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 />
Approximations are implicit in <strong>the</strong> various steps <strong>of</strong> this simplified analysis <strong>of</strong> an<br />
inelastic MDoF system. Implicit in Steps 1 <strong>and</strong> 2 is a lateral force distribution<br />
assumed to be fixed, <strong>and</strong> based only on <strong>the</strong> fundamental vibration mode <strong>of</strong> <strong>the</strong><br />
elastic system; however, extensions to take into account <strong>high</strong>er mode effects have<br />
been proposed. Implicit in Step 4 is <strong>the</strong> belief that <strong>the</strong> earthquake-induced<br />
deformation <strong>of</strong> an inelastic SDoF system can be estimated satisfactorily by an<br />
iterative method requiring analysis <strong>of</strong> a sequence <strong>of</strong> equivalent linear SDoF<br />
systems, thus avoiding <strong>the</strong> dynamic analysis <strong>of</strong> <strong>the</strong> inelastic SDoF system.<br />
Both force distribution <strong>and</strong> target displacement are based on <strong>the</strong> assumption that<br />
<strong>the</strong> response is controlled by a single shape vector (<strong>the</strong> fundamental mode) <strong>and</strong><br />
that <strong>the</strong> mode shape remains unchanged after <strong>the</strong> structure yields. Parameter<br />
studies have shown that for frame <strong>and</strong> wall structures with a first mode period <strong>of</strong><br />
less than 2 seconds this assumption is ra<strong>the</strong>r accurate for elastic systems <strong>and</strong><br />
conservative (overestimates <strong>the</strong> MDoF displacement) for inelastic systems.<br />
In all cases, <strong>the</strong> determined target displacement becomes <strong>the</strong> base line for<br />
predicting <strong>the</strong> inelastic displacement dem<strong>and</strong>, which needs to be accomplished<br />
with due consideration to <strong>the</strong> hysteretic characteristic <strong>of</strong> <strong>the</strong> equivalent SDOF<br />
system. The effects <strong>of</strong> yield strength, strength <strong>and</strong> stiffness degradation, pinching<br />
during hysteretic loops, P-delta incremented forces caused by gravity loads acting<br />
on <strong>the</strong> deformed configuration <strong>of</strong> <strong>the</strong> structure can be taken into account through<br />
cumulative modification factors applied to <strong>the</strong> elastic displacement dem<strong>and</strong>. The<br />
loop illustrated in Figure 2.10 assumes that stable relationships can be found<br />
between <strong>the</strong> spectral displacement dem<strong>and</strong> at <strong>the</strong> first mode period <strong>of</strong> <strong>the</strong> structure<br />
<strong>and</strong> <strong>the</strong> system <strong>and</strong> element deformation dem<strong>and</strong>s (Gupta <strong>and</strong> Krawinkler, 2000),<br />
using <strong>the</strong> following definitions:<br />
30<br />
• MDoF modification factor, αMDOF, a factor that relates <strong>the</strong> elastic spectral<br />
displacement dem<strong>and</strong> at <strong>the</strong> first mode period <strong>of</strong> <strong>the</strong> structure to <strong>the</strong> elastic<br />
ro<strong>of</strong> drift dem<strong>and</strong> <strong>of</strong> <strong>the</strong> MDoF structure, neglecting P-∆ effects.<br />
• Inelasticity modification factor, αINEL, a factor that relates <strong>the</strong> elastic ro<strong>of</strong><br />
drift dem<strong>and</strong> to <strong>the</strong> inelastic ro<strong>of</strong> drift dem<strong>and</strong>, neglecting P-∆ effects.<br />
• P-∆ modification factor, αP∆, a factor that takes into account <strong>the</strong> effect <strong>of</strong> P-<br />
∆ on <strong>the</strong> inelastic ro<strong>of</strong> drift dem<strong>and</strong>.<br />
• Storey drift modification factor, αST, a factor that relates individual storey<br />
drift dem<strong>and</strong>s to <strong>the</strong> ro<strong>of</strong> drift dem<strong>and</strong>.<br />
• Element deformations modification function, a function that relates storey<br />
drift dem<strong>and</strong> to element plastic deformation dem<strong>and</strong>s.