Civil Engineering Reference
In-Depth Information
of the diaphragm configurations shown has varying stiffness caused by the different
depths of the diaphragm. These are represented by moments of inertia
I
1
,
I
2
, and
I
3
.
Under wind loading, the applied loads are uniform along the entire length of the
diaphragm. However, when seismic controls, the uniform loads vary in accordance
with the depth of the diaphragm. Concentrated loads can also occur in the loading
pattern if vertically discontinuous interior shear walls are located above the dia-
phragm and require the transfer of their shear through the diaphragm into adjacent
shear walls below. The procedure for calculating the deflection under nonuniform
loads and varying moments of inertia is accomplished by applying elastic beam the-
ory to derive the bending and shear deflection, then modifying the other terms of the
basic deflection equation in accordance with the configuration of the model. The
maximum deflection will not always occur at midspan of the diaphragm. The deflec-
tions in the examples presented in ATC 7 were calculated using virtual work. Deflec-
tions can now be determined by using available software or by customizing electronic
spreadsheets, thereby eliminating the need to resort to lengthy hand calculations.
Sample computer models are shown at the bottom of Fig. 3.8. The equations below
follow the method used in ATC 7.
∑
(
∆
X
)
C
∆=∆+∆+
0 188
.
Le
+
TL
B
S
n
2
b
where
b
c
mM
EI
mM
EI
∫
∫
∆=
dx
+
dx
B
1
2
a
b
b
c
L
bt
GA
wx
b
b
vV
Gt
∫
∫
=
∫
0
∆=
dx
+
wx dx
dx
S
2
2
2
′
a
b
Example 3.1 provides an easier method for calculating the deflections of a single
notched (offset) diaphragm.
3.4
Single Offset Diaphragms
All the tools that are necessary to analyze a notched diaphragm have been reviewed
and discussed in the preceding sections. The following examples show how those tools
are applied to solve the transfer of the discontinuous chord or strut force across the
offset in both the transverse and longitudinal directions. The direction of the roof or
floor framing will be ignored until a familiarization with the techniques of solving these
problems has been established.
Example 3.1: Single Notched Diaphragm, Analysis in the Transverse Direction
The diaphragm shown in Fig. 3.9 has a length of 125 ft and a depth of 50 ft, with a 15-ft
horizontal offset between grid lines 1 and 2. A 200 plf load is applied uniformly along
the entire length of the diaphragm. The depth of the diaphragm between grid lines A
and B is 35 ft. The diaphragm chord is discontinuous at grid line 2B because of the offset.
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