Design of seismic isolation system (FPS, LRB, HDRB)

Design ground acceleration (including soil factor S and importance factor γ_I)

α_g⋅S

g

In accordance with EN1998-1 §3.2.1(2), 3.2.1(3) and the National Annex

Characteristic period of elastic response spectrum (start of constant velocity branch)

T_C

s

In accordance with EN1998-1 §3.2.2.2(2)P and the National Annex

Characteristic period of elastic response spectrum (start of constant displacement branch)

T_D

s

In accordance with EN1998-1 §3.2.2.2(2)P and the National Annex. It is noted that for seismic isolation systems with long periods the displacement demands are directly proportional to T_D. For bridges a larger value of T_D = 2.5 s is recommended in EN1998-2 §7.4.1(1)P

Seismic weight of the superstructure above the isolation interface

W_d

kN

Typically the weight corresponding to the mass of the superstructure above the isolation interface that oscillates practically as a rigid body. For bridges it corresponds to the weight of the deck including the effect of quasi-permanent masses due to variable traffic actions, in accordance with EN1998-2 §4.1.2. The mass of the superstructure is assumed as m = W_d / g and the force of the sliding elements is assumed proportional to W_d

Total force at zero displacement under cyclic loading of hysteretic devices

F₀

kN

Corresponds to the total effect of all hysteretic devices

Total post-elastic stiffness of hysteretic and spring devices

K_p

kN/m

Corresponds to the total effect of all hysteretic devices and spring devices

Equivalent yield displacement

d_y

m

Representative value for the total isolation system so that the dissipated energy (area of hysteretic loops) is equivalent

Total preloading force of preloaded spring devices

F_p

kN

Corresponds to the total effect of all preloaded spring devices

Equivalent friction coefficient of sliding devices

μ

Corresponds to the total effect of all friction devices

Equivalent radius of curvature of sliding devices

R

m

Corresponds to the equivalent value for all friction devices so that the corresponding post yield stiffness is Kp=W/R. For R=0 the effect of the radius of curvature is ignored i.e. it is assumed that R=∞

Total coefficient of force-velocity law of viscous devices

C

kN⋅(s/m)^α_b

Corresponds to the total effect of all viscous devices

Exponent of force-velocity law of viscous devices

α_b

For linear viscous elements where force is proportional to velocity α_b = 1. For nonlinear viscous elements α_b < 1

Total equivalent stiffness of the substructure elements

K_s

kN/m

Corresponds to the total representative stiffness of the substructure below the seismic isolation system, e.g. the pier stiffness for an isolated bridge. For K_s=0 the effect of substructure stiffness is ignored i.e. it is assumed that K_s=∞

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Eurocode 8 Preliminary SDOF analysis of seismic isolation