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)

Shear failure of beams without shear reinforcement 199
Shear span a"
v €
I
-
v
v
-v
(b)
(a)
v
Diago~al ~~
tenSlOl'l./ .
v
0 1 ... 1
I-b-t
v
Diagonal
/ " crack
(e)
v
Fig. 6.2-1 Traditional concepts of shear and diagonal tension [1]
introduction to the concepts of diagonal tension and diagonal cracking,
does not give a whole picture of the actual behaviour. In fact, the type of
diagonal crack in Fig. 6.2-1(c), called a web-shear crack, occurs mainly in
prestressed concrete beams (see Chapter 9) and only rarely in reinforced
concrete beams. Of course, the behaviour of reinforced concrete beams
is much influenced by the shear stresses, but the trouble is that we do not
know how to calculate their values. In the earlier days it was usual to make
various assumptions (which were not justified) and to prove that, below the
neutral axis, v was everywhere equal to V/bz (b being the beam width
and z the lever-arm distance) and that, above the neutral axis, v varied
parabolically to zero at the compression face of the beam. It was realized
some years ago that things were not so simple. Even today, 'the
distribution of the shear stress across a flexurally cracked beam is not
understood and an accurate determination of the magnitude of v is
impossible' [1]; indeed, present-day designers no longer attempt to
calculate the actual value of the shear stress v. However, there are
advantages in retaining the concept of a nominal shear stress to be used as
some sort of stress coefficient in design. In current British design practice,
BS 8110 refers to this nominal shear stress as the design shear stress and
defines it as
(6.2-1)