reinforcement." To appreciate the way in which
the two materials interact it is necessary to
visualise the distribution of stress which
occurs within a beam when a bending-type
load is applied.
The distribution of stress within a beam of
any material depends on the configuration of
the applied load. The action of a uniformly
distributed load is to bend the beam
downwards and cause tensile stress to be set
up in the lower half of the cross-section and
compressive stress in the upper half. The exact
distribution of the stress is complex but a way
of visualising it is shown in Fig. 4.31.
In Fig. 4.31a a series of circles has been
drawn on the side of the beam. Following the
application of the load these change their
shape to become ellipses (Fig. 4.31b). The
minor and major axes of the ellipses coincide
with the directions of maximum compression
and tension at each location. This allows the
directions of the maximum tensile and
compressive stresses (the principal stresses) to
be plotted (Fig. 4.31c). Thus, at mid-span the
direction of stress is parallel to that of the
beam. Towards the ends of the beam the direc-
tion of the tensile and compressive stresses
become progressively more inclined to the axis
of the beam and the tensile and compressive
stress lines cross each other. The material in
these regions is stressed simultaneously in
tension and compression in two orthogonal
directions.
The diagram of principal stresses (Fig. 4.31c)
shows only the directions of maximum tension
and compression. The magnitudes of the
stresses vary along each line from a maximum
at the mid-span position, where they are paral-
lel to the axis of the beam, to zero where the
curved portions of the lines approach the top
or bottom of the beam. The magnitudes of the
stresses also vary between lines. They are
greatest in the lines which run closest to the
Fig. 4.31 The pattern of stresses in a beam. Circles
drawn on the side of an unloaded beam (a) become
ellipses as a result of the strain caused by the load (b).
This gives an indication of the directions of maximum
tension and compression at every location and allows
principal stress lines to be drawn (c). The magnitude of the
stress varies along each principal stress line from zero at
the point at which it crosses the top or bottom surface of
the beam to a maximum at the mid-span position. The
magnitude of stress also varies between different lines
with those closest to the top and bottom surfaces at the
mid-span position carrying the greatest stress.top and bottom of the beam at mid-span and
decrease towards the interior of the beam.
The highest levels of stress occur on the
cross-section at the mid-span point. The stress
is tensile in the lower half of the cross-section
and compressive in the upper half. Its magni-
tude varies from a maximum tensile stress at
the lower extreme fibre to maximum compres-
sive stress at the upper extreme fibre with zero
stress half-way up at what is called the neutral
axis. 12711 In complex reinforced concrete elements compression
reinforcement is also provided.Reinforced concrete structures(b)(a)(c)Compression
Tension