Civil Engineering Reference
In-Depth Information
For hollow sections
V
u
b
w
d
T
u
p
h
1.7
A
oh
V
c
b
w
d
c
(ACI Equation 11-19)
8
f
Should the wall thickness of a hollow section be less than
A
oh
/
P
h
,
the second term in
T
u
p
h
/1.7
A
oh
ACI Equation 11-19 is to be taken not as
but as
T
u
/1.7
A
oh
, where
t
is the
thickness of the wall where stresses are being checked (ACI 11.6.3.3).
Another requirement given in ACI Section 11.6.4.4 for hollow sections is that the
distance from the centerline of the transverse torsion reinforcing to the inside face of the
wall must not be less than . In this expression,
p
h
is the perimeter of the center-
line of the outermost closed torsional reinforcing, while
A
oh
is the cross-sectional area of
the member that is enclosed within this centerline. The letters
oh
stand for
outside hoop
(of stirrups).
0.5
A
oh
/
p
h
15.7
DESIGN OF TORSIONAL REINFORCING
The torsional strength of reinforced concrete beams can be greatly increased by adding
torsional reinforcing consisting of closed stirrups and longitudinal bars. If the factored
torsional m
om
ent for a particular member is larger than the value given in ACI Section
11.6.1 , the Code provides an expression to compute the absolute mini-
mum area of transverse closed stirrups that may be used.
c
(
A
cp
/
P
h
)]
[
f
c
b
w
s
50
b
w
s
f
yv
(ACI Equation 11-23)
(
A
v
2
A
t
)
0.75
f
f
yv
In this expression,
A
v
is the area of reinforcing required for shear in a distance
s
(which represents the stirrup spacing). You will remember from shear design that the
area
A
v
obtained is for both legs of a two-legged stirrup (or for all legs of a four-legged
stirrup, etc.). The value
A
t
, which represents the area of the stirrups needed for torsion, is
for only one leg of the stirrup. Therefore the value
A
v
2
A
t
is the total area of both legs
of the stirrup (for two-legged stirrups) needed for shear plus torsion. It is considered de-
sirable to use equal volumes of steel in the stirrups and the added longitudinal steel so
that they will participate equally in resisting torsional moments. This theory was fol-
lowed in preparing the ACI equations used for selecting torsional reinforcing. The ACI
Code requires that the area of stirrups
A
t
used for resisting torsion be computed with the
equation that follows.
2
A
o
A
t
f
yv
s
T
n
cot
(ACI Equation 11-21)
This equation is usually written in the following form:
A
t
s
T
n
2
A
o
f
yv
cot
The transverse reinforcing is based on the torsional moment strength
T
n
, which equals
. The term
A
o
represents the gross area enclosed by the shear flow path around the
T
u
/
