Probabilistic versus Deterministic Assessment of the Minimum Structural Damping Required to Prevent Galloping of Dry Bridge Hangers
Publication: Journal of Structural Engineering
Volume 145, Issue 8
Abstract
The risk of large-amplitude vibrations of bridge hangers due to galloping instabilities has posed a challenge to the engineering and research communities. Galloping vibrations can lead to serviceability problems and reduce fatigue life. A number of aeroelastic models have been developed to predict the unstable behavior and to design counteracting measures, i.e., shape modifications and structural damping addition. All the proposed procedures generally consider that the parameters are assigned according to deterministic values. A framework is proposed for the deterministic and probabilistic assessment of the minimum structural damping required to prevent galloping of bridge hangers based on the output of a two-degree-of-freedom sectional quasi-steady aeroelastic model. All the variables required to define the hanger dynamics, the sheath aerodynamics, and the local wind climate are considered. Because of the large uncertainties and of the nonlinear nature of the problem, the distribution of the minimum structural damping required to prevent galloping is obtained by Monte Carlo simulations. An application of the method to the proposed Messina Straits crossing bridge is presented. Starting from wind tunnel measurements of the aerodynamic coefficients of a real plain high-density polyethylene (HDPE) cable sheath, the random nature of the aerodynamics is shown, which is ascribed to the cable irregularities (surface roughness, section distortion, and axis curvature). Then the statistical variation of the parameters of the model is considered, based on real data derived from wind tunnel tests and from the wind climate measured at the site. The distributions of the parameters defining the hanger dynamics are assigned according to typical values. Using a normal and a log-normal model of capacity, the probability of failure is calculated. The results are discussed and compared with conventional approaches based on the definition of the deterministic variables. Finally, using a deterministic model of capacity, a simplified closed-form equation for the evaluation of the structural damping needed to prevent galloping in a probabilistic-based performance approach is proposed.
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Acknowledgments
The authors acknowledge Professor Christos T. Georgakis of Aarhus University for the use of the wind tunnel and Ph.D. candidate Celeste Burlina of the Technical University of Denmark for helping in wind tunnel testing. The first author acknowledges the Jiangsu Provincial Double Innovation Program (2016A407) for providing the cluster used in the numerical simulations.
References
Avossa, A., C. Demartino, and F. Ricciardelli. 2017. “Design procedures for footbridges subjected to walking loads: Comparison and remarks.” Baltic J. Road Bridge Eng. 12 (2): 94–105. https://doi.org/10.3846/bjrbe.2017.12.
Batham, J. 1973. “Pressure distributions on circular cylinders at critical Reynolds numbers.” J. Fluid Mech. 57 (2): 209–228. https://doi.org/10.1017/S0022112073001114.
Benidir, A., O. Flamand, L. Gaillet, and G. Dimitriadis. 2015. “Impact of roughness and circularity-defect on bridge cables stability.” J. Wind Eng. Ind. Aerodyn. 137 (Feb): 1–13. https://doi.org/10.1016/j.jweia.2014.11.010.
Blevins, R. 1977. Flow-induced vibration. New York: Van Nostrand Reinhold.
Brancaleoni, F., et al. 2009. The Messina Strait Bridge: A challenge and a dream. London: CRC Press.
Brownjohn, J. M. W. 1994. “Estimation of damping in suspension bridges.” Proc. Inst. Civ. Eng. Struct. Build. 104 (4): 401–415. https://doi.org/10.1680/istbu.1994.27199.
Brownjohn, J. M. W., and P. Carden. 2007. “Reliability of frequency and damping estimates from free vibration response.” In Proc., 2nd Int. Operational Modal Analysis Conf., 23–30. Copenaghen, Denmark.
Brownjohn, J. M. W., F. Magalhaes, E. de Sá Caetano, and A. Cunha. 2010. “Ambient vibration re-testing and operational modal analysis of the Humber Bridge.” Eng. Struct. 32 (8): 2003–2018. https://doi.org/10.1016/j.engstruct.2010.02.034.
Carassale, L., A. Freda, and G. Piccardo. 2005. “Aeroelastic forces on yawed circular cylinders: Quasi-steady modeling and aerodynamic instability.” Wind Struct. 8 (5): 373–388. https://doi.org/10.12989/was.2005.8.5.373.
Carta, J. A., P. Ramirez, and C. Bueno. 2008. “A joint probability density function of wind speed and direction for wind energy analysis.” Energy Convers. Manage. 49 (6): 1309–1320. https://doi.org/10.1016/j.enconman.2008.01.010.
CEN (European Committee for Standardization). 2005. Actions on structures. Eurocode 1, EN 1991 Part 1–4. Brussels, Belgium: CEN.
Chabart, O., and J. Lilien. 1998. “Galloping of electrical lines in wind tunnel facilities.” J. Wind Eng. Ind. Aerodyn. 74–76 (Apr): 967–976. https://doi.org/10.1016/S0167-6105(98)00088-9.
Chiodi, R., and F. Ricciardelli. 2014. “Three issues concerning the statistics of mean and extreme wind speeds.” J. Wind Eng. Ind. Aerodyn. 125 (Feb): 156–167. https://doi.org/10.1016/j.jweia.2013.12.009.
Cooper, K., E. Mercker, and J. Wiedeman. 1999. “Improved blockage corrections for bluff bodies in closed and open wind tunnels.” In Proc., Wind Engineering into the 21st Century. Rotterdam, Netherlands: A.A. Balkema.
Demartino, C. 2014. “Aerodynamics and aeroelastic behaviour of ice-accreted bridge cables.” Ph.D. thesis, Dept. of Structures for Engineering and Architecture, Univ. of Naples Federico II.
Demartino, C., A. Avossa, F. Ricciardelli, and C. Calidonna. 2017. “Wind profiles identification using wind lidars: An application to the area of lametia terme.” In Proc., 7th European and African Conf. on Wind Engineering, 1–10. Bologna, Italy: Institute of Atmospheric Sciences and Climate.
Demartino, C., A. M. Avossa, and F. Ricciardelli. 2018. “Deterministic and probabilistic serviceability assessment of footbridge vibrations due to a single walker crossing.” Shock Vibr. 2018: 26. https://doi.org/10.1155/2018/1917629.2018.
Demartino, C., H. Koss, C. Georgakis, and F. Ricciardelli. 2015. “Effects of ice accretion on the aerodynamics of bridge cable.” J. Wind Eng. Ind. Aerodyn. 138 (Mar): 98–119. https://doi.org/10.1016/j.jweia.2014.12.010.
Demartino, C., and F. Ricciardelli. 2015. “Aerodynamic stability of ice-accreted bridge cables.” J. Fluids Struct. 52 (Jan): 81–100. https://doi.org/10.1016/j.jfluidstructs.2014.10.003.
Demartino, C., and F. Ricciardelli. 2017. “Aerodynamics of nominally circular cylinders: A review of experimental results for civil engineering applications.” Eng. Struct. 137 (Apr): 76–114. https://doi.org/10.1016/j.engstruct.2017.01.023.
Demartino, C., and F. Ricciardelli. 2018. “Assessment of the structural damping required to prevent galloping of dry HDPE stay cables using the quasi-steady approach.” J. Bridge Eng. 23(4), 04018004. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001168.
Den Hartog, J. 1932. “Transmission line vibration due to sleet.” Trans. Am. Inst. Electr. Eng. 51 (4): 1074–1076. https://doi.org/10.1109/T-AIEE.1932.5056223.
Ekman, V. 1905. “On the influence of the earth’s rotation on ocean currents.” Ark. Mat. Astron. Fys. 11 (2): 1–53.
Flamand, O., and O. Boujard. 2009. “A comparison between dry cylinder galloping and rain-wind induced excitation.” In Proc., 5th European and African Conf. on Wind Engineering, 485–488. Florence, Italy.
Georgakis, C., H. Koss, and F. Ricciardelli. 2009. “Design specifications for a novel climatic wind tunnel for the testing of structural cables.” In Proc., 8th Int. Symp. on Cable Dynamics, 333–340. Paris.
Gimsing, N. J., and C. T. Georgakis. 2011. Cable supported bridges: Concept and design. Chichester, UK: Wiley.
Gjelstrup, H., and C. Georgakis. 2011. “A quasi-steady 3 degree-of-freedom model for the determination of the onset of bluff body galloping instability.” J. Fluids Struct. 27 (7): 1021–1034. https://doi.org/10.1016/j.jfluidstructs.2011.04.006.
Gjelstrup, H., C. Georgakis, and A. Larsen. 2012. “An evaluation of iced bridge hanger vibrations through wind tunnel testing and quasi-steady theory.” Wind Struct. 15 (5): 385–407. https://doi.org/10.12989/was.2012.15.5.385.
He, M., and J. Macdonald. 2016. “An analytical solution for the galloping stability of a 3 degree-of-freedom system based on quasi-steady theory.” J. Fluids Struct. 60 (Jan): 23–36. https://doi.org/10.1016/j.jfluidstructs.2015.10.004.
He, M., and J. Macdonald. 2017. “Aeroelastic stability of a 3dof system based on quasi-steady theory with reference to inertial coupling.” J. Wind Eng. Ind. Aerodyn. 171 (Dec): 319–329. https://doi.org/10.1016/j.jweia.2017.10.013.
Irvine, H. 1981. Cable structures. New York: Dover.
ISO. 1998. General principles on reliability for structures. ISO 2394. Geneva: ISO.
Karadeniz, H., and T. Vrouwenvelder. 2003. Saferelnet Task 5.1: Overview reliability methods. Delft, the Netherlands: Delft Univ. of Technology.
Koss, H. H., H. Gjelstrup, and C. T. Georgakis. 2012. “Experimental study of ice accretion on circular cylinders at moderate low temperatures.” J. Wind Eng. Ind. Aerodyn. 104–106 (May–Jul): 540–546. https://doi.org/10.1016/j.jweia.2012.03.024.
Krenk, S., and J. Høgsberg. 2005. “Damping of cables by a transverse force.” J. Eng. Mech. 131 (4): 340–348. https://doi.org/10.1061/(ASCE)0733-9399(2005)131:4(340).
Kumarasena, S., N. P. Jones, P. Irwin, and P. Taylor. 2007. Wind-induced vibration of stay cables. Washington, DC: Federal Highway Administration.
Leira, B. 2013. “Structural limit states and reliability measures.” In Optimal stochastic control schemes within a structural reliability framework, 3–12. Cham, Switzerland: Springer.
Macdonald, J. H. G., and W. E. Daniell. 2005. “Variation of modal parameters of a cable-stayed bridge identified from ambient vibration measurements and FE modelling.” Eng. Struct. 27 (13): 1916–1930. https://doi.org/10.1016/j.engstruct.2005.06.007.
Macdonald, J. H. G., and G. L. Larose. 2006. “A unified approach to aerodynamic damping and drag/lift instabilities, and its application to dry inclined cable galloping.” J. Fluids Struct. 22 (2): 229–252. https://doi.org/10.1016/j.jfluidstructs.2005.10.002.
Macdonald, J. H. G., and G. L. Larose. 2008a. “Two-degree-of-freedom inclined cable galloping Part 1: General formulation and solution for perfectly tuned system.” J. Wind Eng. Ind. Aerodyn. 96 (3): 291–307. https://doi.org/10.1016/j.jweia.2007.07.002.
Macdonald, J. H. G., and G. L. Larose. 2008b. “Two-degree-of-freedom inclined cable galloping Part 2: Analysis and prevention for arbitrary frequency ratio.” J. Wind Eng. Ind. Aerodyn. 96 (3): 308–326. https://doi.org/10.1016/j.jweia.2007.07.001.
Mardia, K. 1972. Statistics of directional data. London: Academic Press.
Martin, W., E. Naudascher, and I. Currie. 1981. “Streamwise oscillations of cylinders.” J. Eng. Mech. Div. 107 (3): 589–607.
Matteoni, G., and C. T. Georgakis. 2012. “Effects of bridge cable surface roughness and cross-sectional distortion on aerodynamic force coefficients.” J. Wind Eng. Ind. Aerodyn. 104–106 (May–Jul): 176–187. https://doi.org/10.1016/j.jweia.2012.02.029.
Matteoni, G., and C. T. Georgakis. 2015. “Effects of surface roughness and cross-sectional distortion on the wind-induced response of bridge cables in dry conditions.” J. Wind Eng. Ind. Aerodyn. 136 (Jan): 89–100. https://doi.org/10.1016/j.jweia.2014.11.003.
Nguyen, C. H., A. Freda, G. Solari, and F. Tubino. 2015. “Aeroelastic instability and wind-excited response of complex lighting poles and antenna masts.” Eng. Struct. 85 (Feb): 264–276. https://doi.org/10.1016/j.engstruct.2014.12.015.
Nguyen, C. H., and J. H. G. Macdonald. 2017. “Galloping analysis of a stay cable with an attached viscous damper considering complex modes.” J. Eng. Mech. 144 (2): 04017175. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001403.
Nigol, O., and P. Buchan. 1981. “Conductor galloping—Part II torsional mechanism.” IEEE Trans. Power Apparatus Syst. 100 (2): 708–720. https://doi.org/10.1109/TPAS.1981.316922.
Nikitas, N., and J. H. G. Macdonald. 2013. “Misconceptions and generalizations of the Den Hartog galloping criterion.” J. Eng. Mech. 140 (4): 04013005. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000697.
Pagnini, L., A. Freda, and G. Piccardo. 2016. “Uncertainties in the evaluation of one degree-of-freedom galloping onset.” Eur. J. Environ. Civ. Eng. 21 (7–8): 1043–1063. https://doi.org/10.1080/19648189.2016.1150900.
Pagnini, L., and M. Repetto. 2012. “The role of parameter uncertainties in the damage prediction of the alongwind-induced fatigue.” J. Wind Eng. Ind. Aerodyn. 104–106 (May–Jul): 227–238. https://doi.org/10.1016/j.jweia.2012.03.027.
Pagnini, L., and G. Solari. 2001. “Damping measurements of steel poles and tubular towers.” Eng. Struct. 23 (9): 1085–1095. https://doi.org/10.1016/S0141-0296(01)00011-6.
Piccardo, G. 1993. “A methodology for the study of coupled aeroelastic phenomena.” J. Wind Eng. Ind. Aerodyn. 48 (2–3): 241–252. https://doi.org/10.1016/0167-6105(93)90139-F.
Piccardo, G., L. Pagnini, and F. Tubino. 2015. “Some research perspectives in galloping phenomena: Critical conditions and post-critical behavior.” Continuum Mech. Thermodyn. 27 (1–2): 261–285. https://doi.org/10.1007/s00161-014-0374-5.
PTI (Post-Tensioning Institute). 2001. Recommendations for stay cable design, testing and installation. Farmington Hills, MI: PTI.
Ricciardelli, F., and C. Demartino. 2016. “Design of footbridges against pedestrian-induced vibrations.” J. Bridge Eng. 21(8), C4015003. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000825.
Schewe, G. 1986. “Sensitivity of transition phenomena to small perturbations in flow round a circular cylinder.” J. Fluid Mech. 172: 33–46. https://doi.org/10.1017/S0022112086001635.
Sumer, B., and J. Fredsøe. 2006. “Hydrodynamics around cylindrical structures.” In Vol. 26 of Advanced series on ocean engineering. Singapore: World Scientific.
Takle, E. S., and J. M. Brown. 1978. “Note on the use of Weibull statistics to characterize wind-speed data.” J. Appl. Meteorol. 17 (4): 556–559. https://doi.org/10.1175/1520-0450(1978)017%3C0556:NOTUOW%3E2.0.CO;2.
Tennekes, H. 1973. “The logarithmic wind profile.” J. Atmos. Sci. 30 (2): 234–238. https://doi.org/10.1175/1520-0469(1973)030%3C0234:TLWP%3E2.0.CO;2.
Weber, R. 1991. “Estimator for the standard deviation of wind direction based on moments of the cartesian components.” J. Appl. Meteorol. 30 (9): 1341–1353. https://doi.org/10.1175/1520-0450(1991)030%3C1341:EFTSDO%3E2.0.CO;2.
Yu, P., Y. M. Desai, N. Popplewell, and A. H. Shah. 1993a. “Three-degree-of-freedom model for galloping. Part II: Solutions.” J. Eng. Mech. 119 (2): 2426–2448. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:12(2426).
Yu, P., Y. M. Desai, A. H. Shah, and N. Popplewell. 1993b. “Three-degree-of-freedom model for galloping. Part I: Formulation.” J. Eng. Mech. 119 (2): 2404–2425. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:12(2404).
Zdravkovich, M. 1997. Flow around circular cylinders, Volume 1: Fundamentals. Oxford, UK: Oxford University Press.
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Published In
Journal of Structural Engineering
Volume 145 • Issue 8 • August 2019
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©2019 American Society of Civil Engineers.
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Received: Apr 27, 2018
Accepted: Dec 20, 2018
Published online: Jun 8, 2019
Published in print: Aug 1, 2019
Discussion open until: Nov 8, 2019
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