Civil Engineering Reference
In-Depth Information
Assuming that:
C
=
1
2
__
_____
EI
+
AEd
2
From the above equations, M
1
and M
2
can be found.
6
EIC
(
x
2
3
-
x
1
3
)
w
w
_____
_______
_____
M
1
=
(
x
2
-
x
1
)
=
6
EIC
(
x
1
2
+
x
1
x
2
+
x
2
2
)
w
w
_____
_____
M
2
=
6
EIC
(
L
-
x
1
) (
L
+
x
1
+
x
2
) =
6
EIC
(
L
2
+
Lx
2
- x
1
x
2
-
x
1
2
)
The lateral drift at the top of the structure is:
y
x=
0
=
wL
4
12(
EI
)
2
C
[
(
x
1
2
+
x
1
x
2
+
x
2
2
) (
L
2
-
x
1
2
) + (
L
2
+
Lx
2
-
x
1
x
2
-
x
1
2
) (
L
2
-
x
2
2
)
]
w
____
________
8
EI
-
The location of the outrigger levels that have the greatest effect on the lateral drift at
the top of the structure are the locations where the y
rx=0
function has the maximum
values. Therefore, the optimum locations for two outrigger levels are obtained by
differentiating the y
rx=0
function with respect to x
1
and x
2
and equating to zero.
x
1
= 0.31
L
x
2
= 0.69
L
The lateral drift at the top of the structure is:
y
=
wL
4
wL
4
____
________
8
EI
-
12(
EI
)
2
C
1.44
and the restoring moments of the outriggers are:
M
1
=
wL
2
6
EIC
0.79
M
2
=
wL
2
_____
_____
6
EIC
1.38
In the equation of the restoring effect of two outrigger levels on the lateral drift at the
top of the structure, when
x
1
=0, the optimum location
x
2
is obtained by differentiating
the y
rx=0
function with respect to
x
2
and equating to zero.
x
2
= 0.5774
L
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