Civil Engineering Reference
In-Depth Information
calculating
l
1,
the measurements of
K
1
X
N
and
K
2
D
are to be made as usual;
but for calculating
l
3,
the part of the opening that lies outside the shear zone
(shown hatched) is to be ignored. Consequently, the centre C
1
of the opening
is to be determined for the remaining part which lies within the domain of
the shear zone (
Figure 3.12)
.
d) For openings located completely outside the shear zone, the beam may
be assumed to be one with solid web.
e) For larger dimensions of openings beyond the prescribed limits (i.e. for
a
1
x
>
X
N
/2
and
a
2
D
>0.6
D
/2, when values of
X
net
and
Y
net
will be found less
than half the width of the load bearing block) the minimum values for
X
net
and
Y
net
are to be taken as half the width of the load bearing block. In such
cases, the values for
l
3
are to be further reduced by the ratio of the
side (or sides) of the limited (admissible) dimensions to the exceeded side
(or sides) of the actual dimensions of the opening, as the case may be.
f) For marginal extensions of openings into the top and bottom 0.2
D
cover
regions (normally not advised), a procedure similar to that for an opening
partially outside the shear zone might be adopted for computing
l
1
and
l
1
and
l
3
.
3.10.2
Ultimate shear strength
Therefore, after knowing the values of
l
3
from Eqns (3.17)-(3.20),
the general equation for the ultimate shear strength of deep beams with web
openings can be written from Eqn (3.16) as:
l
1,
l
2
and
Q
u
(=
P
u
/2)=
P
c
(
l
1
).(
l
2
).(
l
3
)+
y
s
P
s
+
y
w
P
w
(3.21)
where, y
s
is an empirical coefficient=0.65 and y
w
is an empirical coefficient
=0.50.
The coefficient
y
s
reflects the levels of stress in the main steel, the
value of which was observed (Ray and Reddy, 1979; Ray 1980; 1982) to
be about 60-70% of the corresponding stress in the case of the companion
solid web beams just prior to failure. Further, ultimate strengths of beams
with web openings were found to vary (Ray and Reddy, 1979; Ray, 1980;
1982) within the range 40-90% of those of identical solid web beams.
Again, the coefficient
y
w
reflects the location of placement of web
reinforcement. In beams where the web steel is distributed over the full
depth, the value of
y
w
=0.50 is a reasonable factor. Moreover, from electrical
strain measurements in some typical beams (Ray, 1980, 1982) it was seen
that the steel strains in the neighbourhood of the openings were found to be
maximum. The strain variation of web steel can thus be approximated as
varying linearly from maximum near the opening to a minimum at the top or
bottom faces. This further justifies the stipulated value of
y
w.
Thus, knowing the geometric dimensions of the beam and the openings,
the loading arrangement and the material properties of concrete and steel,
Q
u
(=
P
u
/2) can be calculated easily from Eqn (3.21).
