1. Lecture on CE 4014 Design of Concrete Structures
Yangon Technological University
Department of Civil Engineering
Lecture on CE Design of Concrete Structures
(Bond, Anchorage and Development Length)
Part (I)
Dr. Khin Than Yu Professor and Head

2. Design of Concrete Structures
Text and Reference
Department of Civil Engineering, YTU

3. FUNDAMENTALS OF FLEXURAL BOND
In reinforced concrete beams it is assumed that strain in the embedded reinforcing bar is the same as that in the surrounding concrete.
Therefore, it is essential that bond force is developed on the interface between concrete and steel to prevent significant slip from occurring at the interface.
Department of Civil Engineering, YTU

4. Source of bond strength
Weak chemical adhesion
Mechanical friction between steel and concrete
Slip induced interlocking of natural roughness of the bar with concrete
End anchorage, hooks : providing tie arch action even for bond broken beam.
Force in the steel,
T = Mmax / z
Deformed bar: providing bond force via the shoulders of the projecting ribs bear on the surrounding concrete.
Department of Civil Engineering, YTU

5. Bond Stress Based on Simple Cracked Section Analysis
u = local average unit bond stress ∑o = sum of the perimeter of all bars Jd = internal lever arm between tensile and compressive force resultants dx = short piece of length of beam
dT = dM / jd For local equilibrium, change in bar force = bond force at the contact surface u ∑o dx = dT, u = dT / ∑o dx = dM / ∑o jd dx = dV / ∑o jd
Department of Civil Engineering, YTU

6. b. Actual Distribution of Flexural Bond Stress
Pure bending case
Concrete fails to resist tensile stresses only where the actual crack is located. Steel T is maximum and
T max = M / jd .
Between cracks , concrete does resist moderate amount of tension introduced by bond.
u is proportional to the rate of change of bar force, and highest where the slope of the steel force curve is greatest.
Very high local bond stress adjacent to the crack.
Department of Civil Engineering, YTU

7. Beam under transverse loads,
According to simple crack sectional theory, T is proportional to the moment diagram and u is proportional to shear force diagram.
In actual, T is less than the simple analysis prediction everywhere except at the actual cracks.
Similarly, u is equal with simple analysis prediction only at the location where slopes of the steel force diagrams are equals .If the slope is greater than assumed, bond stress is greater; if the slope is less bond stress is less.
Department of Civil Engineering, YTU

8. ULTIMATE BOND STRENGTH AND DEVELOPMENT LENGTH
Types of bond failure
Direct pullout of bars
(small diameter bars are used with sufficiently large concrete cover distances and bar spacing)
Splitting of the concrete along the bar (cover or bar spacing is insufficient to resist the lateral concrete tension resulting from the wedging effect of bar deformations)
Department of Civil Engineering, YTU

9. a. Ultimate Bond Strength
Direct pull out
For sufficiently confined bar, adhesive bond and friction are overcome as the tensile force on the bar is increased. Concrete eventually crushes locally ahead of the bar deformation and bar pullout results.
When pull out resistance is overcome or when splitting has spread all the way to the end of an unanchored bar, complete bond failure occurs.
Splitting
Splitting comes from wedging action when the ribs of the deformed bars bear against the concrete.
Splitting in vertical plane
Splitting in horizontal plane: frequently begins at a diagonal crack in connection with dowel action. Shear and bond failures are often interrelated.
Local bond failure
Large local variation of bond stress caused by flexural and diagonal cracks immediately adjacent to cracks leads to this failure below the failure load of the beam.
Results small slip and some widening of cracks and increase of deflections.
Harmless as long as the failure does not propagate all along the bar.
Providing end anchorage, hooks or extended length of straight bar (development length concept)
Department of Civil Engineering, YTU

10. b. Development Length
Development length is the length of embedment necessary to develop the full tensile strength of bar, controlled by either pullout or splitting.
In Fig., let
maximum M at a and zero at support
fs at a T = Ab fs _
Development length concept total tension force must be transferred from the bar to the concrete in the distance ‘l ‘ by bond stress on the surface.
To fully develop the strength  T = Ab fy
 ld , development length
Safety against bond failure: the length of the bar from any point of given steel stress to its nearby end must be at least equal to its development length. If the length is inadequate, special anchorage can be provided.
Department of Civil Engineering, YTU

11. c. Factors influencing Development Length
Tensile strength of concrete
Cover distance
Bar spacing
Lateral reinforcement
Vertical bar location relative to beam depth
Epoxy coated bars or not
Excess reinforcement
Bar diameter
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12. ACI CODE PROVISION FOR DEVELOPMENT OF TENSION REINFORCEMENT
Limit
(c + ktr) / db = 2.5 for pullout case
√f’c are not to be greater than 100 psi.
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13. For two cases of practical importance, using (c + ktr) / db = 1.5,
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14. Example:
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15. Continue:
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16. Continue:
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17. ANCHORAGE OF TENSION BARS BY HOOKS
In the event that the desired tensile stress in a bar can not be developed by bond alone, it is necessary to provide special anchorage at the end of the bar.
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18. Department of Civil Engineering, YTU

19. b. Development Length and Modification Factors for Hooked Bars
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20. Department of Civil Engineering, YTU

21. Example
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22. ANCHORAGE REQUIREMENTS FOR WEB REINFORCEMENT
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23. DEVELOPMENT OF BARS IN COMPRESSION
Reinforcement may be required to develop its compressive strength by embedment under various circumstances.
ACI basic development length in compression
ldb = 0.02db fy/√f’c
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24. BAR CUTOFF AND BEND POINTS IN BEAMS
Theoretical points of cutoff or bend
T = As fs = M/z
T = function of (M)
ACI Code: uniformly loaded, continuous beam of fairly regular span may be designed using moment coefficients.
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25. b. Practical Considerations and ACI Code Requirements
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26. If cutoff points are in tension zone (to prevent formation of premature flexural and diagonal tension cracks) no flexural bar shall be terminated unless the following conditions are specified.
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27. Standard Cutoff and Bend Points
For not more than 50% of tensile steel is to be cutoff or bent
Department of Civil Engineering, YTU

28. c. Special Requirements near the Point of Zero Moment
It is necessary to consider whenever the moments over the development length are greater than those corresponding to a linear reduction to zero.
Bond force per unit length , u = dT / dx = dM / zdx, proportional to the slope of the moment diagram.
Maximum bond forces u would occur at point of inflection and pullout resistance is required.
Slope of M diagram at any point = V at that point
Let Mn = nominal flexural
strength provided by those
bars extend to the
point of inflection.
Department of Civil Engineering, YTU

29. Thus a must be greater than or equal to ld ACI Code
For assumed (conservatively) uniformed slope of moment diagram Vu towards the positive moment region, length a at M = Mn
a = Mn/Vu
Thus a must be greater than or equal to ld
ACI Code
Simply support case
Department of Civil Engineering, YTU

30. d. Structural Integrity Provisions
For major supporting elements, such as columns, total collapse can be prevented through relatively minor changes in bar detailing owing to accidental or abnormal loading.
If some reinforcement properly confined is carried continuously through a support catenary action of beam can prevent from total collapse even if the support is damaged.
ACI Code
Department of Civil Engineering, YTU

31. Comment
Consideration for bond and detail design for anchorage, development length and structural integrity requirements are important to have proper structural performance of the building.
Department of Civil Engineering, YTU