Geology Reference
In-Depth Information
Box 1.
0
; if
x
x
> −
x
sl
al
ol
if
=
(13)
β
cl
(
)
  ; if x
x
≤−
x
k x
x
+
x
+
c
x
x
c
sl
al
ol
cl
sl
al
ol
cl
sl
al
Box 2.
0
; if
x
x
<
x
sr
ar
or
if
=
(14)
β
cr
(
)
(
)
  ; if x
x
x
k
x
x
x
+
c
x
x
c
sr
ar
or
cr
sr
ar
or
cr
sr
ar
a d
where ρ is the material density and m if corresponds
to the mass of the span. R if and δ if are calculated
based on the total mass and material properties
of each span and then the contact stiffness k cc is
equal to k c given by Equation 10.
The force due to pounding of the left span to
the left abutment is modeled as left-sided contact
force in Box 1.and similar modeling holds for the
pounding of the right span to the right abutment
(see Box 2).
The contact parameters k cl , k cr and c cl, c cr are
defined similarly to the case of contact between
the spans, using the properties (mass, velocity)
of the colliding bodies of interest. The restitution
coefficients for collision of the left or right span
to their neighboring abutments are denoted by e cl
and e cr respectively.
The damper forces depend on the type of
application. For simplicity only the case of
passive viscous dampers is discussed here, but
the framework presented in the next sections is
directly extendable to the design of other type
of dampers as well. For fluid viscous dampers
the damper forces are a function of the relative
velocity across the end points of the damper. For
the damper connecting the left span to the cor-
responding abutment (Makris & Zhang, 2004)
they may be described in Box 3.
if
=
c
sgn(
x
   
x
)
x
x
(15)
dl
d
sl
al
sl
al
where c d is the damping coefficient and a d an
exponent parameter. These adjustable charac-
teristics are the controllable damper parameters
to de selected at the design stage. Note that for
a d =1 relationship 15 corresponds to a linear
viscous damper. Maximum forcing capabilities
for the damper, related to cost constraints, may
be incorporated into the model as a saturation of
the damper force to if max leading to (see Box 4).
For the damper connecting the right span to
the abutment the damper force is similarly ex-
pressed in Box 4.
EXCITATION MODEL
The analysis and design of any seismic structural
system needs to be performed considering poten-
tial damaging future ground motions. For base-
isolated bridges this translates to consideration
of near-fault ground motions.
The last two decades numerous models have
been proposed for ground motion modeling
(Atkinson & Silva, 2000; Shinozuka, Deodatis,
Zhang, & Papageorgiou, 1999) that incorporate
important characteristics of the seismic source
as well as of the earth medium. Other studies
 
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