Civil Engineering Reference
In-Depth Information
value of
A
s
, a new value of
a
can be computed and the cycle repeated. After two or three cycles, a
very good value of
a
will be obtained.
Assume
a
2
:
M
u
(12)(160,000)
A
s
1.78 in
2
.
d
a
2
21
2
2
f
y
(0.9)(60,000)
A
s
f
y
0.85
f
(1.78)(60,000)
(0.85)(3000)(16)
2.62
a
c
b
Assume
a
2.6
:
(12)(160,000)
1.80 in.
2
A
s
2.62
2
(0.9)(60,000)
21
(1.80)(60,000)
(0.85)(3000)(16)
2.65
a
(close enough)
4.6
BUNDLED BARS
Sometimes when large amounts of steel reinforcing are required in a beam or column, it is
very difficult to fit all the bars in the cross section. For such situations, groups of parallel
bars may be bundled together. Up to four bars can be bundled, provided they are enclosed
by stirrups or ties. The ACI Code (7.6.6.3) states that bars larger than #11 should not be
bundled in beams or girders. This is primarily because of crack control problems, a sub-
ject discussed in Chapter 6 of this text. That is, if the ACI crack control provisions are to
be met, bars larger than #11 cannot practically be used. The AASHTO permits the use of
2-, 3-, and 4-bar bundles for bars up through the #11 size. For bars larger than #11, how-
ever, AASHTO limits the bundles to two bars (AASHTO Sections 8.21.5 ASD and
5.10.3.1.5 strength design).
Typical configurations for 2-, 3-, and 4-bar bundles are shown in Figure 4.6. When
bundles of more than one bar deep vertically are used in the plane of bending, they may
not practically be hooked or bent as a unit. If end hooks are required, it is preferable to
stagger the hooks of the individual bars within the bundle.
Although the ACI permits the use of bundled bars, their use in the tension areas of
beams may very well be counterproductive because of the other applicable code restric-
tions that are brought into play as a result of their use.
When spacing limitations and cover requirements are based on bar sizes, the bun-
dled bars may be treated as a single bar for computation purposes; the diameter of the
fictitious bar is to be calculated from the total equivalent area of the group. When indi-
vidual bars in a bundle are cut off within the span of beams or girders, they should ter-
minate at different points. The Code (7.6.6.4) requires that there be a stagger of at least
40 bar diameters.
Figure 4.6
Bundled-bar arrangements.
