Civil Engineering Reference
In-Depth Information
distributed loading, the critical section is taken as 0.15
l
o
from the face of the
support; for a concentrated load, it is taken as half way between the load and
the face of the support. The shear reinforcement required at the critical
section shall be used throughout the span.
The design is based on:
V
u
<φ
V
n
V
n
=V
c
+V
s
(1.21)
(1.22)
where
V
u
is the design shear force at the critical section (lb),
V
n
is the
nominal shear strength (lb) (Eqn (1.22)) and φ is the capacity reduction
factor for shear, taken as 0.85,
V
c
is the shear strength provided by concrete
(lb) and
V
s
is the shear strength provided by steel (lb). The nominal shear
strength
V
n
should not exceed the following:
(1.23a)
(1.23b)
where ƒ'
c
is the concrete cylinder compressive strength (lb/in
2
),
b
is the
beam width (in) and
d
is the effective depth (in).
The shear provided by concrete is calculated from:
(1.24)
where
M
u
is the design bending moment (lb-in) which occurs simultaneously
with
V
u
at the critical section and ρ is the ratio of the main steel area to the
area of the concrete section (ρ
=A
s
/bd).
The second term on the right-hand side of Eqn (1.24) is the concrete
shear strength for normal beams, given in ACI(318-83) (revised 1986). The
first term on the right-hand side is a multiplier to allow for strength increase
in deep beams, subject to the restrictions that follow:
[3.5-2.5(
M
u
/V
u
d
)]<2.5
(1.25)
(1.26)
In the case where
V
u
exceeds φ
V
c,
a system of orthogonal shear
reinforcement must be provided to carry the excess shear. The contribution
V
s
of shear reinforcement is given by:
(1.27)
Combining between equations (1.21), (1.22) and (1.27) gives
(1.28)
