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Shock and Vibration
Volume 15 (2008), Issue 3-4, Pages 273-290

An Inelastic Beam Element with Hysteretic Damping

K.G. Papakonstantinou, P.C. Dimizas, and V.K. Koumousis

Institute of Structural Analysis and Aseismic Research, National Technical University of Athens, NTUA, Zografou Campus GR -15773, Athens, Greece

Received 29 April 2007; Revised 29 April 2007

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this work, an inelastic beam macro-element that incorporates hysteretic damping is presented. Based on classical theory of plasticity, a Bouc-Wen type model is utilized that simulates the hysteretic behavior of an inelastic spring element. Using this model, an inelastic nonlinear beam element is formulated based on the appropriate combination of two coupled nonlinear spring elements. The equations of motion are determined and are cast in a state-space form for the vector of the end displacements, velocities and hysteretic forces. The system is solved by employing a Runge-Kutta type of algorithm. The proposed inelastic beam model is then employed to simulate the experimental dynamic behavior of steel beams. The model parameters are estimated with the aid of a nonlinear system identification algorithm using existing experimental data. The proposed element approximates the inelastic behavior of steel beams adequately within plastic regions that do not undergo substantial stiffness degradation, or other relevant phenomena. Finally, the hysteretic damping features of the model are demonstrated.