Civil Engineering Reference
In-Depth Information
where
M
is the largest applied bending moment in the span,
f
y
is the
reinforcement characteristic strength,
g
m
the partial safety factor and z the
lever arm which is to be taken as follows:
z
=0.2(
l
+
2h
)
for 1<(
l/h
)<2
z
=0.6
l
for (
l/h)<
1
(1.15)
The two expressions show that in deep beams the lever arm varies at a lower
rate with the depth
h.
When the depth exceeds the span, the lever arm
becomes independent of the beam depth. The main longitudinal
reinforcement so calculated should extend without curtailment from one
support to the other and be adequately anchored at the ends. According to
the CEB-FIP Model Code, vertical hooks cause the development of cracks in
the anchorage zone and should be avoided. The required steel should be
distributed uniformly over a depth of (0.25
h
-0.05
l
) from the soffit of the
beam. The CEB-FIP Model Code recommends the use of small diameter
bars which are more efficient in limiting the width and development of
cracks under service loads and facilitate the anchorage at the supports.
1.5.2
Flexural strength: continuous deep beams
For continuous deep beams, the lever arm z is taken as:
z
=0.2(
l
+1.5
h
) for 1<
l/h
<2.5
z
=0.5
l
for
l/h<
1
The main longitudinal steel in the span should be detailed as for simply
supported beams. Over the support, half the steel should extend across the
full length of the adjacent span; the remaining half is stopped at 0.4
l
or 0.4
h
,
whichever is smaller, from the face of the support.
(1.16)
1.5.3
Shear strength and web reinforcement
The design shear strength should not exceed the lesser of
(1.17)
where
b
is the width,
h
is the beam depth, is the characteristic cylinder
strength of concrete and
g
m
is a partial safety factor for material.
The web reinforcement is provided in the form of a light mesh of
orthogonal reinforcement consisting of vertical stirrups and horizontal bars
placed near each face and surrounding the extreme vertical bars. The web
steel ratio should be about 0.20% in each direction near each face for
smooth round bars and 0.20% for high bond bars. Additional bars should be
provided near the supports, particularly in the horizontal direction.
The aim of the web reinforcement is mainly to limit the crack widths
which may be caused by the principal tensile stresses. For beams loaded at
the bottom edge, vertical stirrups are required to transmit the load into the
