A New Iterative Design Strategy for Steel Frames Modelled by Generalised Multi-stepped Beam Elements

The paper deals with frame steel structures required to ensure sufficient resistance, appropriate ductility and safety against brittle failure. This special aim cannot be reached by utilizing standard procedures and standard beam elements. Therefore, the present study proposes an innovative design strategy devoted to plane steel frames constituted by I-shaped cross-section beam elements and subjected to simultaneous combinations of serviceability limit state conditions and ultimate limit state conditions. Special factory-made I-shaped uniform piecewise steel profiles are utilised to provide the optimal behaviour of the frame. The proposed design strategy consists of two subsequent steps: at first a classical sizing of the frame is performed by utilising standard steel profiles, then a specific optimal design problem is performed to define the optimal geometry of the I-shaped steel profiles that fulfils all the constraints related to the required resistance and the limited deformability as well as special introduced constraints related to the protection against the brittle failure. The reliability of the procedure and the expected optimal behaviour of the frame are checked by performing nonlinear static analyses employing a recently proposed Fibre Smart Displacement-Based (FSDB) beam element model. The proposed beam element is defined by adopting displacement shape functions capable of embedding the cross-section discontinuities by means of the use of generalised functions. Furthermore, the proposed shape functions are addressed to as “smart” since capable of update in accordance with the development of plastic deformations detected by means of fibre discretisation of the cross-section. The results related to a simple steel portal confirmed the expected optimal behaviour of the structure.