Civil Engineering Reference
In-Depth Information
where
A
v
is the area (in
2
) of vertical web reinforcement within a spacing
s
v,
A
h
is the area (in
2
) of horizontal web reinforcement within a spacing
s
h,
f
y
is
the strength of the web steel which should not be taken as more than 60 000
lb/in
2
(410N/mm
2
),
s
v
is the spacing (in) of the vertical web bars—which
must exceed neither
d/
5 nor 18 in—and
s
h
is the spacing (in) of the
horizontal web bars—which must exceed neither
d/
3 nor 18 in.
The orthogonal mesh provided must satisfy not only Eqn (1.28) but also
the minimum web reinforcement requirement of Section 1.6.1.1.
In (Eqn 1.28.) the quantities (1+
l
o
/d
)/12 and (11
-l
o
/d)/
12 represent
weighting factors for the relative effectiveness of the vertical and horizontal
web bars. ACI Code 318-83 (revised 1986) rightly considers that horizontal
web reinforcement is more effective than vertical web reinforcement (Kong
and Robins, 1971; Kong and Singh, 1972). At the limiting
l
o
/d
ratio of 5,
quoted in Section 1.6.2, the weighting factors (1
+l
o
/d
)
/
12 and (11
-l
o
/
d
)/12
are equal. As the
l
o
/d
ratio decreases, horizontal web bars become
increasingly more effective compared with vertical web bars.
1.6.2.2
Shear strength: continuous deep beams
Calculations for continuous
deep beams, unlike those for simply supported ones, are not based on the
design shear force at the critical section as defined in Section 1.6.2.1.
Instead, the shear reinforcement at any section is calculated from the design
shear force
V
u
at that section. The design is based on Eqn (1.29) and (1.30).
(1.29)
V
u
<
φ
V
n
V
n
=
V
c
+
V
s
(1.30)
where
φ
,
V
n,
V
c
and
V
s
are as defined for Eqns (1.21) and (1.22). The
nominal shear strength
V
n
is subject to the same limits as imposed by Eqn
(1.23a, b). However, for continuous deep beams, the concrete nominal shear
strength
V
c
is to be taken as the least value given by Eqns (1.31a-c):
(1.31a)
(1.31b)
(1.31c)
where
M
u
is the design moment occurring simultaneously with
V
u
at the
section considered (lb-in); p is the main steel ratio
A
s
/bd; f '
c
is the concrete
cylinder strength (lb/in
2
).
Where
V
u
exceeds 0.5φ
V
c,
vertical shear reinforcement should be provided
to satisfy the condition:
(
A
v
/bs
v
)
>
(50/
f
y
)
(1.32)
