Modelling of Stirrup Confinement Effects in RC Layered Beam Finite Elements Using a 3D Yield Criterion and Transversal Equilibrium Constraints

Péter Zoltán Berke1, Thierry Jacques Massart1
1Building, Architecture and Town Planning (BATir) department, Université libre de Bruxelles (ULB), Bruxelles, Belgium

Tóm tắt

Apart from its recognized strengthening effect for shear loading, the presence of stirrups in reinforced concrete results in an increase of the ductility of structural members and in the capacity of reaching higher longitudinal compressive stress levels provided by transversal confinement. These effects are usually represented phenomenologically in fibre beam models by artificially increasing the compressive strength and the ultimate compressive strain of concrete. Two numerical formulations for layered beam descriptions accounting explicitly for transversal confinement are implemented and assessed in this contribution. The influence of stirrups is incorporated by means of a multi-dimensional yield surface for concrete, combined with equilibrium constraints for the transversal direction involving concrete and steel stirrups, and with a concrete ultimate strain dependent on the hydrostatic stress. This contribution focuses on the numerical formulations of both frameworks, and on their assessment against experimental results available in the literature.

Tài liệu tham khảo

Ahmad, S. M., & Shah, S. P. (1982). Complete triaxial stress–strain curves of concrete confined by spiral reinforcement. Journal of the Structural Division ASCE, 108, 728–742. Bao, J. Q., Long, X., Tan, K. H., & Lee, C. K. (2013). A new generalized Drucker–Prager flow rule for concrete under compression. Engineering Structures, 56, 2076–2082. Battini, J.-M. (2002) Corotational beam elements in instability problems (PhD thesis, Royal Institute of Technology). Biolzi, L., Cattaneo, S., & Mola, F. (2014). Bending-shear response of self-consolidating and high-performance reinforced concrete beams. Engineering Structures, 59, 399–410. Breveglieri, M., Aprile, A., & Barros, J. A. O. (2015). Embedded through-section shear strengthening technique using steel and CFRP bars in RC beams of different percentage of existing stirrup. Computers and Structures, 126, 101–113. Buyukozturk, O., & Tseng, T.-M. (1984). Concrete in biaxial cyclic compression. Journal of Structural Engineering ASCE, 110, 461–476. Chen, W. F. (1982). Plasticity in reinforced concrete. New York: McAraw-Hill Book Company. Cho, C.-G., & Park, M.-H. (2003). Finite element prediction of the influence of confinement on RC beam-columns under single or double curvature bending. Engineering Structures, 25, 1525–1536. Codina, R., Ambrosini, D., & de Borbón, F. (2016). Alternatives to prevent the failure of RC members under close-in blast loadings. Engineering Failure Analysis, 60, 96–106. Comi, C. (2001). A non-local model with tension and compression damage mechanisms. European Journal of Mechanics A/Solids, 20, 1–22. Comi, C., Kirchmayr, B., & Pignatelli, R. (2012). Two-phase damage modeling of concrete affected by alkali–silica reaction under variable temperature and humidity conditions. International Journal of Solids and Structures, 49, 3367–3380. Crisfield, M. A. (1995). Non linear finite elements analysis of solids and structures-volume 1: The essentials. London: Wiley. Cusson, D., & Paultre, P. (1995). Stress-strain model for confined high-strength concrete. Journal of Structural Engineering ASCE, 121, 468–477. De Corte, W., & Boel, V. (2013). Effectiveness of spirally shaped stirrups in reinforced concrete beams. Engineering Structures, 52, 667–675. Dede, T., & Ayvaz, Y. (2010). Plasticity models for concrete material based on different criteria including Bresler–Pister. Materials & Design, 31, 278–286. Ding, Y., You, Z., & Jalali, S. (2011). The composite effect of steel fibres and stirrups on the shear behaviour of beams using self-consolidating concrete. Engineering Structures, 33, 107–117. Gabet, T., Malécot, Y., & Daudeville, L. (2008). Triaxial behaviour of concrete under high stresses: Influence of the loading path on compaction and limit states. Cement & Concrete Research, 38, 403–412. Garzón-Roca, J., Adam, J. M., Calderón, P. A., & Valente, I. B. (2012). Finite element modelling of steel-caged RC columns subjected to axial force and bending moment. Engineering Structures, 40, 168–186. Hammoud, R., Yahia, A., & Boukhili, R. (2014). Triaxial compressive strength of concrete subjected to high temperatures. Journal of Materials in Civil Engineering ASCE, 26, 705–712. Hong, K. N., & Han, S. H. (2005). Stress–strain model of high-strength concrete confined by rectangular ties. Journal of Structural Engineering ASCE, 9, 225–232. Hou, J., & Song, L. (2016). Progressive collapse resistance of RC frames under a side column removal scenario: The mechanism explained. International Journal of Concrete Structures and Materials, 10, 237–247. Imran, I., & Pantazopoulou, S. J. (1996). Experimental study of plain concrete under triaxial stress. ACI Materials Journal, 93, 589–601. Kent, D. C., & Park, R. (1971). Flexural members with confined concrete. Journal of the Structural Division ASCE, 97, 1969–1990. Lew, H. S., Bao, Y., Sadek, F., Main, J. A., Pujol, S., & Sozen, M. A. (2011). An experimental and computational study of reinforced concrete assemblies under a column removal scenario. NIST Technical Note 1720. Lim, K.-M., Shin, H.-O., Kim, D.-J., Yoon, Y.-S., & Lee, J.-H. (2016). Numerical assessment of reinforcing details in beam-column joints on blast resistance. International Journal of Concrete Structures and Materials, 10, S87–S96. Lu, X. (2005). Uniaxial and triaxial behavior of high strength concrete with and without steel fibers (PhD thesis, New Jersey Institute of Technology). Malécot, Y., Daudeville, L., Dupray, F., Poinard, C., & Buzaud, E. (2010). Strength and damage of concrete under high triaxial loading. European Journal of Environmental and Civil Engineering, 14, 777–803. Mander, J. B., Priestley, M. J. N., & Park, R. (1988a). Theoretical stress–strain model for confined concrete. Journal of Structural Engineering ASCE, 114, 1804–1826. Mander, J. B., Priestley, M. J. N., & Park, R. (1988b). Observed stress–strain behavior of confined concrete. Journal of Structural Engineering ASCE, 114, 1827–1849. Menchel, K., Massart, T. J., Rammer, Y., & Bouillard, Ph. (2009). Comparison and study of different progressive collapse simulation techniques for RC structures. Journal of Structural Engineering ASCE, 135, 685–697. Mullapudi, T. R., & Ayoub, A. (2010). Modeling of the seismic behavior of shear-critical reinforced concrete columns. Engineering Structures, 32, 3601–3615. Mullapudi, T. R. S., & Ayoub, A. (2013). Analysis of reinforced concrete column subjected to combined axial, flexure, shear and torsional loads. Journal of Structural Engineering ASCE, 139, 561–573. Oliveira, C. E. M. (2015). The influence of geometrically nonlinear effects on the progressive collapse of reinforced concrete structures (PhD thesis, Universidade Federal de Ouro Preto). Oliveira, C. E. M., Batelo, E. A. P., Berke, P. Z., Silveira, R. A. M., & Massart, T. J. (2014). Nonlinear analysis of the progressive collapse of reinforced concrete plane frames using a multilayered beam formulation. IBRACON Structures and Materials Journal, 7, 845–855. Oliveira, R. S., Ramalho, M. A., & Corrêa, M. R. S. (2008). A layered finite element for reinforced concrete beams with bond-slip effects. Cement & Concrete Composites, 30, 245–252. Park, R., Priestley, M. J. N., & Gill, W. D. (1982). Ductility of square-confined concrete columns. Journal of the Structural Division ASCE, 108, 929–950. Petrangeli, M., Pinto, P. E., & Ciampi, V. (1999). Fiber element for cyclic bending and shear of RC structures. I: Theory. Journal of Engineering Mechanics, 125, 994–1001. Petrone, F., Shan, L., & Kunnath, S. K. (2016). Modeling of RC frame buildings for progressive collapse analysis. International Journal of Concrete Structures and Materials, 10, 1–13. Rashidian, O., Abbasnia, R., Ahmadi, R., & Nav, F. M. (2016). Progressive collapse of exterior reinforced concrete beam-column sub-assemblages: Considering the effects of a transverse frame. International Journal of Concrete Structures and Materials, 10, 479–497. Richart, F. E., Brantzaeg, A., & Brown, R. L. (1928) A study of the failure of concrete under combined compressive stresses. Engineering Experiment Station, University of Illinois, Urbana, Bulletin No. 185. Richart, F. E., Brantzaeg, A., & Brown, R. L. (1929). The failure of plain and spirally reinforced concrete in compression. Engineering Experiment Station, University of Illinois, Urbana, Bulletin No. 190. Saatcioglu, M., & Razvi, S. R. (1992). Strength and ductility of confined concrete. Journal of the Structural Division ASCE, 118, 1590–1607. Santafé Iribarren, B., Berke, P., Bouillard, Ph, Vantomme, J., & Massart, T. J. (2011). Investigation of the influence of design and material parameters in the progressive collapse analysis of RC structures. Engineering Structures, 33, 2805–2820. Santos, J., & Henriques, A. A. (2015). New finite element to model bond-slip with steel strain effect for the analysis of reinforced concrete structures. Engineering Structures, 86, 72–83. Sargin, M. (1971). Stress–strain relationship for concrete and the analysis of structural concrete section (PhD thesis, University of Waterloo) Saritas, A., & Filippou, F. C. (2009). Numerical integration of a class of 3D plastic-damage concrete models and condensation of 3D stress–strain relations for use in beam finite elements. Engineering Structures, 31, 2327–2336. Scott, B. D., Park, R., & Priestley, M. J. N. (1982). Stress–strain behaviour of concrete confined by overlapping hoops at low and high strain rates. Journal of American Concrete Institute, 79, 13–27. Sfer, D., Carol, I., Gettu, R., & Etse, G. (2002). Study of the behavior of concrete under triaxial compression. Journal of Engineering Mechanics, 128, 156–163. Sheikh, S. A., & Uzumeri, S. M. (1980). Strength and ductility of tied concrete columns. Journal of the Structural Division ASCE, 106, 1079–1102. Simo, J. C., & Taylor, R. L. (1985). Consistent tangent operators for rate independent plasticity. Computer Methods in Applied Mechanics and Engineering, 48, 101–118. Stramandinoli, R. S. B., & La Rovere, H. L. (2012). FE model for nonlinear analysis of reinforced concrete beams considering shear deformation. Engineering Structures, 35, 244–253. Tan, T. H. (2005). Effects of triaxial stress on concrete. In 30th conference on our world in concrete & structures. Xiao, Y. (1989). Experimental study and analytical modeling of triaxial behavior of confined concrete (PhD thesis, Kyushu University). Zendaoui, A., Kadid, A., & Yahiaoui, D. (2016). Comparison of different numerical models of RC elements for predicting the seismic performance of structures. International Journal of Concrete Structures and Materials, 10, 461–478. Zhou, J. J., Pan, J. L., Leung, C. K. Y., & Li, Z. J. (2014). Experimental study on mechanical behavior of high performance concrete under multi-axial compressive stress. Science China Technological Sciences, 57, 2514–2522.