Civil Engineering Reference
In-Depth Information
The location of the center of rigidity for a story can be determined by calculating the coordinates
and
from
x
r
y
r
arbitrary located origin as follows:
()
∑
k
i
y
x
i
x
r
=
(
y
∑
k
i
()
∑
k
i
x
y
i
y
r
=
∑
(
x
k
i
where:
(k
i
)
y
= lateral stiffness of lateral load resisting element (wall or frame) in the y-direction
(k
i
)
x
= lateral stiffness of lateral load resisting element (wall or frame) in the x-direction
x
i
and y
i
= coordinates measured from arbitrary located origin to the centroid of lateral force
resisting element i.
The distribution of the seismic shear force V
x
(at floor x) to the different lateral force resisting element
(shearwalls or frames) can be calculated from the following equations:
For force seismic force V
x
applied in x direction
(
x
k
i
(
x
J
r
k
i
y
i
k
i
(
x
=
V
i
V
x
+
V
x
e
y
(
x
∑
For force seismic force V
x
applied in y direction
(
y
k
i
(
y
J
r
k
i
y
i
k
i
(
y
=
V
i
V
x
+
V
x
e
x
(
x
∑
where:
x
i
, y
i
= perpendicular distances from the lateral force resisting element i to the center of
rigidity parallel to x and y axes respectively
J
r
= rotational stiffness for all lateral force resisting elements in the story
(
y
+
(
x
∑
∑
=
x
i
2
k
i
y
i
2
k
i
e
x
, e
y
= perpendicular distance from the center of mass to the center of rigidity or assumed
eccentricities parallel to x and y axes respectively
(k
i
)
x
, (k
i
)
y
= stiffnesses of lateral force resisting element in x and y direction, respectively
11.6.2.2 Direction of Seismic Load
To determine the seismic force effects on different structural members, a structural analysis for the building needs
to be preformed. The design seismic forces should be applied in the direction which produces the most critical load
effect in each structural component. Provisions on application of loading are given in ASCE 12.5 as a function of
the SDC and the irregularity of the structure. Applications of these provisions for irregular structures are beyond
the scope of this publication.
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