On the optimal strut-and-tie models and design approach for the cable-pylon anchorage zone
Abstract
The cable-pylon anchorage zone is a typical D-region in a cable-stayed bridge, for which there has been no uniform simplified design method until now. In this paper, based on the extensive statistics of actual projects, topology optimization techniques and principle of minimum strain energy, two precise strut-and-tie models for the cable-pylon anchorage zone are proposed, which can clearly reveal the load-transmitting mechanism of the anchorage zone. Th e explicit geometric parameters of the strut-and-tie models are derived; thus, the designers can directly use these models. A simple design procedure to deploy prestressing tendons in the anchorage zone is also introduced, whose effectiveness and convenience are demonstrated by two design examples. A new design named the “one-way prestressing tendons PC cable-pylon” is also discussed regarding its application scope.
Keyword : cable-pylon anchorage zone, strut-and-tie model, topology optimization, prestressing tendon, design approach
How to Cite
Cui, N., & Huang, S. (2019). On the optimal strut-and-tie models and design approach for the cable-pylon anchorage zone. Journal of Civil Engineering and Management, 25(6), 576-586. https://doi.org/10.3846/jcem.2019.10374
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
ACI Committee 318. (2008). Building code requirements for structural concrete (ACI318-08) and commentary (ACI 318R-08). American Concrete Institute, Farmington Hills (MI), USA.
Association of State Highway and Transportation Officials (AASHTO). (1999). Guide specifications for design and construction of segmental concrete bridges. Washington (DC), USA.
Association of State Highway and Transportation Officials (AASHTO). (2004). LRFD bridge specifications SI units (3rd ed.). Washington (DC), USA.
Bendsoe, M. P., & Sigmund, O. (2013). Topology optimization: Theory, methods, and applications. Berlin: Springer Science & Business Media.
Canadian Standards Association (CSA). (1994). Design of concrete structure: Structures design. Rexdale (ON), Canada.
CEB-FIP MC 1990. (1993). Design code. London: Thomas Telford Services Ltd.
Cui, N. N., Jia, B. Y., Yu, X. L., Mai, Z. H., Yang, Z., & Yan, Q. S. (2016). Full-scale model test of pylon anchorage zone with one-way prestressing tendons in cable-stayed bridge. Journal of Hunan University (Natural Sciences), 43(5), 61-69 (in Chinese).
Cui, N. N., Jia, B. Y., Yu, X. L., Yang, Z., & Yan, Q. S. (2015). Investigation into prestress loss of short straight tendons in pylon anchorage zone of cable-stayed bridge. Journal of South China University of Technology (Natural Science), 43(12), 7784 (in Chinese).
Eurocode 2. (2004). Design of concrete structures: Part 1–1: General rules and rules for buildings. London: Thomas Telford Services Ltd.
He, Z.-Q., & Liu, Z. (2010). Optimal three-dimensional strutand-tie models for anchorage diaphragms in externally prestressed bridges. Engineering Structures, 32, 2057-2064. https://doi.org/10.1016/j.engstruct.2010.03.006
Ji, L. (2005). The collection of Runyang Yangtze River bridge construction. Beijing: China Communication Press.
Jia, H., Misra, A., Poorsolhjouy, P., & Liu, C. (2017). Optimal structural topology of materials with micro-scale tensioncompression asymmetry simulated using granular micromechanics. Materials & Design, 115, 422-432. https://doi.org/10.1016/j.matdes.2016.11.059
Liang, Q. Q., & Steven, G. P. (2002). A performance-based optimization method for topology design of continuum structures with mean compliance constraints. Computer Methods in Applied Mechanics and Engineering, 191(13), 1471-1489. https://doi.org/10.1016/S0045-7825(01)00333-4
Liang, Q. Q., Brian, U., & Steven, G. P. (2002) Performance-based optimization for strut-tie modeling of structural concrete. Journal of Structural Engineering, 128(6), 815-823. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:6(815)
Liang, Q. Q., Xie, Y. M., & Steven, G. P. (2000). Topology optimization of strut-and-tie models in reinforced concrete structures using an evolutionary procedure. ACI Structural Journal, 97(2), 322-330. https://doi.org/10.14359/863
Meng, J., Wu, H. W., & Zheng, H. H. (2016). Prestress design for concrete pylon anchorage zone based on the strut-and-tie models. Structural Engineers, 32(1), 5-9 (in Chinese).
Schlaich, J., Kurt, S., & Mattias, J. (1987). Toward a consistent design of structural concrete. PCI Journal. 32(3), 74-150. https://doi.org/10.15554/pcij.05011987.74.150
Su, Q. T., Yang, G. T., Qin, F., & Wu, C. (2012). Investigation on the horizontal mechanical behavior of steel-concrete composite cable-pylon anchorage. Journal of Constructional Steel Research, 24(6), 36-40. https://doi.org/10.1016/j.jcsr.2012.01.004
Tang, H. Y. (2006). Study on key problems of cable-stayed bridge PC pylon (PhD thesis). Southeast University, Nanjing, China.
Tao, H. (2007). Study on key problems of concrete cable-stayed bridges base on three-dimensional analysis (PhD thesis). Tongji University, Shanghai, China.
Tao, H., & Xiao, R. H. (2008). Strut and tie model of prestress design for pylon anchor of concrete cable stayed bridges. Structural Engineers, 24(6), 36-40 (in Chinese).
Tao, Q. Y. (2012). Study on key issues in the PC pylon of long-span cable-stayed bridge (PhD thesis). Southwest Jiaotong University, Chengdu, China.
Tao, Q. Y., Ye, H. W., Hu, J. C., & Xu, X. (2017a). Horizontal STM and application of pre-stressed pylon anchorage zones of cable-stayed bridge. Sichuan Building Science, 43(3), 10-15 (in Chinese).
Tao, Q. Y., Ye, H. W., Hu, J. C., & Xu, X. (2017b). Study on vertical strut-and-tie model in side wall of concrete cable bent tower anchorage zone of large-span cable-stayed bridge. Railway Engineering, 17(7), 16-20 (in Chinese).
Tjhin, T., & Kuchma, D. (2007) Integrated analysis and design tool for the strut-and-tie method. Engineering Structures, 29(11), 3042-3052. https://doi.org/10.1016/j.engstruct.2007.01.032
Wu, B., Lu, H., & Chen, B. (2017). Study on finite element model updating in highway bridge static loading test using spatially distributed optical fiber sensors. Sensors, 17(7), 1657. https://doi.org/10.3390/s17071657
Xia, Z., Li, A, Li, J., & Duan, M. (2017). FE model updating on an in-service self-anchored suspension bridge with extra-width using hybrid method. Applied Sciences, 7(2), 191. https://doi.org/10.3390/app7020191
Xie, Y. M., & Steven, G. P. (1993). A simple evolutionary procedure for structural optimization. Computers & Structures, 49(5), 885-896. https://doi.org/10.1016/0045-7949(93)90035-C
Xiong, Z. H., Liu Y. J., Tian, W. M., & Song, S. L. (2013). Application of topologically optimized strut-and-tie model to pylon anchorage zone. Bridge Construction, 43(4), 74-79 (in Chinese).
Ye, H. W., Li, C. J., Xu, X., Xiao, L., & Qiang, S. Z. (2014). Fullscale model test of pre-stressed cable-pylon anchorage for single-oblique-pylon cable-stayed bridges. Journal of Southwest Jiaotong University, 49(1), 52-58 (in Chinese).
Zhai, H. N. (2008). Experimental study of horizontal behavior of the anchorage zone on pylon of the third Yellow River Bridge in Jinan (MSc thesis). Tongji University, Shanghai, China.
Zhu, J. W., Wang, J. B., & Feng, Y. C. (2017). Topologically optimized strut-and-tie model and structural analysis of prestress for anchorage zone in pylon. Bridge Construction, 47(5), 5964 (in Chinese).
Association of State Highway and Transportation Officials (AASHTO). (1999). Guide specifications for design and construction of segmental concrete bridges. Washington (DC), USA.
Association of State Highway and Transportation Officials (AASHTO). (2004). LRFD bridge specifications SI units (3rd ed.). Washington (DC), USA.
Bendsoe, M. P., & Sigmund, O. (2013). Topology optimization: Theory, methods, and applications. Berlin: Springer Science & Business Media.
Canadian Standards Association (CSA). (1994). Design of concrete structure: Structures design. Rexdale (ON), Canada.
CEB-FIP MC 1990. (1993). Design code. London: Thomas Telford Services Ltd.
Cui, N. N., Jia, B. Y., Yu, X. L., Mai, Z. H., Yang, Z., & Yan, Q. S. (2016). Full-scale model test of pylon anchorage zone with one-way prestressing tendons in cable-stayed bridge. Journal of Hunan University (Natural Sciences), 43(5), 61-69 (in Chinese).
Cui, N. N., Jia, B. Y., Yu, X. L., Yang, Z., & Yan, Q. S. (2015). Investigation into prestress loss of short straight tendons in pylon anchorage zone of cable-stayed bridge. Journal of South China University of Technology (Natural Science), 43(12), 7784 (in Chinese).
Eurocode 2. (2004). Design of concrete structures: Part 1–1: General rules and rules for buildings. London: Thomas Telford Services Ltd.
He, Z.-Q., & Liu, Z. (2010). Optimal three-dimensional strutand-tie models for anchorage diaphragms in externally prestressed bridges. Engineering Structures, 32, 2057-2064. https://doi.org/10.1016/j.engstruct.2010.03.006
Ji, L. (2005). The collection of Runyang Yangtze River bridge construction. Beijing: China Communication Press.
Jia, H., Misra, A., Poorsolhjouy, P., & Liu, C. (2017). Optimal structural topology of materials with micro-scale tensioncompression asymmetry simulated using granular micromechanics. Materials & Design, 115, 422-432. https://doi.org/10.1016/j.matdes.2016.11.059
Liang, Q. Q., & Steven, G. P. (2002). A performance-based optimization method for topology design of continuum structures with mean compliance constraints. Computer Methods in Applied Mechanics and Engineering, 191(13), 1471-1489. https://doi.org/10.1016/S0045-7825(01)00333-4
Liang, Q. Q., Brian, U., & Steven, G. P. (2002) Performance-based optimization for strut-tie modeling of structural concrete. Journal of Structural Engineering, 128(6), 815-823. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:6(815)
Liang, Q. Q., Xie, Y. M., & Steven, G. P. (2000). Topology optimization of strut-and-tie models in reinforced concrete structures using an evolutionary procedure. ACI Structural Journal, 97(2), 322-330. https://doi.org/10.14359/863
Meng, J., Wu, H. W., & Zheng, H. H. (2016). Prestress design for concrete pylon anchorage zone based on the strut-and-tie models. Structural Engineers, 32(1), 5-9 (in Chinese).
Schlaich, J., Kurt, S., & Mattias, J. (1987). Toward a consistent design of structural concrete. PCI Journal. 32(3), 74-150. https://doi.org/10.15554/pcij.05011987.74.150
Su, Q. T., Yang, G. T., Qin, F., & Wu, C. (2012). Investigation on the horizontal mechanical behavior of steel-concrete composite cable-pylon anchorage. Journal of Constructional Steel Research, 24(6), 36-40. https://doi.org/10.1016/j.jcsr.2012.01.004
Tang, H. Y. (2006). Study on key problems of cable-stayed bridge PC pylon (PhD thesis). Southeast University, Nanjing, China.
Tao, H. (2007). Study on key problems of concrete cable-stayed bridges base on three-dimensional analysis (PhD thesis). Tongji University, Shanghai, China.
Tao, H., & Xiao, R. H. (2008). Strut and tie model of prestress design for pylon anchor of concrete cable stayed bridges. Structural Engineers, 24(6), 36-40 (in Chinese).
Tao, Q. Y. (2012). Study on key issues in the PC pylon of long-span cable-stayed bridge (PhD thesis). Southwest Jiaotong University, Chengdu, China.
Tao, Q. Y., Ye, H. W., Hu, J. C., & Xu, X. (2017a). Horizontal STM and application of pre-stressed pylon anchorage zones of cable-stayed bridge. Sichuan Building Science, 43(3), 10-15 (in Chinese).
Tao, Q. Y., Ye, H. W., Hu, J. C., & Xu, X. (2017b). Study on vertical strut-and-tie model in side wall of concrete cable bent tower anchorage zone of large-span cable-stayed bridge. Railway Engineering, 17(7), 16-20 (in Chinese).
Tjhin, T., & Kuchma, D. (2007) Integrated analysis and design tool for the strut-and-tie method. Engineering Structures, 29(11), 3042-3052. https://doi.org/10.1016/j.engstruct.2007.01.032
Wu, B., Lu, H., & Chen, B. (2017). Study on finite element model updating in highway bridge static loading test using spatially distributed optical fiber sensors. Sensors, 17(7), 1657. https://doi.org/10.3390/s17071657
Xia, Z., Li, A, Li, J., & Duan, M. (2017). FE model updating on an in-service self-anchored suspension bridge with extra-width using hybrid method. Applied Sciences, 7(2), 191. https://doi.org/10.3390/app7020191
Xie, Y. M., & Steven, G. P. (1993). A simple evolutionary procedure for structural optimization. Computers & Structures, 49(5), 885-896. https://doi.org/10.1016/0045-7949(93)90035-C
Xiong, Z. H., Liu Y. J., Tian, W. M., & Song, S. L. (2013). Application of topologically optimized strut-and-tie model to pylon anchorage zone. Bridge Construction, 43(4), 74-79 (in Chinese).
Ye, H. W., Li, C. J., Xu, X., Xiao, L., & Qiang, S. Z. (2014). Fullscale model test of pre-stressed cable-pylon anchorage for single-oblique-pylon cable-stayed bridges. Journal of Southwest Jiaotong University, 49(1), 52-58 (in Chinese).
Zhai, H. N. (2008). Experimental study of horizontal behavior of the anchorage zone on pylon of the third Yellow River Bridge in Jinan (MSc thesis). Tongji University, Shanghai, China.
Zhu, J. W., Wang, J. B., & Feng, Y. C. (2017). Topologically optimized strut-and-tie model and structural analysis of prestress for anchorage zone in pylon. Bridge Construction, 47(5), 5964 (in Chinese).