Topology Optimization-Based Reinforced Concrete Beams: Design and Experiment
Publication: Journal of Structural Engineering
Volume 148, Issue 10
Abstract
Though topology optimization has been around for nearly 3 decades, its application in the design of RC structures still is a concern, not only because of the lack of a definite procedure, but also because of the lack of supporting and reassuring experimental evidence. This paper presents a practical integration of topology optimization to the design of RC beams with experimental validation. Concrete and steel reinforcement profiles based on two-material topology optimization were considered as a form suggestion and used for design guidance. The design was refined constantly to alleviate any stress and deflection violations, and the beam successively evolved. A supporting experiment verified that a reduction of approximately 30% in concrete can be achieved while all the relevant design requirements remained satisfied and integrity was maintained, with more than 3 times the beam’s service capacity reserved.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
Funding for this research was provided by the Thailand National Research Council through the Kasetsart University Research and Development Institute (KURDI), Bangkok, Thailand. The Faculty of Engineering and the Faculty of Architecture at Kasetsart University facilitated project execution. The Civil Engineering Department provided laboratory space and time in their newly opened laboratory.
References
Amir, O. 2013. “A topology optimization procedure for reinforced concrete structures.” Comput. Struct. 114–115 (Jan): 46–58. https://doi.org/10.1016/j.compstruc.2012.10.011.
Amir, O., and O. Sigmund. 2013. “Reinforcement layout design for concrete structures based on continuum damage and truss topology optimization.” Struct. Multidiscip. Optim. 47 (2): 157–174. https://doi.org/10.1007/s00158-012-0817-1.
Bendsøe, M. P., and N. Kikuchi. 1988. “Generating optimal topologies in structural design using a homogenization method.” Comput. Methods Appl. Mech. Eng. 71 (2): 197–224. https://doi.org/10.1016/0045-7825(88)90086-2.
Bogomolny, M., and O. Amir. 2012. “Conceptual design of reinforced concrete structures using topology optimization with elastoplastic material modeling.” Int. J. Numer. Methods Eng. 90 (13): 1578–1597. https://doi.org/10.1002/nme.4253.
Bruggi, M. 2009. “Generating strut-and-tie patterns for reinforced concrete structures using topology optimization.” Comput. Struct. 87 (23–24): 1483–1495. https://doi.org/10.1016/j.compstruc.2009.06.003.
EIT (The Engineering Institute of Thailand under H.M. the King’s Patronage). 2010. Standard for reinforced concrete building: Working stress design. [In Thailand.] EIT Standard 1007-34. Bangkok, Thailand: EIT.
EIT (The Engineering Institute of Thailand under H.M. the King’s Patronage). 2012. Standard for reinforced concrete building: Ultimate design. [In Thailand.] EIT Standard 1008-38. Bangkok, Thailand: EIT.
Gaynor, A. T., J. K. Guest, and C. D. Moen. 2013. “Reinforced concrete force visualization and design using bilinear truss-continuum topology optimization.” J. Struct. Eng. 139 (4): 607–618. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000692.
Guan, H. 2005. “Strut-and-tie of deep beams with web openings—An optimization approach.” Struct. Eng. Mech. 19 (4): 361–379. https://doi.org/10.12989/sem.2005.19.4.361.
Huang, X., and Y. M. Xie. 2007. “Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method.” Finite Elem. Anal. Des. 43 (14): 1039–1049. https://doi.org/10.1016/j.finel.2007.06.006.
Jewett, J. L., and J. V. Carstensen. 2019. “Experimental investigation of strut-and-tie layouts in deep RC beams designed with hybrid bi-linear topology optimization.” Eng. Struct. 197 (Oct): 1–10. https://doi.org/10.1016/j.engstruct.2019.109322.
Kim, H., and G. Baker. 2002. “Topology optimization for reinforced concrete design.” In Proc., 5th World Congress on Computational Mechanics, edited by H. A. Mang, F. G. Rammerstorfer, and J. Eberhardsteiner. Madrid, Spain: International Association for Computational Mechanics.
Kwak, H.-G., and S.-H. Noh. 2006. “Determination of strut-and-tie models using evolutionary structural optimization.” Eng. Struct. 28 (10): 1440–1449. https://doi.org/10.1016/j.engstruct.2006.01.013.
Leu, L.-J., C.-W. Haung, C.-S. Chen, and Y.-P. Liao. 2006. “Strut-and-tie design methodology for three-dimensional reinforced concrete structures.” J. Struct. Eng. 132 (6): 929–938. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:6(929).
Liang, Q., B. Uy, and G. P. Steven. 2002. “Performance-based optimization for strut-tie modeling of structural concrete.” J. Struct. Eng. 128 (6): 815–823. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:6(815).
Liang, Q. Q., Y. M. Xie, and G. P. Steven. 2000. “Topology optimization of strut-and-tie models in reinforced concrete structures using an evolutionary procedure.” ACI Struct. J. 97 (2): 322–332. https://doi.org/10.14359/863.
Liu, Y., J. L. Jewett, and J. V. Carstensen. 2020. “Experimental investigation of topology-optimized deep reinforced concrete beams with reduced concrete volume.” In Vol. 28 of Proc., 2nd RILEM Int. Conf. on Concrete and Digital Fabrication, DC 2020, edited by F. Bos, S. Lucas, R. Wolfs, and T. Salet, 601–611. Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-030-49916-7_61.
Luo, Y., and Z. Kang. 2013. “Layout design of reinforced concrete structures using two-material topology optimization with Drucker–Prager yield constraints.” Struct. Multidiscip. Optim. 47 (1): 95–110. https://doi.org/10.1007/s00158-012-0809-1.
Michell, A. G. M. 1904. “The limits of economy of material in frame-structures.” London Edinburgh Dublin Philos. Mag. J. Sci. 8 (47): 589–597. https://doi.org/10.1080/14786440409463229.
Moen, C. D., and J. K. Guest. 2010. “Reinforced concrete design with topology optimization.” In Proc., 19th Analysis and Computation Specialty Conf., 445–454. Reston, VA: ASCE. https://doi.org/10.1061/41131(370)39.
Plianjitdee, A., and B. Wethyaivorn. 2005. “Strength design of optimal topology for composite beams.” [In Thailand.] In Proc., 10th National Convention on Civil Engineering. Bangkok, Thailand: Engineering Institute of Thailand Under H.M. The King’s Patronage.
Querin, O. M., G. P. Steven, and Y. M. Xie. 1998. “Evolutionary structural optimisation (ESO) using a bidirectional algorithm.” Eng. Comput. 15 (8): 1031–1048. https://doi.org/10.1108/02644409810244129.
Querin, O. M., M. Victoria, and P. Martí. 2010. “Topology optimization of truss-like continua with different material properties in tension and compression.” Struct. Multidiscip. Optim. 42 (1): 25–32. https://doi.org/10.1007/s00158-009-0473-2.
Querin, O. M., V. Young, G. P. Steven, and Y. M. Xie. 2000. “Computational efficiency and validation of bi-directional evolutionary structural optimisation.” Comput. Methods Appl. Mech. Eng. 189 (2): 559–573. https://doi.org/10.1016/S0045-7825(99)00309-6.
Rahim, A., and H. Jamelle. 2007. “The economies of elegance migrating coastlines: Residential tower, Dubai.” Archit. Des. 77 (1): 65–75. https://doi.org/10.1002/ad.399.
Surit, S., and B. Wethyavivorn. 2011. “Topology optimization of reinforced concrete beams by a spread-over reinforcement model with fixed grid mesh.” Songklanakarin J. Sci. Technol. 33 (1): 95–100.
Thanadirek, T., and B. Wethyavivorn. 2012a. “Design of reinforced concrete transfer beam by topology optimization method.” [In Thailand.] In Proc., 17th National Convention on Civil Engineering. Bangkok, Thailand: Engineering Institute of Thailand Under H.M. The King’s Patronage.
Thanadirek, T., and B. Wethyavivorn. 2012b. “Reinforced concrete deep beams by topology optimization: Design and experiment.” In Proc., Tokyo Institute of Technology and Kasetsart University joint seminar on Infrastructure Development. Bangkok, Thailand: Tokyo Institute of Technology and Kasetsart Univ.
Vantyghem, G., W. De Corte, E. Shakour, and O. Amir. 2020. “3D printing of a post-tensioned concrete girder designed by topology optimization.” Autom. Constr. 112 (Apr): 103084. https://doi.org/10.1016/j.autcon.2020.103084.
Victoria, M., O. M. Querin, and P. Martí. 2011. “Generation of strut-and-tie models by topology design using different material properties in tension and compression.” Struct. Multidiscip. Optim. 44 (2): 247–258. https://doi.org/10.1007/s00158-011-0633-z.
Wang, C., and C. G. Salmon. 1979. Reinforced concrete design. 3rd ed. New York: T. Crowell.
Wethyavivorn, B., and K. Atchacosit. 2003. “The optimal topology of composite beams: Analysis, design and experiment, system-based vision for strategic and creative design.” In Proc., 2nd Int. Conf. on Structural and Construction Engineering, edited by F. Bontempi. Rotterdam, Netherlands: A.A. Balkema.
Wethyavivorn, B., S. Surit, J. Jirapapan, and T. Thanadirek. 2012. Development of reinforced concrete beams by optimum topology technology. [In Thailand.]. Bangkok, Thailand: Kasetsart Univ.
Wethyavivorn, B., S. Surit, and B. Layangkoon. 2003. “Optimal topology of structures with boundary constrants.” In Proc., 4th Regional Symp. on Infrastructures Development in Civil Engineering (RSID). Bangkok, Thailand: Tokyo Institute of Technology and Kasetsart Univ.
Xie, Y. M., and G. P. Steven. 1993. “A simple evolutionary procedure for structural optimization.” Comput. Struct. 49 (5): 885–896. https://doi.org/10.1016/0045-7949(93)90035-C.
Yang, X. Y., Y. M. Xie, G. P. Steven, and O. M. Querin. 1999. “Bi-directional evolutionary method for stiffness optimization.” J. Am. Inst. Aeronaut. Astronaut. 37 (11): 1483–1488. https://doi.org/10.2514/2.626.
Zhou, M., B. S. Lazarov, F. Wang, and O. Sigmund. 2015. “Minimum length scale in topology optimization by geometric constraints.” Comput. Methods Appl. Mech. Eng. 293 (Aug): 266–282. https://doi.org/10.1016/j.cma.2015.05.003.
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Published In
Journal of Structural Engineering
Volume 148 • Issue 10 • October 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Dec 2, 2021
Accepted: May 20, 2022
Published online: Jul 23, 2022
Published in print: Oct 1, 2022
Discussion open until: Dec 23, 2022
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