Shear and Diagonal Tension - Design of Reinforced Concrete - page 246

vertical cracks will occur. If moment and shear are both large, diagonal tension cracks
will occur at rather large angles from the vertical. This situation has been discussed in
Sections 8.1 through 8.11.
A short cantilever member having a ratio of clear span to depth ( a / d ) of 1.0 or less is
often called a bracket or corbel . One such member is shown in Figure 8.19. The shear
friction concept provides a convenient method for designing for cases where diagonal ten-
sion design is not applicable. The most common locations where shear friction design is
used are for brackets, corbels, and precast connections, but it may also be applied to the
interfaces between concretes cast at different times, to the interfaces between concrete
and steel sections, and so on.
When brackets or corbels or short, overhanging ends or precast connections support
heavy concentrated loads, they are subject to possible shear friction failures. The dashed
lines in Figure 8.19 show the probable locations of these failures. It will be noted that for
the end-bearing situations the cracks tend to occur at angles of about 20

from the direc-

tion of the force application.
Space is not taken in this chapter to provide an example of shear friction design, but a
few general remarks about them are presented. (In Section 12.13 of this text, a numerical
shear friction example is presented in relation to the transfer of horizontal forces at the
base of a column to a footing.) It is first assumed that a crack has occurred as shown by
the dashed lines of Figure 8.19. As slip begins to occur along the cracked surface, the
roughness of the concrete surfaces tends to cause the opposing faces of the concrete to
separate.
As the concrete separates, it is resisted by the tensile reinforcement ( A vf ) provided
across the crack. It is assumed that this steel is stretched until it yields. (An opening of the
crack of 0.01 in. will probably be sufficient to develop the yield strength of the bars.) The
clamping force developed in the bars A vf f y will provide a frictional resistance equal to
A vf f y

is the coefficient of friction (values of which are provided for different sit-
uations in Section 11.7.4.3 of the Code).

where

Figure 8.19 Possible shear friction failures.