Bond and anchorage of embedded steel reinforcement in fib Model Code 2010
6.4 Lapped bars of different diameter
If lapped bars are of different diameters, lap length may be based on the diameter of the smaller bar.
7 Ductility and robustness
The splitting mode of bond failure is invariably non-duc-tile, even where relatively large amounts of confining re-inforcement are present. The options for ensuring ductili-ty are a) to provide sufficient confinement for a pullout mode of failure and b) to ensure the bonded length is long enough for the bar to reach yield. Although it is be-lieved that one of the justifications for the lower values of the coefficient α6 in MC90 when only a proportion of bars is lapped was that bars continuous through the lapped joint would maintain some post-peak capacity in the event of a failure of the lapped proportion, the avail-able evidence shows that where laps are staggered with only 50 % of bars lapped at a section, beams behave in a manner nearly as brittle as those beams with 100 % of bars lapped at the same section [20], Fig 13. Fig. 14 shows the method of determining the ductility index Dresused in Fig. 13.
At end anchorages at supports, Figs. 6a and 6b, para-metric investigations show that where bond demand ex-ceeds basic bond strength, transverse compression will be sufficient to preclude a splitting failure mode. In such situ-ations a moderately ductile failure mode would be ob-tained without the need to design for the bar yielding, and the design stress may be taken as α1.fyd, with α1 = As,cal/As,ef, where As,calis the calculated area of reinforce-ment required by the design and As,efis the area of rein-forcement provided. Bond failure of a lapped joint is like-ly to occur in a splitting mode for all except the smallest diameter bars; hence, they should be designed to ensure an adequate probability that bars can reach yield. Lap length should therefore not be reduced if the area of rein-forcement provided exceeds that required by design, as was permitted in MC90.
8 Economy and constructability
Although the contribution of lapped joints to material costs is small in relation to the overall costs of construc-tion, laps may have a significant impact on locations of construction joints and hence on a construction pro-gramme. Contractors therefore wish to minimize lap lengths consistent with maintaining an appropriate level
0 1 2 3
6.00
5.00
4.00
3.00
2.00
1.00
0.00
Bond strength (MPa)
No. in bundle
Fig. 12. Influence of bundle size on bond strength of lapped joint [22]
0.0 0.2 0.4 0.6 0.8 1.0
0% 25% 50% 75% 100%
Duclity Index Dres
Proporon lapped
Bundle Individual
Fig. 13. How proportion of bars lapped at a section influences post-peak resistance [19]
of safety. Good detailing practice locates laps where stress in reinforcement is low, e.g. near points of contraflexure in continuous beams. Stresses in lapped bars at such loca-tions will never approach the design strength of reinforce-ment under normal service conditions. It is only in the event of accidental loading or damage that bars would be highly stressed, e.g. if an intermediate support were to fail.
In such situations the lap should still be designed so that the bar reaches yield, but the partial safety factor used when determining the basic bond strength should be that appropriate to accidental rather than transient and persis-tent situations. A coefficient α4= 0.7 has been introduced for such circumstances to permit shorter laps where it is safe to do so, and will encourage detailers to locate laps at positions of low reinforcement stress.
9 Local bond-slip relationship
In MC90 it was not apparent how the bond strengths for laps or anchorages presented in section 6.9 related to the local bond-slip relationship presented in section 3. The basic design bond strength for a grade 30 concrete in MC90 is 3.0 MPa, while the peak bond stress τmaxfrom the local bond-slip relationship is 12.3 MPa – over four times greater; hence, the two sections might be perceived to be inconsistent.
There are several reasons for the difference. The lo-cal bond-slip relationship gives a mean value, whereas the basic bond strength is a characteristic value. The local bond-slip relationship is based on a test specification such as that for the RILEM pullout test which has a short bond length of 5φ and a relatively thick concrete cover equal to 4.5φ. As demonstrated in Fig. 4, average bond strength de-creases with increasing bond length. The thick cover, to-gether with arching action within the specimen, provides high confinement. By contrast, the application rules pro-vide design values based on the minimum permissible cov-er of 1φ and thus correspond to a much lower confine-ment, and are also derived for much longer bond lengths.
The values for τbu,splitgiven in the local bond-slip relation-ship and design bond strengths given in fib Model Code 2010 are both derived from Eq. (3), so the common origin
54
J. Cairns · Bond and anchorage of embedded steel reinforcement in fib Model Code 2010
Structural Concrete (2015), No. 1
of these two parts of the fib Model Code 2010 provisions is now explicit.
10 Simplified rules
While it is essential that design rules for bond of embed-ded reinforcement be based on rational physical models of the relevant physical phenomena, refinement of design rules invariably leads to increasing complexity in the cal-culations associated with the detailing process for laps and anchorages, which brings with it an increased possibility of errors. There is therefore an incentive to derive simpli-fied requirements for more common situations and to de-velop a system of classification to define them. Detailing rules in sections 7.13.2.5 and 7.13.2.6 of fib Model Code 2010 are derived from the provisions of section 6.1 for the most common situations and represent a basic attempt at classification.
11 Conclusions
This paper provides an overview of the rationale under-pinning the requirements of fib Model Code 2010 for the design of laps and anchorages of embedded ribbed steel reinforcement. The reader should refer to fib Bulletin 72 [5] for a more comprehensive and detailed review. It is demonstrated that fib Model Code 2010 design rules are linked back to evidence from a large number of physical tests. The most significant changes from MC90 are:
1. An extension of the range of concrete strengths cov-ered.
2. The introduction of a new coefficient η4for steel grade to allow for the non-linear relationship between bond length and the stress developed in a bar.
3. Revisions to the expressions allowing for confinement by concrete and secondary reinforcement and to their respective limiting values, plus the introduction of a clear spacing parameter cmax/cminwhich permits short-er laps in slabs.
4. A change in the way the contribution of hooks or an-chorages is determined.
Fig. 14. Typical plot of load vs. deflection, showing calculation of deformability index Dres
J. Cairns · Bond and anchorage of embedded steel reinforcement in fib Model Code 2010 5. Recognition of the contribution of end bearing to laps
and anchorages for compression bars.
6. A distinction between laps and anchorages based on the presence or absence of transverse pressure instead of function.
7. Discontinuation of the α6coefficient for staggered laps.
8. Recognition of the need to avoid brittle failures of lapped joints and that structural robustness requires bar yield to precede a splitting mode bond failure.
9. A clear link between design rules and the local bond-slip relationship.
Acknowledgements
The author wishes to record his appreciation for the con-tributions to the work summarized in this paper made by members of TG4.5, in particular G. Balazs, R. Elige-hausen, S. Lettow, G. Metelli, S. Pantazopoulou and G.
Plizzari.
References
1. fib – International Federation for Structural Concrete. fib Model Code for Concrete Structures 2010. Berlin: Verlag Ernst & Sohn, 2013.
2. CEB-FIP Model Code 90. CEB, Lausanne, 1993.
3. CEB-FIP Model Code for concrete structures. CEB, 1978.
4. CEB Bulletin 228: High Performance Concrete. Recom-mended Extensions to the Model Code 90 – Research Needs, 1995, ISBN 978-2-88394-031-4.
5. fib: Bond and anchorage of embedded reinforcement: Back-ground to the fib Model Code 2010. fib Bulletin fib, Lau-sanne, May 2014 170pp. ISBN 978-2-88394-112-0
6. ACI 408 bond database – may be obtained from:
http://www.concrete.org/technical/ckc/Additional_Data_R eferenced_from_Technical_Committee_Documents.htm 7. fib TG4.5 bond test database – may be obtained from:
http://fibtg45.dii.unile.it/files%20scaricabili/Database_splic etest%20Stuttgart% 20sept%202005.xls
8. Amin, R.: End Anchorage At Simple Supports In Reinforced Concrete. PhD thesis, London South Bank University, Nov 2009.
9. Canbay, E., Frosch, R. J.: Bond Strength of Lap-Spliced Bars.
ACI Structural Journal, vol. 102, No. 4, Jul 2005.
10. Orangun, C. O., Jirsa, J. O., Breen, J. E.: ‘A Re-evaulation of Test Data on Development Length and Splices’, Proceedings American Concrete Institute. Vol. 74, No. 3, March 1977.
11. Zuo, J., Darwin, D.: ‘Splice Strength of Conventional and High Relative Rib Area Bars in Normal and High-Strength Concrete’, ACI Structural Journal. Vol. 97, No. 4, July 2000.
12. Eurocode 2: Design of concrete structures – Part 1-1: Gener-al rules and rules for buildings. BS EN 1992-1-1:2004. British Standards Institution, London, 2004.
13 Schiessl, P.: Interaction between anchorage of bond, hooks and welded transverse bars. Proc. of Intl. Conf. on Bond in Concrete. Paisley, Applied Science Publishers, London, 1982, pp. 424–433.
14. American Concrete Institute. ACI 318-11: Building Code Re-quirements for Structural Concrete and Commentary. ACI, Michigan, USA, 2008.
15. Ferguson, P. M., Breen, J.: Lapped Splices For High Strength Reinforcing Bars. ACI Proc., vol. 62, No. 9, 1965, pp.
1063–1078.
16. Tepfers, R.: A Theory of bond applied to overlapped rein-forcement splices for deformed bars. Chalmers Technical University, Institution for Betonbyggnad. Pub. No. 73:2, Gothenburg, 1973.
17. Reynolds, G., Beeby, A. W.: Proc. of Intl. Conf. on Bond in Concrete. Paisley, Applied Science Publishers, London, 1982.
18. Magnusson, J.: Bond and anchorage of ribbed bars in high strength concrete. PhD thesis, Div. of Concrete Structures, Chalmers University of Technology, Gothenburg, 2000.
19. Metelli, G., Cairns, J., Plizzari, G.: The influence of percent-age of bars lapped on performance of splices. Materials and Structures, June 2014. DOI: 10.1617/s11527-014-0371-y 20. Cairns, J. (2014), Staggered lap joints for tension
reinforce-ment. Structural Concrete, 15: 45–54. doi: 10.1002/suco.
201300041.
21. Cairns, J.: Bond Strength Of Compression Splices: A Re-eval-uation Of Test Data. ACI Proc., Jul/Aug 1985, pp. 510–516.
22. Cairns, J.: Lap Splices of Bars in Bundles. ACI Structural Journal (110-S16), Mar/Apr 2013.
John Cairns
School of the Built Environment Heriot-Watt University Edinburgh EH14 4AS, UK [email protected]
56 © 2015 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete (2015), No. 1
Technical Paper
DOI: 10.1002/suco.201300101
The effect of concrete grade on the bond between 12 mm diame-ter deformed steel bars and recycled aggregate concrete (RAC) has been investigated with the help of 45 pullout tests with con-centric rebar placement for coarse recycled concrete aggregate (RCA) replacement levels of 25, 50, 75 and 100 %. For all the three concrete grades, the measured bond-slip relationships indicate similar mechanisms of bond resistance in the RAC and the natur-al aggregate (NA) concrete. The most accurate and least conser-vative predictions of the measured bond strengths were obtained from the local bond-slip model in the fib Model Code for Concrete Structures 2010. Bond strength normalized to fc(3/4)resulted in an improved match with test data and increased with an increase in the RCA replacement levels and decreased with an increase in compressive strength. An attempt to explain this behaviour has been sought in terms of brittleness index, an analogous parame-ter from rock mechanics. An empirical bond stress versus slip re-lationship has been proposed for the 12 mm diameter bar and it is conservatively suggested that similar anchorage lengths for this bar in all three concrete grades can be adopted for the RAC and the NA concretes.
Keywords: coarse recycled concrete aggregate, replacement level, natural coarse aggregate, bond, pullout failure, normalized bond strength
1 Introduction
Traditionally, bond strength between steel bars and con-ventional concrete (made with natural coarse aggregates) has been normalized to the square root of the concrete compressive strength fc [1–7], although this practice has not been universal. Zsutty [8], for example, found that fc1/3 provided a better match with data compared with fc1/2.On the basis of a review of a large number of bond test results of concretes with strengths between 17 and 110 MPa, Dar-win et al. [9] and Zuo and DarDar-win [10] have reported that the effect of concrete grade on splice strength for normal-strength as well as high-normal-strength concrete is more accu-rately represented if the bond strength data are normal-ized to fc1/4. The bond test results of Harajli and Al-Hajj [11] show that as the compressive strength of concrete in-creased from about 28 MPa to about 55 MPa, the local
splice strength increased in proportion to fcp, with p > 1/2.
These authors found that for all the parameters they inves-tigated, whenever the local splice strengths were normal-ized to fc1/2, the results of high-strength concrete were about 23 % higher than those of normal-strength concrete.
On the other hand, according to Azizinamini et al. [12], the normalized average bond strength at failure in high-strength concrete reduces relative to normal-high-strength con-crete, and this reduction in bond strength increases with an increase in splice length. In contrast to the results of Azizinamini et al. [12], Esfahani and Rangan [13] found that the average bond stress at failure normalized with re-spect to fc1/2 is higher for high-strength concrete than for normal-strength concrete. According to the literature, fc1/2 does not accurately represent the effect of concrete strength on bond, and ACI Committee 408 [14] states that
“when bond strengths are normalized with respect to fc1/2, the effect of concrete strength is exaggerated, resulting in an overestimation of bond strength for higher strength concretes”.
The brief review presented above indicates the com-plexity of the relationship between local bond strength of deformed steel bars and grade of concrete (made with nat-ural coarse aggregates). In recent years, considerable ef-fort has been directed towards investigating the possibility of using coarse recycled concrete aggregate (RCA) as a substitute for natural coarse aggregate (NCA) in concrete construction. Although the bond behaviour between NCA concrete and steel rebars has been extensively studied [14–16], only a few investigations have looked at the bond between RCA concrete and steel reinforcement [17–21].
This situation is further compounded by the fact that even less information is available in the literature on the bond strength of deformed steel bars embedded in high-strength