F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

204 Shear, band and tarsian
(f)
ately weaker than smaller beams. This is probably because in practice
the aggregate-interlock capacity does not increase in the same
proportion as the beam size. The design shear stress values in Table
6.4-1 allow for the influence of the effective depth d.
the effective shear-span/ depth ratio (M/ V d). The ultimate shear stress
at a beam section increases rapidly as the M/Vd ratio [2] is reduced
below about 2, where M is the bending moment, V the shear force,
and d the effective depth; this is true for both distributed loading or
concentrated loading. For two-point loading, as in Fig. 6.2-1(a), the
critical (i.e. the largest) M/Vd ratio occurs at the loading point, where
M/Vd = avid.
A broad overview of the shear failure of reinforced concrete beams has
been given above. As stated at the beginning of this chapter, shear is a
controversial topic; new and potentially far-reaching concepts are continually
being developed. Interested readers are recommended to study the
latest papers by Kotsovos [3, 4], Regan [5] and Hsu [6], for example.
6.3 Effects of shear reinforcement
Referring to Fig. 6.2-1(a), the shear strength of the beam may be
substantially increased by the suitable provision of shear reinforcement,
or web reinforcement as it is of ten called; more important, such shear
reinforcement increases the ductility of the beam and considerably reduces
the likelihood of a sudden and catastrophic failure, which of ten occurs in
beams without shear reinforcement.
Stirrups or links (Fig. 6.3-1) are the most common type of web
reinforcement, though they are sometimes used in combination with bentup
bars (Fig. 6.3-2). Before diagonal cracking, the extern al shear force V
produces practically no stress in the web reinforcement. When the diagonal
crack forms, any web bar which intercepts the diagonal crack would
suddenly carry a portion of the shear force V; web bars not intercepting
the diagonal crack remain essentially unstressed. The mechanism of shear
transfer is shown in Fig. 6.3-3, in which the meanings of the symbols are
similar to those in Fig. 6.2-5, namely, V cz is the shear carried by the
uncracked concrete compression zone, Va that by aggregate interlock
across the diagonal crack, and V d that carried by the dowel act ion of the
l J
I
1
j
o
1
I
Fig. 6.3-1 Links or stirrups