Analysis and modelling of the seismic behaviour of high ... - Ingegneria

2. DUCTILITY AND SEISMIC RESPONSE OF STRUCTURES
These preliminary concepts are based on grossly simplified physical models,
engineering judgment and a number of empirical coefficients. Influenced by
conventional design concepts, earthquake actions are considered as static loads
and the structures as elastic systems. This simple concept has been the standard
design methodology for several decades, well understood by structural engineers
because relatively easy to implement. These are the reasons for the success of
this design approach, even if, in some cases, it may lead to inadequate protection
(Krawinkler, 1995). Because of this limits new concepts have been developed.
2.2.2 Modern design concepts of ductility
The beginning of the modern design concepts can be fixed in the 1930s, when the
concepts of response spectrum and plastic deformation were introduced into
earthquake engineering. The first concept considering the elastic response
spectrum was used by Benioff in 1934 and Biot in 1941. Linear elastic response
spectra provide a reliable tool to estimate the level of forces and deformations
developed in the structures. In 1935 Tanabashi proposed an advanced theory,
which suggested that the earthquake resistance capacity of a structure should be
measured by the amount of energy that the structure can absorb before collapse.
In term used nowadays, this energy can be interpreted as the dissipated energy
through the ductility of the structure.
The first attempts to combine these two aspects, the response spectrum and the
dissipation of seismic energy through plastic deformations, was made by Housner
(1997), who made a quantitative evaluation of the total amount of energy input that
contributes to the building response, using the velocity response spectra in the
elastic system. Moreover, assuming that the energy input, responsible for the
damage in the elastic-plastic system, is identical to that in the elastic system
(Akiyama, 1985). Housner verified his hypothesis by examining several examples
of damage. So, his method proposed a limit design type analysis to ensure that
there is sufficient energy-absorbing capacity to give an adequate factor of safety
against collapse in the event of extremely strong ground motion. Velestos and
Newmark conducted the first study on the inelastic spectrum in 1960. They
obtained the maximum response deformation for the elastic-perfectly plastic
structures. Since its first application in seismic design, the response spectrum has
become a standard measure of the demand of ground motion. Although it is based
on a simple Single-Degree-of-Freedom (SDoF) linear system, the concept of the
response spectrum has been extended to Multiple-Degree-of-Freedom (MDoF)
systems, non-linear elastic systems and inelastic hysteretic systems. The utility of
the response spectrum lies in the fact that it gives a simple and direct indication of
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