Civil Engineering Reference
In-Depth Information
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
60
-0.1
-0.2
-0.3
-0.4
Time (s)
Figure 7.31
Time history of acceleration during the El Centro earthquake (1940), United
States.
by
x
i
(
t
) and
x
f
(
t
), and these are relative to the ground displacement. The
whole system is subjected to ground shaking with acceleration time his-
tory denoted by
xt
. The equations of motion may be formulated for
linear soil-structure interaction analysis and subsequently solved using the
wavelet-based technique as explained earlier. For the sake of the readers'
interest, the dynamic equations of the tank-fluid-foundation system and
only the tank-fluid system may be written as
g
()
mxtxt
(()
+
( ))
+
mxt Kxtxt
()
+
(()
−
( ))
=
0
(7.10)
i
i
x
g
f
f
f
f
mx tCxt
()
+
()
+
Kx t
()
=−
mxt
()
(7.11)
ii
i
l
i
i
ii
i
and =ω
2
It may be noted here that in the above equation, =ζω
K
i i i
,
and the expression for the term
K
x
is given by Equation (4.16). The expressions
for the base shear,
Q
(
t
), and the base moment,
M
(
t
), developed at the tank
base due to soil-structure interaction effects may be written as
Cm
i
i
{
}
Qt
()
=
mxtxt
i
()
+
()
(7.12)
i
f
{
}
Mt
()
=
mxtxth
i
()
+
()
(7.13)
i
f
i
In the above expression for tank base moment the term
h
i
denotes the
height above the tank base at which the impulsive mass should be located
to give correct moments at a section immediately above the tank base. The
