A Practical Approach for Generating the Strut-and-Tie Models of Anchorage Zones
Publication: Journal of Bridge Engineering
Volume 22, Issue 4
Abstract
This paper presents a practical method for automatically generating optimal strut-and-tie models (STMs) in anchorage zones. In the proposed approach, a new microtruss element pattern is created to build ground structures. In certain conditions, the approach could also be improved by combining the microtruss grids with solid elements. Furthermore, the formula for the cross-sectional areas of bar elements in the microtruss grid is deduced for the purpose of replacing the continuum structures built by solid elements with discrete structures built by truss elements. Then, three examples are illustrated to demonstrate the capability of the proposed optimization procedure to find the optimal STMs of anchorage zones. The existing solutions and numerical experiments indicate that the proposed approach accurately reflects the actual load-transfer mechanism in anchorage zones. The method can be used in practice, especially in the design of some disturbed regions (D-regions) in which optimal STMs cannot be obtained by traditional optimization procedures. It should be noted that at present, the application of the proposed model in this paper is limited to homogeneous material with linear constitutive laws.
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Acknowledgments
This study is supported by the National Nature Science Foundation of P.R. China (Grant 51578479) and the Qingdao Postdoctoral Sustentation Fund of P.R. China (Grant 2015201). The financial support is gratefully acknowledged. The authors would like to extend their heartfelt gratitude to the anonymous reviewers for their helpful suggestions for improving the quality of this paper.
References
AASHTO. (1998). AASHTO LRFD bridge design specifications, Washington, DC.
Achtziger, W., and Stolpe, M. (2007). “Truss topology optimization with discrete design variables—Guaranteed global optimality and benchmark examples.” Struct. Multidiscip. Optim., 34(1), 1–20.
Achtziger, W., and Stolpe, M. (2009). “Global optimization of truss topology with discrete bar areas—Part II: Implementation and numerical results.” Comput. Optim. Appl., 44(2), 315–341.
Ali, M. A., and White, R. N. (2000). “Formulation of optimal strut-and-tie models in design of reinforced concrete structures.” ACI Spec. Publ., 193, 979–998.
Ali, M. A., and White, R. N. (2001). “Automatic generation of truss model for optimal design of reinforced concrete structures.” ACI Struct. J., 98(4), 431–442.
Almeida, V. S., Simonetti, H. L., and Neto, L. O. (2013). “Comparative analysis of strut-and-tie models using smooth evolutionary structural optimization.” Eng. Struct., 56(6), 1665–1675.
Bendsøe, M. P., Ben-Tal, A., and Zowe, J. (1994). “Optimization methods for truss geometry and topology design.” Struct. Optim., 7(3), 141–159.
Biondini, F., Bontempi, F., and Malerba, P. G. (1999). “Optimal strut-and-tie models in reinforced concrete structures.” Comput. Assisted Mech. Eng. Sci., 6(3), 279–293.
Breen, J. E., Burdet, O., Roberts, C., Sanders, D., and Wollmann, G. (1994). “Anchorage zone reinforcement for post-tensioned concrete girders.” NCHRP Rep.10-29, Transportation Research Board, Washington, DC.
Bruggi, M. (2009). “Generating strut-and-tie patterns for reinforced concrete structures using topology optimization.” Comput. Struct., 87(23–24), 1483–1495.
Bruggi, M. (2016). “A numerical method to generate optimal load paths in plain and reinforced concrete structures.” Comput. Struct., 170, 26–36.
Burdet, O. (1990). “Analysis and design of anchorage zones in post-tensioned concrete bridges.” Ph.D. dissertation, Univ. of Texas at Austin, Austin, TX.
De Tommasi, G. D., Monaco, P., and Vitone, C. (2003). “A first approach to the load path method on masonry structure behavior.” Structural studies repairs and maintenance of heritage architecture VIII, C. A. Brebbia, ed., Wessex Institute of Technology, Southampton, U.K., 287–296.
Gaynor, A., Guest, J., and Moen, C. (2012). “Reinforced concrete force visualization and design using bilinear truss-continuum topology optimization.” J. Struct. Eng., 607–618.
Guan, H., and Doh, J. H. (2007). “Development of strut-and-tie models in deep beams with web openings.” Adv. Struct. Eng., 10(6), 697–711.
Guyon, Y., and Johns, W. M. (1953). “Prestressed concrete.” Nature, 171(4359), 854–855.
Hagishita, T., and Ohsaki, M. (2009). “Topology optimization of trusses by growing ground structure method.” Struct. Multidisc. Optim., 37(4), 377–393.
Herranz, J. P., Maria, H. S., Gutierrez, S., and Riddell, R. (2012). “Optimal strut-and-tie models using full homogenization optimization method.” ACI Struct. J., 109(5), 605–613.
Kumar, P. (1978). “Optimal force transmission in reinforced concrete deep beams.” Comput. Struct., 8(2), 223–229.
Liang, Q. Q., Xie, Y. M., and Steven, G. P. (2000a). “Optimal topology selection of continuum structures with displacement constraints.” Comput. Struct., 77(6), 635–644.
Liang, Q. Q., Xie, Y. M., and Steven, G. P. (2000b). “Topology optimization of strut-and-tie models in reinforced concrete structures using an evolutionary procedure.” ACI Struct. J., 97(2), 322–332.
Liang, Q. Q., Xie, Y. M., and Steven, G. P. (2001). “Generating optimal strut-and-tie models in prestressed concrete beams by performance-based optimization.” ACI Struct. J., 98(2), 226–232.
Marti, P. (1985). “Basic tools of reinforced concrete beam design.” ACI J., 82(1), 46–56.
MATLAB [Computer software]. MathWorks, Natick, MA.
Mezzina, M., Palmisano, F., and Raffaele, D. (2012). “Designing simply supported R.C. bridge decks subjected to in-plane actions: Strut-and-tie model approach.” J. Earthquake Eng., 16(4), 496–514.
Nagarajan, P., Jayadeep, U. B., and Pillai, T. M. M. (2010). “Application of micro truss and strut and tie model for analysis and design of reinforced concrete structural elements.” Songklanakarin J. Sci. Tech., 31(6), 647–653.
Oviedo, R., Gutiérrez, S., and Santa María, H. (2016). “Experimental evaluation of optimized strut-and-tie models for a dapped beam.” Struct. Concr., 17(3), 469–480.
Palmisano, F., Alicino, G., and Vitone, A. (2014). “Nonlinear analysis of RC discontinuity regions by using the bi-directional evolutionary structural optimization method.” Proc., OPT-I, Int. Conf. on Engineering and Applied Sciences Optimization, National Technical Univ. of Athens, Athens, Greece, 749–758.
Palmisano, F., and Elia, A. (2009). “Masonry buildings subjected to foundation settlements due to landslide: A preliminary study on the interpretation of structural behavior using the load path method.” Structural studies repairs and maintenance of heritage architecture XI, C. A. Brebbia, ed., 109, Wessex Institute of Technology, Southampton, U.K., 141–150.
Palmisano, F., and Elia, A. (2015). “Shape optimization of strut-and-tie models in masonry buildings subjected to landslide-induced settlements.” Eng. Struct., 84, 223–232.
Palmisano, F., Vitone, A., and Vitone, C. (2003). “From load path method to classical models of structural analysis.” Proc., ISEC-02–Int. Structural Engineering and Construction Conf., F. Bontempi, ed., Vol. 1, A. A. Balkema, Rotterdam, Netherlands, 589–596.
Palmisano, F., Vitone, A., and Vitone, C. (2005). “Load path method in the interpretation of masonry vault behaviour.” Structural studies repairs and maintenance of heritage architecture IX, C. A. Brebbia, ed., Vol. 20, Wessex Institute of Technology, Southampton, U.K., 155–167.
Salem, H. M. (2004). “The micro truss model: an innovative rational design approach for reinforced concrete.” J. Adv. Concr. Technol., 2(1), 77–87.
Sanders, D. (1990). “Design and behavior of anchorage zones in post-tensioned concrete members.” Ph.D. dissertation, Univ. of Texas at Austin, Austin, TX.
Schlaich, J., Schäfer, K., and Jennewein, M. (1987). “Toward a consistent design of structural concrete.” PCI J., 32(3), 74–150.
Wollmann, G. (1992). “Anchorage zones in post-tensioned concrete structures.” Ph.D. dissertation, Univ. of Texas at Austin, Austin, TX.
Xie, Y. M., and Steven, G. P. (1993). “A simple evolutionary procedure for structural optimization.” Comput. Struct., 49(5), 885–896.
Zakhama, R., Abdalla, M. M., Smaoui, H., and Gurdal, Z. (2006). “Topology design of geometrically nonlinear 2D elastic continua using CA and an equivalent truss model.” Proc., 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conf., American Institute of Aeronautics and Astronautics, Inc., Raleigh, NC, 6–8.
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Published In
Journal of Bridge Engineering
Volume 22 • Issue 4 • April 2017
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Aug 11, 2016
Accepted: Oct 5, 2016
Published online: Nov 23, 2016
Published in print: Apr 1, 2017
Discussion open until: Apr 23, 2017
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