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.

Sufficient attention has not been paid to the proper anchorage of the
upper ends of the stirrups. They should extend well into the compression
area of the beam, where they should be properly anchored. They should
not be too near the surface of the beam. They must not be too far apart,
and they must be of sufficient cross-section to develop the necessary
tensile forces at not excessive unit stresses. A working tension in the
stirrups which is too high, will produce a local disintegration of the
cantilevers, and give the beam the appearance of failure due to diagonal
tension. Their distribution should follow closely that of the vertical
or horizontal shear in the beam. Practice must rely on experiment for
data as to the size and distribution of stirrups for maximum efficiency.

The maximum shearing stress in a concrete beam is commonly computed by
the equation:

_V_
_v_ = ------------- (1)
7
--- _b_ _d_
8

Where _d_ is the distance from the center of the reinforcing bars to the
surface of the beam in compression:

_b_ = t