Civil Engineering Reference
In-Depth Information
necessarily a difficult task and it has been shown that, for a simply supported
RC beam at its ultimate limit state, the compressive force at the mid cross-
section is transmitted to the support by following a path which, for any practical
purpose, may be considered to be bi-linear (Kotsovos, 1983b; 1988a). The
change in path direction appears to occur at a distance of approximately twice
the beam depth
d
for the cases of
(a)
two-point loading with a shear span-to-
depth
(a/d)
ratio greater than a value of approximately 2.0 and
(b)
uniformly
distributed loading (UDL) with a span-to-depth
(L/d)
ratio greater than a value
of approximately 6.0 (
Figure 2.15a
);
for smaller ratios it is considered to occur
at the cross-section coinciding with the load point, assuming that UDL can be
replaced by an equivalent two-point loading at the third points (Figure 2.15b).
Although a deep beam is usually considered to be, by definition, a beam with
L/
d
<2.0, investigations of deep beam behaviour often include beams with values
of
L/d
as large as 3.0. It would appear, therefore, that, in all cases, an RC deep
beam should be characterised by a compressive force path similar to that of a
beam with
a/d
<2.0 or
L/d
<6.0 (Figure 2.16).
Figure 2.16
Path of compressive force and corresponding outline of compressive stress trajectories
for a typical deep beam.
2.5
Deep beam behaviour at ultimate limit state
It is well known that the behaviour of an RC beam with a rectangular cross-
section and without shear reinforcement may be divided into four types of
behaviour depending on either
a/d,
for beams subjected to two-point
