where:
G = the shear modulus
w =
uniform lateral shear load on the
diaphragm, K/ft. (N/m).
noting that:
R, the end reaction, equals W/2 and qave =
L = diaphragm span, ft. (m).
R/2D = W/4D, L = 2L1, and Aw = Dt
D = depth of diaphragm, ft. (m).
Where t is the thickness of the web, and D is the
depth of the diaphragm, the formula for shearing
G' =
effective shear modulus calculated
deflection can also be expressed as:
from tabulated values based on profile and thickness
q Lα
of deck and type and spacing of connectors.
∆ω
= ave 1
(7-8)
tG
The effective shear modulus , G' is related to the
,
flexibility factor, F, as follows:
As noted above, this is only applicable to webs of
uniform properties. For a concrete slab with " = 1.5,
3
G'= 10
(7-11)
1.5
'
f , the formula in
F
G = 0.4 E, and E = 33w
c
English units becomes:
c.
Design of Diaphragms.
A deep-beam
analogy is used in the design.
Diaphragms are
qave L1
∆ω =
(7-9)
envisioned as deep beams with the web (decking or
1.5
'
8.8tw
f .
c
sheathing) resisting shear and the flanges (spandrel
beams or other members) at the edges resisting the
where:
bending moment.
t = thickness of the slab, in.
(1) Unit shears. Diaphragm unit shears are
obtained by dividing the diaphragm shear by the
w = unit weight of the concrete, lbs. /cu. ft.
length or area of the web, and are expressed in
pounds per foot (N/m) (for wood and metal decks) or
Recent editions of the SDI Diaphragm Design
pounds per square inch (MPa) (for concrete). These
Manual provide the following alternative equation for
unit shears are checked against allowable values for
the deflection of steel deck diaphragms:
the material.
Webs of precast concrete units or
metal-deck units will require details for joining the
2
wL
units to each other and to their supports so as to
)w =
(7-10)
8DG '
distribute shear forces.
7 -121
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