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

2. DUCTILITY AND SEISMIC RESPONSE OF STRUCTURES
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the system with stiffness ksec. Substituting the expressions of Ed and Es in
Eq. (2.10) on gets:
ξ
eq
( µ − )( −α
)
( 1+
− )
2 1 1
=
πµ αµ α
The total viscous damping of the equivalent linear system is
( 2.11 )
ξeq = ξ + ξeq
( 2.12 )
where ξ is the viscous damping ratio of the bilinear system vibrating within
its linearly elastic range (u < uy).
For elasto-perfect plastic systems, α = 0 and both Eqs. (2.9) and (2.11)
reduce to
2 µ −1
Teq = TN
µ ξeq
= ( 2.13 )
π µ
Eqs. (2.9) and (2.11) are plotted in Figure 2.9 where the variation of Teq/TN
and ξeq vs. µ is shown for four values of α. For yielding systems, viz. α > 1,
Teq is longer than TN and ξeq > 0. The period of the equivalent linear
system increases monotonically with µ for all α.. For a fixed µ, Teq is
longest for elasto-plastic systems and is shorter for systems with α > 0. For
α = 0, ξeq increases monotonically with µ but not for α > 0. For the latter
case, ξeq reaches its maximum value at a µ value, which depends on α,
and then decreases gradually.
5. Convert the displacement demand determined in Step 4 to global (roof)
displacement and individual component deformation and compare them to
the limiting values for the specified performance goals.