Abstract
In bridge erection, a steel girder undergoing in-plane loading is commonly subjected to the interaction of several forces. Many previous studies have highlighted the effects of single in-plane loads on plate buckling but only a few works concentrated on the combined effects. For this reason, the stability of steel plates subjected to the combined action of patch loading, bending moment, and shear stress was studied through parametric analysis in this work. In particular, the effect of patch loading length combined with bending and shear stress was investigated. Other parameters like patch loading magnitude, panel aspect ratio, and plate slenderness have also been considered to characterize the plate stability. Through an intensive finite element method (FEM) analysis, new design equations have been defined to describe the influence of plate and load parameters on critical buckling loads of plates subjected to combined loads, with regard to plates subjected to patch loading. A comparison with the FEM results offers good accuracy, with a maximum deviation equal to 5%. To validate the analytical equations, a practical example is given.
目 的
通过深入的数值分析研究面内综合加载条件下钢板的临界屈曲荷载变化规律。
创新点
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1.
提出一个确定钢梁在平面荷载作用下的临界屈曲系数的新公式;
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2.
通过与有限元分析结果对比以修正参数并获得解析公式的高精度。
方 法
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1.
采用有限元分析软件Strand 7 研究矩形钢板在节点荷载、 弯矩和剪应力综合作用下的弹性稳定性;
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2.
针对节点荷载长度、 载荷大小、 板长宽比和长径比等参数分析对综合加载条件下的钢板稳定性的影响;
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3.
借助一个实际的例子验证解析公式的有效性。
结 论
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1.
通过与有限元结果的比较, 解析公式均表现出较高的精度, 误差均在有限范围内且不受板几何形状的影响;
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2.
节点荷载、 弯矩和剪应力的综合作用通过减小板临界抗屈曲性导致钢板的屈曲失效;
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3.
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综合加载会导致临界抗屈曲性减小一半。
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References
Alinia MM, 2005. A study into optimization of stiffeners in plates subjected to shear loading. Thin-Walled Structures, 43(5):845–860. https://doi.org/10.1016/j.tws.2004.10.008
Alinia MM, Moosavi SH, 2009. Stability of longitudinally stiffened web plates under interactive shear and bending forces. Thin-Walled Structures, 47(1):53–60. https://doi.org/10.1016/j.tws.2008.05.005
Basler K, 1961. New Provisions for Plate Girder Design. American Institute of Steel Construction, p.65–74. Braun B, 2010. Stability of Steel Plates under Combined Loading. PhD Thesis, Universität Stuttgart, Stuttgart, Germany.
Braun B, 2010. Stability of Steel Plates under Combined Loading. PhD Thesis, Universität Stuttgart, Stuttgart, Germany.
CEN (European Committee for Standardization), 2006. Eurocode 3-Design of Steel Structures-part 1-5: Plated Structural Elements, EN 1993-1-5:2006. CEN.
Duchene Y, Maquoi R, 1994. Contribution, par voie numérique, à l’étude de la résistance des âmes aux charges transversales. Construction Métallique, 2:43–56 (in French).
Graciano C, Edlund B, 2003. Failure mechanism of slender girder webs with a longitudinal stiffener under patch loading. Journal of Constructional Steel Research, 59(1): 27–45. https://doi.org/10.1016/S0143-974X(02)00022-6
Graciano C, Lagerqvist O, 2003. Critical buckling of longitudinally stiffened webs subjected to compressive edge loads. Journal of Constructional Steel Research, 59(9): 1119–1146. https://doi.org/10.1016/S0143-974X(03)00055-5
Graciano C, Ayestarán A, 2013. Steel plate girder webs under combined patch loading, bending and shear. Journal of Constructional Steel Research, 80:202–212. https://doi.org/10.1016/j.jcsr.2012.09.018
Graciano C, Mendes J, 2014. Elastic buckling of longitudinally stiffened patch loaded plate girders using factorial design. Journal of Constructional Steel Research, 100:229–236. https://doi.org/10.1016/j.jcsr.2014.04.030
Graciano C, Zapata-Medina DG, 2015. Effect of longitudinal stiffening on bridge girder webs at incremental launching stage. Ingeniería e Investigación, 35(1):24–30. https://doi.org/10.15446/ing.investig.v35n1.42220
Jager B, Kövesdi B, Dunai L, 2017. I-girders with unstiffened slender webs subjected by bending and shear interaction. Journal of Constructional Steel Research, 131:176–188. https://doi.org/10.1016/j.jcsr.2017.01.009
Khan MZ, Walker AC, 1972. Buckling of plates subjected to localized edge loadings. The Structural Engineer, 50(6): 225–232.
Kövesdi B, Dunai L, 2016. Bending, shear and patch loading interaction behaviour of slender steel sections. Procedia Engineering, 156:199–206. https://doi.org/10.1016/j.proeng.2016.08.287
Kövesdi B, Alcaine J, Dunai L, et al., 2014. Interaction behaviour of steel I-girders part I: longitudinally unstiffened girders. Journal of Constructional Steel Research, 103 327–343. https://doi.org/10.1016/j.jcsr.2014.06.018
Loaiza N, Graciano C, Chacón R, et al., 2017. Influence of bearing length on the patch loading resistance of multiple longitudinally stiffened webs. Proceedings of Eurosteel, 1(2-3):4199–4204.
Maiorana E, Pellegrino C, Modena C, 2008. Linear buckling analysis of unstiffened plates subjected to both patch load and bending moment. Engineering Structures, 30(12): 3731–3738. https://doi.org/10.1016/j.engstruct.2008.07.002
Maiorana E, Pellegrino C, Modena C, 2011. Influence of longitudinal stiffeners on elastic stability of girder webs. Journal of Constructional Steel Research, 67(1):51–64. https://doi.org/10.1016/j.jcsr.2010.07.005
Matlab, 2017. Matlab User’s Manual, Version R2017a. MathWorks, Inc., USA.
Porter DM, Rockey KC, 1975. The collapse behaviors of plate girders loaded in shear. Structural Engineering, 53(8): 313–325.
Quang-Viet V, Papazafeiropoulos G, Graciano C, et al., 2019. Optimum linear buckling analysis of longitudinally multistiffened steel plates subjected to combined bending and shear. Thin-Walled Structures, 136:235–245. https://doi.org/10.1016/j.tws.2018.12.008
Ren T, Tong GS, 2005. Elastic buckling of web plates in I-girders under patch and wheel loading. Engineering Structures, 27(10):1528–1536. https://doi.org/10.1016/j.engstruct.2005.05.006
Rockey KC, Bagchi DK, 1970. Buckling of plate girder webs under partial edge loadings. International Journal of Mechanical Sciences, 12(1):61–76. https://doi.org/10.1016/0020-7403(70)90007-X
Shahabian F, Roberts TM, 1999. Buckling of slender web plates subjected to combinations of in-plane loading. Journal of Constructional Steel Research, 51(2):99–121. https://doi.org/10.1016/S0143-974X(99)00020-6
Strand 7, 2005. Strand 7 User’s Manual. G+D Computing, Sydney, Australia.
Tetougueni CD, Maiorana E, Zampieri P, et al., 2019. Plate girders behaviour under in-plane loading: a review. Engineering Failure Analysis, 95:332–358. https://doi.org/10.1016/j.engfailanal.2018.09.021
Timoshenko S, Woinowsky-Krieger S, 1959. Theory of Plates and Shells. McGraw-Hill Book Company, New York, USA.
Tong GS, Feng YX, Tao WD, et al., 2016. Elastic stability of plate simply supported on four sides subjected to combined bending shear and patch loading. Thin-Walled Structures, 107:377–396. https://doi.org/10.1016/j.tws.2016.06.021
Zetlin L, 1955. Elastic instability of flat plates subjected to partial edge loads. Proceedings of the American Society of Civil Engineers, 81(9):1–24.
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Prof. Carlo PELLEGRINO has been the Editorial Board Member of Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering) since 2018. Carlo PELLEGRINO is a Full Professor of Structural Analysis and Design and Head of the Department of Civil, Environmental and Architectural Engineering, University of Padova, Italy. He is elected member of the Academic Senate, University of Padova, Italy. He obtained the PhD in Mechanics of Structures, University of Bologna, Italy. Prof. PELLEGRINO is coordinator of several national and international research projects, participant in COST Actions and referee for the selection of international research projects. He is member of various national and international technical and scientific associations.
He is author of over 300 scientific publications, over 100 of them in referred ISI/Scopus journals with more than 2500 citations (h-index 30) about the following topics: assessment, rehabilitation, strengthening and retrofit of buildings and bridges; seismic vulnerability and risk of existing buildings and bridges; integrated risk assessment and management of bridges in transportation networks; advanced strengthening techniques by means of innovative techniques; use of recycled components for structural materials.
He is a keynote speaker and member of the editorial board/international scientific committee of several international conferences and organizer of various special sessions/mini-symposia in international conferences. He is member of the organizing committee of various national and international conferences and Editorial Board Member of International Journals.
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Maiorana, E., Tetougueni, C.D., Zampieri, P. et al. Interaction between patch loading, bending moment, and shear stress in steel girders. J. Zhejiang Univ. Sci. A 20, 389–410 (2019). https://doi.org/10.1631/jzus.A1900024
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DOI: https://doi.org/10.1631/jzus.A1900024