Combined shear and bending of reinforced concrete members
The object of the research reported in this
thesis, was to formulate a theory of shear in
reinforced concrete, which was both logically
acceptable and reasonably accurate, while at the
same time being simple enough to be of practical use.
The main outline of the known behaviour of
members subject to shear is described, and existing
shear theories are reviewed in the light of it. The
inadequacies of the various theories are discussed.
To a large extent, these stem from the fact that the
majority of the present-day methods was derived
empirically on the basis of very limited test data
and is found to be inapplicable in more general cases.
A few analytical approaches are so complicated as to
be virtually unusable.
The approach to shear, developed in the major
part of this thesis, consists of two separate theories.
The first is concerned with shear cracking, and is
based on an analysis of the stresses in beams immediately
prior to the occurence of shear cracks. The determination
of stress distributions is dependent on widely accepted
stress-strain relations, and the criteria of local
failure, or cracking, used is shown to be as accurate
as any and generally safe. The results obtained by the
analysis are approximated to by simple equations.
The second part of the theory relates to the
behaviour of beams with shear cracks. This requires
a new analysis of stresses, as the internal structure
of a beam is radically changed by such cracks. The
internal structure is complex and indeterminate, both
in the statical sense and in the sense that its
geometry is unknown due to the unknown disposition
of cracks. Under some circumstances this structure
is incapable of supporting the load that causes the
shear cracks to form. In these cases the previous
shear cracking equations also serve to determine ultimate
loads. In other cases, in which an increased load can
be sustained following shear cracking, a solution for
the ultimate strength is obtained by using a set of
three simultaneous equations. One relates the area
of uncracked concrete, capable of supporting load, to
the properties of the beam and the lengths of shear cracks.
It is based on a compatibility condition not very
different from those used in other recent shear theories.
The second equation is an extension of the original
shear cracking theory, and enables the lengths of shear
cracks to be related to the properties of the beam.
This is a type of equation that has not been used
previously. The third and final equation is the basic
failure criterion and very simply relates the ultimate
load to the strength of the uncracked zone of concrete,
in which failure occurs.
It is shown that there exists a number of
secondary modes of failure associated with shear
cracking; that the resistance of a beam to such
failures cannot be determined by the theory outlined
above, and is not in fact amenable to precise analysis.
Simple methods of dealing with such secondary modes
are given, in terms of safe limiting strengths and/
or detailing requirements.
The details of 25 tests are also presented.
The object of the tests was to investigate the effects
on shear strength of a number of quite normal types
of detailing for which little or no previous data was
available. In some eases the results are inconclusive,
but in general the behaviour of the beams was in agreement
with the predictions of the proposed theory.
In the form described, the theory constitutes a
relatively comprehensive and theoretically reasonable
method of analysis. Its accuracy and those of the
more accepted earlier theories are checked against a
very large number of test results, and it is shown
that the proposed method is more accurate and more
economical than the others.
Suggestions are made as to ways in which the range
of applicability of the theory could be extended, and
the work required to do this is discussed.
Although the theory is simpler to use than
previous analytical methods, and could be used by
a competent designer, it is more complex than some
empirical approaches - in particular it is more
complex than the recently published American design
recommendations. A final chapter is therefore
devoted to the development of very simple design
proposals suitable for inclusion in a Code of Practice.