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
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
2. DUCTILITY AND SEISMIC RESPONSE OF STRUCTURES<br />
in <strong>the</strong> elastic range, or some limited plastic deformations can occur in agreement<br />
with <strong>the</strong> design assumptions. The rigidity check is generally related to <strong>the</strong><br />
serviceability limit state, for which <strong>the</strong> structure displacements must remain within<br />
certain limits, which assure that no damage occurs in non-structural elements.<br />
Although it is recognized that damage is also due to deformations, strength<br />
checking plays <strong>the</strong> leading role in designs for conventional loads. Conversely, in<br />
case <strong>of</strong> earthquake design, a new dem<strong>and</strong> must be added to <strong>the</strong> two previous<br />
ones, that is <strong>the</strong> ductility dem<strong>and</strong>. The performance <strong>of</strong> a structure under strong<br />
<strong>seismic</strong> actions relies on its capacity to deform beyond <strong>the</strong> elastic range, <strong>and</strong> to<br />
dissipate <strong>seismic</strong> energy through plastic deformations. So, <strong>the</strong> ductility check<br />
controls whe<strong>the</strong>r <strong>the</strong> structure is able to dissipate <strong>the</strong> given quantity <strong>of</strong> <strong>seismic</strong><br />
energy considered in structural analysis or not (Gioncu <strong>and</strong> Mazzolani, 2002).<br />
2.2 Ductility in <strong>seismic</strong> design<br />
2.2.1 First developments <strong>of</strong> ductility concept<br />
The preliminary design concepts were conceived after <strong>the</strong> severe earthquakes at<br />
<strong>the</strong> beginning <strong>of</strong> <strong>the</strong> 20 th century. The great builder Gustave Eiffel had <strong>the</strong> intuition<br />
to model <strong>the</strong> earthquake forces by means <strong>of</strong> an equivalent wind load. The city <strong>of</strong><br />
San Francisco was rebuilt after <strong>the</strong> 1906 great earthquake using a 1.4 kPa<br />
equivalent wind load. It was not until after <strong>the</strong> Santa Barbara earthquake in 1925<br />
<strong>and</strong> <strong>the</strong> Long Beach earthquake in 1933, that <strong>the</strong> concept <strong>of</strong> lateral forces<br />
proportional to <strong>the</strong> mass was introduced into practice. The buildings have been<br />
designed to withst<strong>and</strong> lateral forces <strong>of</strong> about 7.5 percent for rigid soil <strong>and</strong> 10<br />
percent for s<strong>of</strong>t soil <strong>of</strong> <strong>the</strong>ir dead load. This rule was a consequence <strong>of</strong> <strong>the</strong><br />
observation that <strong>the</strong> great majority <strong>of</strong> well designed <strong>and</strong> constructed buildings<br />
survived strong ground motions, even if <strong>the</strong>y were designed only for a fraction <strong>of</strong><br />
<strong>the</strong> forces that would develop if <strong>the</strong> structure behaved entirely linearly elastic<br />
(Fajfar, 1995). In 1943, <strong>the</strong> Los Angeles city code recognized <strong>the</strong> influence <strong>of</strong><br />
flexibility <strong>of</strong> structures, <strong>and</strong> considered <strong>the</strong> number <strong>of</strong> structure levels in design<br />
forces. The San Francisco recommendations were <strong>the</strong> first ones where <strong>the</strong><br />
influence <strong>of</strong> <strong>the</strong> fundamental period <strong>of</strong> <strong>the</strong> structure was introduced with a relation<br />
stating that <strong>the</strong> <strong>seismic</strong> forces are inversely proportional to this period (Bertero,<br />
1992, Popov 1994).<br />
8