Civil Engineering Reference
In-Depth Information
where
V
is the shear force,
Q
c
=
A
c
y
na
is the statical moment of the concrete slab
about the neutral axis,
A
c
is the transformed area of the concrete slab,
b
f
is the width
of the girder flange,
y
na
is the distance from the centroid of the concrete slab to the
neutral axis, and
I
cp
is the moment of inertia of the composite section.
Shear transfer connectors must be designed to resist the shear flow at the steel to
concrete interface. AREMA (2008) recommends that shear studs be at least 3
long
(4
long shear studs are commonly used) and have the following strength:
(d
s
)
2
4
C
sr
π
S
r
=
kips,
(d
s
)
2
π
20.0
S
m
=
kips.
4
For channels the recommended strength is
S
r
=
D
sr
w
c
kips,
S
m
=
3600
w
c
kips,
where
S
r
is the allowable horizontal design force for fatigue per connector, kips;
S
m
is the allowable maximum horizontal design force per connector, kips;
d
s
is the
diameter of the shear stud (3/4 or 7/8 in.);
C
sr
is 7.0 for fatigue design cycles
N
≥
=
2,000,000 cyclesand10.0forfatiguedesigncycles
N
2,000,000 cycles;
D
sr
is2100
≥
for fatigue design cycles
N
2,000,000 cycles and 2400 for fatigue design cycles
N
2,000,000 cycles;
w
c
is the length of the channel perpendicular to the shear flow
(transverse to the flange).
The distribution of shear connectors along the span is made based on the mag-
nitude of the shear flow along the span length. Since live load shear flow varies
along the span length,
L
, the shear connector spacing may also vary. The form of
a typical shear flow influence line for the determination of live load maximum and
range of shear flow is shown in Figure 7.23. Based on the maximum shear flow and
live load shear flow range, a practical spacing over a length,
s
i
, with some acceptable
overstress (usually about 10%) can be made as illustrated in
Figure 7.24.
=
q
max
= maximum live load shear flow
q
max
(
x
1
) = maximum live load shear flow at
x
1
q
r
(
x
2
) = live load shear flow range at
x
2
x
1
x
2
L
/2
FIGURE 7.23
Distribution of shear flow along the span length.
