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 Δ 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, Δ 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:
| (1) |
Where d is the distance from the center of the reinforcing bars to the surface of the beam in compression:
b = the width of the flange, and
V = the total vertical shear at the section.
This equation gives very erratic results, because it is based on a continuous web. For a non-continuous web, it should be modified to