What is Development
Length?
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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 ≤ Ï„ _{bd }× 2Ï€Ï†/2 × L_{d } (surface
area = 2Ï€r × L_{d})
T =
Ïƒ_{ st }× Ï€/4 ×Ï†^{2 }(
T = Ïƒ_{ st} × AÏ†)
Ïƒ_{ st }×
Ï€/4 ×Ï†^{2 }≤
Ï„ _{bd }× 2Ï€Ï†/2 × L_{d }
L_{d} ≥
Ïƒ_{ st }Ï†_{/ 4 }Ï„ _{bd}
Where
L_{d }=
Embedded length of steel bar
Ïƒ_{ st} = Permissible
stress in steel
Ï„ _{bd} =
Bond stress
Ï† = Diameter
of bar
L_{d }is
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
L_{d} =
Ïƒ_{ st }Ï†_{/ 4 }Ï„ _{bd}
The permissible
bond stress Ï„ _{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

Ï„ _{bd} For plain bars(N/mm^{2})

Ï„ _{bd} For deformed bars(N/mm^{2})

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 = Ïƒ_{ st }Ï†_{/ 4(1.25) }Ï„ _{bd}
_{
}
_{
= }Ïƒ_{ st }Ï†_{/ 5 }Ï„ _{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 = Ïƒ_{ st }Ï†_{/ 4 }Ï„ _{bd}
Development length
in compression = Ïƒ_{ st }Ï†_{/ 5 }Ï„ _{bd}
_{Development
Length For Single Bars}
Type of steel bar

Ïƒ_{ st }N/mm^{2}

L_{d} in tension(mm)

L_{d} in
compression(mm)


M20

M25

M30

M20

M25

M30


Fe 250 plain bars

130

41 Ï†

39 Ï†

33 Ï†

33 Ï†

30 Ï†

27 Ï†

140

44 Ï†

39 Ï†

35 Ï†

36 Ï†

32 Ï†

28 Ï†


Deformed bars

230

45 Ï†

40 Ï†

36 Ï†

36 Ï†

32 Ï†

29 Ï†

Note :
1. Ï† 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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