NOVEL COMPUTATIONAL APPROACHES TO OLD AND NEW PROBLEMS IN MECHANICS
The multiple slope discontinuity beam element for nonlinear
analysis of RC framed structures
Mohsen Rezaee Hajidehi
.
Antonino Spada
.
Giuseppe Giambanco
Received: 3 May 2017 / Accepted: 5 January 2018 / Published online: 11 January 2018
Ó Springer Science+Business Media B.V., part of Springer Nature 2018
Abstract The seismic nonlinear response of rein-
forced 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 clas-
sifiable 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 solu-
tions 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 hypoth-
esis 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.
Keywords Slope discontinuity Á Nonlinear pushover
analysis Á Lumped plasticity Á Plastic hinge
1 Introduction
Reinforced concrete (RC) is one of the most com-
monly used materials for constructions. It gives
numerous advantages that include great compressive
strength, suitable rigidity, relative low cost, long
service life, and vast geometrical creativity.
A considerable number of existing RC buildings
worldwide suffer when experience seismic actions,
and are prone to serious structural damages. This is
particularly evident in those cases where regulations
for seismic-resistant design were not promulgated at
This article has been corrected.
M. Rezaee Hajidehi Á A. Spada (&) Á G. Giambanco
University of Palermo, Viale delle Scienze, Ed. 8,
Palermo, Italy
e-mail: antonino.spada@unipa.it
M. Rezaee Hajidehi
e-mail: mohsen.rezaeehajidehi@unipa.it
G. Giambanco
e-mail: giuseppe.giambanco@unipa.it
123
Meccanica (2018) 53:1469–1490
https://doi.org/10.1007/s11012-018-0817-3
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