diaphragm is presented in the following equation:
Diaphragms shall be considered rigid when the
maximum lateral deformation of the diaphragm is
T =( 0.1∆ w + 0.078∆ d )
less than half the average interstory drift of the
0.5
(7-5)
associated story. Diaphragms that are neither flexible
nor rigid shall be classified as stiff. The interstory
where ∆ w and ∆ d are in-plane wall and diaphragm
drift and diaphragm deformations shall be estimated
displacements in inches, due to a lateral load, in the
using the seismic lateral forces from Section 5.3 or
direction under consideration, equal to the weight of
5.4 of FEMA 302.
the building.
For the displacements in mm, the
calculated value of T shall be multiplied by 5. Wall
(2) Flexibility considerations. The in-plane
displacements shall be estimated for each line of
deflection of the floor diaphragm shall be calculated
framing. For multiple-bay diaphragms, lateral load
for an in-plane distribution of lateral force consistent
equal to the gravity weight tributary to the diaphragm
with the distribution of mass, as well as all in-plane
bay under consideration shall be applied to each bay
lateral forces associated with offsets in the vertical
of the building to calculate a separate period for each
seismic framing at that floor. The deformation of the
diaphragm bay.
The period so calculated that
diaphragm may be neglected in mathematical models
maximizes the equivalent base shear shall be used for
of buildings with rigid diaphragms. Mathematical
design of all walls and diaphragms in the building.
models of buildings with stiff diaphragms shall
explicitly
include
diaphragm
flexibility.
(3) Rotation. In cases where there is a lack of
Mathematical models of buildings with flexible
symmetry either in the load or the reactions, the
diaphragms
should
explicitly
account
for
the
diaphragm will experience a rotation. Rotation is of
flexibility of the diaphragms.
For buildings with
concern because it can lead to vertical instability.
flexible diaphragms at each floor level, the vertical
This is illustrated in the following cases: the
lines
of
seismic
framing
may
be
designed
cantilever diaphragm, and the diaphragm supported
independently, with seismic masses assigned on the
on three sides.
basis of tributary area. Diaphragm flexibility results
in: (1) an increase in the fundamental period of the
(a) Building with a cantilever diaphragm
building, (2) decoupling of the vibrational modes of
(an example is shown in Figure 7-48). The layout of
the horizontal and vertical seismic framing, and (3)
the resisting walls is shown in Figure 7-48, part a. If
modification of the inertia force distribution in the
the backspan is flexible relative to the walls (Figure
plane of the diaphragm. There are numerous single-
7-48, part b), the forces exerted on the backspan by
story buildings with flexible diaphragms.
For
the cantilever are resisted by walls B, C, and D,
example, precast concrete tilt-up buildings with
provided there are adequate collectors.
If the
timber-sheathed diaphragms are common throughout
backspan is relatively rigid (Figure 7-48, part c), the
the United States. An equation for the fundamental
load from the cantilever is resisted by all four walls
period of a single-story building with a flexible
7 -114
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