Bond Strength-Splice Length in Concrete Beams Confined by Transverse Reinforcement

This work aim to study the effect of transverse reinforcement , area of splice bar, concrete cover thickness , rib area and the increasing in concrete strength (high-strength concrete) on bond strength between concrete and reinforcing spliced bars . Therefore, a new simple equation is derived for beams with spliced bars and confined by transverse reinforcement to calculate bond strength and reflects the effects of these factors .Where many of existing codes and provisions used to calculate the spliced strength do not include or reflect the influencing of these factors in bond strength estimation . Based on experimental results from previous works , (116) confined beams with spliced bars are investigated in this study , where concrete compressive strength ( c f ¢ ) ranging from 25 MPa to 113.793 MPa ,amount of transverse reinforcement vary in a wide range and , conventional and high relative rib area of deformed bars are present in these beams . The proposed method exceed the limitation of ( MPa f c 69 £ ¢ ) that given by ACI code .Where the proposed method is examined and applicable for concrete compressive strength up to 113 MPa . Also, in this work the second root of c f ¢ is examined , as concrete strength increased with high-strength concrete , to reach a suitable value for both normal and high-strength concrete and to be more appropriate with the heavy present of transverse reinforcement . Power of (0.35) is adopted and used in this work instead of the second root of c f ¢ .


Introduction
Over the years , the estimation of bond strength between concrete and reinforcing bars has been improved .This improvement added a significant knowledge on bond behavior.The accuracy of the bond strength prediction increased and improved due to the increase in available test results that recently studied the effect of many factors on bond strength .The effect of admixtures of silica fume and other admixtures , the effect of lightweight aggregate and the effect of epoxy-coated reinforcing bars has been studied for their influence on bond strength [1][2][3][4][5] .In the last few years , high-strength concrete ( HSC ) has gained popularity for diverse applications such as bridges ,tall buildings , pavements ,etc .As the effect of concrete strength has been investigated 2,[6][7][8] , a comparison of the effects on bond strength of normal-strength concrete ( NSC ) and HSC has been made .Research indicates that bond strength increased with the increase of compressive strength of concrete and cover thickness 4,6 .The extent of damage at the steel-concrete interface depends on concrete strength and bar deformation pattern 2 .This damage was more extensive near the discontinuous ends of splices 6 .Bond failure of ribbed reinforcing bars generally involves splitting of the surrounding concrete cover unless heavy confinement reinforcement are present .Splitting failure results from a fracture of the concrete along the bar due to the lateral tension caused by wedging action provided by the bar deformations 6,9-13 .The use of transverse reinforcement is useful for ductility problems, where the unconfined beams tend to fail in more brittle mode than the confined ones-especially , when HSC is used , in which the drop in ductility is obvious 6,12 .
Azizinamini et al. 13  Where the use of term (u avg. ) is due to the non-uniform distribution of bond strength along the reinforcing bar 14,15 .When a reinforcement bar reaches the yield stress , the term Δf s will be replaced by steel yield stress (f y ), Eq.( 4) Bond Strength-Splice Length, In ACI 08 16

and Previous Provisions
Many studies tried to obtain a reliable formula that gives a suitable estimation for the bond strength between the concrete and the reinforcing bars that are being spliced or developed .Also, several equations have been derived to determine the splice or development length .As for the ACI code 08 16 , the estimation of splice or development length has been expressed in a reliable formula Eq.( 5 In which , the term shall not be taken greater than 2.5 , the product of

….(6)
Other studies proposed different approaches to predict the splice/development length and the bond strength .Esfahani et al. 8 provided a set of equations to calculate the bond strength and the splice length Where A t in this provision represents the area of one transverse reinforcing bar .In which Also, Esfahani et al. 8 derived another equation to obtain the development / splice length as in Eq.( 11) Where :

New Approach for Bond Strength Calculation
In order to obtain a better understanding for bond between concrete and reinforcing bars in spliced beams, a new equation is derived to calculate the bond strength and try to reflect the effect of different factors on bond behavior .Transverse reinforcement , concrete strength , cover thickness and the rib area of bars have been considered and represented in the proposed equation .The new formula is more simple than others6,8,17except for ACI 0816 .The effect of transverse reinforcement is represented as total area along the spliced region(At) .And the effect of transverse reinforcement is related with the spacing between stirrups within the spliced length (S) .Cover thickness, also has an effect on bond strength of concrete surrounding the spliced bars.The proposed equations examine this effect .A term of is given by the factor (K),Eq.(15) .Where (Ab) is the individual splice bar diameter , and (C) factor represent the minimum concrete thickness concrete surrounding the spliced bars .
Where , factor (K) reflects the influence of the surrounding matrix of spliced bar .Factor (K) can be used only for spliced beams confined by transverse reinforcement.This factor will be added to the nominal bond strength (u o ) to get the final bond strength expression , Eqs.16-19 Where ( ) for beams not confined by transverse reinforcement .By using regression analysis a factor (H) is found to reflect the increase in concrete strength( in case of HSC ) .This factor will vary as concrete strength increased .In order to simplify the proposed equation , this factor can be taken as a constant value equal to (1.176) .Therefore Eq.( 18) will be written as follows :

Bond Strength and the Effect of Transverse Reinforcement Within Splice Region
Generally , transverse reinforcement has a significant effect on bond strength due to the ductility problems .For spliced not confined beams the failure occurred suddenly , with a quick drop in load after the peak .In contrast, beams confined by transverse reinforcement gave a more ductile behavior , with a slow drop in load after the peak .And failure occurred in more ductile manner .When HSC is used in spliced beams the failure occurred in a more brittle manner than beams made with NSC 6 .From the above , the important effects of transverse reinforcement are obvious , as a solution for ductility problems .Confinement is more essential for HSC than NSC .This work studies the effect of transverse reinforcement on bond strength , in which NSC and HSC are used , by using experimental data from existing research .

Effect of Concrete Strength , Rib Area and Cover Thickness on Bond Strength
Bond failure at the concretesteel interface occurred due to the concrete crushing at the face of rib .Concrete damage depended on the concrete strength and bar deformation pattern.Usually damage is more extensive near the discontinuous ends of splices 6 .For conventional bars , concrete crushed between the bars ribs .In contrast, high rib area concrete both crushed and sheared 10 .In confined beams with HSC, concrete damage at the interface surface is similar in NSC beams , but the damage occurred over a longer region in the former 6 .In general, the use of high rib deformed bars reduction the splice length for both NSC and HSC .limited because a pullout failure is expected and the increase in cover is unlikely to increase the anchorage capacity 16 .

Discussion and Conclusions
This work studies the effect of different factors on bond strength between concrete and reinforcing bars .The influence of transverse reinforcement , area of individual splice bar (A b ) , concrete cover , rib area and concrete strength (NSC & HSC) are investigated by using experimental results from previous works 2,6,7,11,18,19 .This study tries to cover a very wide range of these factors values .Beams with different amounts of transverse reinforcement along splice region are studied , where transverse reinforcement varies in a very wide range .Concrete compressive strength ( c f ′ ) varies in a range of ( 25.0 MPa to 113.8 MPa ) to give a realistic indication to the increase in concrete strength behavior , deformed bars with conventional and high relative rib area has been covered and beam geometrical dimensions are also varied in a wide range .Table (      PDF created with pdfFactory Pro trial version www.pdffactory.comPDF created with pdfFactory Pro trial version www.pdffactory.com studied the effect of HSC on bond in spliced beam tests .When results indicate that the average bond stress values along the spliced reinforcing bars normalized with respect to the square PDF created with pdfFactory Pro trial version www.pdffactory.comEng.& Tech.Journal ,Vol.28,No..splice length increases .They also noticed that the bearing capacity of concrete is related to c f ′ while tensile capacity is related to ( c f ′ ) .HSC development failure in beams proved to be more brittle than with NSC .Therefore a suitable amount of transverse reinforcement must be used especially in the case of HSC .Zuo et al.6 have applied the influence of c f ′ in their proposed design .Instead of using providing a new simple and more accurate approach .Concrete strength properties , availability of transverse reinforcement within the splice region and the relative rib area are studied and examined .The proposed equations effect of these factors on the estimation of the splice strength.Also, the use of the square root of concrete bars and the surrounding matrix , and bearing against the face of the ribs .The total bond force is the sum of the components of the bearing and friction forces on the rib acting parallel to the reinforcing bar axis.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 transformed by bearing on the deformations of the bars ,Fig.(1a).Equal and opposite bearing stresses act on the concrete ,Fig.(1b).The forces on the concrete have both a longitudinal and a radial component , Fig.(1 c and d) .The concrete will split parallel to the bar and the resulting crack will propagate out to the side or bottom surface of the beam 14 ., flexural tensile forces are provided by reinforcing bars .Therefore there must be a force transfer (bond) between the two materials .Internal forces acting in the beam and forces acting in the reinforcing bars are illustrated in Fig.(2a and 2b) 14 .When this bond strength is lost the reinforcing bar will pull out of the concrete and the tensile force (T) will drop to zero causing the beam to fail .Stresses or forces in the reinforcing bars vary from point to pint along the length of bar, Fig.(3) 14 .If f s2 is greater than f s1 ,bond strength (u) must act on the surface of reinforcing bar to ensure equilibrium .By summing PDF created with pdfFactory Pro trial version www.pdffactory.comEng.& Tech.Journal ,Vol.28,No..

5 )
And f s is the tensile stress in the reinforcing bar at failure .Conservatively f s can be replaced by f y which also provides a margin of safety8 .Zuo et al.6 obtained a new design expression for the splice length ,in which the effects of concrete strength , coarse aggregate quantity , type and reinforcing bar geometry and amount of transverse reinforcement are evaluated .The power ¼ of compressive strength c f ′ best characterizes the effect of concrete strength on splice strength without transverse reinforcement .While the power ¾ characterizes the effect of concrete strength on the additional splice strength provided by transverse reinforcement .Reference 6 gives : PDF created with pdfFactory Pro trial version www.pdffactory.comEng.& Tech.Journal ,Vol.28,No..et al. 17 tried to derived a simple equation to estimate the splice length based on physical model of tension cracking of concrete in the lap spliced region .
Also, in this work the power of c f ′ is examined , as concrete strength increased with HSC , to reach a suitable value for both ( NSC & HSC ) and to be more appropriate with the heavy presence of transverse reinforcement .Power of (0.35) is used instead of the second root of c f ′ , Fig.(4).Fig.(4( changed to SI units)….(14)PDF created with pdfFactory Pro trial version www.pdffactory.comEng.& Tech.Journal ,Vol.28,No..2

Fig
Fig.(6).The effect of transverse reinforcement present shall not be taken without the use of HSC considerations , where both of transverse reinforcement and HSC have a simultaneous effects on bond between concrete and reinforcing bars .

Fig.( 7 )
provides a relationship between area of individual splice bar (A b ) and ( effect of (A b ) on bond strength for beams confined by transverse reinforcement is illustrated .Similarly , concrete thickness factor (C) have a great effect on the splice bond strength , in which the increase in concrete cover thickness has provides an increase in bond strength .This increased in bond strength is PDF created with pdfFactory Pro trial version www.pdffactory.comEng.& Tech.Journal ,Vol.28,No..
c f ′ ( or other powers )in order to reflect the effect of HSC and the heavy present of transverse reinforcement.Notations A b = area of an individual bar being spliced or developed .A tr , A t = total cross-sectional area of all b ,c = smaller of (a) the distance from center of a bar to nearest concrete surface , and (b) one-half the centerto-center spacing of bars being spliced or developed .C med = median of side and bottom concrete cover and one-half the center-to-center spacing of bars being spliced or developed .COV = coefficient of variation .d b = longitudinal reinforcing bar diameter .d t = transverse reinforcing bar diameter .f ′ c = concrete compressive strength .f s1 and f s2 =stresses acting in the reinforcement bar .f y = specified steel yield strength .f yt = specified yield strength of transverse reinforcement .H = factor used to reflect the effect of high-strength concrete on bond strength .HSC = high-strength concrete .L,l d = splice or development length .n = number of bars being spliced or developed .-strength concrete .S,s= center-to-center spacing of transverse reinforcement .u = calculated bond strength along the reinforcement bar being spliced .u avg.=average bond strength along the reinforcement bar .u o = nominal bond strength between concrete and reinforcing bars .u test = experimental (measured)bond strength .λ = modification factor related to density of concrete .ψ e = factor used to modify spliced or development length based on reinforcement coating .ψ s = factor used to modify spliced or development length based on reinforcement size .ψ t = factor used to modify spliced or development length based on reinforcement location .

Figure ( 5 )
Figure (5) Relationship between bondstrength ratio and the total area of transverse reinforcement (A t ) mm 2 along the spliced bars.

Figure ( 6 )
Figure (6) Effect of concrete compressive strength ( c f ′ )MPa on the bond strength ratio .

Figure ( 7 )
Figure (7) Relationship between bond strength ratio and the area of individual splice bar (A b ) mm 2 .

Bond Strength-Splice Length in Concrete Beams Confined by Transverse Reinforcement 332 Table (1) Details and test result for splice beams confined by transverse reinforcement
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Journal ,Vol.28,No..2,2010 Bond Strength-Splice Length in Concrete Beams Confined by Transverse Reinforcement 335 Table (2) Statistical results for provisions studied in this work Statistical measurements Provisions studied in this work
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