Shear-shear-torsional homogenous beam models for nonlinear periodic beam-like structures

In this paper, the proper modeling of a class of nonlinear periodic beam-like structures, behaving as shear beams in the 3D environment, is critically considered. Multi-story frame buildings are taken as an example of these structures and the suitability of the (unflexurable) shear-shear-torsional beam model in describing the behavior of the building, is investigated. In this context, the range of applicability of the equivalent beam model is detected through an order-of-magnitude analysis, which is developed in linear regime and corroborated by means of finite-element analyses. A new continuous shear-shear-torsional beam model, here referred to as ‘complete model’, is formulated in the framework of the direct one-dimensional approach, while its nonlinear hyperelastic constitutive law is obtained by identification with a three-dimensional body, through an energy equivalence. In addition, a ‘minimal model’ is derived from the complete one for which only the cubic terms generated by the stretch of the columns are retained, while the remaining cubic terms and all the quadratic terms, generated by the finite twist angle, are neglected. Perturbation solutions for both the complete and the minimal model are obtained. The limits of applicability of the minimal model are discussed in terms of nonlinear static responses of some structures taken as case-studies.