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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2. DUCTILITY AND SEISMIC RESPONSE OF STRUCTURES<br />
dem<strong>and</strong>s on beam-to-column connections, shear force dem<strong>and</strong>s in deep<br />
reinforced concrete beams, shear force dem<strong>and</strong>s in unreinforced masonry<br />
wall piers, etc;<br />
• estimates <strong>of</strong> <strong>the</strong> deformation dem<strong>and</strong>s for elements that have to deform<br />
inelastically in order to dissipate <strong>the</strong> energy imparted to <strong>the</strong> structure by<br />
ground motion;<br />
• consequences <strong>of</strong> strength deterioration <strong>of</strong> individual elements on <strong>the</strong><br />
<strong>behaviour</strong> <strong>of</strong> a structural system;<br />
• identification <strong>of</strong> <strong>the</strong> critical regions in which <strong>the</strong> deformation dem<strong>and</strong>s are<br />
expected to be <strong>high</strong> <strong>and</strong> that have to become <strong>the</strong> focus <strong>of</strong> detailing;<br />
• identification <strong>of</strong> strength discontinuities in plan <strong>and</strong> elevation that will lead<br />
to changes in <strong>the</strong> dynamic characteristic in <strong>the</strong> inelastic range;<br />
• estimates <strong>of</strong> <strong>the</strong> interstorey drifts that account for strength or stiffness<br />
discontinuities <strong>and</strong> that may be used to control damage <strong>and</strong> to evaluate P-<br />
delta effects.<br />
Clearly, this benefits come at <strong>the</strong> cost <strong>of</strong> additional analysis effort, associated with<br />
incorporation <strong>of</strong> all important elements, <strong>the</strong> <strong>modelling</strong> <strong>of</strong> <strong>the</strong>ir inelastic load-<br />
deformation characteristic, <strong>and</strong> <strong>the</strong> execution <strong>of</strong> incremental inelastic analysis,<br />
preferably with a three-dimensional (3D) analytical model. At this time adequate<br />
analytical tools for this purpose ere ei<strong>the</strong>r cumbersome or not available, but several<br />
good tools are under development, primarily through <strong>the</strong> recent publication <strong>of</strong> <strong>the</strong><br />
FEMA 273 document (1997), that includes extensive recommendations for load-<br />
deformation <strong>modelling</strong> <strong>of</strong> individual elements <strong>and</strong> for acceptable values <strong>of</strong> force<br />
<strong>and</strong> deformation parameters for performance evaluation. Based on <strong>the</strong> capacity<br />
spectrum method originally developed by Freeman et al. (1975) <strong>and</strong> Freeman<br />
(1978), <strong>the</strong> NSP procedure could be summarized in <strong>the</strong> following steps (Chopra<br />
<strong>and</strong> Goel, 1999):<br />
1. Develop <strong>the</strong> relationship between base shear Vb <strong>and</strong> ro<strong>of</strong> (N th floor)<br />
displacement uN, depicted in Figure 2.6, commonly known as pushover<br />
curve.<br />
u N<br />
F<br />
V b<br />
Pushover Curve<br />
u<br />
V N<br />
b<br />
Figure 2.6. Development <strong>of</strong> a pushover curve<br />
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