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

2. DUCTILITY AND SEISMIC RESPONSE OF STRUCTURES
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2. Convert the pushover curve to a capacity diagram, see Figure 2.7, where
N
m φ
j j1
j j1
j = 1 * j = 1
1 N 1 N
2
mjφ j1 2
mjφ
j1
j = 1 j = 1
N
m φ
2
Γ = Μ = ( 2.6 )
and mj = lumped mass at the j th floor level, φj1 is the j th -floor element of the
*
fundamental mode φj, N is the number of floors, and M1 is the effective
modal mass for the fundamental vibration mode.
V b
Pushover Curve
u N
A =
V b
M 1 *
Capacity Diagram
u N
D = Γ1 φ N1
Figure 2.7. Conversion of a pushover curve to a capacity diagram
3. Convert the elastic response (or design) spectrum from the standard
pseudo-acceleration A versus natural period TN format to the A-D format,
where D is the deformation spectrum ordinate, defined as
2
N
2
T
D = ⋅ A
( 2.7 )
4π
4. Plot the demand diagram and capacity diagram together and determine the
displacement demand as illustrated in Figure 2.8. Involved in this step are
dynamic analyses of a sequence of equivalent linear systems with
successively updated values of the natural vibration period Teq and
equivalent viscous damping ξeq. To define the above-mentioned quantities
we have to consider an inelastic SDoF system with bi-linear force-
deformation relationship on initial loading. The stiffness of the elastic
branch is k and that of the yielding branch is αk.