Civil Engineering Reference
In-Depth Information
2.3.4 Other Design Considerations
2.3.4.1 Compatibility Torsion
In the case of compatibility torsion, where a torsional moment in a statically indeterminate
structure can be redistributed to other adjoining members after the formation of a plastic hinge,
the ACI code allows the torsional moment to be reduced to the cracking torsional moment
under combined loadings. For nonprestressed members, the cracking torque of solid sections
subjected to combined torsion, shear and bending
T
cr
has been suggested by Hsu and Burton
(1974) and Hsu and Hwang (1977):
33
f
c
(MPa)
A
cp
p
cp
4
f
c
(psi)
A
cp
p
cp
T
cr
=
0
.
or
(2.116)
where
f
c
and
f
c
have the same stress units (MPa or psi). Detailed derivation of the cracking
torsional moment (Equation 2.116), is given in Section 7.2.5 (Chapter 7).
In the case of prestressed concrete, however, the expression on the right-hand side of
Equation (2.116) must be multiplied by a factor which reflects the increase of cracking
strength by the longitudinal prestress. Using the well-known square-root factor derived from
either the Mohr stress circle (Hsu, 1984) or from the skew bending theory (Hsu, 1968b), the
cracking torsional moment of solid prestressed members is expressed as follows:
1
A
cp
p
cp
33
f
c
f
pc
T
u
=
φ
T
cr
=
φ
0
.
(MPa)
+
33
f
c
(2.117)
0
.
where
f
pc
in the square-root factor is the compressive stress of concrete at the centroid of
cross-section due to effective prestress after allowing for all losses, or at the junction of web and
flange when the centroid lies within the flange. In the case of nonprestressed solid members,
f
pc
=
0 and the square-root factor becomes unity.
2.3.4.2 Threshold Torque
In order to simplify the design processes, the ACI Code allows a small torsional moment in a
structure to be neglected. The limit of this small torsional moment was taken for solid sections
as 25% of the cracking torque, Equation (2.117), which results in:
1
083
f
c
(MPa)
A
cp
p
cp
f
pc
T
u
=
φ
0
.
+
33
f
c
(2.118)
0
.
In the case of hollow sections, Mattock (1995) suggested a simple relationship between the
cracking torque of a hollow section (
T
cr
)
hollow
and that of a solid section with the same outer
dimensions (
T
cr
)
solid
:
(
T
cr
)
hollow
(
T
cr
)
solid
=
A
g
A
cp
(2.119)
