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 body, C b b’
C’.

At any section, let

C or C’ represent the total concrete compression; T or T’ represent the total steel tension; J or J’ represent the total vertical shear; P represent the total vertical load for the length, b — b’;

and let [Delta] T = T’ — T = C’ — C represent the total transverse shear for the length, b — b’.

Assuming that the tension cracks extend to the neutral surface, n n, that portion of the beam C b b’ C’, acts as a cantilever fixed at a b and a’ b’, and subjected to the unbalanced steel tension, [Delta] T.  The vertical shear, J, is carried mainly by the concrete above the neutral surface, very little of it being carried by the steel reinforcement.  In the case of plain webs, the tension cracks are the forerunners of the sudden so-called diagonal tension failures produced by the snapping off, below the neutral surface, of the concrete cantilevers.  The logical method of reinforcing these cantilevers is by inserting vertical steel in the tension side.  The vertical reinforcement, to be efficient, must be well anchored, both in the top and in the bottom of the beam.  Experience has solved the problem of doing this by the use of vertical steel in the form of stirrups, that is, U-shaped rods.  The horizontal reinforcement rests in the bottom of the U.