Reliability Evaluation Based on Multiple Response Surfaces Method Considering Construction Uncertainties of Cable Tension for a Hybrid Roof Structure
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7, Issue 3
Abstract
For large-span hybrid roof structures, the construction uncertainties of cable tension usually have significant influences on the roof’s mechanical performance and should be considered in reliability evaluation. An effective approach to quantify uncertainties of cable tensions and evaluate structural reliability is proposed to carry out the studies by combining finite-element simulation with the multiple response surfaces method. Taking a hybrid roof structure with cables and steel trusses as an example, the main procedures on this issue are illustrated. First, a finite-element model is established for the hybrid roof structure considering construction deviations, such as the deviations of cable force between the design values and the real measured values. The ultimate bearing capacity of the structure is calculated for models with and without deviations, and the effects of construction deviations on structural bearing capacity are analyzed. Then, an uncertainty model of cable tension for structural reliability evaluation is proposed by establishing the statistics of initial strain in a structural analysis based on the monitored deviations. With subspace division and limit state sample (or sample pair), the multiple response surfaces method is developed to solve reliability for examples with complex failure functions. It is found that the hybrid roof structure has a high reliability index about 6.76; and the uncertainties of cable tensions have a large impact on the reliability, especially the uncertainties of the upper suspension cable tensions and the back cable tensions.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The research is supported by the National Natural Science Foundation of China (Grant No. 51678072), National Key Research and Development Program of China (2019YFC1511000), and Key Discipline Foundation of Civil Engineering of Changsha University of Science and Technology (18ZDXK01). This support is gratefully acknowledged.
References
Cai, J. G., and J. Feng. 2015. “Form-finding of tensegrity structures using an optimization method.” Eng. Struct. 104 (Dec): 126–132. https://doi.org/10.1016/j.engstruct.2015.09.028.
Cai, J. G., R. G. Yang, X. Y. Wang, and J. Feng. 2019a. “Effect of initial imperfections of struts on the mechanical behavior of tensegrity structures.” Compos. Struct. 207 (Jan): 871–876. https://doi.org/10.1016/j.compstruct.2018.09.018.
Cai, J. G., Q. Zhang, J. Feng, and Y. X. Xu. 2019b. “Modeling and kinematic path selection of retractable kirigami roof structures.” Comput.-Aided Civil Infrastruct. Eng. 34 (4): 352–363. https://doi.org/10.1111/mice.12418.
Cheng, J. 2010. “Determination of cable forces in cable-stayed bridges constructed under parametric uncertainty.” Eng. Comput. 27 (3): 301–321. https://doi.org/10.1108/02644401011029907.
Cheng, M. 2014. “Probability analysis and parameters identification of cable tested tension by frequency method.” [In Chinese.] Master dissertation, School of Transportation Science and Engineering, Harbin Institute of Technology.
Dai, L., H. Bian, L. Wang, and M. Potier-Ferry. 2020. “Prestress loss diagnostics in pretensioned concrete structures with corrosive cracking.” J. Struct. Eng. 146 (3): 04020013. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002554.
Deng, H., M. R. Zhang, H. C. Liu, S. L. Dong, Z. H. Zhang, and L. Q. Chen. 2016. “Numerical analysis of the pretension deviations of a novel crescent-shaped tensile canopy structural system.” Eng. Struct. 119 (Jul): 24–33. https://doi.org/10.1016/j.engstruct.2016.04.005.
Deng, H., Y. Z. Zu, J. J. Shen, G. B. Bai, S. L. Dong, Z. H. Zhang, and L. Q. Chen. 2013. “Analysis and experiment on erection process of a crescent-shaped cable-truss canopy structure.” [In Chinese.] J. Zhejiang Univ. (Eng. Sci.) 47 (3): 488–494. https://doi.org/10.3785/j.issn.1008-973X.2013.03.013.
Dubourg, V., B. Sudret, and F. Deheeger. 2013. “Metamodel -based importance sampling for structural reliability analysis.” Probab. Eng. Mech. 33 (Jul): 47–57. https://doi.org/10.1016/j.probengmech.2013.02.002.
Fang, K. T. and Y. Wang. 1994. Number-theoretic methods in statistics. London: Chapman & Hall.
Feng, F. 2005. “Structural behavior and design methods of Tensegrity domes.” J. Constr. Steel Res. 61 (1): 23–35. https://doi.org/10.1016/j.jcsr.2004.06.004.
Fuller, B. R. 1975. Synergetics: Explorations in the geometry of thinking. New York: Macmillan.
Geiger, D. H., A. Stefaniuk, and D. Chen. 1986. “The design and construction of two cable domes for the Korean Olympics.” In Vol. 2 of Proc., IASS Symp. Osaka, Shells, Membranes and Space Frames, 265–272. Amsterdam, Netherlands: Elsevier.
Guimarães, H., J. C. Matos, and A. A. Henriques. 2018. “An innovative adaptive sparse response surface method for structural reliability analysis.” Struct. Saf. 73 (Jul): 12–28. https://doi.org/10.1016/j.strusafe.2018.02.001.
Hadidi, A., B. F. Azar, and A. Rafiee. 2017. “Efficient response surface method for high-dimensional structural reliability analysis.” Struct. Saf. 68 (Sep): 15–27. https://doi.org/10.1016/j.strusafe.2017.03.006.
Jiang, Y. B., Q. Cao, X. Kong, and G. Y. Liao. 2016. “Stiffness study of inner concave cable–arch structure based on an efficient method.” Adv. Struct. Eng. 19 (12): 1927–1939. https://doi.org/10.1177/1369433216649394.
Jiang, Y. B., J. Luo, G. Y. Liao, Y. L. Zhao, and J. R. Zhang. 2015. “An efficient method for generation of uniform support vector and its application in structural failure function fitting.” Struct. Saf. 54 (May): 1–9. https://doi.org/10.1016/j.strusafe.2014.12.004.
Jiang, Y. B., L. J. Zhao, M. Beer, E. Patelli, M. Broggi, J. Luo, Y. H. He, and J. R. Zhang. 2017. “Multiple response surfaces method with advanced classification of samples for structural failure function fitting.” Struct. Saf. 64 (Jan): 87–97. https://doi.org/10.1016/j.strusafe.2016.10.002.
Ju, S., R. A. Shenoi, D. Jiang, and A. J. Sobey. 2013. “Multi-parameter optimization of lightweight composite triangular truss structure based on response surface methodology.” Compos. Struct. 97 (2): 107–116. https://doi.org/10.1016/j.compstruct.2012.10.025.
Juan, S. H., and J. M. M. Tur. 2008. “Tensegrity frameworks: Static analysis review.” Mech. Mach. Theory 43 (7): 859–881. https://doi.org/10.1016/j.mechmachtheory.2007.06.010.
Kebiche, K., M. N. Kazi, and R. Motro. 1999. “Geometrical non-linear analysis of tensegrity systems.” Eng. Struct. 21 (9): 864–876. https://doi.org/10.1016/S0141-0296(98)00014-5.
Kmet, S., and M. Mojdis. 2013. “Time-dependent analysis of cable domes using a modified dynamic relaxation method and creep theory.” Comput. Struct. 125 (1): 11–22. https://doi.org/10.1016/j.compstruc.2013.04.019.
Kmet, S., M. Tomko, and J. Brda. 2007. “Time-dependent analysis and simulation-based reliability assessment of suspended cables with rheological properties.” Adv. Eng. Software 38 (8–9): 561–575. https://doi.org/10.1016/j.advengsoft.2006.08.022.
Marelli, S., and B. Sudret. 2018. “An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis.” Struct. Saf. 75 (Nov): 67–74. https://doi.org/10.1016/j.strusafe.2018.06.003.
MOHURD (Ministry of Housing and Urban-Rural Development of the People’s Republic of China). 2012. Load code for the design of building structures. [In Chinese.] GB50009-2012. Beijing: China Building Industry Press.
Morino, S. 1998. “Recent developments in hybrid structures in Japan—Research, design and construction.” Eng. Struct. 20 (4–6): 336–346. https://doi.org/10.1016/S0141-0296(97)00022-9.
Papadopoulos, V., D. G. Giovanis, N. D. Lagaros, and M. Papadrakakis. 2012. “Accelerated subset simulation with neural networks for reliability analysis.” Comput. Meth. Appl. Mech. Eng. 223–224 (Jun): 70–80. https://doi.org/10.1016/j.cma.2012.02.013.
Phocas, M. C., and K. Alexandrou. 2018. “Numerical analysis and cable activation in hybrid bending-active structures with multiple cables.” Eng. Struct. 174 (Nov): 561–572. https://doi.org/10.1016/j.engstruct.2018.07.089.
Rosenblatt, M. 1952. “Remarks on a multivariate transformation.” Ann. Math. Stat. 23 (3): 470–472. https://doi.org/10.1214/aoms/1177729394.
Schobi, R., B. Sudret, and J. Wiart. 2015. “Polynomial-chaos-based kriging.” Int. J. Uncertainty Quantif. 5 (2): 171–193. https://doi.org/10.1615/Int.J.UncertaintyQuantification.2015012467.
Sultan, C., M. Corless, and R. E. Skelton. 2001. “The prestressability problem of tensegrity structures: Some analytical solutions.” Int. J. Solids Struct. 38 (30): 5223–5252. https://doi.org/10.1016/S0020-7683(00)00401-7.
Sultan, C., M. Corless, and R. E. Skelton. 2002. “Linear dynamics of tensegrity structures.” Eng. Struct. 24 (6): 671–685. https://doi.org/10.1016/S0141-0296(01)00130-4.
Teixeira, R., N. María, and A. O’Connor. 2020. “Adaptive approaches in metamodel-based reliability analysis: A review.” Struct. Saf. 89 (2021): 102019. https://doi.org/10.1016/j.strusafe.2020.102019.
Tibert, G., and S. Pellegrino. 2003. “Review of form-finding methods for tensegrity structures.” Int. J. Space Struct. 18 (4): 209–223. https://doi.org/10.1260/026635103322987940.
Wakefield, D. S. 1999. “Engineering analysis of tension structures: Theory and practice.” Eng. Struct. 21 (8): 680–690. https://doi.org/10.1016/S0141-0296(98)00023-6.
Wang, L., L. Z. Dai, H. B. Bian, and Y. F. Ma. 2019. “Concrete cracking prediction under combined prestress and strand corrosion.” Struct. Infrastruct. Eng. 15 (3): 285–295. https://doi.org/10.1080/15732479.2018.1550519.
Wang, Z. Y., and A. Shafieezadeh. 2019. “REAK: Reliability analysis through error rate-based adaptive kriging.” Reliab. Eng. Syst. Saf. 182 (Feb): 33–45. https://doi.org/10.1016/j.ress.2018.10.004.
Williamson, D., R. E. Skelton, and J. Han. 2003. “Equilibrium conditions of a tensegrity structure.” Int. J. Solids Struct. 40 (23): 6347–6367. https://doi.org/10.1016/S0020-7683(03)00400-1.
Xiao, N. C., H. Y. Zhan, and K. Yuan. 2020. “A new reliability method for small failure probability problems by combining the adaptive importance sampling and surrogate models.” Comput. Meth. Appl. Mech. Eng. 372 (Dec): 113336. https://doi.org/10.1016/j.cma.2020.113336.
Xue, G. F., H. Z. Dai, H. Zhang, and W. Wang. 2017. “A new unbiased metamodel method for efficient reliability analysis.” Struct. Saf. 67 (Jul): 1–10. https://doi.org/10.1016/j.strusafe.2017.03.005.
Yan, X. Y., Y. Yang, Z. H. Chen, and Q. Ma. 2019. “Mechanical properties of a hybrid cable dome under non-uniform snow distribution.” J. Constr. Steel Res. 153 (Feb): 519–532. https://doi.org/10.1016/j.jcsr.2018.10.022.
Yasuhiko, H. G., and M. Wu. 1999. “Analytical method of structural behaviors of a hybrid structure consisting of cables and rigid structures.” Eng. Struct. 21 (8): 726–736. https://doi.org/10.1016/S0141-0296(98)00027-3.
Zhang, J. Y., and M. Ohsaki. 2006. “Adaptive force density method for form-finding problem of tensegrity structures.” Int. J. Solids Struct. 43 (18): 5658–5673. https://doi.org/10.1016/j.ijsolstr.2005.10.011.
Zhang, Q., N. Pan, M. Meloni, D. Lu, J. G. Cai, and J. Feng. 2020. “Reliability analysis of radially retractable roofs with revolute joint clearances.” Reliab. Eng. Syst. Saf. 208 (2021): 107401. https://doi.org/10.1016/j.ress.2020.107401.
Zhang, X. P. 2001. Reliability analysis and design for building structures. [In Chinese.] Beijing: Science Press.
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Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7 • Issue 3 • September 2021
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© 2021 American Society of Civil Engineers.
History
Received: Sep 18, 2020
Accepted: Mar 31, 2021
Published online: Jun 22, 2021
Published in print: Sep 1, 2021
Discussion open until: Nov 22, 2021
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