Civil Engineering Reference
In-Depth Information
studying this information, the reader probably will be pleased to find at the end of this
section a discussion of simplified design office practices for determining bar lengths.
Positive-Moment Reinforcement
Section 12.11 of the Code provides several detailed requirements for the lengths of positive-
moment reinforcement. These are briefly summarized in the following paragraphs.
1.
At least one-third of the positive steel in simple beams and one-fourth of the posi-
tive steel in continuous members must extend uninterrupted along the same face
of the member at least 6 in. in the support (12.11.1). The purpose of this require-
ment is to make sure that the moment resistance of a beam will not be reduced
excessively in parts of beams where the moments may be changed due to settle-
ments, lateral loads, and so on.
2.
The positive reinforcement required in the preceding paragraph must,
if the mem-
ber is part of a primary lateral load resisting system
, be extended into the support
a sufficient distance to develop the yield stress in tension of the bars at the face of
the support. This requirement is included by the Code (12.11.2) to assure a ductile
response to severe overstress as might occur with moment reversal during an
earthquake or explosion. As a result of this requirement, it is necessary to have
bottom bars lapped at interior supports and to use additional embedment lengths
and hooks at exterior supports.
3.
Section 12.11.3 of the Code says that at simple supports and at points of inflec-
tion, the positive-moment tension bars must have their diameters limited to certain
maximum sizes. The purpose of the limitation is to keep bond stresses within rea-
son at these points of low moments and large shears. (It is to be remembered that
when bar diameters are smaller, the bars have greater surface area in proportion to
their cross-sectional areas. Thus for bonding to concrete, the larger the bars' diam-
eters the larger must be their development lengths. This fact is reflected in the ex-
pressions for
d
.) It has not been shown that long anchorage lengths are fully
effective in developing bars in a short distance between a P.I. and a point of maxi-
mum bar stress, a condition that might occur in heavily loaded short beams with
large bottom bars. It is specified that
d
as computed by the requirements pre-
sented in Chapter 7 may not exceed the following:
M
n
d
V
u
a
(ACI Equation 12-3)
In this expression,
M
n
is the computed theoretical flexural strength of the member if
all reinforcing in that part of the beam is assumed stressed to
f
y
and
V
u
is the factored
shear at the section. At a support,
a
is equal to the sum of the embedment length beyond
the
L
of the support and the equivalent embedment length of any furnished hooks or me-
chanical anchorage. (Mechanical anchorage, which is permitted in Section 12.6.3 of the
Code, consists of bars or plates or angles or other pieces welded or otherwise attached
transversely to the flexural bars in locations where sufficient anchorage length is not
available.) At a point of inflection,
a
is equal to the larger of the effective depth of the
member or 12
d
(ACI 12.11.3). When the ends of the reinforcement are confined by a
