Diaphragms With End Horizontal Offsets - The Analysis of Irregular Shaped Structures - page 91

occurs below the collector at the same location. The directions of the shears trans-
ferred into the collector oppose each other with the largest shear value acting to the
right. Visually, the directions of the shears indicate that the 225 plf shear must be sub-
tracted from the 550 plf shear, with a resulting shear of 325 plf acting to the right. At
the opposite end of the collector, it can be seen that the +150 plf shear must also be
subtracted from the +475 plf shear, with a resulting shear value of 325 plf also acting
to the right.

Shear left = 550-(225) = 325 plf, acting to the right (tension)

Shear right = 475-(150) = 325 plf, acting to the right (tension)
The resulting shear diagram is shown at the bottom of the figure. The force on the
collector is the average shear multiplied by the length of the collector, or, simply put,
the area of the shear diagram. The resulting force should equal the calculated chord
force at the discontinuity. If it does not, an error exists.

( 325 + 325

2

)( L )

F =

collector

tensiondirection of forceisactingtoright ,

Tables could be generated to compile the diaphragm shear, transfer shear, and net
shear data. However, as with tables, it is often difficult to mentally visualize the overall
picture of how the shears are flowing through the diaphragm. The method shown
above provides a clear visual representation of the direction of the shears that are
transferred into the elements and visually verifies if the chords, struts, or collectors are
in tension or compression.
Diekmann 1 and ATC 7 4 recommended that the aspect ratio of the transfer dia-
phragm be limited to that of the main diaphragm, a maximum ratio of 4 : 1. Code limits
the aspect ratio for blocked wood diaphragms to 4 : 1 and 3 : 1 for unblocked dia-
phragms. This should be carefully considered when determining the initial size of the
transfer diaphragm. Whenever tie straps are installed, the tendency is to make the exten-
sion of the collector as short as possible to minimize cost, especially when the framing is
oriented perpendicular to the collector. This can create two problems: first, transfer
diaphragm shears will be high, which will increase the nailing requirements, cause
splitting, and potentially create localized failures; second, if the collector length is too
short, the required aspect ratio cannot be maintained and the transfer diaphragm will
not be stiff enough to distribute the shears as anticipated. To prove the first point, a
comparison of transfer diaphragms with aspect ratios of 2 : 1 and 4 : 1 will be examined
as shown in Fig. 3.6. A chord force of 6000 lb is applied to each transfer diaphragm. The
basic diaphragm shear diagram loads acting at the transfer diaphragm area are as
shown at the bottom of the figure. The transfer diaphragm reaction and unit shears at
grid lines A and C are as follows:

Transfer Diaphragm Reactions A/R = 2 : 1 A/R = 4 : 1

6000 10
50

() 1200

25

1200
12 5

R A = = 1200 lb v A = = - 48 plf v A = = - 96 plf

.

6000 40
50

()

4800
25

4800
12 5

R C = = 4800 lb

v C = = + 192 plf v C = = + 384 plf

.