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7.26 Vertically offset diaphragms, both sides.
order to avoid the time required to model a three-dimensional structure. The vertical
distribution of the seismic forces is typically calculated in the first mode in accordance
with ASCE 7-05 Section 12.8.3 and then applied to the respective diaphragm levels.
As an example, the structures similar to the one shown in Fig. 7.27 are occasionally
analyzed incorrectly by assuming that frames A and B can be designed independently,
each of which supports its respective sections at grid line A. The two frames are incor-
rectly assumed to safely enclose and support the high roof section. Alternately, frames
A, B, and C are combined and analyzed as a single frame. The problem of using a plane
frame analysis for this type of structure is that the analysis does not account for rotation
of the diaphragm sections or the effects of that rotation, which could cause secondary
stresses in the members.
Figure 7.26 is a photograph of an actual project that has low roof diaphragms on
each side of a higher vertically offset section. The entire lateral resisting system con-
sists of moment-resisting frames. The results of a modal analysis for a similar struc-
ture are shown in Figs. 7.27 through 7.29. There are two things that can be observed
in the first mode shape, which is shown in Fig. 7.27. The horizontal displacements of
the individual low diaphragms will not be equal if the frames have different stiff-
nesses. The lower roof sections impose a horizontal force on the columns located at
grid lines 2 and 3. In mode 3 shown in Fig. 7.28, all the individual diaphragms rotate
in a counterclockwise direction. In mode 4, shown in Fig. 7.29, the diaphragms
rotate in opposite directions. Each of these modes causes a different load condition
on the two-story columns. Three-dimensional computer programs will account for
these effects. A plane frame analysis will not. The modal analysis shows that special
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