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 = 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

V
v = -------------                     (2)
K b d

In this equation K b d represents the concrete area in compression.  The value of K is approximately equal to 0.4.

Three large concrete beams with web reinforcement, tested at the University of Illinois[K], developed an average maximum shearing resistance of 215 lb. per sq. in., computed by Equation 1.  Equation 2 would give 470 lb. per sq. in.

Three T-beams, having 32 by 3-1/4-in. flanges and 8-in. webs, tested at the University of Illinois, had maximum shearing resistances of 585, 605, and 370 lb. per. sq. in., respectively.[L] They did not fail in shear, although they appeared to develop maximum shearing stresses which were almost three times as high as those in the rectangular beams mentioned.  The concrete and web reinforcement being identical, the discrepancy must be somewhere else.  Based on a non-continuous concrete web, the shearing resistances become 385, 400, and 244 lb. per sq. in., respectively.  As none of these failed in shear, the ultimate shearing resistance of concrete must be considerably higher than any of the values given.

About thirteen years ago, Professor A. Vierendeel[M] developed the theory of open-web girder construction.  By an open-web girder, the speaker means a girder which has a lower and upper chord connected by verticals.  Several girders of this type, far exceeding solid girders in length, have been built.  The theory of the open-web girder, assuming the verticals to be hinged at their lower ends, applies to the concrete beam reinforced with stirrups.  Assuming that the spaces between the verticals of the girder become continually narrower, they become the tension cracks of the concrete beam.[N]