diaphragm is presented in the following equation:

Diaphragms shall be considered rigid when the

maximum lateral deformation of the diaphragm is

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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