Civil Engineering Reference
In-Depth Information
The reinforcement is assumed to be anchored behind the support,
symbolised by an anchor plate in
Figure 8.7
,
resulting in a compressive
concrete force
T
distributed over the depth
y.
If the reinforcement is not
cocentral with the concrete compression (i.e.
y
>2
c
) this gives rise to a
moment, which must equal the moment delivered by the support reaction.
Hence:
V
(
s
/
2
-
x
/2)=
T
(
y
/2-
c
), from which the required length
s
of the support
platen is determined. This is equivalent with the geometrical relation:
cot
=
y/x
=(
s
-
x
)/(
y
--2
c
)
which can also be deduced from Figure 8.7.
Although the stress distribution of Figure 8.7 formally satisfies
equilibrium, the detailed load transfer at the support is left unexplained.
Figure 8.8 shows a more consistent stress distribution at the support for the
case where the reinforcement is concentrated in a single stringer (in Figure
8.7 the reinforcement may in principle be located anywhere in the beam
section, as long as the effective depth to the centroid is
d
=
h
-
c
). The shaded
areas are under the biaxial hydrostatic compression a and the vertical stress
over the central part of the support platen is
q
(8.6)
, the inclined
concrete stresses being transferred to the reinforcement by bond shear.
s
v
=
s
sin
2
q
Figure 8.8
Alternative stress distribution at support.
2
c
it is
possible to place the concrete compression symmetrically about the
reinforcement centroid, and the stress distribution at the support is modified
as shown in
Figure 8.9
.
Figure 8.7 yields an expression for the strut inclination:
cot
The stress distributions mentioned are topical for
y
>2
c.
If
y
£
q
=
y/x
=
l
/(
h
-
c
-
y
/2)
(8.7)
