Structural Concrete - Hassoun

268 Chapter 7 Development Length of Reinforcing Bars
The value of ψ e is 1.5 because the concrete cover is less than 3d b = 3 in. Check that
ψ t ψ e = 1.0(1.5) = 1.5 < 1.7 (Assuming k tr = 0).
2.
l d
= R s ψ t ψ e f y
d b 20λ √ (for bars > no. 7)
f c
′
= 0.89(1.0)(1.5)(60,000)
(20)(0.75) √ = 97.5in. say, 98in.
3000
3. The development length l d can be obtained from Table 7.2 (l d = 55 in. for no. 8 bars) and then
divided by the factor 0.75.
Example 7.3
A reinforced concrete column is reinforced with eight no. 10 bars, which should extend to the footing.
Determine the development length needed for the bars to extend down in the footing. Use normal-weight
concrete with f c ′ = 4ksi and f y = 60 ksi.
Solution
The development length in compression is
l dc = 0.02d b f y
λ √ f ′ c
≥ 0.0003d b f y
= 0.02(1.27)(60,000)
(1) √ = 24.1in. (controls)
4000
The minimum l dc is 0.0003(1.27)(60,000) = 22.86 in., but it cannot be less than 8 in. Because there
are no other multiplication factors, then l d = 24.1 in., or 25 in. (The same value is shown in Table 7.4.)
7.6 CRITICAL SECTIONS IN FLEXURAL MEMBERS
The critical sections for development of reinforcement in flexural members are
• At points of maximum stress
• At points where tension bars within the span are terminated or bent
• At the face of the support
• At points of inflection at which moment changes signs
The critical sections for a typical uniformly loaded continuous beam are shown in Fig. 7.6.
The sections and the relative development lengths are explained as follows:
1. Three sections are critical for the negative moment reinforcement:
Section 1 is at the face of the support, where the negative moment as well as stress is at
maximum values. The distance x 1 should be greater or equal the development length in
tension l d for all bars.
Section 2 is the section where part of the negative reinforcement bars are no longer needed
to resist negative moment and can be terminated. To develop full tensile force, the bars
should extend a distance x 2 before they can be terminated. Once parts of the bars are
terminated, the remaining bars develop maximum stress. The distance x 2 should be the
larger of d or 12 bar diameters.