Civil Engineering Reference
In-Depth Information
K
i
= p
i
d =
A
i
Ed
2
_____
2
L
where E is the modulus of elasticity.
Considering all the couple of columns (in elongation and contraction) on the two
facades perpendicular to the bending direction:
n
n
K
i
=
Ed
2
A
i
=
AEd
2
K
=
∑
i
= 1
____
2
L
∑
i
= 1
_____
2L
K =
AEd
2
_____
2
L
The rotational stiffness of outriggers at distance x from the top of the structure is:
AEd
2
_______
K =
2(
L - x
)
The function of the rotational stiffness of the spring, representing the effect of the
outrigger on the core, shows that the rotational stiffness of the outrigger is directly
proportional to the distance of its location from the top of the structure.
X
Figure 3.50
Location of a single outrigger level at distance x from the top
For the location of a single outrigger level at distance x from the top of the structure
(
Figure 3.50
),
the lateral drift at distance x from the top of the structure is:
8EI
-
M
x
y
x=0
=
wL
4
____
___
2EI
(
L
2
- x
2
)
and the restoring effect of the outrigger on the lateral drift at the top of the structure is:
y
rx=0
=
M
x
___
2EI
(
L
2
- x
2
)
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