Civil Engineering Reference
In-Depth Information
Figure 2.16
Various cross sections
2.3.1.2 Torsional Longitudinal Steel
The torsional longitudinal steel can be designed according to Equation (2.47) assuming yield-
ing of steel,
f
=
f
y
, where
f
y
is yield strength of longitudinal torsional reinforcement.
However, a more convenient equation relating the torsional longitudinal steel to the torsional
transverse steel can be derived by equating Equation (2.47) to Equation (2.48). Noticing in
Equation (2.47) that
N
=
A
f
y
, where
A
is now defined as the total area of torsional lon-
gitudinal steel in the cross-section. Also assuming that
p
o
=
p
h
, where
p
h
is defined as the
perimeter of the centerline of the outermost hoop bars, we derive the ACI equation:
A
t
s
p
h
f
yt
f
y
cot
2
A
=
θ
(2.104)
The angle
θ
is the same one used for transverse torsional steel in Equation (2.99).
2.3.1.3 Minimum Longitudinal Torsional Steel
In order to avoid a brittle torsional failure, a minimum amount of torsional reinforcement
(including both transverse and longitudinal steel) is required in a member subjected to torsion.
The basic criterion for determining this minimum torsional reinforcement is to equate the
post-cracking strength
T
n
to the cracking strength
T
cr
. The formula derived by Hsu (1997) is:
42
f
c
(
MPa
)
A
g
f
y
A
t
s
p
h
0
.
f
yt
f
y
A
,
min
=
−
(2.105)
where
A
,
min
is the total area of minimum longitudinal steel;
A
g
is the cross-sectional area of
the hollow section, considering only the concrete and not including the hole(s).
A
g
becomes
A
cp
for solid sections, where
A
cp
is the area of the same hollow section including the hole(s).
Detailed derivation of Equation (2.105) is given in Section 7.2.6 (Chapter 7).
