Numerical-Computational Model of semi-rigid connection based on Damage Mechanics

Beam-to-column connections in steel structures are traditionally designed with the assumption of ideally flexible or fully rigid behavior, which simplifies the analysis and structural design processes. However, these two cases are extreme, as most connections used in practical field transmit some partial moment. Experimental results obtained for beam-column connections show that the moment-rotation relation is non-linear and varies depending on connection flexibility. In this context, a connection one-dimensional constitutive model based on Continuous Damage Mechanics is proposed, which takes into account the progressive reduction of rotational stiffness. A computational code is developed for the static analysis of plane frames with geometric nonlinear behavior and semi-rigid connection. The damage variable is calculated as a function of three parameters - initial rotational stiffness, rotational deformation and damage modulus -, being these obtained from the moment - rotation curve of the connection. In order to verify the proposed formulation, this model is applied to two numerical problems - a cantilever beam and a two-story frame. The structures are discretized with the Co-rotational formulation of the Finite Element Method, considering the Euler-Bernoulli theory for beam bending. The connection is simulated by a null-length finite element, whose elementary stiffness matrix considers the axial, translational and rotational stiffnesses. The system of nonlinear equations, which describes the structural problem, is solved by a two-step iterative-incremental procedure with cubic convergence. The numerical results with the Scilab program show the good agreement of the equilibrium paths of the structures obtained with the proposed model and those found in the literature.