Civil Engineering Reference
In-Depth Information
Y
net
=(0.6
D-a
2
D
)
In the case of a circular opening these measurements are made with
reference to the equivalent square opening, the side of which is equal to the
diameter of the circular opening.
and
(3.2)
3.9
Criterion of failure and strength theory
From the mode of failure shown in
Figures 3.2,
3.3
and
3.5
for beams with
web openings and in Figure 3.8 for a beam without web opening, it is clear
that the failure along the critical diagonal path is by sliding. This particular
mode of failure can be interpreted in terms of Coulomb's internal friction
theory and Mohr's generalised failure criterion with straight line envelopes,
combined as used by Guralnick (1959) in the case of an ordinary reinforced
concrete beam,
Figure 3.9.
By this, two independent physical properties of
concrete, namely cylinder compressive strength
f'
C
and cylinder splitting
tensile strength
f'
t
are accounted for. The ratio
f'
t
/f '
C
varies widely (from
about 1/8 to 1/16) with the quality of concrete. In absence of any practical
test data, adoption of a suitable ratio for
f'
t
/f '
C
may be erratic. Therefore, it is
advisable that the parameters
f'
C
and
f'
t
to be used for deep beams be
determined by independent tests.
Figure 3.8
Crack patterns at failure of a typical deep beam with solid web (under two-point
loading).
