Structural Concrete - Hassoun

7.3 Development Length in Tension 261
Figure 7.4 Examples of spalling of concrete cover. (a) High bottom cover, (b) wide
spacing, and (c) small bottom cover.
7.3 DEVELOPMENT LENGTH IN TENSION
7.3.1 Development Length, I d
If a steel bar is embedded in concrete, as shown in Fig. 7.2, and is subjected to a tension force T,
then this force will be resisted by the bond stress between the steel bar and the concrete. The
maximum tension force is equal to A s f y ,whereA s is the area of the steel bar. This force is resisted
by another internal force of magnitude U u Ol d ,whereU u is the ultimate average bond stress, l d is
the embedded length of the bar, and O is the perimeter of the bar (πD). The two forces must be
equal for equilibrium:
A s f y = U u Ol d and l d = A s f y
U u O
For a combination of bars,
l d =
A s f y
∑ (7.3)
U u O
The length l d is the minimum permissible anchorage length and is called the development length:
l d =
πd2 b f y
4U u (πd b ) = d b f y
(7.4)
4U u
where d b is the diameter of reinforcing bars.
This means that the development length is a function of the size and yield strength of the
reinforcing bars in addition to the ultimate bond stress, which in turn is a function of √ f c. ′ The bar
length l d given in Eq. 7.4 is called the development length, l d . The final development length should
also include the other factors mentioned in Section 7.1. Equation 7.4 may be written as follows:
( )
l fy
d
= K √ (7.5)
d b f
′
c
where K is a general factor that can be obtained from tests to include factors such as the bar characteristics
(bar size, spacing, epoxy coated or uncoated, location in concrete section, and bar splicing),
amount of transverse reinforcement, and the provision of excess reinforcement compared to that
required from design.
The ACI Code, Section 25.4.2.3, evaluated K as follows:
K =
( 3
40λ
) ( )
ψ t ψ e ψ s
( )
cb + K tr ∕db
(7.6)