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
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4. SEISMIC RESPONSE OF PARTIAL-STRENGTH COMPOSITE JOINTS<br />
from <strong>the</strong> linear distribution point <strong>of</strong> view. Moreover, <strong>the</strong> third shape, calculated as<br />
SRSS combinations <strong>of</strong> <strong>the</strong> load distributions is obtained from modal analyses <strong>of</strong><br />
<strong>the</strong> buildings. The choice <strong>of</strong> this load shape is made to take into consideration <strong>the</strong><br />
anticipated effect <strong>of</strong> <strong>high</strong>er modes <strong>of</strong> vibrations for moderate long period <strong>and</strong><br />
irregular structures, as well as for buildings with hybrid lateral resistance systems.<br />
Ano<strong>the</strong>r difference between <strong>the</strong> two approaches, i.e. <strong>the</strong> EC8 procedure <strong>and</strong> <strong>the</strong><br />
FEMA-273 procedure, is <strong>the</strong> evaluation <strong>of</strong> <strong>the</strong> target displacement. Following <strong>the</strong><br />
indication contained in <strong>the</strong> EC8 (2002), <strong>the</strong> capacity curve, which represents <strong>the</strong><br />
relation between base shear force <strong>and</strong> control node displacement, is determined<br />
by pushover analysis for values <strong>of</strong> <strong>the</strong> control displacement ranging between zero<br />
<strong>and</strong> <strong>the</strong> value corresponding to 150% <strong>of</strong> <strong>the</strong> target displacement. The target<br />
displacement is defined as <strong>the</strong> <strong>seismic</strong> dem<strong>and</strong> derived from <strong>the</strong> elastic response<br />
spectrum in terms <strong>of</strong> <strong>the</strong> displacement <strong>of</strong> an equivalent SDoF system. The<br />
procedure presented in <strong>the</strong> Annex B <strong>of</strong> <strong>the</strong> EC8 (2002) is articulated as follows.<br />
i. The MDoF system is firstly converted into an SDoF system. The following<br />
152<br />
relation between normalized lateral forces Fi <strong>and</strong> normalized displacements Φi<br />
is assumed:<br />
Fi = mi<br />
Φ i<br />
( 4.28 )<br />
where mi is <strong>the</strong> mass in <strong>the</strong> i-th storey. Displacements are normalized in such a<br />
way that Φn=1, where n is <strong>the</strong> control node (usually, n denotes <strong>the</strong> ro<strong>of</strong> level),<br />
so that Fn = mn<br />
. The mass <strong>of</strong> an equivalent SDoF system m * is determined as:<br />
*<br />
m = m Φ = F<br />
( 4.29 )<br />
i i i<br />
<strong>and</strong> <strong>the</strong> transformation factor is given by:<br />
Γ =<br />
*<br />
m<br />
m Φ<br />
i<br />
2<br />
i<br />
=<br />
F<br />
i<br />
F<br />
m<br />
2<br />
i<br />
i<br />
( 4.30 )<br />
The force F * <strong>and</strong> <strong>the</strong> displacement d * <strong>of</strong> <strong>the</strong> equivalent SDoF system are <strong>the</strong>n<br />
computed as:<br />
=<br />
Γ<br />
b F<br />
F *<br />
,<br />
=<br />
Γ<br />
n d<br />
d *<br />
( 4.31 )