disbalance on bimoments in connecting nodes of rods reinforced with transversal ribs can be taken into account on the basis of the eccentric moments transfer on the bar junctions. An approach based on the Lagrange variational principle to the construction of equations of finite element analysis while taking into account such disbalances is proposed. Herewith, some additional nodal bimoments are introduced. They allow us to correct the solution of the problem and do not affect the global stiffness matrix of the finite element system. A presented rapidly converging iterative process makes it possible to estimate the values of such bimoments. The performance of the suggested methodology has been illustrated via an example of the calculation of frames made of I-beams and U-beams. The comparison of the results of bimoments definition using the developed bar calculation schemes and shell models have shown that the suggested algorithm allows describing the disbalance of bimoments in bar connection nodes to a fairly high degree of precision for practical goals. This result may have significant importance for improving computer modelling of deformations of the thin-walled open-section bar structures.