Homogenization of a vierendeel girder with elastic joints into an equivalent polar beam

In this paper, a homogenization procedure of a Vierendeel girder with elastic joints is shown. The method is based on the Stephen transfer matrix analysis and employs (as a substitute continuum) a polar Timoshenko beam. The polar character of the equivalent beam arises quite naturally from the analysis of the pure bending eigenvector components of the girder force transfer matrix. Through the girder unit cell, two bending moments are transmitted: one is generated by the couple of axial forces acting on each nodal section of the beam, and the other is produced by the moments applied at the nodes of every section by the adjacent cells and is modeled as the resultant of the micropolar moments. Transfer force eigenvector analysis reveals that the unit cell bends while maintaining undeformed webs, a property that allows the evaluation of both the bending stiffnesses and the equivalent material micropolar scale parameter by means of straightforward equations.The accuracy of the proposed method is verified by comparing the predictions of the homogenized model with literature data and with the results of the analysis of a series of girders carried out by the finite element method.