Abstract
Due to the limitations of the bridge deck modeling and wind tunnel installations, the parametric uncertainties of aerostatic displacement-dependent wind loads have become an urgent problem for reliability analysis in bridge engineering. Computational fluid dynamic (CFD) simulations were conducted to investigate the distribution model of aerostatic coefficients. The Monte Carlo simulation (MCS) was used to generate random samples of stream-lined box cross-sections. Among these samples, wind attack angles of −8°–8° were considered, and the sample size of each angle group was set as 30. Then, the statistical properties for the variation and distribution of aerostatic coefficients were discussed. In addition, sub-samples with sizes of 5–20 were randomly sampled from the initial sample group to evaluate the influence of the sample scale. The coefficient of variation (COV) of aerostatic coefficients with respect to geometric uncertainties increased up to 0.217, which occurred at −7° wind attack angle. Lognormal distribution models obtained by hypothesis tests maintained a low deviation for estimating the distribution of aerostatic coefficients. The sample size had a significant effect on quantifying the error between empirical and theoretical distribution models. Simulation method proposed in this paper provides a systematic approach for probabilistic problems involving fluid-structure interaction and parametric uncertainties.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- B :
-
Width of the bridge deck
- C D :
-
Drag coefficient
- C M :
-
Pitch moment coefficient
- D n :
-
Deviation of hypothesis testings
- \(D_n^{{\alpha _0}}\) :
-
Critical values of the K-S test
- C V :
-
Lift coefficient
- D ω :
-
Cross-diffusion term
- F D :
-
Drag force
- F V :
-
Lift force
- G K :
-
Turbulent generation of K
- \({{\tilde G}_k}\) :
-
Turbulence kinetic energy arises from the mean velocity gradients
- G ω :
-
Turbulent generation of ω
- H :
-
Height of bridge deck cross-section
- H 1 :
-
Height of upper part of the bridge deck
- H 2 :
-
Height of lower part of the bridge deck
- K :
-
Turbulent kinetic energy
- L :
-
Span length of projection in the windward direction
- M :
-
Pitch moment
- n′ :
-
The size of sub-samples
- P :
-
Mean pressure
- S ij :
-
Mean strain-rate tensor
- S K :
-
User-defined parameter related to K
- S ω :
-
User-defined parameter related to ω
- T :
-
Calculating time
- U :
-
Flow speed
- u i :
-
Mean velocity vector
- u i′:
-
Fluctuating velocity at point i
- u j′:
-
Fluctuating velocity at point j
- X i :
-
Position vector
- Y K :
-
Dissipation of K
- Y ω :
-
Dissipation of ω
- α :
-
Wind angle of attack
- α 0 :
-
The confidence level in hypothesis testing
- α 1 :
-
Angle of the upper part of the wind faring
- α 2 :
-
Angle of the lower part of the wind faring
- α 3 :
-
Angle of the bridge panel
- Γ K :
-
Effective diffusivity of K
- Γ ω :
-
Effective diffusivity of ω
- μ :
-
Location parameter
- μ 0 :
-
Fluid viscosity
- ρ :
-
Density of constant fluid
- σ :
-
Scale parameter
- ω :
-
Specific dissipation rate
References
Biondini F, Bontempi F, Frangopol DM, Malerba PG (2004) Reliability of material and geometrically non-linear reinforced and prestressed concrete structures. Computers and Structures 82(13–14):1021–1031, DOI: https://doi.org/10.1016/j.compstruc.2004.03.010
Booyapinyo V, Yamada H, Miyata T (1994) Wind-induced nonlinear lateral-torsional buckling of cable-stayed bridges. Journal of Structural Engineering 120(2):486–506, DOI: https://doi.org/10.1061/(ASCE)0733-9445(1994)120:2(486)
Bruno L, Fransos D (2011) Probabilistic evaluation of the aerodynamic properties of a bridge deck. Journal of Wind Engineering and Industrial Aerodynamics 99(6–7):718–728, DOI: https://doi.org/10.1016/j.jweia.2011.03.007
Brusiani F, Miranda S, Patruno L, Ubertini F, Vaona P (2013) On the evaluation of bridge deck flutter derivatives using RANS turbulence models. Journal of Wind Engineering and Industrial Aerodynamics 119:39–47, DOI: https://doi.org/10.1016/j.jweia.2013.05.002
Castaldo P, Gino D, Marano GC, Mancini G (2022) Aleatory uncertainties with global resistance safety factors for non-linear analyses of slender reinforced concrete columns. Engineering Structures 255:113920, DOI: https://doi.org/10.1016/j.engstruct.2022.113920
Cheng J (2013) Serviceability reliability analysis of prestressed concrete bridges. KSCE Journal of Civil Engineering 17(2):415–425, DOI: https://doi.org/10.1007/s12205-013-1374-x
Cheng J, Cai CS, Xiao R, Chen SR (2005) Flutter reliability analysis of suspension bridges. Journal of Wind Engineering and Industrial Aerodynamics 93(10):757–775, DOI: https://doi.org/10.1016/j.jweia.2005.08.003
Cheng J, Dong F (2017) Application of inverse reliability method to estimation of flutter safety factors of suspension bridges. Wind and Structures 24(3):249–265, DOI: https://doi.org/10.12989/was.2017.24.3.249
Cheng J, Jiang JJ, Xiao RC (2003) Aerostatic stability analysis of suspension bridges under parametric uncertainty. Engineering Structures 25(13): 1675–1684, DOI: https://doi.org/10.1016/S0141-0296(03)00146-9
Cheng J, Jiang JJ, Xiao RC, Xiang HF (2002) Advanced aerostatic stability analysis of cable-stayed bridges using finite-element method. Computers and Structures 80(13):1145–1158, DOI: https://doi.org/10.1016/S0045-7949(02)00079-2
Cheng J, Li QS (2009) Reliability analysis of long span steel arch bridges against wind-induced stability failure. Journal of Wind Engineering and Industrial Aerodynamics 97(3–4):132–139, DOI: https://doi.org/10.1016/j.jweia.2009.02.001
Der Kiureghian A, Zhang Y, Li CC (1994) Inverse reliability problem. Journal of Engineering Mechanics 120(5):1154–1159, DOI: https://doi.org/10.1061/(ASCE)0733-9399(1994)120:5(1154)
Dong F, Cheng J (2017) A new method for estimation of aerostatic stability safety factors of cable-stayed bridges. Proceedings of the Institution of Civil Engineers-Structures and Buildings 172(1):17–29, DOI: https://doi.org/10.1680/jstbu.17.00083
Dong F, Cheng J, Sun B (2018) Estimation of the parameters of the Normal flutter derivatives distribution. Journal of Wind Engineering and Industrial Aerodynamics 174:358–368, DOI: https://doi.org/10.1016/j.jweia.2018.01.012
Dong F, Shi, F, Wang L, Wei Y, Zheng K (2021) Probabilistic assessment approach of the aerostatic instability of long-span symmetry cable-stayed bridges. Symmetry 13(12):2413, DOI: https://doi.org/10.3390/sym13122413
Gaxiola-Camacho JR, Azizsoltani H, Villegas-Mercado FJ, Haldar A (2017) A novel reliability technique for implementation of Performance-Based Seismic Design of structures. Engineering Structures 142:137–147, DOI: https://doi.org/10.1016/j.engstruct.2017.03.076
Gino D, Castaldo P, Giordano L, Mancini G (2021) Model uncertainty in non-linear numerical analyses of slender reinforced concrete members. Structural Concrete 22(2):845–870, DOI: https://doi.org/10.1002/suco.202000600
Han Y, Chen H, Cai CS, Xu G, Shen L, Hu P (2016) Numerical analysis on the difference of drag force coefficients of bridge deck sections between the global force and pressure distribution methods. Journal of Wind Engineering and Industrial Aerodynamics 159:65–79, DOI: https://doi.org/10.1016/j.jweia.2016.10.004
Haque MN, Katsuchi H, Yamada H, Nishio M, (2016) Investigation of edge fairing shaping effects on aerodynamic response of long-span bridge deck by unsteady RANS. Archives of Civil and Mechanical Engineering 16(4):888–900, DOI: https://doi.org/10.1016/j.acme.2016.06.007
Herzog MAM (1994) Aerodynamic stability of cable-stayed bridges simplified. ICE Proceedings Structures and Buildings 104(2):205–210, DOI: https://doi.org/10.1680/istbu.1994.26329
Kareem A (1988) Effect of parametric uncertainties on wind excited structural response. Journal of Wind Engineering and Industrial Aerodynamics 30:233–241, DOI: https://doi.org/10.1016/0167-6105(88)90088-8
Kumar A, Chakrabarti A, Bhargava P, Chowdhury R (2015) Probabilistic failure analysis of laminated sandwich shells based on higher order zigzag theory. Journal of Sandwich Structures & Materials 17(5):546–561, DOI: https://doi.org/10.1177/1099636215577368
Kusano I, Baldomir A, Jurado JA, Hernandez S (2014) Reliability based design optimization of long-span bridges considering flutter. Journal of Wind Engineering and Industrial Aerodynamics 135:149–162, DOI: https://doi.org/10.1016/j.jweia.2014.10.006
Kusano I, Montoya MC, Baldomir A, Nieto F, Jurado JA, Hernandez S (2020) Reliability based design optimization for bridge girder shape and plate thicknesses of long -span suspension bridges considering aeroelastic constraint. Journal of Wind Engineering and Industrial Aerodynamics 202:104176, DOI: https://doi.org/10.1016/j.jweia.2020.104176
Lee I, Choi KK, Du L, Gorsich D (2008) Inverse analysis method using MPP-based dimension reduction for reliability-based design optimization of nonlinear and multi-dimension systems. Computer Methods in Applied Mechanics and Engineering 198:12–27, DOI: https://doi.org/10.1016/j.cma.2008.03.004
Li Y, Chen Z, Dong S, Li J (2021) Study on the effects of pedestrians on the aerostatic response of a long-span pedestrian suspension bridge. KSCE Journal of Civil Engineering 25(10):3866–3878, DOI: https://doi.org/10.1007/s12205-021-2127-x
Li H, Foschi RO (1998) An inverse reliability method and its application. Structural Safety 20(3):257–270, DOI: https://doi.org/10.1016/S0167-4730(98)00010-1
Liu ZW, Chen AR, He SH (2004) Probabilistic finite element analysis of cable-stayed bridges under wind. Journal of Chang’an University (Natural Science Edition) 24(2):53–57, DOI: https://doi.org/10.19721/j.cnki.1671-8879.2004.02.013 (in Chinese)
Ma C, Duan Q, Li Q, Liao H, Tao Q (2019) Aerodynamic characteristics of a long-span cable-stayed bridge under construction. Engineering Structures 184:232–246, DOI: https://doi.org/10.1016/j.engstruct.2018.12.097
Mannini C, Bartoli G (2015) Aerodynamic uncertainty propagation in bridge flutter analysis. Structural Safety 52:29–39, DOI: https://doi.org/10.1016/j.strusafe.2014.07.005
Melchers RE, Beck AT (2017) Structural reliability analysis and prediction. John Wiley & Sons, Hoboken, NJ, USA, 65–73
Mishra BB, Kumar A, Samui P, Roshni T (2020a) Buckling of laminated composite skew plate using FEM and machine learning methods. Engineering Computations 38(1):501–528, DOI: https://doi.org/10.1108/EC-08-2019-0346
Mishra BB, Kumar A, Topal U (2020b) Stochastic normal mode frequency analysis of hybrid angle ply laminated composite skew plate with opening using a novel approach. Mechanics Based Design of Structures and Machines, DOI: https://doi.org/10.1080/15397734.2020.1840393
Mishra BB, Kumar A, Zaburko J, Sadowska-Buraczewska B, Barnat-Hunek D (2021) Dynamic response of angle ply laminates with uncertainties using MARS, ANN-PSO, GPR and ANFIS. Materials 14(2):395, DOI: https://doi.org/10.3390/ma14020395
Pagnini L (2010) Reliability analysis of wind-excited structures. Journal of Wind Engineering and Industrial Aerodynamics 98(1):1–9, DOI: https://doi.org/10.1016/j.jweia.2009.08.010
Pourzeynali S, Datta TK (2002) Reliability analysis of suspension bridges against flutter. Journal of Sound and Vibration 254(1):143–162, DOI: https://doi.org/10.1006/jsvi.2002.4090
Rashki M, Miri M, Moghaddam MA (2012) A new efficient simulation method to approximate the probability of failure and most probable point. Structural Safety 39:22–29, DOI: https://doi.org/10.1016/j.strusafe.2012.06.003
Rojiani K, Wen Y (1981) Reliability of steel buildings under winds. Journal of the Structural Division 107(1):203–221, DOI: https://doi.org/10.1061/JSDEAG.0005622
Sarkar A, Deep S, Datta D, Vijaywargiya A, Roy R, Phanikanth VS (2019) Weibull and generalized extreme value distributions for wind speed data analysis of some locations in India. KSCE Journal of Civil Engineering 23(8):3476–3492, DOI: https://doi.org/10.1007/s12205-019-1538-4
Schuller GI, Hirtz H, Booz G (1983) The effect of uncertainties in wind load estimation on reliability assessments. Journal of Wind Engineering and Industrial Aerodynamics 14(1):15–26, DOI: https://doi.org/10.1016/0167-6105(83)90006-5
Su C, Luo J, Xiao C (2013) Efficient approach for reliability assessments on aeroinstability of long-span bridges. Journal of Bridge Engineering 18(6):570–575, DOI: https://doi.org/10.1061/(ASCE)BE.1943-5592.0000447
Su C, Luo X, Yun T (2010) Aerostatic reliability analysis of long-span bridges. Journal of Bridge Engineering 15(3):260–268, DOI: https://doi.org/10.1061/(ASCE)BE.1943-5592.0000069
Tang H, Shum KM, Li Y (2019) Investigation of flutter performance of a twin-box bridge girder at large angles of attack. Journal of Wind Engineering and Industrial Aerodynamics 186:192–203, DOI: https://doi.org/10.1016/j.jweia.2019.01.010
Xie S, Pan B, Du X (2019) An inverse reliability analysis method for reliability-based design optimization with random and dependent interval variables constrained within ellipsoids. Engineering Optimization 51(12):2109–2126, DOI: https://doi.org/10.1080/0305215X.2019.1573896
Xu F, Zhang Z (2017) Free vibration numerical simulation technique for extracting flutter derivatives of bridge decks. Journal of Wind Engineering and Industrial Aerodynamics 170:226–237, DOI: https://doi.org/10.1016/j.jweia.2017.08.018
Zhang Z, Zhang X, Yang Y, Ge Y (2017) Nonlinear aerodynamic and energy input properties of a twin-box girder bridge deck section. Journal of Fluids and Structures 74:413–426, DOI: https://doi.org/10.1016/j.jfluidstructs.2017.06.016
Zhou R, Yang Y, Ge Y, Zhang L (2018) Comprehensive evaluation of aerodynamic performance of twin-box girder bridges with vertical stabilizers. Journal of Wind Engineering and Industrial Aerodynamics 175:317–327, DOI: https://doi.org/10.1016/j.jweia.2018.01.039
Zhou Z, Mao W, Ding Q (2019) Experimental and numerical studies on flutter stability of a closed box girder accounting for ground effects. Journal of Fluids and Structures 84:1–17, DOI: https://doi.org/10.1016/j.jfluidstructs.2018.09.009
Zhu SP, Keshtegar B, Chakraborty S, Trung NT (2020) Novel probabilistic model for searching most probable point in structural reliability analysis. Computer Methods in Applied Mechanics and Engineering 366:113027, DOI: https://doi.org/10.1016/j.cma.2020.113027
Acknowledgments
This work was supported by the Natural Science Foundation of Jiangsu Province (Grant No. BK20200793).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shi, F., Wang, L., Dong, F. et al. Probabilistic Analysis on Aerostatic Displacement-dependent Wind Loads on a Stream-lined Box Girder. KSCE J Civ Eng 27, 299–312 (2023). https://doi.org/10.1007/s12205-022-0742-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-022-0742-9