Lecture onCE 4014 Design of Concrete StructuresYangon Technological UniversityDepartment of Civil EngineeringDr. Khin Than Yu Professor and Head(Bond, Anchorage and Development Length) Part (I)20-3-2008

Design of Concrete Structures

Text and Reference

FUNDAMENTALS OF FLEXURAL BONDIn 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.

Source of bond strengthWeak chemical adhesionMechanical friction between steel and concreteSlip induced interlocking of natural roughness of the bar with concreteEnd 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.

Bond Stress Based on Simple Cracked Section Analysis dT = dM / jdFor local equilibrium, change in bar force = bond force at the contact surfaceu o dx = dT, u = dT / o dx = dM / o jd dx = dV / o jd u = local average unit bond stresso = sum of the perimeter of all barsJd = internal lever arm between tensile and compressive force resultantsdx = short piece of length of beam

b. Actual Distribution of Flexural Bond StressPure bending caseConcrete 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.

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.

ULTIMATE BOND STRENGTH AND DEVELOPMENT LENGTHTypes 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)

a. Ultimate Bond StrengthDirect pull outFor 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.SplittingSplitting comes from wedging action when the ribs of the deformed bars bear against the concrete.Splitting in vertical planeSplitting 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)

b. Development LengthDevelopment length is the length of embedment necessary to develop the full tensile strength of bar, controlled by either pullout or splitting.In Fig., letmaximum M at a and zero at supportfs 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.

c. Factors influencing Development LengthTensile strength of concreteCover distanceBar spacingLateral reinforcementVertical bar location relative to beam depthEpoxy coated bars or notExcess reinforcementBar diameter

ACI CODE PROVISION FOR DEVELOPMENT OF TENSION REINFORCEMENTLimit(c + ktr) / db = 2.5 for pullout casefc are not to be greater than 100 psi.

For two cases of practical importance, using (c + ktr) / db = 1.5,

Example:

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ANCHORAGE OF TENSION BARS BY HOOKSIn 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.

b. Development Length and Modification Factors for Hooked Bars

Example

ANCHORAGE REQUIREMENTS FOR WEB REINFORCEMENT

DEVELOPMENT OF BARS IN COMPRESSIONReinforcement may be required to develop its compressive strength by embedment under various circumstances.

ACI basic development length in compression ldb = 0.02db fy/fc

BAR CUTOFF AND BEND POINTS IN BEAMSTheoretical points of cutoff or bendT = As fs = M/zT = function of (M)

ACI Code: uniformly loaded, continuous beam of fairly regular span may be designed using moment coefficients.

b. Practical Considerations and ACI Code Requirements

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.

Standard Cutoff and Bend PointsFor not more than 50% of tensile steel is to be cutoff or bent

c. Special Requirements near the Point of Zero MomentIt 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 pointLet Mn = nominal flexural strength provided by those bars extend to the point of inflection.

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 CodeSimply support case

d. Structural Integrity ProvisionsFor 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

CommentConsideration for bond and detail design for anchorage, development length and structural integrity requirements are important to have proper structural performance of the building.