Keywords: distributed plasticity frame element, fibre discretization, displacement based method, hysteresis, Bouc-Wen model, dynamic non-linear analysis.

The need for robust structural response estimation in seismic prone regions has led to the development of detailed beam-column elements capable of tracking their inherent hysteretic behaviour. A subset of these models are the distributed plasticity beam elements whose cross sections are discretized with fibres, which, as a bundle, obey the plane section - remain plane, Euler-Bernoulli assumption [1]. Consequently, they are capable of describing the behaviour of complex cross sections with different materials at full bond, where each fibre obeys its own axial constitutive relation. In this paper the uniaxial hysteretic behaviour of the fibres is based on the Bouc-Wen hysteretic model with kinematic hardening [2]. In this approach, every fibre's stress is decomposed into an "elastic" and hysteretic part. By integrating the contribution of all fibres in a cross section along the element, the total coupled actions at the centroid are evaluated. Subsequently, numerical integration of the control sections along the element's length determines its overall coupled axial and flexural behaviour. This procedure leads to the development of additional nodal hysteretic stress resultants that correspond to additional degrees of freedom, doubling the total degrees of freedom of the element [3]. The decomposition of the elemental behaviour into an "elastic" and hysteretic one, which describes the material non-linearity, can be treated separately. The "elastic" elemental stiffness relations are assembled to form a system of linear global equations of motion, while the hysteretic nodal forces form a global hysteretic load vector, which is subtracted from the external one. This approach leads to a system of equations of motion with constant matrices on the left hand side, whose numerical iterative solution is marching regularly, with the non-linearity being included in the updating of the hysteretic force vector at each time step. Numerical results are presented to validate the proposed method, which verify the accuracy and efficiency of the entire computational scheme.

1

E. Spacone, F.C. Filippou, F.F. Taucer, "Fibre beam column model for nonlinear analysis of R/C frames. I: Formulation", Earthquake Engrg. and Struct. Dyn., 25(7), 711-725, 1996.

2

R. Bouc, "Forced vibration of mechanical systems with hysteresis", Proceedings of the Fourth Conference on Non-linear oscillation, Prague, Czechoslovakia, 1967.

3

S. Triantafyllou, V. Koumousis, "Small and Large Displacement Dynamic Analysis of Frame Structures Based on Hysteretic beam Elements", Journal Of Engineering Mechanics, 138(1), 36-49, July 2011.

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