Acknowledgement
This work is supported by National Natural Science Foundation of China (NSFC) (Grand number: 51978013), China Scholarship Council (Grand number: 201906545013), China Postdoctoral Science Foundation (Grand number: 2017M620789) and Beijing University of Technology (Grand number: 004000514118567, 004000514119060).
References
- ANSYS Inc. (2005), ANSYS Structural Analysis Guide, http://www.ansys.com.
- Boswell, L.F. and Li, Q. (1995), "Consideration of the relationships between torsion, distortion and warping of thinwalled beams", Thin Wall. Struct., 21, 147-161. https://doi.org/10.1016/ 0263-8231(94)00030-4.
- Chaudhari, S.C. and Deshmukh, S.K. (2020a), "Distortional analysis of laminated composite box girder: A review", Mater. Today Proc., 27(2), 1479-1486. https://doi.org/10.1016/j.matpr.2020.02.974.
- Chaudhari, S.C. and Deshmukh, S.K. (2020b), "Distortional response of doubly symmetric laminated composite box girder", Mater. Today Proc., 27(2), 1381-1388. https://doi.org/10.1016/j.matpr.2020.02.765.
- Choi, Y.J., Park, N.H. and Hong, S.S. (2003), "A consideration on intermediate diaphragm spacing of horizontally curved steel box girders", J. Korean Soc. Civ. Eng., 23, 345-353.
- Harashima, M. and Usugi, K. (1980), "Distortional analysis of random box girders considering the shear deformation", Foreign Bridge, 1, 1-29.
- Hsu, Y.T. and Schelling, D.R. (1995), "EBEF method for distortional analysis of steel box-girder bridges", J. Struct. Eng., 121, 557-566. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:8(982).
- Hsu, Y.T. and Fu, C.C. (2002), "Application of EBEF method for the distortional analysis of steel box girder bridge superstructures during construction", Adv. Struct. Eng., 5, 211-221. https://doi.org/10.1260/136943302320974581.
- Kolekova, Y., Kovac, M. and Balaz I. (2017), "influence lines of bridges with box-girder cross-section under torsion and distortion", Procedia Eng., 190, 603-610. https://doi.org/10.1016/j.proeng.2017.05.386.
- Lee, J.H., Lee, S.K. and Lim, J.H. (2015), "Spacing of intermediate diaphragms horizontally curved steel box girder bridges considering bending-distortional warping normal stress ratio", J. Korea Acad.-Ind. Coorp. Soc., 16, 6325-6332. https://doi.org/10.5762/KAIS.2015.16.9.6325.
- Lee, J.H., Lee, K.S., Choi, J.H and Kang, Y.J. (2020), "Intermediate diaphragm spacing for single-cell rectangular steel box girder bridges considering aspect-ratio", J. Constr. Steel Res., 168, 105877. https://doi.org/10.1016/j.jcsr.2019.105877.
- Li, Q. (1993), "Investigation of the warping functions of thin walled bars with closed cross section", J. Southw. Jiaotong Univ., 6, 1-6.
- Li, H.F. and Luo, Y.F. (2010), "Application of stiffness matrix of a beam element considering section distortion effect", J. Southeast Univ., 26, 431-435.
- Liu, Y., Yang, C.X. and Tan, Z.C. (2017), "Hybrid element-based virtual distortion method for finite element model updating of bridges with wide-box girders", Eng. Struct., 143, 558-570. https://doi.org/10.1016/j.engstruct.2017.04.030.
- Park, N.H., Choi, Y. and Yi, G. (2002), "Distortional analysis of steel box girders", Steel Struct., 2(1), 51-58. https://doi.org/10.12989/scs.2002.2.1.051
- Park, N.H., Lim, N. and Kang, Y. (2003), "A consideration on intermediate diaphragm spacing in steel box girder bridges with a doubly symmetric section", Eng. Struct., 25, 1665-1674. https://doi.org/10.1 016 /S0141-0296(03)00145-7. https://doi.org/10.1016/S0141-0296(03)00145-7
- Park, N.H., Yoon, K.Y. and Cho, S.K. (2004), "Effective distortional stiffness ratio and spacing of intermediate diaphragms in steel box girder bridges", Steel Struct., 4, 93-102.
- Park, N.H., Choi, Y. and Kang, Y. (2005a), "Spacing of intermediate diaphragms in horizontally curved steel box girder bridges", Finite Elem. Anal. Des., 41, 925-943. https://doi.org/10.1016/j.finel.2004.12.006.
- Park, N.H., Choi, S. and Kang, Y. (2005b), "Exact distortional behavior and practical distortional analysis of multicell box girders using an expanded method", Compos. Struct., 83, 1607-1626. https://doi.org/10.1016/j.compstruc.2005.01.003.
- Park, N.H., Kang, Y.J. and Kim, H.J. (2005c), "An independent distortional analysis method of thin-walled multicell box girders", Struct. Eng. Mech., 21(3), 275-293. https://doi.org/10.12989/sem.2005.21.3.275.
- Ren, Y.Z., Cheng, W.M., Wang, Y.Q., Chen, Q.R. and Wang, B. (2017a), "Distortional analysis of simply supported box girders with inner diaphragms considering shear deformation of diaphragms using initial parameter method", Eng. Struct., 145, 44-59. https://doi.org/10.1016/j.engstruct.2017.05.004.
- Ren, Y.Z., Cheng, W.M., Wang, Y.Q. and Wang, B. (2017b), "Analysis of the distortion of cantilever box girder with inner flexible diaphragms using initial parameter method", Thin Wall. Struct., 117, 140-154. https://doi.org/10.1016/j.tws.2017.04.010.
- Ren, Y.Z., Wang, B., Li, Y.Q. and Liu, X.C. (2019), "New research for the distortion of steel box girders with inner solid diaphragms", Adv. Struct. Eng., 22, 3026-3041. https://doi.org/10.1177/1369433219856754.
- Suetake, Y. and Hirashima, M. (1997), "Extended trigonometric series analysis of box girders with diaphragms", J. Eng. Mech., 123, 293-301. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:4(293).
- Wright, R.N., Abdel-Samad, S.R. and Robinson, A.R. (1968), "BEF analogy for analysis of box girders", J. Struct. Div., 94, 1719-1743. https://doi.org/10.1061/JSDEAG.0002013.
- Xu, X. and Qiang, S.Z. (2013a), "Research on distortion analysis theory of thin-walled box girder", Eng. Mech., 30, 192-201. https://doi.org/10.6052/j.issn.1000-4750.2012.07.0554.
- Xu, X., Ye, H.W. and Qiang, S.Z. (2013b), "Distortional analysis of thin-walled box girder taking account of shear deformation", Chin. J. Comput. Mech., 30, 860-866. https://doi.org/10.7511/jslx201306018.
- Ye, Y.S., Zhang, J. and Zhao, X.M. (2007), "Kalman filtering identification for displacement parameters of continuous curved box girder bridge based on novozhilov flexibility theory", China J. Highw. Transp., 20, 65-69. https://doi.org/10.1063/1.3137898.
- Zhang, J., Ye, J.S. and Zhao, X.M., (2007), "Dynamic Bayesian stochastic estimation to displacement parameters of continuous curved box with segregating slab", Chin. J. Appl. Mech., 24, 69-74.
- Zhang, Z.W., Wang, J.N. and Cheng, W.M. (2013), Crane Design Manual, Chin. Railway Pub. House.
- Zhao, Z.M. (1997), "The calculating analysis for multiple span continuous curved box girder by the finite strip method", J. Fuzhou Univ. (N. Sci.), 25, 90-94.
- Zhao, Z.M., Fang, Z.Z. and Guo, J.Q. (1993a), "Analysis of continuous box girders with diaphragms by finite strip method", Bridge Constr., 4, 35-53.
- Zhao, Z.M. (1993b), "Analysis of continuous curved box-girder bridge with flexible transverse diaphragms by finite strip method", Comput. Struct. Mech. Appl., 10, 473-484.
- Zhu, L., Su, R.K.L. and Li, M.J. (2021), "Finite beam element with 26 DOFs for curved composite box girders considering constrained torsion, distortion, shear lag and biaxial slip", Eng. Struct., 232, 111797. https://doi.org/10.1016/j.engstruct.2020.111797.