Bond and Development Length
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Plain and Reinforced Concrete II
Reference Books:
Concrete Structures by Prof. Dr. Zahid Ahmed Siddiqi
Reinforced concrete mechanics and design by James G. Macgregor
Design of concrete structures by Arthur H. Nilson David Darwin Charles W.
Dolan
Reinforced Concrete by Edward G. Nawy
Code:
Building Code Requirements for Structural Concrete (ACI318-11)
American Society for Testing and Materials (ASTM)
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Bond and Development Length
Reference:
Reinforced concrete mechanics and design
by James G. Macgregor
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Bond and Development Length
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Bond and Development Length
�In a reinforced concrete beam, the flexural
compressive forces are resisted by
concrete, while the flexural tensile forces
are provided by reinforcement.
�For this process to exist, there must be a
force transfer, or bond, between the two
materials.
�For the bar to be in equilibrium, bond
stresses must exist.
�If these disappear, the bar will pull out of
the concrete and the tensile force, T, will
drop to zero, causing the beam to fail.
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Bond and Development Length
Need for Bond Stresses
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Relationship between change in bar stress and
average bond stress
If “fs2” is greater than “fs1” bond stress, µ, must act on the surface of the bar to maintain equilibrium
ldd
ff bavgb
s )(4
)(
2
12sπµ
π=−
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Bond and Development Length
Average flexural bond stress
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Bond Stresses in an Axially Loaded Prism
Steel, concrete, and bond stresses in a cracked prism
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Steel, concrete and bond stresses in a cracked beam
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Stress distribution in a pull-out test
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Mechanism of Bond Transfer
�A smooth bar embedded in concrete develops
bond by adhesion between the concrete and the
bar and by a small amount of friction.
�Both of these effects are quickly lost when the
bar is loaded in tension, particularly because the
diameter of the bar decreases slightly, due to
Poisson’s ratio.
�For this reason, smooth bars are generally not
used as reinforcement.
�In cases where smooth bars must be
embedded in concrete mechanical anchorage in
the form of hooks are used.
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Mechanism of Bond Transfer
�Although adhesion and friction are present when a deformed bar is loaded for the first time, these bond-transfer mechanisms are quickly lost, leaving the bond to be transferred by bearing on the deformations of the bar.�Equal and opposite bearing stresses act on the concrete.�The forces on the concrete have both a longitudinal and a radial component.�The latter causes circumferential tensile stresses in the concrete around the bar.
�Eventually, the concrete will split parallel to the bar, and the resulting crack will propagate out to the surface of the beam. �The splitting cracks follow the reinforcing bars along the bottom or side surfaces of the beam.
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Bond-transfer mechanism
Once these cracks develop, the bond transfer drops rapidly unless reinforcement is provided to restrain the opening of the splitting crack
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Typical splitting-failure surfaces
If the cover and bar spacings are large compared to the bar diameter, a pull-out failure can occur, where the bar and the annulus of concrete between successive deformations pull out along a cylindrical failure surface joining the tips of the deformations.
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Development Length (ld)
�Because the actual bond stress varies along the length of a bar anchored in a zone of tension, the ACI Code
uses the concept of ld rather than bond stress. �ld, is the shortest length of bar in which the bar stress can increase from zero to the yield strength (fy).�If the distance from a point where the bar stress equals fy to the end of the bar is less than the development length, the bar will pull out of the concrete. �The lds are different in tension and compression, because a bar loaded in tension is subject to in-and-out bond stresses and hence requires a considerably longer development length. �Also, for a bar in compression, bearing stresses at the end of the bar will transfer part of the compression force into the concrete.
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Development Length (ld)
The development length can be expressed in terms of the ultimate value of the average bond stress by setting (fs2 - fs1) = fy in equation.
d
avg
by
bavgb
y
bavgb
s
ldf
ldd
f
ldd
ff
=
=
=−
µ
πµπ
πµπ
4
)(4
)(
)(4
)(
2
2
12s
Here, µavg is the value of µavg at bond failure in a beam test.
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Basic Development Equation ACI318-11
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Basic Development Equation ACI318-11
Case2
Case 1
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Explanation of Cases 1 and 2
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Basic Development Equation ACI318-11
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Basic Development Equation ACI318-11
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Basic Development Equation ACI318-11
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Development of deformed bars and deformed wire in compression
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Development of deformed bars and deformed wire in compression
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Development of standard hooks in tension
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Development of standard hooks in tension
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Development of standard hooks in tension
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Standard Hooks
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Development length of headed bars in tension
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