Civil Engineering Reference
In-Depth Information
where
A
g
is the cross-sectional area of the concrete only and not including the hole(s), while
A
cp
is the area of the same hollow section including the hole(s). For solid sections,
A
g
=
A
cp
.
This very simple relation expressed by Equation (2.119) has been validated by tests.
In view of Equation (2.119), the ACI Code allows
A
cp
in Equation (2.118) for the threshold
torque to be replaced by
A
g
in the case of hollow sections. In Equation (2.117) for compatibility
torsion, however,
A
cp
is not allowed to be replaced by
A
g
in the case of hollow sections, because
of the lack of experimental studies and the lack of need for such an application.
2.3.4.3 Location of Torsional Steel in Shear Flow Zone
The internal torsional moment of a member is contributed by the circulatory shear stresses
acting along the centerline of shear flow (Figure 2.6). To be theoretically correct, the centroidal
line of the steel cage should be designed to coincide with the centerline of shear flow. Because
a steel cage is made up of hoop bars and longitudinal bars, the centroidal line of the steel
cage is best represented by the inner edge of the hoop bars, (Figure 2.16a, b). Define
c
as
the distance measured from the outer face of the cross-section to the inner edge of the hoop
bars. When the centerline of the steel cage defined by
c
lies in the middle of the shear flow
zone with a thickness
t
d
, then the theoretically correct case of design is
c
=
0.5
t
d
.If
t
d
is
taken conservatively as the maximum thickness,
t
d
,
max
=
0
.
8
A
c
/
p
c
in Equation (7.85) (Section
7.2.4, Chapter 7), then
c
p
c
.
In the case of a hollow beam as shown in Figure 2.16(b), the inner concrete cover measured
from the inside face of wall to the inner edge of hoop bars should also be 0.5
t
d
in theory. This
theoretical requirement of the inner concrete cover is replaced in the ACI Code by a provision
specifying that the distance from the inside face of wall to the centerline of the hoop bars
shall be not less than 0
=
0
.
4
A
c
/
.
5
A
oh
/
p
h
. This requirement is conservative because the thickness
t
d
=
p
h
represents the maximum thickness required to resist a maximum torque for the given
outer cross-section. It is obvious that this provision is intended for application to the hollow
section with one layer of hoop steel as shown in Figure 2.16(b), not to the inner cover of large
hollow cross-sections with two layers of hoop steel as shown in Figure 2.16(c).
A
oh
/
2.3.4.4 Box Sections with Outstanding Flanges
When the outstanding flanges of a box section are very thin compared with the height of the
section, the parameter
A
cp
/
p
cp
for the box section with flanges may be less than the same
parameter for the box section without flanges. This is conceptually wrong because the addition
of flanges is supposed to increase the torsional resistance. Physically, this inconsistency means
that the cross-section is not 'bulky' enough and that St. Venant torsional stresses, as expressed
by the parameter
A
cp
/
p
cp
, can not flow into the flanges. When this happens, the outstanding
flanges should be neglected in the calculation of the cross-sectional properties of
A
cp
,
A
g
and
p
cp
(see 'Check Outstanding Flanges' in the Design Example, Section 2.3.5).
2.3.4.5 Limitation of Angle
θ
to Prevent Excessive Cracking
deviates too much from 45
◦
, cracking will become excessive. In order to
control the crack widths, the ACI Code limits the range of
θ
When the angle
θ
to
30
◦
≤
θ
≤
60
◦
(2.120)
