What is Development Length?

What is Development Length?

For understanding the concept of bond and development length, let us consider a steel bar embedded in concrete. the bar is subjected to a tensile load T. due to the tensile force, the steel bar will tend to come out and slip out of the concrete. This tendency of slipping is resisted by the bond stress developed over the surface of the bar.
                                                       Bond stress is the shear stress developed along the contact surface between the reinforcing steel and the surrounding concrete which prevent the bar from slipping out of concrete. To avoid slipping 

                                         
                         T ≤ τ bd × 2πφ/2 × Ld             (surface area = 2πr × Ld)
                         T = σ st × π/4 ×φ2                                 ( T = σ st × Aφ)
                        σ st × π/4 ×φ≤  τ bd × 2πφ/2 × Ld                         
                         Ld ≥ σ st φ/ 4 τ bd

Where

Ld   = Embedded length of steel bar
σ st = Permissible stress in steel
τ bd = Bond stress
φ    =  Diameter of bar

Lis called as the development length. It is the minimum length of the bar which must be embedded in concrete beyond any section to develop its full strength. This is also called as an anchorage length in case of axial tension or axial compression and development length in case of flexural tension or flexural compression. As per code IS456:2000, development length is given by

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                                  Ld = σ st φ/τ bd        
                                                        
 The permissible bond stress τ bd depends upon the grade of concrete and type of steel. The values of permissible bond stress are given in the table.

Permissible Bond Stress For Plain Bars And Deformed Bars

Grade of Concrete
τ bd For plain bars(N/mm2)
τ bd For deformed bars(N/mm2)
        M20
          0.8
           1.28
        M25
          0.9
           1.44
        M30
          1.0
           1.60
        M35
          1.1
           1.76
M40 and above
          1.2
           1.92





Here 

a.) For deformed bars is 60% more than that of plain bars.
b.) It is easier to pull a bar than to push it inside. Therefore permissible bond stress for plain and deformed bars in compression is taken 25% more than that for the bars in tension.

Development length in compression = σ st φ/ 4(1.25) τ bd
                                                                      
                                                                       = σ st φ/ 5 τ bd

The development length for steel bars of different grades are computed by the following formula and data are given in the table

Development length in tension = σ st φ/ 4 τ bd 

Development length in compression = σ st φ/ 5 τ bd

Development Length For Single Bars

Type of steel bar
σ st N/mm2
       Ld in tension(mm)
    Ld in compression(mm)
M20
M25
M30
M20
M25
M30
Fe 250 plain bars
130 
41 φ
39 φ
33 φ
33 φ
30 φ
27 φ
140
44 φ
39 φ
35 φ
36 φ
32 φ
28 φ
Deformed bars
230
45 φ
40 φ
36 φ
36 φ
32 φ
29 φ

Note :

1. φ is the diameter of the bar.
2. In case of bundled bars in contact, the development length is given by that for the individual bars and increased as follows:
a.) 10% for two bars in contact.
b.) 20% for three bars in contact.
3.) 33% for four bars in contact.



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