building codes with low-strength mortars
Eurocode 2 Part 1–6: Plain concrete structures
5 Results taken from the literature
6.1 Comparison with Eurocode 2
6.1.3 Evaluation of the modulus of elasticity Estimates based on the compressive strength
Figs. 7 and 8 show the predictions of Eqs. (5) and (8). For the results taken from the literature, the mean and maxi-mum relative errors are 8 and 56 % respectively for Eq.
(5), and 11 and 25 % for Eq. (8). The predictions of both equations seem to overestimate the results from [16], [15]
and [17], which are the ones containing rubber or light-weight aggregates.
For the experimental results, the mean and maxi-mum relative errors are 62 and 147 % respectively for Eu-rocode 2 (Eq. (5)), and 13 and 45 % for ACI 318 (Eq. (7)).
As can be seen in Fig. 9, the prediction of Eurocode 2 is an overestimation for all experimental results. As shown in Fig. 10, ACI 318 (Eq. (8)) provides a better estimation for this range of compressive strength (but still overestimates its actual value).
It can be seen in the previous section that the impact of the modulus of elasticity of the cement paste on that of the concrete changes when the granular skeleton incorpo-rates low-stiffness aggregates. For those materials, the modulus of elasticity should not be estimated with the compressive strength as the only input data. As will be shown in the next section, the consideration of a second input, the unit weight, allows the estimation of the modu-lus of elasticity of those materials to be acceptable.
Fig. 5. Correlation between 7- and 28-day moduli of elasticity – results from the literature
Fig. 6. Correlation between 7- and 28-day moduli of elasticity – experimen-tal results
F. Duplan/A. Abou-Chakra/A. Turatsinze/G. Escadeillas/S. Brûlé/E. Javelaud/F. Massé · On the use of European and American building codes with low-strength mortars
Estimates based on the compressive strength and unit weight
For Eurocode 2 Part 1-4, only concretes with dry densities
< 2000 kg/m3are supposed to be concerned. For ACI 318, Eq. (7) can be used with unit weights between 1440 and 2560 kg/m3.
The addition of the correcting factor gE (Eq. (6)) to Eq. (5) significantly improves the prediction for the studies of [16], [15], [17] and [18]: the mean and maximum relative errors are 21 and 78 % respectively, compared with 96 and 132 % when the correcting factor gEwas not taken into ac-count.
The prediction of Eq. (7) from ACI 318 gives lower re-sults than Eurocode 2 Part 1–4 and seems to be closer to the actual values of the modulus of elasticity of light-weight concrete: the mean and maximum relative errors are 14 and 31 % respectively. The predicted and experi-mental moduli from the literature are presented in Table 5.
As for the results from the literature, the addition of the coefficient gEto Eq. (5) improves the prediction of the moduli of elasticity of the mortars investigated: mean and maximum relative errors are 15 and 45 % respectively, compared with 62 and 147 % without the correcting factor gE.
Eq. (7) underestimates the modulus of elasticity of the mortars investigated. The mean and maximum relative errors were 13 and 45 % respectively, compared with 29 and 41 % for Eq. (7). The predicted and experimental moduli are presented in Table 6.
7 Conclusion
The evolution of the compressive strength of low-strength mortars over time is predicted with accuracy by Euro -code 2 and ACI 209.
The time dependence of the modulus of elasticity can be predicted with the Eurocode 2 formula for normal-Fig. 7. Correlation between compressive strength and modulus of elasticity
– results from the literature – Eurocode 2
Fig. 8. Correlation between compressive strength and modulus of elasticity – results from the literature – ACI
Fig. 9. Correlation between compressive strength and modulus of elasticity – experimental results – Eurocode 2t
Fig. 10. Correlation between compressive strength and modulus of elas -ticity – experimental results – ACI
42
F. Duplan/A. Abou-Chakra/A. Turatsinze/G. Escadeillas/S. Brûlé/E. Javelaud/F. Massé · On the use of European and American building codes with low-strength mortars
Structural Concrete (2015), No. 1
weight concretes. When specific (and less stiff) aggregates are incorporated in the cement mix, those formulas lose their precision because the impact of the cement paste hy-dration on the overall elastic properties of the material is changed.
Estimating the modulus of elasticity of low-strength mortars with Eurocode 2 should take into account their unit weights in order to improve the precision. With ACI building codes, the consideration of the unit weight does
not give a better accuracy, and systematically underesti-mates the modulus of elasticity.
Acknowledgements
The authors would like to thank the Menard company for their financial support and for showing great interest in this work.
Table 5. Predicted moduli of elasticity with unit weight and compressive strength – results from the literature
fcm q (EC2), wc(ACI) Eexp EACl EEC2 error EACl error EEC2 Reference
(MPa) (kg/m3) (GPa) (GPa) (GPa) (%) (%) –
63.0 2300 34.0 37.6 41.8 11 % 23 % [16]
40.0 2150 23.5 26.3 31.8 12 % 36 % [16]
27.0 2090 18.0 20.4 26.7 13 % 49 % [16]
18.0 2040 17.0 15.8 22.6 7 % 33 % [16]
44.0 2300 35.0 31.5 37.5 10 % 7 % [15]
34.0 2240 30.0 26.4 32.9 12 % 10 % [15]
22.5 2190 24.5 20.6 27.8 16 % 13 % [15]
13.8 2050 19.5 14.5 21.0 26 % 8 % [15]
7.5 1950 13.5 9.8 15.9 27 % 17 % [15]
6.0 1850 10.0 8.1 13.3 19 % 33 % [15]
44.0 2300 35.0 31.5 37.5 10 % 7 % [15]
36.0 2170 27.0 25.9 31.4 4 % 16 % [15]
30.0 2050 22.0 21.5 26.6 2 % 21 % [15]
20.0 2008 18.0 16.9 22.6 6 % 25 % [15]
16.0 1975 15.0 14.6 20.4 2 % 3 % [15]
12.0 1927 10.0 12.1 17.8 21 % 78 % [15]
40.2 1970 28.6 23.8 26.8 17 % 6 % [17]
36.5 1850 23.5 20.3 22.9 14 % 2 % [17]
30.8 1720,0 20.7 16.4 18.8 21 % 9 % [17]
27.2 1560 16.7 13.0 14.9 22 % 11 % [17]
24.9 1530 15.7 11.9 14.0 24 % 11 % [17]
50.0 2456 45.7 37.0 44.4 19 % 3 % [18]
22.6 2226 22.1 21.5 28.8 3 % 30 % [18]
17.0 2121 23.3 17.3 24.0 26 % 3 % [18]
21.7 2233 22.0 21.1 28.6 4 % 30 % [18]
18.5 2069 25.4 17.4 23.4 31 % 8 % [18]
19.4 2053 17.5 17.6 23.4 1 % 34 % [18]
17.8 2067 21.9 17.1 23.1 22 % 5 % [18]
17.8 2093 18.0 17.4 23.7 3 % 32 % [18]
7.1 1823 10.8 8.9 13.7 17 % 26 % [18]
F. Duplan/A. Abou-Chakra/A. Turatsinze/G. Escadeillas/S. Brûlé/E. Javelaud/F. Massé · On the use of European and American building codes with low-strength mortars
Notation Eurocode 2
fcm(MPa) average concrete compressive strength after 28 days of curing
fctm(MPa) average concrete tensile strength after 28 days of curing
Ecm(GPa) average concrete modulus of elasticity after 28 days of curing
t days of curing
βcc(t) time evolution term
fcm(t) (MPa) average concrete compressive strength after t days of curing
Ecm(t) (GPa) average concrete modulus of elasticity after t days of curing
Eurocode 2 Part 1–4 q (kg/m3) dry unit weight
gE reduction factor for lightweight concrete ACI 318
Ec(psi) modulus of elasticity of concrete wc(lb/ft3) dry unit weight of concrete
fc′ (psi) specified compressive strength of concrete ACI 209
(fc′)t (psi) compressive strength of concrete after t days of curing
(fc′)28 (psi) compressive strength of concrete after 28 days of curing
(fc′)u (psi) ultimate compressive strength of concrete over time
References
1. ACI Committee 318: American Concrete Institute and Inter-national Organization for Standardization. Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary, 2008.
2. Guide for structural lightweight-aggregate concrete, ACI, 213R-03, 2003.
3. ACI Committee 209R-92-Creep and Shrinkage: Prediction of Creep, Shrinkage, and Temperature Effects in Concrete Structures. ACI standard, American Concrete Institute, 2008.
4. Turatsinze, A., Garros, M.: On the modulus of elasticity and strain capacity of self-compacting concrete incorporating rubber aggregates. Resour. Conserv. Recycling, 52 (10):
1209–1215, 2008.
5. Panesar, D. K., Shindman, B.: Elastic properties of self con-solidating concrete. Construction and Building Materials, 25: 3334–3344, 2011.
6. Parra, C., Valcuende, M., Gomez, F.: Splitting tensile strength and modulus of elasticity of self-compacting concrete. Con-struction and Building Materials, 25: 201–207, 2011.
7. Shariq, M., Prasad, J., Masood, A.: Effect of gbbfs on time dependent compressive strength of concrete. Construction and Building Materials, 24: 1469–1478, 2010.
8. Shariq, M., Prasad, J., Masood, A.: Effect of gbbfs on age de-pendent modulus of elasticity of concrete. Construction and Building Materials, 41: 411–418, 2013.
9. Aslani, F., Nejadi, S.: Self compacting concrete incorporat-ing steel and polypropylene fibers. Composites: Part B, 53:
121–133, 2013.
10. Wild, S., Sabir, B. B., Khatib, J. M.: Factors influencing strength development of concrete containing silica fume. Ce-ment and Concrete Research, 25 (7): 1567–1580, 1995.
11. Malaikah, A. S.: A proposed relationship for the modulus of elasticity of high strength concrete using local materials in Riyadh. Journal of King Saud University, 7, 2004.
12. Nazari, A., Riahi, S.: Improvement compressive strength of concrete in different curing media by Al2O3 nanoparticles.
Materials Science and Engineering, 528: 1183–1191, 2011.
13. Kim, J. K., Moon, Y. H., Eo, S. H.: Compressive strength de-velopment of concrete with different curing time and tem-perature. Cement and Concrete Research, 28 (12):
1761–1773, 1998.
14. Zain, M. F. M., Mahmud, H. B., Ilham, A., Faizal, M.: Pre-diction of splitting tensile strength of high-performance con-crete. Cement and Concrete Research, 32: 1251–1258, 2002.
15. Garros, M.: Composites cimentaires incorporant des granu-lats caoutchouc issus du broyage de pneux usagés: optimisa-tion de la formulaoptimisa-tion et caractérisaoptimisa-tion – Cementitious composites incorporating waste tire rubber aggregates. PhD thesis, Université de Toulouse, 2007.
16. Ho, A. C.: Optimisation de la composition et caractérisation d’un béton incorporant des granulats issus du broyage de pneus usagés. Application aux éléments de grande surface. – Mix design optimization and characterization of concrete in-corporating waste tire rubber aggregates. PhD thesis, Univer-sité de Toulouse, 2010.
17. Ke, Y., Beaucour, A. L., Ortola, S., Dumontet, H., Cabrillac, R.: Influence of volume fraction and characteristics of light-weight aggregates on the mechanical properties of concrete.
Construction and Building Materials, 23: 2821–2828, 2009.
18. Panesar, D. K., Shindman, B.: The mechanical, transport and thermal properties of mortar and concrete containing waste cork. Cement and Concrete Composites, 34: 982–992, 2012.
Francois Duplan PhD
Université de Toulouse, UPS, INSA LMDC (Laboratoire Materiaux et Durabilite des Constructions) 135, Avenue de Rangueil F-31 077 Toulouse cedex 4, France Menard, 91 620 Nozay, France [email protected] Tel.: +3356 155 9916
Table 6. Predicted moduli of elasticity with unit weight and compressive strength – experimental results
fcm ρm Eexp EACl EEC2 error EACl error EEC2
44
F. Duplan/A. Abou-Chakra/A. Turatsinze/G. Escadeillas/S. Brûlé/E. Javelaud/F. Massé · On the use of European and American building codes with low-strength mortars
Structural Concrete (2015), No. 1 Ariane Abou-Chakra, Assistant professor Université de Toulouse, UPS, INSA LMDC (Laboratoire Materiaux et Durabilite des Constructions) 135, Avenue de Rangueil F-31 077 Toulouse cedex 4, France [email protected] Tel.: +3356155 9930
Anaclet Turatsinze, Professor Université de Toulouse, UPS, INSA LMDC (Laboratoire Materiaux et Durabilite des Constructions) 135, Avenue de Rangueil F-31 077 Toulouse cedex 4, France [email protected] Tel.: +3356155 9934
Gilles Escadeillas, Head of departement Université de Toulouse, UPS, INSA LMDC (Laboratoire Materiaux et Durabilite des Constructions) 135, Avenue de Rangueil F-31 077 Toulouse cedex 4, France [email protected] Tel.: +3356155 7498
Stéphane Brûlé Menard, 91 620 Nozay France
[email protected] Tel.: +33478513394
Emmanuel Javelaud Menard, 91 620 Nozay France
[email protected] Tel.: +33478513394
Frédéric Massé
Menard, 150 East Main Street,
Suite 500 Carnegie, PA 15106, United States [email protected] Tel. : +14126206000
This paper describes the changes to design provisions for em-bedded steel reinforcement in the fib Model Code for Concrete Structures 2010. The changes introduce new coefficients for steel grade and clear spacing between bars, and extend the range of concrete strengths covered. The way in which the con-tribution of hooks or anchorages is calculated has been revised and the contribution of end bearing to laps and anchorages of compression bars is recognized. The revised rules represent a move away from a distinction between laps and anchorages per se towards a distinction based on the presence or absence of transverse pressure perpendicular to the bar axis within the bond length. The benefits of staggering laps with only a proportion of bars lapped at a section are also reviewed. Finally, the potential impact of lap and anchorage performance on structural robust-ness is discussed, and it is concluded that this can only be achieved if bar yield precedes splitting mode bond failures.
Keywords: fib Model Code, bond, anchorage, lapped joints, hooks and bends
1 Introduction
The fib Model Code for Concrete Structures 2010 [1] was published in its final version in 2013. As part of the revi-sion process, fib Task Group 4.5 “Bond Models” under-took a thorough review of the content for bond of embed-ded steel reinforcement, the outcome of which has resulted in section 6.1 of fib Model Code 2010. This paper reviews the major changes between MC90 [2] and fib Model Code 2010 with the aim of helping users to under-stand the revised rules and the underlying physical basis for the changes introduced. The scope of the paper is re-stricted to conventional non-coated ribbed reinforcing bars.
The basic expressions for bond strength in the Model Codes have remained essentially unchanged since MC78 [3]. Since then there has been a general increase in the strengths of both concrete and reinforcement used in con-struction. For example, the characteristic strength of rein-forcement in many European countries was about 410 MPa in 1978, but is currently 500 MPa. The CEB Bul-letin on High Performance Concrete [4] recommended that the range of concrete grades covered in the 1990
Model Code be extended from the limit of C80/100 then up to C100/125 now, and that the validity of current rules for bond and anchorage should be reconsidered. In addi-tion, the source of many rules in MC90 was unknown and evidence to support them lacking. A rigorous review of the Model Code provisions for bond and anchorage was there-fore considered necessary.