Civil Engineering Reference
In-Depth Information
Figure 1.3
Shear stresses in a composite section with the neutral
axis in the concrete slab
assumed to be cracked. As in the theory for reinforced concrete beams, it
resists no longitudinal stress but is capable of transferring shear stress.
Equation 1.15 is based on rate of change along the beam of bending
stress, so in applying it here, area ABCD is omitted when the 'excluded
area' is calculated. Let the cross-hatched area of flange be
A
f
, as before.
The longitudinal shear stress on plane 6-5 is given by
v
65
=
VA
f
K/
It
w
(1.18)
where K
is the distance from the centroid of the excluded area to the
neutral axis,
not to plane 6-5
. If
A
and K are calculated for the cross-
hatched area below plane 6-5, the same value
v
65
is obtained, because it is
the equality of the two products '
A
K' that determines the value
x
.
The preceding theory relies on the assumption that the flexibility of
shear connectors is negligible, and is used in bridge design and for fatigue
generally. Ultimate-strength theory (Sections 3.3.2 and 3.6.2) provides an
alternative that takes advantage of the plastic behaviour of stud connec-
tors and is widely used in design for buildings.
For a plane such as 2-3 in Fig. 1.3, the shear flow is
v
L,23
=
VA
23
K/
I
(1.19)
The design shear stress for the concrete on this plane is
v
L,23
/
h
c
. It is not
equal to
v
L,23
/
x
because the cracked concrete can resist shear. The depth
h
c
