Title:
Cracking and Crushing in Prestressed Concrete Beams
Author(s):
Federico Accornero, Renato Cafarelli, and Alberto Carpinteri
Publication:
Structural Journal
Volume:
118
Issue:
2
Appears on pages(s):
101-109
Keywords:
concrete cracking; concrete crushing; ductile-to-brittle transition; non-linear fracture mechanics; prestressed concrete; scale effects
DOI:
10.14359/51728184
Date:
3/1/2021
Abstract:
The cohesive/overlapping crack model represents an effective tool in the study of failure transition phenomena occurring in plain or reinforced concrete structures. In the present paper, this non-linear fracture mechanics model is applied to study the global structural behavior of prestressed concrete beams casted by means of pre-tensioning technique or, more generally, having a straight steel strand layout. In this context, a thorough analysis of scale effects is presented to investigate local mechanical instabilities such as snap-back and snap-through phenomena due to concrete cracking or crushing, highlighting the crucial role of the ductile-to-brittle transition in the design of prestressed concrete structural elements.
Related References:
1. Carpinteri, A.; Marega, C.; and Savadori, A., “Ductile-Brittle Transition by Varying Structural Size,” Engineering Fracture Mechanics, V. 21, No. 2, 1985, pp. 263-271. doi: 10.1016/0013-7944(85)90015-3
2. Carpinteri, A., and Corrado, M., “Upper and Lower Bounds for Structural Design of RC Members with Ductile Response,” Engineering Structures, V. 33, No. 12, 2011, pp. 3432-3441. doi: 10.1016/j.engstruct.2011.07.007
3. Hillerborg, A.; Modéer, M.; and Petersson, P.-E., “Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements,” Cement and Concrete Research, V. 6, No. 6, 1976, pp. 773-781. doi: 10.1016/0008-8846(76)90007-7
4. Gustafsson, P. J., and Hillerborg, A., “Sensitivity in Shear Strength of Longitudinally Reinforced Concrete Beams to Fracture Energy of Concrete,” ACI Structural Journal, V. 85, No. 3, May-June 1988, pp. 286-294.
5. Jenq, Y. S., and Shah, S. P., “Shear Resistance of Reinforced Concrete Beams – A Fracture Mechanics Approach,” Fracture Mechanics: Application to Concrete, SP-118, American Concrete Institute, Farmington Hills, MI, 1990, pp. 237-258.
6. Carpinteri, A., “A Fracture Mechanics Model for Reinforced Concrete Collapse,” IABSE Reports of the Working Commissions, 1981.
7. Carpinteri, A., “Sensitivity and Stability of Progressive Cracking in Plain and Reinforced Cement Composites,” International Journal of Cement Composites and Lightweight Concrete, V. 4, No. 1, 1982, pp. 47-56. doi: 10.1016/0262-5075(82)90007-0
8. Carpinteri, A., “Stability of Fracturing Process In RC Beams,” Journal of Structural Engineering, ASCE, V. 110, No. 3, 1984, pp. 544-558. doi: 10.1061/(ASCE)0733-9445(1984)110:3(544)
9. Carpinteri, A., “Interpretation of the Griffith Instability as a Bifurcation of the Global Equilibrium,” Application of Fracture Mechanics to Cementitious Composite (edited by Surenda P. Shah), NATO ASI Series, Series E: Applied Sciences, V. 94, 1985, pp. 287-316.
10. Carpinteri, A., “Size Effects on Strength, Toughness, and Ductility,” Journal of Engineering Mechanics, ASCE, V. 115, No. 7, 1989, pp. 1375-1392. doi: 10.1061/(ASCE)0733-9399(1989)115:7(1375)
11. Carpinteri, A., Minimum Reinforcement in Concrete Members, Elsevier, 1999.
12. Carpinteri, A.; Colombo, G.; and Giuseppetti, G., “Accuracy of the Numerical Description of the Cohesive Crack Propagation,” Fracture Toughness and Fracture Energy of Concrete, Elsevier Science Publisher, 1985, pp. 189-195.
13. Bosco, C.; Carpinteri, A.; and Debernardi, P. G., “Fracture of Reinforced Concrete: Scale Effects and Snap-Back Instability,” Engineering Fracture Mechanics, V. 35, No. 4-5, 1990, pp. 665-677. doi: 10.1016/0013-7944(90)90149-B
14. Bosco, C., and Carpinteri, A., “Softening and Snap-through behavior of Reinforced Elements,” Journal of Engineering Mechanics, ASCE, V. 118, No. 8, 1992, pp. 1564-1577. doi: 10.1061/(ASCE)0733-9399(1992)118:8(1564)
15. NCHRP, “LRFD Minimum Flexural Reinforcement Requirements,” National Cooperative Highway Research Program (NCHRP) Research Report 906, 2019.
16. Carpinteri, A.; Corrado, M.; Paggi, M.; and Mancini, G., “Cohesive Versus Overlapping Crack Model for a Size Effect Analysis of RC Elements in Bending,” Proceedings of the 6th International Conference on Fracture Mechanics of Concrete and Concrete Structures, V. 2, 2007, pp. 655-663.
17. Carpinteri, A.; Corrado, M.; Mancini, G.; and Paggi, M., “Size-Scale Effects on Plastic Rotational Capacity of Reinforced Concrete Beams, ACI Structural Journal, V. 106, No. 6, Nov.-Dec. 2009, pp. 887-896.
18. Carpinteri, A.; Corrado, M.; and Paggi, M., “An Integrated Cohesive/Overlapping Crack Model for the Analysis of Flexural Cracking and Crushing in RC Beams,” International Journal of Fracture, V. 161, No. 2, 2010, pp. 161-173. doi: 10.1007/s10704-010-9450-4
19. Dugdale, D. S., “Yielding of Steel Sheets Containing Slits,” Journal of the Mechanics and Physics of Solids, V. 8, No. 2, 1960, pp. 100-104. doi: 10.1016/0022-5096(60)90013-2
20. Barenblatt, G. I., “The Formation of Equilibrium Cracks during Brittle Fracture, General Ideas and Hypothesis, Axially Symmetric Cracks,” Journal of Applied Mathematics and Mechanics, V. 23, 1959, pp. 434-444.
21. Barenblatt, G. I., “The Mathematical Theory of Equilibrium Cracks in Brittle Fracture,” Advances in Applied Mechanics, V. 7, 1962, pp. 55-129. doi: 10.1016/S0065-2156(08)70121-2
22. Hillerborg, A., “Numerical Methods to Simulate Softening and Fracture of Concrete,” Fracture Mechanics of Concrete: Structural Application and Numerical Calculation (edited by George C. Sih and Angelo Di Tommaso), 1985, pp. 141-170.
23. Carpinteri, A., “Cusp Catastrophe Interpretation of Fracture Instability,” Journal of the Mechanics and Physics of Solids, V. 37, No. 5, 1989, pp. 567-582. doi: 10.1016/0022-5096(89)90029-X
24. Ruiz, G.; Elices, M.; and Planas, J., “Size Effect and Bond-Slip Dependence of Lightly Reinforced Concrete Beams,” Minimum Reinforcement in Concrete Members (edited by Alberto Carpinteri), 1999, pp. 67-97.
25. Petersson, P.-E., “Crack Growth and Development of Fracture Zone in Plain Concrete and Similar Materials,” PhD thesis, 1981, Lund University.
26. Kotsovos, M. D., “Effect of Testing Techniques on the Post-Ultimate Behaviour of Concrete in Compression,” Matériaux et Construction, V. 16, 1983, pp. 3-12.
27. van Mier, J. G. M., “Strain-Softening of Concrete under Multiaxial Loading Conditions,” PhD thesis, 1984, Eindhoven University of Technology, Eindhoven, the Netherlands.
28. Vonk, R. A.; Rutten, H. S.; Van Mier, J. G. M.; and Fijneman, H. J., “Influence of Boundary Conditions on Softening of Concrete Loaded in Compression,” Fracture of Concrete and Rock – Recent Developments (edited by S.P. Shah, S.E. Swartz and B. Barr), Elsevier Applied Science, 1989, pp. 711-720
29. Hillerborg, A., “Fracture Mechanics Concepts Applied to Moment Capacity and Rotational Capacity of Reinforced Concrete Beams,” Engineering Fracture Mechanics, V. 35, No. 1-3, 1990, pp. 233-240. doi: 10.1016/0013-7944(90)90201-Q
30. Bažant, Z. P., “Identification of Strain-Softening Constitutive Relation from Uniaxial Tests by Series Coupling Model for Localization,” Cement and Concrete Research, V. 19, No. 6, 1989, pp. 973-977. doi: 10.1016/0008-8846(89)90111-7
31. van Mier, J. G. M.; Shah, S. P.; Arnaud, M.; Balayssac, J. P.; Bascoul, A.; Choi, S.; Dasenbrock, D.; Ferrara, G.; French, C.; Gobbi, M. E.; Karihaloo, B. L.; König, G.; Kotsovos, M. D.; Labuz, J.; Lange-Kornbak, D.; Markeset, G.; Pavlovic, M. N.; Simsch, G.; Thienel, K.-C.; Turatsinze, A.; Ulmer, M.; van Geel, H. J. G. M.; van Vliet, M. R. A.; and Zissopoulos, D., “Strain-softening of Concrete in Uniaxial Compression,” Materials and Structures, V. 30, No. 4, 1997, pp. 195-209. doi: 10.1007/BF02486177
32. Ferrara, G., and Gobbi, M.E., “Strain Softening of Concrete under Compression,” Report to RILEM Committee 148, 1995.
33. Carpinteri, A.; Corrado, M.; Mancini, G.; and Paggi, M., “The Overlapping Crack Model for Uniaxial and Eccentric Concrete Compression Tests,” Magazine of Concrete Research, V. 61, No. 9, 2009, pp. 745-757. doi: 10.1680/macr.2008.61.9.745
34. Jansen, D. C., and Shah, S. P., “Effect of Length on Compressive Strain Softening of Concrete,” Journal of Engineering Mechanics, ASCE, V. 123, No. 1, 1997, 25 pp., doi: 10.1061/(ASCE)0733-9399(1997)123:1(25)
35. Suzuki, M.; Akiyama, M.; Matsuzaki, H.; and Dang, T. H., “Concentric Loading Test of RC Columns with Normal and High-Strength Materials and Averaged Stress-Strain Model for Confined Concrete Considering Compressive Fracture Energy,” Proceedings of the 2nd Fib Congress, 2006
36. International Federation for Structural Concrete, fib Model Code for Concrete Structures, International Federation for Structural Concrete, Ernst&Sohn, 2013.
37. Carpinteri, A., and Colombo, G., “Numerical Analysis of Catastrophic Softening Behavior (Snap-Back Instability),” Computers & Structures, V. 31, No. 4, 1989, pp. 607-636. doi: 10.1016/0045-7949(89)90337-4
38. Carpinteri, A., and Accornero, F., “Rotation Versus Curvature Fractal Scaling in Bending Failure,” Physical Mesomechanics, V. 22, No. 1, 2019, pp. 46-51. doi: 10.1134/S1029959919010089
39. Carpinteri, A., and Accornero, F., “Multiple Snap-Back Instabilities in Progressive Microcracking Coalescence,” Engineering Fracture Mechanics, V. 187, 2018, pp. 272-281. doi: 10.1016/j.engfracmech.2017.11.034
40. Carpinteri, A., and Accornero, F., “The Bridged Crack Model with Multiple Fibers: Local Instabilities, Scale Effects, Plastic Shake-Down, and Hysteresis,” Theoretical and Applied Fracture Mechanics, V. 104, 2019, 102351 pp., doi: 10.1016/j.tafmec.2019.102351
41. Warwaruk, J.; Sozen, M. A.; and Siess, C. P., Investigation of Prestressed Reinforced Concrete for Highway Bridges, Part III, 1962, University of Illinois.
42. Biolzi, L.; Cangiano, S.; Tognon, G.; and Carpinteri, A., “Snap-Back Softening Instability in High Strength Concrete Beams,” Materials and Structures, V. 22, No. 6, 1989, pp. 429-436. doi: 10.1007/BF02472220
43. Wittmann, F. H., “Fracture Mechanics of Concrete,” Elsevier, 1983.
44. Elfgren, L., ed., “Fracture Mechanics of Concrete Structures: From Theory to Applications,” Report of the Technical Committee 90 – FMA Fracture Mechanics to Concrete/Applications, RILEM (the International Union of Testing and Research Laboratories for Materials and Structures), Chapman and Hall, Taylor and Francis Group, 1989
45. Elfgren, L., and Shah, S. P., eds., “Analysis of Concrete Structures by Fracture Mechanics: Proceedings of a RILEM Workshop dedicated to Professor Arne Hillerborg,” Chapman and Hall, Taylor and Francis Group, 1991.
46. Shah, S. P., and Carpinteri, A., “Fracture Mechanics Test Methods for Concrete,” Report of the Technical Committee 89 FMT Fracture Mechanics of Concrete – Test Methods, Chapman and Hall, 1991.
47. Bažant, Z. P., and Planas, J., Fracture and Size Effect in Concrete and Other Quasibrittle Materials, CRC Press, Boca Raton, FL, 1997
48. ACI Committee 446, “Fracture Mechanics of Concrete: Concepts, Models and Determination of Materials Properties (ACI 446.1R-91),” American Concrete Institute, Farmington Hills, MI, 1999, 146 pp.
49. ACI Committee 446, “Finite Element Analysis of Fracture in Concrete Structures (ACI 446.3R-97),” American Concrete Institute, Farmington Hills, MI, 1997, pp. 33.