Design Considerations for Earthquake Forces - Simplified Design of Reinforced Concrete Buildings - page 287

h i and h x = the height in feet from the base level to i or x
w i and w x = the portion of W assigned to level i or x

For most of the structures covered in this publication, the fundamental period T is less than 0.5 second.
For this case the above equation simplifies to:

w x h x

C vx =

n
∑

w i h i

i = 1

11.6.2.1 Distribution of Seismic Forces to Vertical Elements of the Lateral Force
Resisting System

The seismic design story shear V x in any story x is the sum of the lateral forces acting at that story in addition
to the lateral forces acting on all the floor levels above (ASCE Eq. 12.8-13):

n
∑

V x = F i

i = x

Figure 11-9 shows the vertical distribution of the seismic force F x and the story shear V x in buildings with T ≤ 0.5.

The lateral shear force V x is typically transferred to the lateral force resisting elements (shearwalls or frames)
by the roof and floors acting as diaphragms. At each level the floor diaphragm distributes the lateral forces from
above to the shearwalls and frames below. The distribution of the lateral force to the lateral force resisting
elements (shearwalls or frames) depends on the relative rigidity of the diaphragm and the lateral force resisting
elements. For analysis purposes the diaphragms are typically classified as rigid, semi-rigid, and flexible.
Cast-in-place concrete floor systems are considered and modeled as rigid diaphragms. In rigid diaphragms, the
lateral force V x is distributed to the shearwalls and frames in proportion to their relative stiffnesses.

V x

F x

Force Shear

Figure 11-9 Vertical Distribution of Seismic Base Shear in Low-rise Buildings (T ≤ 0.5 sec)

For building frame system (consisting of shearwalls and frames) the shearwalls are designed to resist the entire
story shear V x . For SDC D, E, and F the frames must be designed to resist the effects caused by the lateral
deflections, since they are connected to the walls through the floor slab (ASCE 12.2.4).

The seismic design story shear V x is considered to act at the center of mass of the story. The center of mass is
the location where the mass of an entire story may be assumed to be concentrated. The location of the center
of mass can be determined by taking the moment of the components weights about two orthogonal axes x and y.
The distribution of V x to the walls and frames depends on the relative location of the center of mass with