A novel box girder beam element considering equivalent shear deformation freedom of corrugated steel webs
-
摘要: 为研究横隔板对波形钢腹板组合箱梁弯曲内力和变形的影响，提出了一种考虑波形钢腹板等效剪切变形自由度的新型箱梁单元(TBT-CSW)；根据波形钢腹板组合箱梁的受力特点和变形协调关系，建立了等效弯曲转角与等效剪切变形的几何关系表达式；针对多室波形钢腹板组合箱形截面边腹板和中腹板弯曲剪力流分布的差异，基于剪切应变能等效原理，提出了波形钢腹板等效剪切变形系数的取值公式；通过最小势能原理，推导了考虑等效弯曲转角和等效剪切变形影响的控制微分方程，并利用其齐次解构造了广义位移(含竖向挠度、波形钢腹板等效剪切变形和等效弯曲转角)的插值函数；基于能量变分原理，开发了一种能考虑端(中)横隔板对波形钢腹板等效剪切变形影响的两节点六自由度箱梁单元，并推导了单元刚度矩阵和等效结点荷载向量；通过算例分析，验证了TBT-CSW梁单元的计算精度和广泛适用性。研究结果表明：与传统TBTS梁单元相比，TBT-CSW梁单元在关键部位的应力计算精度最高提升了30.8%；端横隔板对主梁整体内力和变形的影响较小，但对其周边翼缘板的应力分布具有显著影响；中横隔板的布置则会显著改变主梁截面的局部内力分配，增加结构内部的超静定次数，导致翼缘板顶面和底面的应力发生明显变化，而翼缘板中面应力变化相对较小；随着中横隔板数量的增加，主梁的竖向挠度逐渐减小，但整体内力分布未发生变化。Abstract: To investigate the influence of diaphragms on the bending forces and deformations of composite box girders with corrugated steel webs (CBG-CSWs), a novel box girder beam element named TBT-CSW, which incorporates the equivalent shear deformation degree of freedom of the CSWs, was proposed. Based on the mechanical characteristics and deformation compatibility of CBG-CSWs, a geometric relationship expression between the equivalent bending rotation and the equivalent shear deformation was established. Addressing the difference in bending shear flow distribution between the side webs and central webs in multi-cell CBG-CSW sections, a formula for determining the equivalent shear deformation coefficient of CSWs was proposed based on the principle of equivalent shear strain energy. The governing differential equations, considering the effects of equivalent bending rotation and equivalent shear deformation, were derived using the principle of minimum potential energy. Their homogeneous solutions were employed to construct interpolation functions for the generalized displacements (vertical deflection, equivalent shear deformation of CSWs, and equivalent bending rotation). Based on the energy variational principle, a two-node, six-degree-of-freedom box girder element (TBT-CSW) was developed, capable of accounting for the influence of end and intermediate diaphragms on the equivalent shear deformation of corrugated steel webs. The element stiffness matrix and equivalent nodal load vector were also derived. Numerical examples validated the computational accuracy and broad applicability of the TBT-CSW beam element. Research results show that, compared to the traditional TBTS beam element, the TBT-CSW beam element achieves up to a 30.8% higher accuracy in stress calculation at critical locations. End diaphragms have a minor influence on the global internal forces and deformation of the girder, but significantly affect the stress distribution in the adjacent flanges. The arrangement of intermediate diaphragms, however, markedly alters the local internal force distribution within the girder cross-section, increases the degree of static indeterminacy, and leads to significant changes in the stress at the top and bottom surfaces of the flanges, while the mid-surface stress remains relatively stable. As the number of intermediate diaphragms increases, the vertical deflection of the girder gradually decreases, but the overall internal force distribution remains essentially unchanged.
-
图 3 波形钢腹板组合箱梁“等效弯曲转角”
Figure 3. "Equivalent bending rotation" for composite box girder with CSWs
图 4 多室波形钢腹板组合箱形截面弯曲剪力流分布
Figure 4. Bending shear flow distribution of multi-cell box section with CSWs
图 6 简支波形钢腹板试验梁模型(单位：mm)
Figure 6. Simply supported test beam model with CSWs (unit: mm)
图 9 横隔板数量对竖向挠度和内力分布的影响
Figure 9. Influence of diaphragm quantity on vertical deflection and bending force distribution
图 10 横隔板数量对混凝土翼缘板应力分布的影响
Figure 10. Influence of diaphragm quantity on stress distribution of concrete flanges
图 11 变高度单箱三室波形钢腹板组合连续梁(单位: m)
Figure 11. Single-box three-cell composite continuous girder with CSWs and variable height (unit: m)
图 12 波形钢腹板组合连续箱梁有限元模型(Solid-FEM)
Figure 12. Finite element model of continuous box girder with CSWs (Solid-FEM)
图 13 波形钢腹组合连续箱梁竖向挠度和内力分布
Figure 13. Vertical deflection and bending force distribution of continuous box girder with CSWs
表 1 简支波形钢腹板试验梁跨中截面竖向挠度
Table 1. Vertical deflection at mid-span section of simply supported test beam with CSWs
mm 
下载: 导出CSV
表 2 简支波形钢腹板试验梁跨中截面应力(P=5 kN)
Table 2. Stresses at mid-span section of simply supported test beam with CSWs (P=5 kN)
MPa 应力点 上翼缘板 下翼缘板 顶面 中面 底面 顶面 中面 底面 TBTS -0.38 -0.38 -0.38 1.08 1.08 1.08 TBT-CSW -1.03 -0.36 0.31 0.52 1.02 1.52 Solid-FEM -0.90 -0.34 0.21 0.83 0.99 1.16
下载: 导出CSV
表 3 波形钢腹组合箱梁截面(Ⅰ-Ⅰ和Ⅱ-Ⅱ)应力
Table 3. Stresses at sections (Ⅰ-Ⅰ and Ⅱ-Ⅱ) of composite box girder with CSWs
MPa 应力点位置 Ⅰ-Ⅰ截面(x=6 m) Ⅱ-Ⅱ截面(x=22 m) 上翼缘板 下翼缘板 上翼缘板 下翼缘板 顶面 中面 底面 顶面 中面 底面 顶面 中面 底面 顶面 中面 底面 TBTS -1.56 -1.56 -1.56 2.32 2.32 2.32 2.01 2.01 2.01 -3.00 -3.00 -3.00 TBT-CSW -2.25 -1.52 -0.80 1.55 2.27 3.00 2.29 2.00 1.70 -2.69 -2.98 -3.28 Solid-FEM -2.24 -1.58 -0.91 1.64 2.30 2.96 2.42 2.08 1.74 -2.67 -3.03 -3.38
下载: 导出CSV
-
[1] 刘玉擎. 组合结构桥梁[M]. 北京: 人民交通出版社, 2005.LIU Yu-qing. Steel-concrete hybrid bridge[M]. Beijing: China Communications Press, 2005. [2] 聂建国, 陶慕轩, 吴丽丽, 等. 钢-混凝土组合结构桥梁研究新进展[J]. 土木工程学报, 2012, 45(6): 110-122.NIE Jian-guo, TAO Mu-xuan, WU Li-li, et al. Advances of research on steel-concrete composite bridges[J]. China Civil Engineering Journal, 2012, 45(6): 110-122. [3] HE J, LIU Y Q, CHEN A R, et al. Mechanical behavior and analysis of composite bridges with corrugated steel webs: State-of-the-art[J]. International Journal of Steel Structures, 2012, 12(3): 321-338. doi: 10.1007/s13296-012-3003-9 [4] JIANG R J, KWONG AU F T, XIAO Y F. Prestressed concrete girder bridges with corrugated steel webs: Review[J]. Journal of Structural Engineering, 2015, 141(2): 04014108. doi: 10.1061/(ASCE)ST.1943-541X.0001040 [5] 陈康明, 黄汉辉, 吴庆雄, 等. 波形钢腹板-钢管混凝土桁式弦杆组合梁桥疲劳性能[J]. 交通运输工程学报, 2022, 22(5): 200-216. doi: 10.19818/j.cnki.1671-1637.2022.05.012 CHEN Kang-ming, HUANG Han-hui, WU Qing-xiong, et al. Fatigue performance of composite girder bridge with corru-gated steel webs-concrete filled steel tubular truss chords[J]. Journal of Traffic and Transportation Engineering, 2022, 22(5): 200-216. doi: 10.19818/j.cnki.1671-1637.2022.05.012 [6] 董桔灿, 陈宜言, BRISEGHELLA B, 等. 波形钢腹板-双管弦杆-混凝土板组合连续箱梁受弯性能[J]. 交通运输工程学报, 2016, 16(3): 35-45. doi: 10.19818/j.cnki.1671-1637.2016.03.005DONG Ju-can, CHEN Yi-yan, BRISEGHELLA B, et al. Flexural behaviors of composite continuous box girder with corrugated steel webs, double concrete filled steel tubular chords and concrete slabs[J]. Journal of Traffic and Transportation Engineering, 2016, 16(3): 35-45. doi: 10.19818/j.cnki.1671-1637.2016.03.005 [7] 邓文琴, 刘朵, 冯杰, 等. 波形钢腹板箱梁桥异步施工节段足尺模型试验研究[J]. 桥梁建设, 2019, 49(1): 53-58.DENG Wen-qin, LIU Duo, FENG Jie, et al. Segmental full-scale model test for asynchronous construction of box girder bridge with corrugated steel webs[J]. Bridge Construction, 2019, 49(1): 53-58. [8] 李宏江, 叶见曙, 万水, 等. 剪切变形对波形钢腹板箱梁挠度的影响[J]. 交通运输工程学报, 2002, 2(4): 17-20. http://transport.chd.edu.cn/article/id/200204004LI Hong-jiang, YE Jian-shu, WAN Shui, et al. Influence of shear deformation on deflection of box girder with corrugated steel webs[J]. Journal of Traffic and Transportation Engineering, 2002, 2(4): 17-20. http://transport.chd.edu.cn/article/id/200204004 [9] 聂建国, 李法雄. 考虑腹板剪切行为的波形钢腹板梁理论模型[J]. 中国公路学报, 2011, 24(6): 40-48.NIE Jian-guo, LI Fa-xiong. Theory model of corrugated steel web girder considering web shear behavior[J]. China Journal of Highway and Transport, 2011, 24(6): 40-48. [10] ZHOU M, LIU Z, ZHANG J D, et al. Deformation analysis of a non-prismatic beam with corrugated steel webs in the elastic stage[J]. Thin-Walled Structures, 2016, 109: 260-270. doi: 10.1016/j.tws.2016.10.001 [11] 吴文清, 叶见曙, 万水, 等. 波形钢腹板-混凝土组合箱梁截面变形的拟平截面假定及其应用研究[J]. 工程力学, 2005, 22(5): 177-180, 198.WU Wen-qing, YE Jian-shu, WAN Shui, et al. Quasi plane assumption and its application in steel-concrete composite box girders with corrugated steel webs[J]. Engineering Mechanics, 2005, 22 (5): 177-180, 198. [12] CHENG J, YAO H. Simplified method for predicting the deflections of composite box girders[J]. Engineering Structures, 2016, 128: 256-264. doi: 10.1016/j.engstruct.2016.09.049 [13] 姚浩, 程进. 基于变分原理的波形钢腹板箱梁挠度计算解析法[J]. 工程力学, 2016, 33(8): 177-184.YAO Hao, CHENG Jin. Analytical method for calculating defection of corrugated box girders based on variational principle[J]. Engineering Mechanics, 2016, 33(8): 177-184. [14] 冀伟, 刘世忠, 蔺鹏臻. 均布荷载作用下波形钢腹板简支箱梁的挠度[J]. 公路交通科技, 2012, 29(12): 69-73, 89.JI Wei, LIU Shi-zhong, LIN Peng-zhen. Deflection of simple-supported box girder with corrugated steel webs under uniform load[J]. Journal of Highway and Transportation Research and Development, 2012, 29(12): 69-73, 89. [15] SHIRATANI H, IKEDA H, IMAI, Y, et al. Flexural and shear behavior of composite bridge girder with corrugated steel webs around middle support[C]//JSCE. Proceedings of the Japan Society of Civil Engineers. Tokyo: JSCE, 2003: 49-67. [16] MACHIMDAMRONG C, WATANABE E, UTSUNOMIYA T. An extended elastic shear deformable beam theory and its application to corrugated steel web girder[J]. Journal of Structural Engineering, 2003, 49A: 29-38. [17] MACHIMDAMRONG C, WATANABE E, UTSUNOMIYA T. Analysis of corrugated steel web girders by an efficient beam bending theory[J]. Structural Engineering/Earthquake Engineering, 2004, 21(2): 131s-142s. doi: 10.2208/jsceseee.21.131s [18] CHEN X C, AU F T K, BAI Z Z, et al. Flexural ductility of reinforced and prestressed concrete sections with corrugated steel webs[J]. Computers and Concrete, 2015, 16(4): 625-642. doi: 10.12989/cac.2015.16.4.625 [19] 贺君, 刘玉擎, 陈艾荣, 等. 折腹式组合梁桥考虑剪切变形的挠度计算[J]. 同济大学学报(自然科学版), 2009, 37(4): 440-444.HE Jun, LIU Yu-qing, CHEN Ai-rong, et al. Deflection calculation of composite girder bridge with corrugated steel web with consideration of shear deformation[J]. Journal of Tongji University (Natural Science), 2009, 37(4): 440-444. [20] 冯建祥, 吕思忠, 杜进生. 考虑腹板剪切变形及滑移的波形钢腹板梁理论模型[J]. 建筑结构学报, 2020, 41(增1): 355-363.FENG Jian-xiang, LV Si-zhong, DU Jin-sheng. A theory model of corrugated steel web girder considering shear deformation of web and shear slip[J]. Journal of Building Structures, 2020, 41(S1): 355-363. [21] ZHANG Y, LIU Y Q, WANG S H, et al. Concrete additional stress near intermediate support for composite girder bridges with corrugated steel webs[J]. Journal of Bridge Engineering, 2022, 27(3): 04021112. doi: 10.1061/(ASCE)BE.1943-5592.0001817 [22] 乔朋, 狄谨, 秦凤江. 单箱多室波形钢腹板组合箱梁的腹板剪应力分析[J]. 工程力学, 2017, 34(7): 97-107.QIAO Peng, DI Jin, QIN Feng-jiang. Shear stress in the webs of single-box multi-cell composite box girders with corrugated steel webs[J]. Engineering Mechanics, 2017, 34(7): 97-107. [23] 乔朋, 钟承星, 狄谨, 等. 单箱多室波形钢腹板箱梁的横向受力分析[J]. 工程力学, 2020, 37(9): 161-172.QIAO Peng, ZHONG Cheng-xing, DI Jin, et al. Analysis of single-box multi-cell composite box girder with corrugated steel webs due to transverse force[J]. Engineering Mecha-nics, 2020, 37(9): 161-172. [24] ZHOU M, LIU Z, ZHANG J D, et al. Equivalent computational models and deflection calculation methods of box girders with corrugated steel webs[J]. Engineering Structures, 2016, 127: 615-634. doi: 10.1016/j.engstruct.2016.08.047 [25] JOHNSON R P, CAFOLLA J, BERNARD C. Corrugated webs in plate girders for bridges[J]. Proceedings of the Insti-tution of Civil Engineers-Structures and Buildings, 1997, 122(2): 157-164. doi: 10.1680/istbu.1997.29305 [26] 李夏元. 基于有限元法的单箱多室波形钢腹板组合箱梁空间力学性能研究[D]. 南京: 东南大学, 2021.LI Xia-yuan. Study on the spatial mechanical properties of single-box multi-cell composite box girders with corrugated steel webs based on finite element analysis[D]. Nanjing: Southeast University, 2021. [27] 郭金琼, 房贞政, 郑振. 箱形梁设计理论[M]. 北京: 人民交通出版社, 2008.GUO Jin-qiong, FANG Zhen-zheng, ZHENG Zhen. Design theory of box girder[M]. Beijing: China Communications Press, 2008. [28] 徐芝纶. 弹性力学简明教程[M]. 北京: 高等教育出版社, 2013.XU Zhi-lun. A concise course in elasticity[M]. Beijing: Higher Education Press, 2013. [29] 夏桂云, 曾庆元, 李传习, 等. 建立Timoshenko深梁单元的新方法[J]. 交通运输工程学报, 2004, 4(2): 27-32. http://transport.chd.edu.cn/article/id/200402007XIA Gui-yun, ZENG Qing-yuan, LI Chuan-xi, et al. New method for formulations of Timoshenko deep beam element[J]. Journal of Traffic and Transportation Engineering, 2004, 4(2): 27-32. http://transport.chd.edu.cn/article/id/200402007 [30] LI X Y, WAN S, ZHANG Y H, et al. Beam finite element for thin-walled box girders considering shear lag and shear deformation effects[J]. Engineering Structures, 2021, 233: 111867. doi: 10.1016/j.engstruct.2021.111867 -
计量
- 文章访问数: 42
- HTML全文浏览量: 14
- PDF下载量: 3
- 被引次数: 0
