Novel Finite Element Analysis of Curved Concrete Box Girders Using Hybrid Box Elements
Publication: Journal of Structural Engineering
Volume 147, Issue 1
Abstract
Horizontally curved concrete bridges are widely used in urban viaducts and overpasses all over the world. A box cross-section is often used in curved concrete girders because of its high resistance to both bending and torsion. This study focuses on the development of a new finite element analysis (FEA) methodology incorporating a novel formulation for curved box sections using orthotropic constitutive models for reinforced concrete, along with a layered shell theory approach. In the new approach, the box section is treated as a frame consisting of curved shell elements modeling webs and flanges and curved beam elements in the web-flange junctions. The use of shell and beam elements in the formulation significantly reduces the number of elements needed to model the box-section girder while maintaining the accuracy of the model. A degenerate superparametric shell element with reduced integration is used to avoid shear-locking, membrane-locking, and zero-energy problems. Prestrain effects are considered in the formulation to account for prestressing forces. The simulation results are compared to the available experimental results on four straight and curved, reinforced and prestressed, concrete box-section girders, with good agreement in terms of the deflections, twist angles, and strains in the prestressed reinforcement. Some critical issues in the analysis of concrete box girders, such as postpeak-strength behaviors, distortion of box section, are also discussed.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request: material properties data, geometric dimension data, finite element mesh data, and model behavior data.
Acknowledgments
This study was sponsored by the National Natural Science Foundation of China (Nos. 51778468 and 51208376) and Tongji Architectural Design (Group) Co. Ltd. (No. 2020KY07). This study was also supported by China Scholarship Council (CSC). Additional support was provided by the Georgia Institute of Technology. The authors thank the editors and reviewers for their time and effort in reviewing our manuscript.
References
Angelakos, D., E. C. Bentz, and M. P. Collins. 2001. “Effect of concrete strength and minimum stirrups on shear strength of large members.” ACI Struct. J. 98 (3): 290–300.
Aparicio, A. C., G. Ramos, and J. R. Casas. 2002. “Testing of externally prestressed concrete beams.” Eng. Struct. 24 (1): 73–84. https://doi.org/10.1016/S0141-0296(01)00062-1.
Batoz, J. L., and G. Dhatt. 1979. “Incremental displacement algorithms for non-linear problems.” J. Numer. Methods Eng. 14 (8): 1262–1267. https://doi.org/10.1002/nme.1620140811.
Bazant, Z. P., and M. T. Kazermi. 1991. “Size effect on diagonal shear failure of beams without stirrups.” ACI Struct. J. 88 (3): 268–276.
Belarbi, A., and T. T. Hsu. 1995. “Constitutive laws of softened concrete in biaxial tension compression.” ACI Struct. J. 92 (5): 562–573.
Bentz, E. C., and S. Buckley. 2005. “Repeating a classic set of experiments on size effect in shear of members without stirrups.” ACI Struct. J. 102 (6): 832–838.
Bergan, P. G., G. Horrigmoe, B. Krakeland, and T. H. Soreide. 1978. “Solution techniques for non-linear finite element problems.” Int. J. Numer. Methods Eng. 12 (11): 1577–1696. https://doi.org/10.1002/nme.1620121106.
Collins, M. P., and D. Mitchell. 1991. Prestressed concrete structures. Englewood Cliffs, NJ: Prentice-Hill.
del Viso, J. R., J. R. Carmona, and G. Ruiz. 2008. “Shape and size effect on the compressive strength of high-strength concrete.” Cem. Concr. Res. 38 (3): 386–395. https://doi.org/10.1016/j.cemconres.2007.09.020.
Du, X. L., H. Cao, and L. Jin. 2012. “A new finite element displacement control method of the whole process simulation of force-displacement relation.” [In Chinese.] Eng. Mech. 29 (1): 1–6.
Hadj-arab, A. 1987. “Behaviour of a one-cell prestressed concrete box girder bridge—Experimental study.” M.Eng. dissertation, Dept. of Civil Engineering and Applied Mechanics, McGill Univ.
Hinton, E., and D. R. J. Owen. 1984. Finite element software for plates and shells. Swansea, UK: Pineridge Press.
Hrynyk, T. D., and F. J. Vecchio. 2015. “Capturing out-of-plane shear failures in the analysis of reinforced concrete shells.” J. Struct. Eng. 141 (12): 04015058. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001311.
Hsu, T. T. C., and Y. L. Mo. 2010. Unified theory of concrete structures. Hoboken, NJ: Wiley.
Hsu, T. T. C., and R. R. H. Zhu. 2002. “Softened membrane model for reinforced concrete elements in shear.” ACI Struct. J. 99 (4): 460–469.
Kani, G. N. J. 1967. “How safe are our large reinforced concrete beams?” Proc. ACI J. 64 (3): 128–141.
Kurian, B., and D. Menon. 2007. “Estimation of collapse load of single-cell concrete box-girder bridges.” J. Bridge Eng. 12 (4): 518–526. https://doi.org/10.1061/(ASCE)1084-0702(2007)12:4(518).
Luu, C. H., Y. L. Mo, and T. T. C. Hsu. 2017. “Development of CSMM-based shell element for reinforced concrete structures.” Eng. Struct. 132 (Feb): 778–790. https://doi.org/10.1016/j.engstruct.2016.11.064.
Mansour, M., and T. T. C. Hsu. 2005. “Behavior of reinforced concrete elements under cyclic shear. II: Theoretical model.” J. Struct. Eng. 131 (1): 54–65. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:1(54).
NCHRP (National Cooperative Highway Research Program). 2008. Development of design specifications and commentary for horizontally curved concrete box girder bridges. Washington, DC: NCHRP.
Ng, S. F., M. S. Cheung, and J. Q. Zhao. 1993. “A materially nonlinear finite element model for the analysis of curved reinforced concrete box-girder bridges.” Can. J. Civ. Eng. 20 (5): 754–759. https://doi.org/10.1139/l93-100.
Pang, X. B., and T. T. C. Hsu. 1995. “Behavior of reinforced concrete membrane elements in shear.” ACI Struct. J. 92 (6): 665–679.
Pang, X. B., and T. T. C. Hsu. 1996. “Fixed-angle softened-truss model for reinforced concrete.” ACI Struct. J. 93 (2): 197–207.
Polak, M. A. 1992. “Nonlinear analysis of reinforced-concrete shells.” Ph.D. dissertation, Dept. of Civil Engineering, Univ. of Toronto.
Polak, M. A., and F. J. Vecchio. 1993. “Nonlinear analysis of reinforced-concrete shells.” J. Struct. Eng. 119 (12): 3439–3462. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:12(3439).
Polak, M. A., and F. J. Vecchio. 1994. “Reinforced concrete shell elements subjected to bending and membrane loads.” ACI Struct. J. 91 (3): 261–268.
Roberts-Wollmann, C. L., M. E. Kreger, D. M. Rogowsky, and J. E. Breen. 2005. “Stresses in external tendons at ultimate.” ACI Struct. J. 102 (2): 206.
Scordelis, A. C., J. C. Bouwkaup, and P. K. Larsen. 1974. Structural behavior of a curved two span reinforced concrete box girder bridge model; Volumes I, II, and III. Berkeley, CA: Univ. of California.
Seible, F., and A. C. Scordelis. 1984. “Nonlinear behavior and failure analysis of multi-cell reinforced concrete box girder bridges.” Can. J. Civ. Eng. 11 (3): 411–422. https://doi.org/10.1139/l84-062.
Sennah, K. M., and J. B. Kennedy. 2001. “State-of-the-art in curved box-girder bridges.” J. Bridge Eng. 15 (4): 159–167. https://doi.org/10.1061/(ASCE)1084-0702(2001)6:3(159).
Shen, Y., G. P. Li, and A. R. Chen. 2003. “Nonlinear models of externally prestressed concrete beams.” [In Chinese.] J. Tongji Univ. 31 (7): 803–807.
SIMULIA. 2011. Abaqus user’s manual 6.11. Providence, RI: SIMULIA.
Soliman, M. I. 1994. “Different aspects affecting the torsional stiffness of RC straight and curved box-girder bridges.” In Proc., 4th Int. Conf. on Short and Medium Span Bridges, 129–140. Halifax, NS, Canada: International Conference on Short and Medium Span Bridges.
Soliman, M. I., and M. K. Ghali. 1994. “Effect of diaphragms on the behavior of RC box-girder bridges.” Proc., 4th Int. Conf. on Short and Medium Span Bridges, 211–222. Halifax, NS, Canada: International Conference on Short and Medium Span Bridges.
Song, T. Y. 2019. “Analysis and calculation methods of curved reinforced and prestressed concrete box-section girder bridges.” [In Chinese.] Ph.D. dissertation, Dept. of Civil Engineering, Tongji Univ.
Song, T. Y., Y. Shen, and G. P. Li. 2017. “Moment redistribution in EPC continuous curved box beams.” J. Bridge Eng. 22 (8): 04017035. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001055.
Stevens, N. J., S. M. Uzumeri, and M. P. Collins. 1987. Analytical modelling of reinforced concrete subjected to monotonic and reversed loadings. Toronto: Univ. of Toronto.
Vecchio, F. J. 1981. “The response of reinforced concrete to in-plane shear and normal stresses.” Ph.D. dissertation, Dept. of Civil Engineering, Univ. of Toronto.
Vecchio, F. J. 1989. “Nonlinear finite element analysis of reinforced concrete membranes.” ACI Struct. J. 86 (1): 26–35.
Vecchio, F. J. 1990. “Reinforced concrete membrane element formulations.” J. Struct. Eng. 116 (3): 730–750. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:3(730.
Vecchio, F. J. 2002. “Disturbed stress field model for reinforced concrete: Formulation.” J. Struct. Eng. 126 (9): 12–20. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:9(1070.
Vecchio, F. J., and M. P. Collins. 1982. The response of reinforced concrete to in-plane shear and normal stresses. Toronto: Univ. of Toronto.
Vecchio, F. J., and M. P. Collins. 1986. “The modified compression-field theory for reinforced concrete elements subjected to shear.” ACI Struct. J. 83 (2): 219–231.
Vecchio, F. J., and R. G. Selby. 1991. “Toward compression-field analysis of reinforced concrete solids.” J. Struct. Eng. 117 (6): 1740–1758. https://doi.org/10.1061/(ASCE)0733-9445(1991)117:6(1740).
Wang, X. C. 2003. Finite element method. [In Chinese.] Beijing: Tsinghua University Press.
Yang, B. 1987. “Nonlinear finite element analysis and experiments of prestressed and reinforced concrete curved box-section beams.” [In Chinese.] Ph.D. dissertation, Dept. of Civil Engineering, Tongji Univ.
Yu, Q., and Z. P. Bazant. 2011. “Can stirrups suppress size effect on shear strength of RC beams?” J. Struct. Eng. 137 (5): 607–707. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000295.
Zhou, S. Y. 1995. “Linear and nonlinear finite element analysis and model experiments of reinforced concrete box girders.” [In Chinese.] M.Eng. dissertation, Dept. of Civil Engineering, Beijing Jiaotong Univ.
Information & Authors
Information
Published In
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Oct 11, 2018
Accepted: Jun 22, 2020
Published online: Oct 18, 2020
Published in print: Jan 1, 2021
Discussion open until: Mar 18, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.