Civil Engineering Reference
In-Depth Information
perimeter of the tube. This area is defined in terms of
A
oh
, which is the area enclosed by
the outermost closed hoops. Figure 15.12 illustrates this definition of
A
oh
for several beam
cross sections.
The value of
A
o
may be determined by analysis, or it may be taken as 0.85
A
oh
. The
term
represents the angle of the concrete “compression diagonals” in the analogous
space truss. It may not be smaller than 30
or larger than 60
, and it may be taken equal to
45
, according to ACI Section 11.6.3.6. In ACI Section 11.6.3.6, the value of
may be
45
for nonprestressed members, and that practice is followed herein. Suggested
values
for prestressed concrete are given in this same ACI section.
As given in the ACI Commentary (R11.6.3.8), the required stirrup areas for shear and
torsion are added together as follows for a two-legged stirrup:
A
v
t
s
A
v
2
A
t
Total
s
s
The spacing of transverse torsional reinforcing may not be larger than or 12 in.,
where
p
h
is the perimeter of the centerline of the outermost closed transverse reinforcing
(ACI 11.6.6.1). Remember also the maximum spacings of stirrups for shear
p
h
/8
d
2
d
4
and
given
in ACI Sections 11.5.4.1 and 11.5.4.3.
It has been found that reinforced concrete specimens with less than about 1% tor-
sional reinforcing by volume which are loaded in pure torsion fail as soon as torsional
cracking occurs. The percentage is smaller for members subject to both torsion and shear.
The equation to follow, which provides a minimum total area of longitudinal torsional re-
inforcing, is based on using about 0.5% torsional reinforcing by volume. In this expres-
sion,
A
cp
is the area enclosed by the outside concrete cross section. The value
A
t
/
s
may not
be taken as less than
25
b
w
/
f
yv
, according to ACI Section 11.6.5.3.
c
A
cp
f
yt
4
f
p
h
f
yv
A
t
s
A
min
(ACI Equation 11-24)
f
y
The longitudinal torsion reinforcement must be developed at both ends, states ACI
Section 11.6.4.3.
Maximum torsion generally acts at the ends of beams, and as a result the longitudi-
nal torsion bars should be anchored for their yield strength at the face of the supports.
To do this it may be necessary to use hooks or horizontal
-shaped bars lap spliced
with the longitudinal torsion reinforcing.
A rather common practice is to extend the
closed stirrup
A
oh
= shaded area
Figure 15.12
Values of
A
oh
.
