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The multiple slope discontinuity beam element for nonlinear analysis of RC framed structures

TitleThe multiple slope discontinuity beam element for nonlinear analysis of RC framed structures
Publication TypeArticolo su Rivista peer-reviewed
Year of Publication2018
AuthorsM. Hajidehi, Rezaee, Spada A., and Giambanco G.
KeywordsBending moments, Chemical activation, Closest point projection methods, Differential equations, Distributed plasticities, Equations of state, Finite element method, Inelastic phenomena, Iterative methods, Iterative solutions, Lumped plasticity model, Non-linear pushover analysis, Nonlinear analysis, Plastic hinges, plasticity, Reinforced concrete, Slope discontinuities, Stiffness matrix, Structural frames

The seismic nonlinear response of reinforced concrete structures permits to identify critical zones of an existing structure and to better plan its rehabilitation process. It is obtained by performing finite element analysis using numerical models classifiable into two categories: lumped plasticity models and distributed plasticity models. The present work is devoted to the implementation, in a finite element environment, of an elastoplastic Euler–Bernoulli beam element showing possible slope discontinuities at any position along the beam span, in the framework of a modified lumped plasticity. The differential equation of an Euler–Bernoulli beam element under static loads in presence of multiple discontinuities in the slope function was already solved by Biondi and Caddemi (Int J Solids Struct 42(9):3027–3044, 2005, Eur J Mech A Solids 26(5):789–809, 2007), who also found solutions in closed form. These solutions are now implemented in the new beam element respecting a thermodynamical approach, from which the state equations and flow rules are derived. State equations and flow rules are rewritten in a discrete manner to match up with the Newton–Raphson iterative solutions of the discretized loading process. A classic elastic predictor phase is followed by a plastic corrector phase in the case of activation of the inelastic phenomenon. The corrector phase is based on the evaluation of return bending moments by employing the closest point projection method under the hypothesis of associated plasticity in the bending moment planes of a Bresler’s type activation domain. Shape functions and stiffness matrix for the new element are derived. Numerical examples are furnished to validate the proposed beam element. © 2018, Springer Science+Business Media B.V., part of Springer Nature.


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Citation KeyRezaeeHajidehi20181469