Learn how to calculate the reinforcement development length required in both tension and compression according to AS3600.
Introduction
What is the development length?
In reinforced concrete design, for strength limit states the Australian Standard specifies a minimum length called the development length \(L_{sy.t}\) over which a straight bar in tension is to be embedded in the concrete in order to develop the yield stress in the bar. In other words, it is the length required to fully transfer stress from the bar to the concrete by bond.
.png)
Common applications for development lengths are:
- to lap bars, since bar lengths are limited for transportation
- to transfer stresses developed in one section to adjoining sections (e.g. slab-to-column, beam-to-column)
If the development length is not met, the capacity of the concrete section is reduced in proportion to the lack of full development.
.png)
left) beam-to-column
right) column-to-footing
What is the difference between development, lap and anchorage lengths?
You may be familiar with the terms lap length \(L_{sy.t.lap}\) or anchorage length, which are provisions in excess of the development length. The lap length is used for bars being lapped (called a lapped slice), while the anchorage length is to ensure anchorage or bond failure does not occur before the design strength at a critical section is achieved.
Does the development vary for bars in tension vs compression?
The development length varies for bars in tension and compression. When in tension, the bar experiences bond stresses as it tries to pull out. When in compression, the end of the bar is bearing against the concrete and part of the bearing stresses are transferred as compression. Hence, the required development length of a bar in tension is longer.
When the bar is experiencing a force, the deformations (threads) on the bar bear on the surrounding concrete, see image (a) above. This exerts an outward radial force, causing tensile stresses in the surrounding concrete, see images (b) and (c), which may lead to splitting cracks if the tensile strength of concrete is exceeded, see image (d). Achieving minimum reinforcement development length aids in reducing the occurrence of these cracks, which could cause failure. For bars in compression, the reduction in bond stress caused by flexure and tension doesn't occur. Hence, the required development length is shorter for bars in compression.
Calculating the Development Length
AS3600-2018 Section 13 prescribes how to calculate the reinforcement development length.
\( \bf{1.} \) Basic Tensile Development Length
As per Clause 13.1.2.2, the basic development length, \( L_{sy.tb} \) of a bar is given by:
$$ L_{sy.tb}=\dfrac{0.5k_1k_3f_{sy}d_b}{k_2\sqrt{f'_c}}\geq0.058f_{sy}k_1d_b $$
Where:
\( \rlap{k_1}\hspace{2.5em}= 1.3 \) for a horizontal bar with more than 300mm of concrete cast below of the bar, otherwise \( k_1 = 1 \). This accounts for reduction in bond strength due to accumulation of bleed water along the bar's underside when there is a considerable depth of concrete cast below
\( \rlap{k_2}\hspace{2.5em}= (132 - d_b)/100 \)
\( \rlap{k_3}\hspace{2.5em}= 1.0 - 0.15(c_d -d_b)/d_b \) within limits of \( 0.7\leq k_3 \leq 1.0 \)
\( \rlap{d_b}\hspace{2.5em} \): diameter of the developing bar
\( \rlap{c_d}\hspace{2.5em} \): effective cover, which as per Figure 13.1.2.2, differs depending on the reinforcement shape, spacing and cover.
The value of \( L_{sy.tb} \) calculated from above should be multiplied by:
1.5 if bars are epoxy-coated, coating around bars increase durability by protecting it against corrosion but reduces bonding strength to concrete
1.3 when lightweight concrete is used, mechanical properties of lightweight concrete are weaker than normal weight concrete
\( \textbf{2.} \) Refined Tensile Development Length - AS3600 Cl. 13.1.2.3
The development length \( L_{sy.t} \) may be taken as the basic development length or may be refined to include the beneficial effects of confinements by transverse reinforcement. As per Clause 13.1.2.3, this refined development length is given by:
$$ L_{sy.t}=k_4k_5L_{sy.tb}\hspace{0.2cm} \text{for } \hspace{0.2cm}k_3k_4k_5 \leq0.7 $$
The reduction depends on the following factors:
\( \rlap{k_4}\hspace{2.5em}= 1.0 - K\lambda \)
\( \rlap{k_5}\hspace{2.5em}= 1.0 - 0.04\rho_p \)
Where:
\( \rlap{K}\hspace{3.0em} \): factor that accounts for the effectiveness of transverse reinforcement (shear fitments) in controlling splitting cracks along a development length.
\( \rlap{\rho_p}\hspace{3.0em} \): stress in the transverse reinforcement around the bar being developed. As the transverse stress, \( p_p \) increases, it delays the formation of splitting cracks and thereby increases bond stress within the development length
\( \rlap{A_{tr}}\hspace{3.0em} \): area of the provided shear reinforcement
\( \rlap{A_{tr.min}}\hspace{3.0em} \): area of the minimum shear reinforcement
\( \rlap{A_s}\hspace{3.0em} \): area of the developing bar
\( \rlap{K}\hspace{2.5em} = 0.05 \times (1+n_f/n_{bs}) \leq 0.10 \), where values of \( K \), \( n_f \) and \( n_{bs} \) are provided in Table 13.1.2.3 for typicla fitment arrangements.
\( \rlap{\lambda}\hspace{2.5em} = (\Sigma A_{tr} - \Sigma A_{tr.,min}) / A_s \geq 0 \)
\( \textbf{3.} \) Additional Provisions for Tensile Development Length
\( \textbf{3.1.} \) Developing to less than Yield Strength
As per Clause 13.1.2.4, the development length may be reduced by the ratio of the actual stress in the reinforcement \( \sigma_{st} \) and the yield strength \( f_{sy} \) if the full yield strength is not required.
$$ L_{st} = L_{sy.t} \frac{\sigma_{st}}{f_{sy}} \geq 12d_b $$
\( \textbf{3.2.} \) Plain Bars
As per Clause 13.1.3, the development length of a plain bar in tension is taken as 50% longer than basic development length but no less than 300mm.
$$ 1.5 \times L_{sy.tb} \geq 300\text{ mm} $$
\( \textbf{3.3.} \) Hooked or Cogged Bars
A standard hook or cog is considered to provide just over 50% of the development length to a bar.
As per Clause 13.1.2.6 and 13.1.2.7, if a deformed bar ends in a hook or a hog, then the tensile development length of the bar is taken as \( 0.5L_{st} \) where \( L_{st} \) is the reduced lap length calculated using the actual stress in the bar. If a plain bar ends in a hook or a hog, then the tensile development length is taken as \( 0.5L_{sy.t} \) or \( 0.5L_{st} \).
For hooked or cogged bars, its length \( L \) as per figure below, and bend diameter \( d_p \) must meet minimum dimensions to be considered effective in providing anchorage. Table C13.1.2.7 in AS3600 Commentary provides the minimum dimensions table for bars bent at different angles.
\( \textbf{4.} \) Basic Compressive Development Length
The development length of bars in compression are much simpler to calculate than bars in tension. As per Clause 13.1.5.1, the basic development length for a bar in compression, \( L_{sy.cb} \) is given by:
$$ L_{sy.cb} = \frac{0.22f_{sy}}{\sqrt{f'_c}}d_b \geq 0.0435f_{sy}d_b \space\space\text{or}\space\space\text{200mm} $$
\( \textbf{5.} \) Refined Compressive Development Length
Again the development length may be taken as the basic development length or may be refined to include the beneficial effects of confinements by transverse reinforcement. As per Clause 13.1.5.4, this refined development length for bars in compression is given by:
$$ L_{sy.c} = k_6L_{sy.cb} $$
Where \( k_6=0.75 \) if \( \large\frac{\Sigma A_{tr}}{s} \geq \frac{A_s}{600} \) where \( s \) is the spacing of transverse reinforcement, otherwise \( k_6=1.0 \).
\( \textbf{6.} \) Additional Provisions for Compressive Development Length
\( \textbf{6.1.} \) Developing to Less than Yield Strength
As per Clause 13.1.5.4, the development length may be reduced by the ratio of the actual stress in the reinforcement \( \sigma_{st} \) and the yield strength \( f_{sy} \) if the full yield strength is not required.
$$ L_{sc} = L_{sy.c} \frac{\sigma_{sc}}{f_{sy}} \geq 200\text{ mm} $$
\( \textbf{6.2.} \) Plain Bars
As per Clause 13.1.6, the development length of a plain bar in compression is taken as twice of the basic or refined development length of a deformed bar.
$$ 2\times L_{sy.c}\space\space\text{or}\space\space2\times L_{sy.cb} $$
\( \textbf{6.3.} \) Hooked and Cogged Bars
Unlike bars in tension, hooks and cogs are not considered effective in developing stress for bars in compression. This is because hooks and cogs do not engage in load-resisting action in compression the same way they do in tension. The governing stress is bearing stress for bars in compression.
