Geology Reference
In-Depth Information
(
)
small vertical deflection
δ
1 cos
of the
bearing and thus of the building. The base isola-
tion element can be arranged in compact units;
e.g. a four spring pendulum unit with a mass of
about 50 kg, which can be manipulated and ex-
changed easily.
To avoid abrasive dry friction, a novel sliding
element has been developed by Khalid (2010)
that consists of a bronze-steel interface of two
contacting circular plates to provide the static
friction. The adjustable pressure of the contacting
plates is provided by an axially pre-stressed
conical steel spring. Above the static friction
limit the relative horizontal motion will cause a
small vertical deflection of the basement, thereby
separating the friction elements via a magnifying
lever mechanism and thus avoiding continuous
contact and the abrasive sliding in dry friction.
Figure 4b shows the design applied in the base
isolation.
The effectiveness of TLCGD in providing
efficient damping of the three base isolated rigid
body modes is demonstrated by the numerical
analysis of a simple single-storey asymmetric
building, see again Khalid (2010). It has a rect-
angular plan rigid base of
A a b
=
l
−
ϕ
=
. Hz
. Assuming small
modal displacements, the modal centers of veloc-
ity, determined from Eq. (11), are given by, Kha-
lid (2010),
f
2
=
. Hz
, and
f
3
0 50
0 82
v
=
−
−
30 3
23 1
.
.
2 6
3 5
.
C
m C
,
10
15
m
,
=
V
1
V
2
−
.
(31)
1 5
0 9
.
.
C
=
m
V
3
The first rigid body mode is dominated by a
translation, the second is a pure translational mode,
both refer to moderate asymmetry of the building.
The center of modal velocity of the third mode,
lies within the floor plan, but distinct from
C
M
and is dominated by a rotational seismically forced
motion thus referring to strong asymmetry of the
building for this mode. The placement of the
absorber would be optimal with a maximum
normal distance from the modes of vibration, see
dashed TLCGD in Figure 4c. However, to avoid
a diagonal installation in the building, the less
effective three TLCGD might be aligned parallel
to the outer perimeter.
For efficient design the geometric dimensions
of the TLCGD are selected to utilize the maximum
available lengths in the plan of the base isolated
building. The vertical liquid column length
H
is
selected to fulfill the limiting conditions of a
maximum stroke of
u
12 8m
2
= ⋅ = ⋅
and a total mass of
m
244 10
3
. Due to
asymmetric walls and distributed load the center
of mass is defined by
C
=
×
kg
=
, , 0
,
y
C
M
=
1 0. m
,
z
C
M
=
0 5. m
with respect to the
origin
O y z
y
z
M
C
C
M
M
max
=
2
H
3
and
,
( )
, see Figure 4c. To decouple foun-
dation and basement 60 spring pendulum units
(240 spring pendulum elements) are distributed
over the floor plan as well as eight novel sliding
elements. The horizontal stiffness of the spring
pendulum units was determined by demanding
that the natural frequencies of the first three modes
of vibration (base isolation modes) of the iso-
lated building are around 0.5 Hz. A modal analy-
sis of the system modeled as three DOF rigid body
renders a set of three ortho-normalised modal
vectors with natural frequencies of
f
1
max
=
3
for the design earthquake load
given by the El Centro 1940 seismogram scaled
to 0.32 g. It is checked that the maximum liquid
speed remains well below the limit of
u
max
≤
12m/s
, Ziegler (2008), for three TLC-
GD with a fluid mass of
m
f
1
u
H
a
=
kg
,
m
f
2
420
=
kg
and
m
f
3
100
=
kg
, Khalid
(2010). The extremely low structural damping
of such a base isolated building is less than 1%,
even with linearized frictional damping of the
5000
=
. Hz
,
0 49
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