Development Length Hook Splice Of Reinforcements

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CHAPTER
DEVELOPMENT LENGTH,
23 HOOK
REINFORCEMENTS
& SPLICE OF

23.1 INTRODUCTION
The failure of the reinforced concrete structure commonly caused by incorrect reinforcements detail.
Reinforcement detail includes the development length, hook (anchorage) and splice between
reinforcements.

The strength of reinforcing bar is based on the bond strength between steel reinforcement and
concrete material. Due to external load the bond stress between steel reinforcement and concrete can
be exceeded and cause crushing and splitting of the surrounding concrete.

The followings are the major factors of the bond strength, as follows :
Adhesion between concrete and steel reinforcement.
Gripping effect from drying shrinkage of the surrounding concrete.
Shear interlock of bar deformation and surrounding concrete.
Concrete quality.
Diameter of the steel reinforcement.

This chapter describes the analysis of development length, standard hook, development of flexural
reinforcement, bar cut off and splice of reinforcements.

23.2 DEVELOPMENT OF BOND STRESS
23.2.1 GENERAL
Bond stress is the primary result of the shear interlock between the steel reinforcement and
surrounding concrete. Bond stress can be defined as local shearing stress per unit area of the bar
surface. Three types of test can be used to determine the bond quality which is pull-out test,
embedded rod test and beam test.

23.2.2 PULL OUT BOND
The pull out bond is determined based on the pull out force applied to the embedded steel
reinforcement with prescribed embedded length.

The pull out bond strength can be calculated based on the average bond stress μ, as follows :

Tnb = μ(πdb )ld [23.1]

23 - 1


where :
Tnb = bond strength of embedded reinforcement
μ = average bond stress per unit area of bar surface
db = diameter of reinforcement
ld = embedded length (development length)

The tensile force at the bar cross section is :

1 2
T= πdb fs [23.2]
4

where :
T = tensile force at bar cross section
fs = stress of bar

The two variables above must be in static horizontal equilibrium, as follows :

μ(πdb )ld =
1 2
πdb fs [23.3]
4

So the development length is derived as :

db fs
ld = [23.4]
4μ

23.3 DEVELOPMENT LENGTH
23.3.1 GENERAL
Development length is defined as minimum length of bar in which the bar stress can increase
from zero to the yield strength. If the distance is less than the development length the bar will pull
out the concrete. The development length is a function of yield stress, bar diameter and average
bond stress at surrounding concrete.

23.3.2 BASIC DEVELOPMENT LENGTH
ACI code uses the concept of development length rather than average bond stress. The average bond
stress is determined based on the test result and function of the concrete compressive strength.

Empirically the average bond stress is calculated, as follows :

9.5 f 'c lb
μ= ≤ 800 [23.5]
db in2
where :

23 - 2


μ = average bond stress per unit area of bar surface
f’c = concrete compressive strength

or can be simply written as :

μ = k f 'c [23.6]

Rewritten the above condition we can obtain the basic development length, as follows :

μ(πdb )ld = A b fy

k f 'c (πdb )ld = A b fy
[23.7]
⎛ A b fy ⎞
ldb = k1⎜ ⎟
⎜ f' ⎟
⎝ c ⎠

23.3.3 DEVELOPMENT LENGTH OF TENSION BAR

A. Original Development Length
The basic development length of tension bar is :

TABLE 23.1 DEVELOPMENT LENGTH OF TENSION BAR
SI psi

ld 15fy αβγλ ld 3fy αβγλ
= =
db ⎛ c + K tr ⎞ db ⎛ c + K tr ⎞
16 f 'c ⎜
⎜ d
⎟
⎟ 40 f 'c ⎜
⎜ d
⎟
⎟
⎝ b ⎠ ⎝ b ⎠

⎛ c + K tr ⎞
≤ 1.5⎜
⎜ d
⎟ ≤ 2. 5
⎟
⎝ b ⎠

The transverse reinforcement index is defined as :

TABLE 23.2 KTR
SI psi

A tr fyt A tr fyt
K tr = K tr =
260sn 1500sn

where :
Ktr = transverse reinforcement index
Atr = area of transverse reinforcement through the
longitudinal bar being developed
fyt = yield strength of transverse reinforcement

Ktr can be used conservatively = 0.

23 - 3


B. α, β, γ, λ & c Factor
The α factor is bar location factor determined, as follows :

TABLE 23.3 BAR LOCATION FACTOR α
LOCATION α
Horizontal reinforcement placed more than 12” (300 mm) fresh concrete 1.3
Other Reinforcement 1.0

The β factor is coating factor determined, as follows :

TABLE 23.4 COATING FACTOR β
COATING β
Epoxy coated bar with cover less than 3db / clear spacing less than 6db 1.5
All epoxy coated bar 1.2
Uncoated reinforcement 1.0

The product of αβ must not exceed 1.7.

The γ factor is bar size factor determined, as follows :

TABLE 23.5 BAR SIZE FACTOR γ
BAR SIZE γ
< 20 mm 0.8
> 25 mm 1.0

The c factor is spacing / cover dimension factor determined as the smaller of :
Distance from center of bar to the nearest concrete surface.
0.5 of center to center spacing of the bar being developed.

C. Simplified Development Length
For the design purpose the simplified development length formula is often used, as follows :

TABLE 23.6 SIMPLIFIED DEVELOPMENT LENGTH OF TENSION BAR – PSI UNIT
≤ NO. 6
CASE > NO. 7
(DEFORMED BAR)

Clear spacing of developed bar
> db, stirrup not less than the
ld fy αβλ ld fy αβλ
code minimum requirement = =
db 25 f 'c db 20 f 'c
> 2db, clear cover > db

ld 3fy αβλ ld 3fy αβλ
Other = =
db 50 f 'c db 40 f 'c

The development length ld must be greater than 12 inch.

23 - 4


TABLE 23.7 SIMPLIFIED DEVELOPMENT LENGTH OF TENSION BAR – SI UNIT
≤ NO. 6
CASE > NO. 7
(DEFORMED BAR)

> db, stirrup not less than the
ld 12fy αβλ ld 12fy αβλ
code minimum requirement = =
db 25 f 'c db 20 f 'c
> 2db, clear cover > db

ld 18 fy αβλ ld 18 fy αβλ
Other = =
db 25 f 'c db 20 f 'c

The development length ld must be greater than 300 mm.

23.3.4 DEVELOPMENT LENGTH OF COMPRESSION BAR
The development length for compression bar is shorter than in the tension bar, because there is no
concrete cracking occurs.

The development length of compression bar is :

TABLE 23.8 DEVELOPMENT LENGTH OF COMPRESSION BAR
psi SI

0.02fy db fy db
ld = ≥ 0.0003 fy db ld = ≥ 0.044 fy db
f 'c 4 f 'c

The development length of compression bar ld must be greater than 8 inch / 200 mm.

23.3.5 DEVELOPMENT LENGTH OF BUNDLED BAR
The development length of bundled bar either in tension or compression is greater than development
length of single bar, because the bundled bar reduce the surface area surrounding concrete.

TABLE 23.9 DEVELOPMENT LENGTH OF BUNDLED BAR
3 BUNDLED 4 BUNDLED

1.2ld 1.33ld

ld is calculated based on the equivalent single bar area having the same area of bundled bar.

23.3.6 DEVELOPMENT LENGTH OF WELDED WIRE FABRIC
The development length of plain welded wire fabric in tension is :

⎛ A w fy λ ⎞
ld = 0.27⎜ ⎟
⎜ s f' ⎟ [23.8]
⎝ w c ⎠

where :
Aw = cross section area of wire

23 - 5


sw = spacing of wire
fy = yield strength of wire (psi)
f’c = concrete compressive strength (psi)

The development length must be greater than 6 inch or (sw + 2 inch).

23.3.7 DEVELOPMENT LENGTH OF WEB REINFORCEMENT
The following figure shows the development length of double U stirrup, as follows :

FIGURE 23.1 DOUBLE U STIRRUP

If the development length above can not fit the depth of the member, the development length
can be extended to full depth of member.

23.4 STANDARD HOOK
23.4.1 GENERAL
When the insufficient length can not be provided to develop a bar then the bar needed to be
anchorage. Two type of standard hooks can be used which is 90o hook and 180o hook.

23.4.2 EMBEDMENT LENGTH OF HOOK
The hook development length is obtained from the basic development length for standard hook lhb
multiplied with factor.

The basic development length for standard hook is :

TABLE 23.10 BASIC DEVELOPMENT LENGTH OF STANDARD HOOK
psi SI

1200 db 100db
lhb = lhb =
f 'c f 'c

23 - 6


The hook development length then calculated as follows :

ldh = λlhb [23.9]

where :
ldh = hook development length
λ = multiplier factor
lhb = basic development length of standard hook
The following is the multiplier factor λ, as follows :

TABLE 23.11 MULTIPLIER FACTOR OF HOOK DEVELOPMENT LENGTH
CONDITION λ

fy
λ=
400
fy different from 400 MPa / 60000 psi
fy
λ=
60000
o
For 90 hook cover not less than 2”
λ = 0 .7
No. 11 bar and smaller cover not less than 2.5”
No. 11 bar and smaller stirrup spacing less than 3d
b
λ = 0 .8
Light weight concrete λ = 1 .3
Epoxy coating λ = 1 .2

23.4.3 90O HOOK AND 180O HOOK
The figure below is the standard hook for 90o hook and 180o hook.

FIGURE 23.2 STANDARD HOOK

The diameter of the bend of hook is :

TABLE 23.12 BEND DIAMETER OF HOOK
NO. 3 – 8 NO. 9, 10, 11 NO. 14 & 18

D = 6db D = 8db D = 10db

23 - 7


The figure below is the hook for No. 3 bar stirrup.

FIGURE 23.3 HOOK FOR STIRRUP NO. 3

The diameter of the bend of stirrup is :

TABLE 23.13 BEND DIAMETER OF STIRRUP
NO. 3 – 5 NO. 6 – 8

D = 4db D = 6db

23.5 DEVELOPMENT OF FLEXURAL REINFORCEMENT & CUT OFF POINT
23.5.1 GENERAL
Flexural reinforcement has different treatment of development length. The flexural reinforcement in one
span may designed due to different value of bending moment so the reinforcement is different.

We have to determine the location where the bar can be cut and the development length from the point
of maximum moment.

23.5.2 DEVELOPMENT LENGTH OF FLEXURAL REINFORCEMENT
A. General
The flexural reinforcements are designed using the maximum bending moment value such as at
mid span (positive moment) and at support (negative moment). To ensure the full development the
flexural reinforcement must be extended at least development length ld from the point of maximum
bending moment.

B. Rules of Positive Moment Reinforcement
The followings are the rules of the development length of flexural reinforcement for positive moment, as
follows :
The reinforcement must be extended at least development length ld from the point of
maximum bending moment.

23 - 8


In simple beam structure, at least 1/3 of positive moment reinforcement must be extended at
least 6 inch into support without bending.
In continuous beam, at least ¼ of positive moment reinforcement must be extended at least
6 inch into support without bending.

Interior continuous beam without closed stirrup, at least ¼ of positive moment
reinforcement shall be spliced with spliced class A.

C. Rules of Negative Moment Reinforcement
The followings are the rules of the development length of flexural reinforcement for negative moment,
as follows :
The reinforcement must be extended at least development length ld from the point of
maximum bending moment.
Negative moment reinforcement must be anchored to the supporting column or member.
At least 1/3 of total reinforcement for negative moment must be extended beyond the
inflection point > d or 12 db or 1/16 of clear span the larger value is taken.

23 - 9


23.5.3 BAR CUT OFF POINT
A. General
The critical location of the flexural reinforcement is where there is rapid drop in the bending moment
such as inflection point (zero moment). To ensure the full development length the flexural
reinforcement must be extended beyond the inflection point with a distance 12db or d which is
greater.

B. Rules for All Reinforcements
The followings are the rules of the bar cut off for all reinforcements, as follows :
Bars must be extended d or 12 db beyond the theoretical flexural cut off points except at
support / end of cantilever.
Bars must be extended ld from the theoretical flexural cut off point of adjacent bar.

23.5.4 SKETCH OF FLEXURAL DEVELOPMENT LENGTH
A. General
This section shows the flexural development sketch of positive moment reinforcement and negative
moment reinforcement based on the all rules at previous section.

B. Positive Moment Reinforcement
The figure below shows the flexural development length of positive moment reinforcement.

FIGURE 23.4 FLEXURAL DEVELOPMENT LENGTH – POSITIVE MOMENT REINFORCEMENT

23 - 10


C. Negative Moment Reinforcement
The figure below shows the flexural development length of negative moment reinforcement.

FIGURE 23.5 FLEXURAL DEVELOPMENT LENGTH – NEGATIVE MOMENT REINFORCEMENT

23.6 SPLICE OF REINFORCEMENTS
23.6.1 GENERAL
The bars are produced in standard length so sometime it is needed to be spliced. The splice of the
reinforcement must ensure that it can develop yield stress along the splice length.

There are three types of splice, as follows :
Lap Splice, lapping of two bars with determined splice length (< bar No. 11).
Mechanical Connecting, splice of reinforcement using the connector / coupler.
Welding, splice by weld the two reinforcements (> bar No. 11).
23.6.2 LAP SPLICE OF TENSION BAR
There are two types of lap splice of tension bar according to ACI code, as follows :
Class A.
Class B.

The splice length of splice class A is :

ls = 1.0ld ≥ 12" [23.10]

where :
ls = splice length
ld = development length

23 - 11


The splice length of splice class B is :

ls = 1.3ld ≥ 12" [23.11]

where :
ls = splice length
ld = development length

The following table shows the conditions of tension lap splice, as follows :

TABLE 23.14 TENSION LAP SPLICE
MAXIMUM % OF SPLICED BAR
As PROVIDED / As REQUIRED
50% 100%

≥2 Class A Class B
<2 Class A Class B

23.6.3 LAP SPLICE OF COMPRESSION BAR
The lap splice of compression bar is :

TABLE 23.15 COMPRESSION LAP SPLICE
fy psi SI

≤ 60000 psi / 400 MPa ls ≥ 0.0005 fy db ls ≥ 0.07 fy db

> 60000 psi / 400 MPa (
ls ≥ 0.0009fy − 24 db ) (
ls ≥ 0.13fy − 24 db )

23.7 DETAIL OF REINFORCEMENTS
23.7.1 GENERAL
The most important thing in the reinforced concrete structure is the reinforcement detail. After the
reinforced concrete member is analyzed and designed a structural engineer must make a
reinforcement detail, splice of reinforcement, bar bending schedule because the engineer is the
only person who knows the location of critical section of the member, these information then used by
the contractor when they build the structure.

23.7.2 SPACING LIMITS
A. General
For ensure the workability of the concrete the spacing of the reinforcement must be limited so the
spacing is not o small compared to the size of the coarse aggregate.

B. Minimum Spacing
Minimum clear spacing of between bars is :

db ≥ 1" [23.12]

23 - 12


where :
db = diameter of bar

Minimum clear spacing of bar more than one layers is :
1" [23.13]

Minimum clear spacing of longitudinal reinforcement in compression member with tied and spiral
transverse reinforcement is :
(1 − 1.5)db ≥ 1"−1.5" [23.13]
where :
db = diameter of bar

C. Maximum Spacing
Maximum spacing between bars must not spaced greater than :
3hf ≤ 18" [23.14]
where :
hf = slab thickness

23.7.3 END SPAN OF CONTINUOUS BEAM
The figure below shows the typical detail of reinforcement for end span in continuous reinforced
concrete structure.

FIGURE 23.6 END SPAN OF CONTINUOUS BEAM

23 - 13


23.7.4 INTERIOR SPAN OF CONTINUOUS BEAM
The figure below shows the typical detail of reinforcement for interior span in continuous reinforced
concrete structure.

FIGURE 23.7 INTERIOR SPAN OF CONTINUOUS BEAM

23.7.5 COLUMN
The figure below shows the typical detail of reinforcement for column.

FIGURE 23.8 COLUMN

23 - 14

Development Length Hook Splice Of Reinforcements

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