Civil Engineering Reference
In-Depth Information
maximum steel
stress here
less than
ties or stirrup-ties
required
C
s
dh
2
2
"
A
C
e
less than
2
2
"
A
≥ 2"
Section A-A
Figure 7.14
Concrete cover per Section 12.5.4 of ACI Code.
C
e
is the clear cover over the end of
the hook, while
C
s
is the clear side cover of the hooked bar. For the situation shown, ties or stirrups
are required if both side cover and top (or bottom) cover are
2
2
in.
(b)
Ties or stirrups.
When hooks made of #11 or smaller bars are enclosed vertically
and horizontally within ties or stirrup ties along their full development length
dh
and
the stirrups or ties are spaced no farther apart than 3
d
b
(where
d
b
is the diameter of
the hooked bar), multiply by 0.8. This situation is shown in Figure 7.14. (Detailed
dimensions are given for stirrup and tie hooks in Section 7.1.3 of the ACI Code.)
(c)
When 180
hooks consisting of #11 or smaller bars are used and are enclosed within
ties or stirrups placed perpendicular to the bars being developed and spaced no fur-
ther than 3
d
apart along the development length
dh
of the hook, multiply by 0.8.
(d)
Should anchorage or development length not be specially required for
f
y
of the
bars, it is permissible to multiply
dh
by
A
s
required/
A
s
provided.
The danger of a concrete splitting failure is quite high if both the side cover (perpendicu-
lar to the hook) and the top and bottom cover (in the plane of the hook) are small. The Code
(12.5.4), therefore, states that when standard hooks with less than in. side and top or bot-
tom cover are used at discontinuous ends of members, the hooks shall be enclosed within ties
or stirrups spaced no farther than 3
d
b
for the full development length
2
2
dh
. The first tie or stir-
rup must enclose the bent part of the hook within a distance of 2
d
bh
of the outside of the bend.
Furthermore, the modification factor of 0.8 of items (b) and (c) herein shall not be applicable.
Example 7.6, which follows, illustrates the calculations necessary to determine the
development lengths required for the tensile bars of a cantilever beam. The lengths for
straight or hooked bars are determined.
EXAMPLE 7.6
Determine the development or embedment length required for the epoxy-coated bars of the beam
shown in Figure 7.15.
(a)
If the bars are straight, assuming
K
tr
0.
(b)
If a 180
hook is used.
(c)
If a 90
hook is used.
c
The six #9 bars shown are considered to be top bars.
f
4000 psi and
f
y
60,000 psi.
