Civil Engineering Reference
In-Depth Information
X,
*2
Figure 3.51
Location of two outrigger levels at distances x
1
and x
2
from the top
For the location of two outrigger levels at distances x
1
and x
2
from the top of the
structure, the lateral drift at the top of the structure is (
Figure 3.51
):
y
x=
0
wL
4
2
EI
[
M
1
(
L
2
-
x
1
2
) +
M
2
(
L
2
-
x
2
2
)
]
1
____
___
8
EI
-
and the restoring effect of the outriggers on the lateral drift at the top of the structure is:
2
EI
[
M
1
(
L
2
-
x
1
2
) +
M
2
(
L
2
-
x
2
2
)
]
1
___
y
rx
=0
=
M
1
and M
2
must be found in the above equations. This is done using the rotation
equations.
The rotations of the core at the levels where the outriggers are located are:
6
EI
(
L
3
-
x
1
3
) -
M
1
EI
(
L
-
x
1
) -
M
2
q
x
1
=
w
___
___
___
EI
(
L
-
x
2
)
6
EI
(
L
3
-
x
2
3
) -
M
1
EI
(
L
-
x
2
) -
M
2
q
x
2
=
w
___
___
___
EI
(
L
-
x
2
)
On the other hand, since
q
=
M
__
K
M
1
M
2
=
2
M
1
(
L - x
1
)
AEd
2
+
2
M
2
(
L - x
2
)
________
________
__________
__________
q
x
1
=
+
AEd
2
AEd
2
AEd
2
_______
_______
2(
L - x
1
)
2(
L - x
2
)
M
1
M
2
=
2
M
1
(
L - x
2
)
AEd
2
+
2
M
2
(
L - x
2
)
________
________
__________
__________
q
x
2
=
+
AEd
2
AEd
2
AEd
2
_______
_______
2(
L - x
2
)
2(
L - x
2
)
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