es an elongation
of from 0.01 to 0.02 of 1%, corresponding to tensile stresses in the
steel of from 3,000 to 6,000 lb. per sq. in. At this stage plain
concrete would have reached its ultimate elongation. It is known,
however, that reinforced concrete, when well made, can sustain without
rupture much greater elongations; tests have shown that its ultimate
elongation may be as high as 0.1 of 1%, corresponding to tensions in
steel of 30,000 lb. per sq. in.

Reinforced concrete structures ordinarily show tensile cracks at very
much lower unit stresses in the steel. The main cause of these cracks is
as follows: Reinforced concrete setting in dry air undergoes
considerable shrinkage during the first few days, when it has very
little resistance. This tendency to shrink being opposed by the
reinforcement at a time when the concrete does not possess the necessary
strength or ductility, causes invisible cracks or planes of weakness in
the concrete. These cracks open and become visible at very low unit
stresses in the steel.

Increase the vertical loads, [Sigma] _P_, and the neutral surface will
rise and small tensile cracks will appear in the concrete below the
neutral surface (Fig. 8). These cracks are most numerous in the central
part of the span, where they are nearly vertical. They decrease in
number at the ends of the span, where they curve slightly away from the
perpendicular toward the center of the span. The formation of these
tensile cracks in the concrete relieves it at once of its highly
stressed condition.

It is impossible to predict the unit tension in the steel at which these
cracks begin to form. They can be detected, though not often visible,
when the unit tensions in the steel are as low as from 10,000 to 16,000
lb. per sq. in. As soon as the tensile cracks form, though invisible,
the neutral surface approaches the position in the beam assigned to it
by the common theory of flexure, with the tension in the concrete
neglected. The internal static conditions in the beam are now modified
to the extent that the concrete below the neutral surface is no longer
continuous. The common theory of flexure can no longer be used to
calculate the web stresses.

To analyze the internal static conditions developed, the speaker will
treat as a free body the shaded portion of the beam shown in Fig. 8,
which lies between two tensile cracks.

[Illustration: FIG. 9.]

In Fig. 9 are shown all the forces which act on this free