2. Bond, Development Lengths, and
Splices
1. Bond stress
- A basic assumption made for RC design: there must be
absolutely no slippage of the bars in relation to the
surrounding concrete. That means the steel and the
concrete should stick together or bond so they will act as a
unit. If not, the bars are not anchored at their ends.
3. Development of Bond Stresses: flexural bond
Flexure bond
1 2 1 2 1 2
; and
T T M M C C
4. But
At any section, dT = dM/jd
Where u is the average bond stress and ΣO is the sum of
perimeters of bars in the tension side.
The rate of change of the moment with respect to x is the shear, or
dM/dx = V
5. For practical calculations, j = 0.87
0.87
V
u
d O
In the strength design method, the nominal bond strength is
reduced by capacity reduction factor ϕ = 0.85 , thus
0.87
u
u
V
U
d O
11. 2. Development length for tension reinforcing
The minimum length of embedment of bars that is necessary
to permit them to be stressed to their yield point plus some
extra distance to ensure member toughness.
12. 2. Development length for tension reinforcing
2
For equilibrium condition:
and
For a combination of bars,
The length is the minimum permissible anchorage length
and is called the development length.
4
s y
s y u d d
u
s y
d
u
d
b y
d
u b
A f
A f U Ol l
U O
A f
l
U O
l
d f
l
U d
4
where = diameter of reinforcing bars
b y
u
b
d f
U
d
13. ► The development length in tension may not be less than the
value computed from Eq. below or 300mm.
Where
• ld = development length, mm.
• db = nominal diameter of bar or wire, mm.
• fy = specified yield strength of nonprestressed bar or wire, MPa
• fc′ = specified compressive strength of concrete, MPa
9
10
y
d t e s
b c b tr
b
f
l
d f c K
d
14. • ψt = reinforcement location factor
= 1.3 for horizontal reinforcement placed such that
more than 300mm of fresh concrete is cast below
the development length or splice
= 1.0 for other reinforcement
• ψe = coating factor
= 1.5 for epoxy-coated bars or wires with cover less
than 3db or clear spacing less than 6db
= 1.2 for all other epoxy-coated bars or wires
= 1.0 for uncoated reinforcement
The product of ψt and ψe need not be taken greater than 1.7
15. • ψs = reinforcement size factor
= 0.8 for DB20mm and smaller bars and deformed wires
= 1.0 for DB22mm and larger bars
• λ = lightweight aggregate concrete factor
= 0.75 when lightweight concrete is used or
= when fct is specified, but not less than 1.0
= 1.0 for normal weight concrete
• cb = spacing or cover dimension, mm.
= the smaller of
(a) distance from center of bar or wire being developed to
the nearest concrete surface,
(b) one-half the center-to-center spacing of bars or
wires being developed
1.8
c ct
f f
16. Concrete stresses in a circular concrete prism containing a
reinforcing bar that is subjected to bond stresses, shown
in section.
17. • Ktr = transverse reinforcement index
where
• Atr = total cross-sectional area of all transverse reinforcement
which is within the spacing s and which crosses the
potential plane of splitting through the reinforcement
being developed, mm2
• s = maximum spacing of transverse reinforcement within ld,
center-to-center, mm.
• n = number of bars or wires being developed along the
plane of splitting
10
tr tr
tr
A f
K
sn
18. • Note that the term not greater than 2.5 (ACI code
section 12.2.3) to safeguard against pullout type failures.
To simplify the calculation the code also permit to use Ktr = 0
b tr
b
c K
d
Definition of Atr
19. If the flexural reinforcement provided exceeds the amount
required to resist the factored moment, the bar stress that must
be developed is less than fy. In such a case, ACI Code Section
12.2.5 allows to be multiplied by (As required/ As provided).
This multiplier is not applied in the design of members
resisting seismic loads.
The value of can not be greater than 8.3 MPa
c
f
20. DB20 mm and
smaller bars and
deformed wires
DB22 mm and
larger bars
(Case 1) Clear spacing of bars
or wires being developed or
spliced not less than db, clear
cover not less than db, and
stirrups or ties throughout ld not
less than the code minimum
or
(Case 2) Clear spacing of bars
or wires being developed or
spliced not less than 2db and
clear cover not less than db
Other cases
2.1
y t e
d
b c
f
l
d f
1.7
y t e
d
b c
f
l
d f
1.4
y t e
d
b c
f
l
d f
1.1
y t e
d
b c
f
l
d f
21.
22.
23. 2. Compression-Development length
Development length of bars in compression should be greater
than below Eq.
and
and
0.24 y
dc
b c
f
l
d f
0.043
dc
y
b
l
f
d
200
dc
l mm
It can be reduced by factor Rs = As, required/As, provided
24. 3. Development of bundle bars
• Development length of individual bars within a bundle, in
tension or compression, shall be that for the individual bar,
increased 20 percent for three-bar bundle, and 33 percent for
four-bar bundle.
• For determining the appropriate spacing and cover values, and
the ψe factor, a unit of bundled bars shall be treated as a single
bar of a diameter derived from the equivalent total area and
having a centroid that coincides with that of the bundled bars.
27. 4. Critical Section In Flexural Members
The critical sections for development of reinforcement in flexural
members are
• At points of maximum stress
• At points where tension bars within the span are terminated or bent
• At the face of the support
• At points of inflection at which moment changes signs
36. Development length of hooked bar ldh :
ldh = development length for hooked bar, mm.
Ψe = coating factor
= 1.2 for all other epoxy-coated bars or wires
= 1.0 for uncoated reinforcement
0.24
(Modification Factor)
e y
dh
b c
f
l
d f
37. • (a) For No. 36 bar and smaller hooks with side cover (normal
to plane of hook) not less than 65 mm, and for 90-degree hook
with cover on bar extension beyond hook not less than
50mm....................... 0.7
38. • (b) For 90-degree hooks of No. 36 and smaller bars that are
either enclosed within ties or stirrups perpendicular to the bar
being developed, spaced not greater than 3db along ldh; or
enclosed within ties or stirrups parallel to the bar being
developed, spaced not greater than 3db along the length of the
tail extension of the hook plus bend .................... 0.8
39. • (c) For 180-degree hooks of No. 36 and smaller bars that are
enclosed within ties or stirrups perpendicular to the bar being
developed, spaced not greater than 3db along
ldh ...................................................... 0.8
• (d) Where anchorage or development for fy is not specifically
required, reinforcement in excess of that required by
analysis ....... (As required)/(As provided)
40.
41.
42.
43.
44.
45. Lap Splices in Tension, lst
Shall be as required for Class A or B splice, but not
less than 300 mm, where:
• Class A splice................................................... 1.0ld
• Class B splice................................................... 1.3ld
where ld is the development length
46. Lap Splices in Compression, lsc
Shall not be less than 300 mm
For bars with 420 0.071
For bars with 420 0.13 24
For 21 , Required lap is increased by 1/3
y sc y b
y sc y b
c
f MPa l f d
f MPa l f d
f MPa
47.
48.
49.
50.
51. Moment-Resistance Diagram(Bar Cutoff Points)
The factored moment capacity of an under-reinforced
concrete beam at any section is:
2
u s y
a
M A f d
The factored moment resistance of one bar, is
2
0.85
area of one bar
ub
ub sb y
s y
c
sb
M
a
M A f d
A f
where a
f b
A
52.
53.
54.
55. • Note (a): Portion
of total negative
reinforcement (As
-)
must be continuous
(or spliced with a
Class B splice or
a mechanical or
welded splice
satisfying 12.14.3)
along full length of
perimeter beams
(7.13.2.2).
(a) Negative Moment
Reinforcement
56. • Note (b): Portion of total
positive reinforcement
(As
+) must be continuous
(or spliced with a Class
B splice or
a mechanical or welded
splice satisfying 12.14.3)
along full length of
perimeter beams and of
beams without
closed stirrups (7.13.2.2).
See also 7.13.2.4.
(b) Positive Moment
Reinforcement
