Analysis and modelling of the seismic behaviour of high ... - Ingegneria

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