Structural Concrete - Hassoun

270 Chapter 7 Development Length of Reinforcing Bars
Section 3 is at the point of inflection. The bars shall extend a distance x 3 , which must be
equal to or greater than the effective depth, d, 12 bar diameters, or 1/16th the clear span,
whichever is greater. At least one-third of the total reinforcement provided for negative
moment at the support shall be extended a distance x 3 beyond the point of inflection,
according to the ACI Code, Sections 7.7.3.8 and 9.7.3.8.
2. Three sections are critical for positive moment reinforcement:
Section 4 is that of maximum positive moment and maximum stresses. The distance x 5
should be greater or equal the development length in tension l d for all bars.
Section 5 is where parts of the positive reinforcement bars are no longer needed to resist
positive moment and may be terminated. To develop full tensile force, the bars should
extend a distance x 6 . The remaining bars will have a maximum stress due to the termination
of part of the bars. The distance x 6 should be the larger of d or 12 bar diameters.
At the face of support, section 1, at least one-third the positive moment reinforcement
in simple members and one-fourth of the positive moment reinforcement in continuous
members shall extend along the same face of the member into the support. In beams
such reinforcement shall extend into the support 6 in. (ACI Code, Section 9.7.3.8.1).
At the face of support section 1, the bottom bars should extend a distance x 7 equal
to the development length for compression l dc when bottom bars used as compression
reinforcement (ACI Code, Section 18.4.2).
Section 6 is at the point of inflection. ACI Code, Sections 7.7.3.8.3 and 9.7.3.8.3, specifies
at simple supports and at points of inflection positive moment tension reinforcement
shall be limited to a diameter such that the l d computed for f y shall satisfy following
equation:
l d ≤ M n
+ l
V a (See Fig. 7.6b)
u
This equation needs not be satisfied for reinforcement terminating beyond centerline of simple
support by standard hook.
M n = is the nominal flexural strength of cross section (without the φ factor). M n is calculated assuming
all reinforcement at the section to be stressed to f y . M n is not the applied factored moment.
V u = is shear force calculated at the section. l a = At support, shall be the embedded length beyond
center of support
= At point of inflection, shall be limited to d or 12 bar diameters, whichever is greater.
l a
An increase of 30% in the value of M n /V u shall be permitted when the ends of the bars are
confined by a compressive reaction such as provided by a column below, but not when a beam
frames into a girder (Fig. 7.6a).
Example 7.4
A continuous beam has the bar details shown in Fig. 7.7. The bending moments for maximum positive
and negative moments are also shown. We must check the development lengths at all critical sections.
Given: f c ′ = 3ksi normal-weight concrete, f y = 40 ksi, b = 12 in., d = 18 in., and span L = 24 ft.
Solution
The critical sections are section 1 at the face of the support for tension and compression reinforcement;
sections 2 and 5 at points where tension bars are terminated within span; sections 3 and 6 at point of
inflection, and at midspan section 4.