Analysis and modelling of the seismic behaviour of high ... - Ingegneria
Analysis and modelling of the seismic behaviour of high ... - Ingegneria
Analysis and modelling of the seismic behaviour of high ... - Ingegneria
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
2. DUCTILITY AND SEISMIC RESPONSE OF STRUCTURES<br />
These preliminary concepts are based on grossly simplified physical models,<br />
engineering judgment <strong>and</strong> a number <strong>of</strong> empirical coefficients. Influenced by<br />
conventional design concepts, earthquake actions are considered as static loads<br />
<strong>and</strong> <strong>the</strong> structures as elastic systems. This simple concept has been <strong>the</strong> st<strong>and</strong>ard<br />
design methodology for several decades, well understood by structural engineers<br />
because relatively easy to implement. These are <strong>the</strong> reasons for <strong>the</strong> success <strong>of</strong><br />
this design approach, even if, in some cases, it may lead to inadequate protection<br />
(Krawinkler, 1995). Because <strong>of</strong> this limits new concepts have been developed.<br />
2.2.2 Modern design concepts <strong>of</strong> ductility<br />
The beginning <strong>of</strong> <strong>the</strong> modern design concepts can be fixed in <strong>the</strong> 1930s, when <strong>the</strong><br />
concepts <strong>of</strong> response spectrum <strong>and</strong> plastic deformation were introduced into<br />
earthquake engineering. The first concept considering <strong>the</strong> elastic response<br />
spectrum was used by Beni<strong>of</strong>f in 1934 <strong>and</strong> Biot in 1941. Linear elastic response<br />
spectra provide a reliable tool to estimate <strong>the</strong> level <strong>of</strong> forces <strong>and</strong> deformations<br />
developed in <strong>the</strong> structures. In 1935 Tanabashi proposed an advanced <strong>the</strong>ory,<br />
which suggested that <strong>the</strong> earthquake resistance capacity <strong>of</strong> a structure should be<br />
measured by <strong>the</strong> amount <strong>of</strong> energy that <strong>the</strong> structure can absorb before collapse.<br />
In term used nowadays, this energy can be interpreted as <strong>the</strong> dissipated energy<br />
through <strong>the</strong> ductility <strong>of</strong> <strong>the</strong> structure.<br />
The first attempts to combine <strong>the</strong>se two aspects, <strong>the</strong> response spectrum <strong>and</strong> <strong>the</strong><br />
dissipation <strong>of</strong> <strong>seismic</strong> energy through plastic deformations, was made by Housner<br />
(1997), who made a quantitative evaluation <strong>of</strong> <strong>the</strong> total amount <strong>of</strong> energy input that<br />
contributes to <strong>the</strong> building response, using <strong>the</strong> velocity response spectra in <strong>the</strong><br />
elastic system. Moreover, assuming that <strong>the</strong> energy input, responsible for <strong>the</strong><br />
damage in <strong>the</strong> elastic-plastic system, is identical to that in <strong>the</strong> elastic system<br />
(Akiyama, 1985). Housner verified his hypo<strong>the</strong>sis by examining several examples<br />
<strong>of</strong> damage. So, his method proposed a limit design type analysis to ensure that<br />
<strong>the</strong>re is sufficient energy-absorbing capacity to give an adequate factor <strong>of</strong> safety<br />
against collapse in <strong>the</strong> event <strong>of</strong> extremely strong ground motion. Velestos <strong>and</strong><br />
Newmark conducted <strong>the</strong> first study on <strong>the</strong> inelastic spectrum in 1960. They<br />
obtained <strong>the</strong> maximum response deformation for <strong>the</strong> elastic-perfectly plastic<br />
structures. Since its first application in <strong>seismic</strong> design, <strong>the</strong> response spectrum has<br />
become a st<strong>and</strong>ard measure <strong>of</strong> <strong>the</strong> dem<strong>and</strong> <strong>of</strong> ground motion. Although it is based<br />
on a simple Single-Degree-<strong>of</strong>-Freedom (SDoF) linear system, <strong>the</strong> concept <strong>of</strong> <strong>the</strong><br />
response spectrum has been extended to Multiple-Degree-<strong>of</strong>-Freedom (MDoF)<br />
systems, non-linear elastic systems <strong>and</strong> inelastic hysteretic systems. The utility <strong>of</strong><br />
<strong>the</strong> response spectrum lies in <strong>the</strong> fact that it gives a simple <strong>and</strong> direct indication <strong>of</strong><br />
9