Civil Engineering Reference
In-Depth Information
h
f
h
w
h
w
≤
4
h
f
h
w
≤
4
h
f
Figure 15.11
Portions of monolithic T beam that
may be used for torsion calculations.
For statically indeterminate structures where reductions in torsional moments can
occur due to redistribution of internal forces, Section 11.6.2.2 of the ACI Code permits
the maximum factored torsional moment to be reduced to the following value:
A
cp
p
cp
c
4
f
In other words, the applied torque may be limited to a member's calculated cracking
moment. (If the computed torque for a particular member is larger than the above value,
the above value may be used in design.) Should the torsional moments be reduced as de-
scribed here, it will be necessary to redistribute these moments to adjoining members. The
ACI Commentary (R11.6.2.1 and R11.6.2.2) does say that when the layout of structures is
such as to impose significant torsional rotations within a short length of a member (as
where a large torque is located near a stiff column), a more exact analysis should be used.
For isolated members with or without flanges,
A
cp
equals the area of the entire cross
sections (including the area of any voids in hollow members) and
p
cp
represents the
perimeters of the entire cross sections. Should a beam be cast monolithically with a slab,
the values of
A
cp
and
p
cp
may be assumed to include part of the adjacent slabs of the re-
sulting T- or L-shaped sections. The widths of the slabs that may be included as parts of
the beams are described in ACI Section 13.2.4 and illustrated in Figure 15.11. Those
widths or extensions may not exceed the projections of the beams above or below the slab
or four times the slab thickness, whichever is smaller.
When appreciable torsion is present, it may be more economical to select a larger
beam than would normally be selected so that torsion reinforcing does not have to be
used. Such a beam may very well be more economical than a smaller one with the closed
stirrups and additional longitudinal steel required for torsion design.
On other occasions
such a practice may not be economical, and sometimes architectural considerations may
dictate the use of smaller sections.
15.6
TORSIONAL MOMENT STRENGTH
The sizes of members subject to shear and torsion are limited by the ACI Code so that un-
sightly cracking is reduced and crushing of the surface concrete caused by inclined com-
pression stresses is prevented. This objective is accomplished with the equations that
follow, in which the left-hand portions represent the shear stresses due to shear and tor-
sion. The sum of these two str
es
ses in a particular member may not exceed the stres
s
that
will cause shear cracking ( as per ACI R11.6.3). In these expressions,
V
c
(ACI Equation 11-3). For solid sections
c
c
b
w
d
8
f
2
f
V
u
b
w
d
T
u
p
h
1.7
A
oh
V
c
b
w
d
2
2
c
8
f
(ACI Equation 11-18)
