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Reinforcement Development Length Calculator to AS3600's banner

Reinforcement Development Length Calculator to AS3600

The development length is the minimum length of a reinforcing bar over which the stress in the bar can increase from zero to the yield strength. If the development length is not met, the section capacity of the section is reduced to compensate. This CalcTree template calculates the minimum reinforcement development length required in both tension and compression.
All calculations are performed in accordance with AS3600-2018.

Calculation

Inputs

Material Properties

Concrete:


f'c
:25MPa​



Concrete elastic modulus, Ec
:26700MPa​


Reinforcement:


Shape
:Straight​



Type
:Deformed​



fsy
:500MPa​



Section Geometry and Reinforcement



B
:700mm​



D
:450mm​


Longitudinal Reinforcement:


Longitudinal reinforcement size, db
:16mm​



Number of bars
:5​



c
:60mm​



a
:109.0mm​



Is there more than 300mm of concrete cast below the reinforcement?
:No​


Shear Reinforcement:


dsv
:16mm​



s
:200mm​



Number of ligs in cross-section
:4​



Considerations for Development Length



Lightweight concrete?
:No​



Epoxy-coated bars?
:No​



Bundled?
:Single bar​



σ
:500MPa​

❗If calculating the full development length, input

= fsy = 500 MPa


ρp
:0MPa​

❗If there is transverse reinforcement around the bar being developed, the stress in the transverse reinforcement is to be calculated. For a conservative approach, use

MPa.

Outputs

Multiplication Factors



Factor for lightweight concrete
:1​



Factor for epoxy-coated bars
:1.0​



Factor for developing less than yield stress
:1​



Factor for plain bars in tension
:1.0​



Factor for hook or cog
:1.0​



Factor for bundling
:1​



Basic Development Length in Tension,



Lsy.tb=0.5k1k3fsydbk2fc′≥0.058fsyk1dbL_{sy.tb}=\frac{0.5k_1k_3f_{sy}d_b}{k_2\sqrt{f'_c}}\geq0.058f_{sy}k_1d_b


k1
:1​



k2
:1.16​



k3
:0.7​



Lsy.tb
:483mm​


Details



cd
:54.5mm​



Refined Development Length in Tension,




Lsy.t=k4k5Lsy.tbL_{sy.t}=k_4k_5L_{sy.tb}
If

, minimum condition governs i.e.

.


k4
:0.7​



k5
:1​



Lsy.t
:483mm​


Details



λ
:3.7499999999999996​



ΣAtr
:804.247719318987mm2​



ΣAtr.min
:50.26548245743669mm2​



nbs
:5.0​



nf
:4.0​



K
:0.09000000000000001​



Basic Development Length in Compression,




Lsy.cb=max(0.22fsyfc′≥0.0435fsydb , 200mm)L_{sy.cb}=\text{max}(\frac{0.22f_{sy}}{\sqrt{f'_c}}\geq0.0435f_{sy}d_b\space,\space\text{200mm})


Lsy.cb
:348mm​



Refined Development Length in Compression,



Lsy.c=k6Lsy.cbL_{sy.c}=k_6L_{sy.cb}


k6
:0.75​



Lsy.c
:261mm​



Explanation

Minimum development length must be met to develop a safe bond between the surface of the reinforcing bar and surrounding concrete. If the development length is not met, the section capacity of the section is reduced to compensate. The development length of a bar transfers stresses developed in one section to adjoining sections (e.g. slab-column, beam-column, etc.).
Development length in common structural configurations

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.
Adopted from AS3600-2018 Supplement 1, Figure C13.1.1

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

Code References

AS3600-2018 Section 13 prescribes how to calculate the minimum reinforcement development length.

Basic Tensile Development Length - AS3600 Cl. 13.1.2.2


Lsy.tb=0.5k1k3fsydbk2fc′≥0.058fsyk1dbL_{sy.tb}=\dfrac{0.5k_1k_3f_{sy}d_b}{k_2\sqrt{f'_c}}\geq0.058f_{sy}k_1d_b
The basic development length,

of a deformed bar depends on the following factors:
  1. 
    
    for a horizontal bar with more than 300mm of concrete cast below of the bar, otherwise
    
    . 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.
  2. 
    
  3. 
    
    within limits of
    
    .
Where:
  1. 
    
    is the diameter of the developing bar
  2. 
    
    is the effective cover, see below
The effective cover,

differs depending on the reinforcement shape, spacing and cover:
Effective cover, - AS3600-2018 Figure 13.1.2.2

The value of

calculated from above should be multiplied by:
  1. 1.5 if bars are epoxy-coated - coating around bars increase durability by protecting it against corrosion but reduces bonding strength to concrete
  2. 1.3 when lightweight concrete is used - mechanical properties of lightweight concrete are weaker than normal weight concrete


Refined Tensile Development Length - AS3600 Cl. 13.1.2.3


Lsy.t=k4k5Lsy.tbfor k3k4k5≤0.7L_{sy.t}=k_4k_5L_{sy.tb}\hspace{0.2cm} \text{for } \hspace{0.2cm}k_3k_4k_5 \leq0.7
The basic development length,

may be reduced to the refined development length,

depending on the following factors:
  1. 
    
    
  1. 
    
Where:
  1. 
    
    = factor that accounts for the effectiveness of transverse reinforcement (shear fitments) in controlling splitting cracks along a development length.
    
    
  2. 
    
  1. 
    
    = stress in the transverse reinforcement around the bar being developed. As the transverse stress,
    
    increases, it delays the formation of splitting cracks and thereby increases bond stress within the development length.
  2. 
    
    = area of the provided shear reinforcement
  3. 
    
    = area of the minimum shear reinforcement
  4. 
    
    = area of the developing bar
It should be noted that as per Clause 13.1.2.3, the product

should not be less than 0.7 - if less than 0.7, then factors must be adjusted.
For typical fitment arrangements, values of

,

and

are:
AS3600-2018 Table 13.1.2.3



Additional Provisions for Tensile Development Length

  1. Developing to less than Yield Strength - AS3600 Cl. 13.1.2.4

Lst=Lsy.tσstfsy≥12dbL_{st} = L_{sy.t} \frac{\sigma_{st}}{f_{sy}} \geq 12d_b
The development length may be reduced by the ratio of the actual stress in the reinforcement (

) and the yield strength (

) if the full yield strength is not required.
  1. Plain Bars - AS3600 Cl. 13.1.3

1.5×Lsy.tb≥300 mm1.5 \times L_{sy.tb} \geq 300\text{ mm}
The development length of a plain bar in tension is taken as 50% longer than basic development length but no less than 300mm.
  1. Hooked or Cogged Bars - AS3600 Cl. 13.1.2.6 / 13.1.2.7
Adopted from AS3600-2018 Figure 13.1.2.6

  1. If a deformed bar ends in a hook or a hog, then the tensile development length of the bar is taken as
    
    where
    
    is the reduced lap length calculated using the actual stress in the bar.
  2. If a plain bar ends in a hook or a hog, then the tensile development length is taken as
    
    or
    
    .
Adopted from Figure C13.1.2.7 - AS3600-2018 Supplement 1

For hooked or cogged bars, its length

and bend diameter

must meet minimum dimensions to be considered effective in providing anchorage. Supplement 1 to AS3600 provides the following table for bars bent at different angles:
Adopted from AS3600-2018 Supplement 1, Table C13.1.2.7



Basic Compressive Development Length - AS3600 Cl. 13.1.5.1

Development length of bars in compression are much simpler to calculate than bars in tension:

Lsy.cb=0.22fsyfc′db≥0.0435fsydb  or  200mmL_{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}

Refined Compressive Development Length - AS3600 Cl. 13.1.5.4


Lsy.c=k6Lsy.cbL_{sy.c} = k_6L_{sy.cb}
  1. 
    
    if
    
    where
    
    spacing of transverse reinforcement, otherwise
    
    


Additional Provisions for Compressive Development Length

  1. Developing to Less than Yield Strength - AS3600 Cl. 13.1.5.4

Lsc=Lsy.cσscfsy≥200 mmL_{sc} = L_{sy.c} \frac{\sigma_{sc}}{f_{sy}} \geq 200\text{ mm}
  1. Plain Bars - AS3600 Cl. 13.1.6

2×Lsy.c  or  2×Lsy.cb2\times L_{sy.c}\space\space\text{or}\space\space2\times L_{sy.cb}
The development length of a plain bar in tension is taken as twice of the basic or refined development length of a deformed bar.
  1. 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.

Related Resources

  1. Concrete Beam Design Calculator to AS3600
  2. Concrete Column Design Calculator to AS3600
  3. Concrete Slab-on-Grade Designer to AS3600
  4. Rectangular Footing Designer to AS3600
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