Beam & Shell Models for Composite Straight or Curved Bridge Decks with Intermediate Diaphragms & Assessment of Design Specifications

Document Type: Research Paper


1 Department of Civil Engineering, Aalto University, Rakentajanaukio 4, Espoo, 02150, Finland

2 Department of Civil Engineering, National Technical University of Athens, Zografou Campus, Athens, 15780, Athens, Greece


In this research effort, the generalized warping and distortional problem of straight or horizontally curved composite beams of arbitrary cross section, loading and boundary conditions is presented. An inclined plane of curvature is considered. Additionally, the stiffness of diaphragmatic plates has been introduced in the formulation in order to compare with the case where rigid diaphragms are assumed. Isogeometric tools (NURBS) are employed in order to obtain the results for the 1D formulation and 3D shell models are developed in FEM commercial software for composite cross sections with diaphragms. The number of intermediate diaphragms according to bridges design specifications is compared to the analyzed diaphragmatic arrangements in order to assess the overall structural behavior of bridges decks. For this purpose, examples of curved beam models with open or closed cross sections and various arrangements of diaphragms have been studied.


Main Subjects

[1] Tsiptsis, I.N., Sapountzakis, E.J., Generalized Warping and Distortional Analysis of Curved Beams with Isogeometric Methods, Computers & Structures, 191, 2017, 33-50.

[2] Tsiptsis, I.N., Sapountzakis, E.J., Higher order beam theories and isogeometric methods in the analysis of curved bridges - assessment of diaphragms’ guidelines, International Journal of Bridge Engineering, 5(3), 2017, 133-182.

[3] Vlasov, V., Thin Walled Elastic Beams, 2nd Edn, National Science Foundation, Washington DC, 1961.

[4] Dabrowski, R., Warping torsion of curved box girders of non-deformable cross-section, Der Stahlbau, 34, 1965, 135-141.

[5] Dabrowski, R., Curved thin-walled girders theory and analysis, Cement and Concrete Association, 1968.

[6] Lili, Z., Yinghua, Z., Guangxin, W., Exact solution for in-plane displacement of redundant curved beam, Structural Engineering and Mechanics, 34(1), 2010, 139-142.

[7] Luo, Q.Z., Li, Q.S., Shear Lag of Thin-Walled Curved Box Girder Bridges, Journal of Engineering Mechanics, 126(10), 2000, 1111-1114.

[8] Heins, C.P., Spates, K.R., Behavior of single horizontally curved girder, Journal of the Structural Division ASCE, 96, 1970, 1511-1524.

[9] Koo, K.K., Cheung, Y.K., Mixed variational formulation for thin-walled beams with shear lag, Journal of Engineering Mechanics ASCE, 115, 1989, 2271-2286.

[10] Rosen, A., Abromovich, H., Galerkin method as a tool to investigate the planar and non-planar behaviour of curved beams, Computers & Structures, 18, 1984, 165-174.

[11] Yoo, C.H., Matrix formulation of curved girders, Journal of Engineering Mechanics ASCE, 105, 1979, 971-987.

[12] Gendy, A.S., Saleeb, A.F., On the finite element analysis of the Spatial response of curved beams with arbitrary thin-walled sections, Computers & Structures, 44(3), 1992, 639-652.

[13] Arici, M., Granata, M.F., Unified theory for analysis of curved thin-walled girders with open and closed cross section through HSA method, Engineering Structures, 113, 2016, 299-314.

[14] Sakai, F., Nagai, M., A proposal for intermediate diaphragm design in curved steel box girder bridges, Proceedings of the Japan Society of Civil Engineers, 305, 1981, 11-22.

[15] Nakai, H., Murayama, Y., Distortional stress analysis and design aid for horizontally curved box girder bridges with diaphragms, Proceedings of the Japan Society of Civil Engineers, 309, 1981, 25-39.

[16] Yabuki, T., Arizumi, Y., A provision on intermediate diaphragm spacing in curved steel-plated box-bridge-girders, Structural engineering/earthquake engineering JSCE, 6(2), 1989, 207-216.

[17] Park, N.H., Lim, N.H., Kang, Y.J., A consideration on intermediate diaphragm spacing in steel box girder bridges with a doubly symmetric section”, Engineering Structures, 25, 2003, 1665-1674.

[18] Park, N.H., Choi, Y.J., Kang, Y.J., Spacing of intermediate diaphragms in horizontally curved steel box girder bridges, Finite Elements in Analysis and Design, 41, 2005, 925-943.

[19] Kang, Y.J., Yoo, C.H., Thin-walled curved beams, I: formulation of nonlinear equations, Journal of Engineering Mechanics, 120(10), 1994, 2072-2101.

[20] Zhang, Y., Hou, Z., Li, Y., Wang, Y., Torsional behaviour of curved composite beams in construction stage and diaphragm effects, Journal of Constructional Steel Research, 108, 2015, 1-10.

[21] Yoo, C.H., Kang, J., Kim, K., Stresses due to distortion on horizontally curved tub-girders, Engineering Structures, 87, 2015, 70-85.

[22] Yangzhi, R., Wenming, C., Yuanqing, W., Bin, W., Analysis of the distortion of cantilever box girder with inner flexible diaphragms using initial parameter method, Thin-Walled Structures, 117, 2017, 140-154.

[23] Yangzhi, R., Wenming, C., Yuanqing, W., Qingrong, C., Bin, W., Distortional analysis of simply supported box girders with inner diaphragms considering shear deformation of diaphragms using initial parameter method, Engineering Structures, 145, 2017, 44-59.

[24] Vu, Q.V., Thai, D.K., Kim, S.E., Effect of intermediate diaphragms on the load-carrying capacity of steel-concrete composite box girder bridges, Thin-Walled Structures, 122, 2018, 230-241.

[25] Jung, J. H., Jang, G.W., Shin, D., Kim, Y.Y., One-dimensional analysis of thin-walled beams with diaphragms and its application to optimization for stiffness reinforcement, Computational Mechanics, 61(3), 2018, 331-349.

[26] Sapountzakis, E.J., Tsiptsis, I.N., Generalized warping analysis of curved beams by BEM, Engineering Structures, 100, 2015, 535-549.

[27] Katsikadelis, J.T., The Analog Equation Method. A Boundary - only Integral Equation Method for Nonlinear Static and Dynamic Problems in General Bodies, Theoretical and Applied Mechanics, 27, 2002, 13-38.

[28] American Association of State Highway and Transportation Officials (AASHTO), AASHTO LRFD bridge design specifications, 7th ed. Washington, DC, 2014.

[29] American Association of State Highway and Transportation Officials (AASHTO), AASHTO Guide specifications for horizontally curved steel girder highway bridges with design examples for I-girder and box-girder bridges, Washington, DC, 2003.

[30] Hanshin Expressway Public Corporation (HEPC), Guidelines for the design of horizontally curved girder bridges (draft), Osaka, Japan: Hanshin Expressway Public Corporation and Steel Struct Study Com, 1988.

[31] Cantieni R., Dynamic load test on highway bridges in Switzerland, 60 years experience of EMPA, Report no.211, Dubendorf, Switzerland, 1983.

[32] Ontario Highway Bridge Design Code (OHBDC), Ministry of Transportation and Communication, Ontario, Canada, 1983.

[33] Billing, J.R., Green, R., Design provisions for dynamic loading of highway bridge, Transportation Research Report 950, Ontario Ministry of Transportation and Communications, Dowsview, Ontario, Canada, 94-103, 1984.

[34] Heins, C.P., Hall, D.H., Designer’s guide to steel box-girder bridges, Bethlehem, Bethlehem Steel Corporation, 1981.

[35] Hamed, E., Frosting, Y., Free vibrations of multi-girder and multi-cell box bridges with transverse deformations effects, Journal of Sound and Vibration, 279, 2005, 699-722.

[36] Petrolo, M., Zappino, E., Carrera, E., Refined free vibration analysis of one-dimensional structures with compact and bridge-like cross-sections, Thin-Walled Structures, 56, 2012, 49-61.

[37] Bathe, K. J., ADINA System. ADINA R&D Inc, 2016.

[38] Dikaros, I.C., Sapountzakis, E.J., Distortional Analysis of Beams of Arbitrary Cross Section Using BEM, Journal of Engineering Mechanics, 143(10), 2017, 04017118.

[39] Bendsøe, M.P., Sigmund, O., Topology optimization, theory, methods, and applications, Springer, Berlin, 2004.

[40] Oleinik, J.C., Heins, C.P., Diaphragms for curved box beam bridges, Journal of the Structural Division ASCE, 101(10), 1975, 2161-2178.

[41] Eurocode 3, Design of steel structures - Part 1-5: Plated structural elements, Brussels, Belgium: European Committee for Standardization, 2006.

[42] Lacki, P., Derlatka, A., Strength evaluation of beam made of the aluminum 6061-T6 and titanium grade 5 alloys sheets joined by RFSSW and RSW, Composite Structures, 159, 2017, 491-497.

[43] Lacki, P, Derlatka, A, Kasza, P., Comparison of steel-concrete composite column and steel column, Composite Structures, 202, 2018, 82-88.

[44] Lacki, P., Nawrot, J., Derlatka, A., Winowiecka, J., Numerical and experimental tests of steel-concrete composite beam with the connector made of top-hat profile, Composite Structures, 211, 2019, 244-53.

[45] FEMAP for Windows. Finite element modeling and post-processing software. Help System Index Version, 11(1), 2010.

[46] Aminbaghai, M., Murin, J., Hrabovsky, J., Mang, H.A., Torsional warping eigenmodes including the effect of the secondary torsion moment on the deformations, Engineering Structures, 106, 2016, 299-316.

[47] Peng, H., Xiaojie, Y., Chen, L., Bo, W., Hongliang, L., Gang, L., Fei, N., An integrated framework of exact modeling, isogeometric analysis and optimization for variable-stiffness composite panels, Computer Methods in Applied Mechanics and Engineering, 339, 2018, 205-238.

[48] Peng, H., Yutian, W., Rui, M., Hongliang, L., Bo, W., Gang, L., A new reliability-based design optimization framework using isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, 345, 2019, 476-501.

[49] Peng, H., Chen, L., Xuanxiu, L., Xiaojie, Y., Bo, W., Gang, L., Manhong, D., Liang, C., Isogeometric analysis and design of variable-stiffness aircraft panels with multiple cutouts by level set method, Composite Structures, 206, 2018, 888-902.