Numerical modeling of diagonal cracks in concrete beams

• Autorzy: Słowik M. , Smarzewski P.

Identyfikatory

DOI

10.2478/ace-2014-0021

• Języki publikacji: EN

Abstrakty

EN

In the paper, the method of a numerical simulation concerning diagonal crack propagation in concrete beams was presented. Two beams reinforced longitudinally but without shear reinforcement were considered during the Finite Element Method analysis. In particular, a nonlinear method was used to simulate the crack evaluation in the beams. The analysis was performed using the commercial program ANSYS. In the numerical simulation, the limit surface for concrete described by Willam and Warnke was applied to model the failure of concrete. To solve the FEM-system of equations, the Newton-Raphson method was used. As the results of FEM calculations, the trajectories of total stains and numerical images of smeared cracks were obtained for two analyzed beams: the slender beam S5 of leff = 1.8 m and the short beam S3k of leff = 1.1 m. The applied method allowed to generate both flexural vertical cracks and diagonal cracks in the shear regions. Some differences in the evaluation of crack patterns in the beams were observed. The greater number of flexural vertical cracks which penetrated deeper in the beam S5 caused the lower stiffness and the greater deformation in the beam S5 compared to the short beam S3k. Numerical results were compared with the experimental data from the early tests performed by Słowik [3]. The numerical simulation yielded very similar results as the experiments and it confirmed that the character of failure process altered according to the effective length of the member. The proposed numerical procedure was successfully verified and it can be suitable for numerical analyses of diagonal crack propagation in concrete beams.

Słowa kluczowe

EN

concrete beam; diagonal crack; numerical analysis

PL

belka betonowa; pęknięcie ukośne; analiza numeryczna

• Wydawca: Komitet Inżynierii Lądowej i Wodnej PAN ; Politechnika Warszawska, Wydział Inżynierii Lądowej
• Czasopismo: Archives of Civil Engineering
• Rocznik: 2014
• Tom: Vol. 60, nr 3
• Strony: 307--322
• Opis fizyczny: Bibliogr. 24 poz., il.

Twórcy

autor

Słowik M.

• Lublin University of Technology, Faculty of Civil Engineering and Architecture, Lublin

autor

Smarzewski P.

• Lublin University of Technology

Bibliografia

• 1. A. M. BRANDT, Cement Based Composites. Materials, Mechanical Properties and Performance, 2nd edition, Taylor & Francis, London and New York, 2009.
• 2. Z. P. BAŽANT, J. PLANAS, Fracture and Size Effect in Concrete and Quasibrittle Materials, CRC Press LLC, Boca Raton, 1998.
• 3. M. SŁOWIK, Experimental study of shear failure mechanism in concrete beams, Brittle Matrix Composites 10, IFTR and Woodhead Publishing Limited, Warsaw, 345–354, 2012 (proceeding of the Tenth International Symposium on Brittle Matrix Composites).
• 4. M. SŁOWIK, T. NOWICKI, The Analysis of Diagonal Crack Propagation in Concrete Beams, Computational Materials Science, 52, 261–7, 2012.
• 5. M. SŁOWIK, P. SMARZEWSKI, The Study of the Scale Effect on Diagonal Crack Propagation in Concrete Beams, Computational Materials Science, 64, 216–20, 2012.
• 6. K. J. WILLAM, E. P. WARNKE, Constitutive Model for the Triaxial Behavior of Concrete, proceedings, International Association for Bridge and Structural Engineering, Vol. 19, ISMES, Bergamo, Italy, 1–30, 1975.
• 7. N. S. OTTOSEN, A Failure Criterion for Concrete, Journal of the Engineering Mechanics Division, American Society of Civil Engineering, 103 (EM 4), 527–535, 1977.
• 8. M. KLISIŃSKI, Degradation and plastic deformation of concrete (in Polish), Institute of Fundamental Technological Research Polish Academy of Sciences Report 38, Warsaw, 1984.
• 9. J. PODGÓRSKI, Critical States in Solids with Internal Friction (in Polish), Institute of Fundamental Technological Research Polish Academy of Sciences Report 25, Warsaw, 1986.
• 10. A. STOLARSKI, Dynamic Strength Criterion for Concrete, Journal of Engineering Mechanics, ASCE, 130, 1428–1435, 2004.
• 11. J. BOBIŃSKI, J. TEJCHMAN, Modelling of size effects in concrete using elasto-plasticity with non-local softening, Archives of Civil Engineering, 52, 1, 7–35, 2006.
• 12. Ł. WIDULIŃSKI, J. BOBIŃSKI, J. TEJCHMAN, FE-analysis of spacing of localized zones in reinforced concrete bars under tension using elasto-plasticity with non-local softening, Archives of Civil Engineering, LV, 2, 257–281, 2009.
• 13. T. JANKOWIAK, T. ŁODYGOWSKI, Quasi-static failure criteria for concrete, Archives of Civil Engineering, LVI, 2, 123–154, 2010.
• 14. P. SMARZEWSKI, Modeling of Static Behavior of Inelastic Reinforced High-Strength Concrete Beams (in Polish), Monographs – Lublin University of Technology, 2011.
• 15. P. DESAYI,, S. KRISHNAN, Equation for the Stress-Strain Curve of Concrete, Journal of the American Concrete Institute, 61, 345–350, 1964.
• 16. M. SUIDAN, W. C. SCHNOBRICH, Finite Element Analysis of Reinforced Concrete, Journal of the Structural Division, ASCE, ST10, 2109–2122, 1973.
• 17. K. J. BATHE, Finite Element Procedures, Prentice-Hall, Inc., Upper Saddle River, New Jersey, 1996.
• 18. O. C. ZIENKIEWICZ, R. L. TAYLOR, The Finite Element Method for Solid and Structural Mechanics, 6th edition, Elsevier Butterworth Heinemann, Oxford, UK, 2005.
• 19. J. BONET, R. D. WOOD, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, Cambridge, UK, 1997.
• 20. M. A. CRISFIELD, Non-Linear Finite Element Analysis of Solids and Structures, John Wiley & Sons, Inc., Chichester, UK, 2000.
• 21. S. A. ASHOUR, Effect of Compressive Strength and Tensile Reinforcement Ratio on Flexural Behaviour of High-Strength Concrete Beams, Engineering Structures, 22, 413–423, 2000.
• 22. M. A. RASHID, M. A. MANSUR, Reinforced High-Strength Concrete Beams in Flexure, ACI Structural Journal, 102, 462–471, 2005.
• 23. E. RIKS, An Incremental Approach to the Solution of Snapping and Buckling Problems, International Journal of Solids and Structures, 15, 529–551, 1979.
• 24. M. A. CRISFIELD, An Arc-Length Method Including Line Searches and Accelerations, International Journal for Numerical Methods in Engineering, 19, 1269–1289, 1983.