Analytical method for a steel gate wide flange I-shaped deep beam with shear over the whole section
WU Siyuan1,2, WANG Zhengzhong3
1. State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China; 2. Research Institute of Structural Engineering and Disaster Reduction, Tongji University, Shanghai 200092, China; 3. Cold & Arid Regions Water Engineering Safety Research Center, Northwest A & F University, Yangling 712100, China
Abstract：The shear deformation transversal section effect can have a large effect on the mechanical properties of thin-walled beam, which can lead to enormous calculation errors when using primary beam theory in traditional designs. The faceplate of a hydraulic steel gate in a dam acts as a flange on the main beam with the main beam having the nonlinear stress characteristics of short deep beams at high heads. The energy-variational method for the shear deformation energy of the whole I-beam section is used in this study with proper selection of the longitudinal displacement function and the warping function to derive formulas for the deflection, bending normal stress and natural frequency of the beam. The results compare well with various analytical methods and finite element results. The results indicate that when the span-depth ratio or the span-width ratio is small, the bending normal stress is greatly affected by the transverse shear with concentrated loads giving greater effects, but the shear effect reduces the nature frequency calculated using other methods. The current method gives more accurate results than existing analytical methods with an extended range of applications for structural designs.
吴思远, 王正中. 考虑全截面剪切的钢闸门宽翼工字形深梁解析计算方法[J]. 清华大学学报（自然科学版）, 2019, 59(5): 380-387.
WU Siyuan, WANG Zhengzhong. Analytical method for a steel gate wide flange I-shaped deep beam with shear over the whole section. Journal of Tsinghua University(Science and Technology), 2019, 59(5): 380-387.
[1] 国家质量监督检验检疫总局, 中国国家标准化管理委员会. 水利水电工程钢闸门设计规范:SL74-2013[S]. 北京:中国标准出版社, 2013. State Administration of Quality Supervision, Inspection and Quarantine, China National Standardization Management Committee. Hydraulic and hydroelectric engineering specification for design of steel gate:SL74-2013[S]. Beijing:China Standard Press, 2013. (in Chinese) [2] 铁摩辛柯. 材料力学[M]. 汪一麟, 译. 北京:科学出版社, 1964. TIMOSHENKO S. Strength of materials[M]. WANG Y L, Trans. Beijing:Science Press, 1964. (in Chinese) [3] 甘亚南, 周广春, 王根会, 等. 宽翼薄壁工字形梁剪滞效应分析的能量变分法[J]. 工程力学, 2009, 26(2):42-47. GAN Y N, ZHOU G C, WANG G H, et al. Energy-variational method for the analysis of shear lag effect of thin-walled I-beams with wide flange[J]. Engineering Mechanics, 2009, 26(2):42-47. (in Chinese) [4] 张玉平, 胡火全, 李传习, 等. 薄壁箱梁剪力滞翘曲位移函数的改进与对比分析[J]. 应用力学学报, 2016, 33(6):1099-1105. ZHANG Y P, HU H Q, LI C X, et al. An improvement and comparative analysis of shear lag warping displacement function in thin-walled box girder[J]. Chinese Journal of Applied Mechanics, 2016, 33(6):1099-1105. (in Chinese) [5] 张慧, 张玉元, 张元海, 等. 单箱双室简支箱梁剪切变形及剪力滞双重效应分析[J]. 应用数学和力学, 2016, 37(8):791-803. ZHANG H, ZHANG Y Y, ZHANG Y H, et al. Analysis on shear deformation and shear-lag effects on twin-cell box girders[J]. Applied Mathematics and Mechanics, 2016, 37(8):791-803. (in Chinese) [6] 冀伟, 邓露, 刘世忠, 等. 多跨等截面波形钢腹板PC连续箱梁桥竖向弯曲振动频率的计算[J]. 振动与冲击, 2016, 35(18):140-146. JI W, DENG L, LIU S Z, et al. Calculation of the vertical bending vibration frequencies of multi-span PC continuous box girder with corrugated steel webs of uniform cross-section[J]. Journal of Vibration and Shock, 2016, 35(18):140-146. (in Chinese) [7] 李法雄, 聂建国. 钢-混凝土组合梁剪力滞效应弹性解析解[J]. 工程力学, 2011, 28(9):1-8. LI F X, NIE J G. Elastic analytical solutions of shear lag effect of steel-concrete composite beam[J]. Engineering Mechanics, 2011, 28(9):1-8. (in Chinese) [8] 甘亚南, 周广春, 吴亚平. 曲线薄壁箱梁侧向静力分析的能量变分法[J]. 固体力学学报, 2011, 32(4):411-418. GAN Y N, ZHOU G C, WU Y P. Energy-variational method of lateral static analysis of thin-walled curved box girders[J]. Acta Mechanica Solida Sinica, 2011, 32(4):411-418. (in Chinese) [9] 王正中, 刘计良, 牟声远, 等. 深孔平面钢闸门主梁应力计算方法研究[J]. 水力发电学报, 2010, 29(3):170-176. WANG Z Z, LIU J L, MOU S Y, et al. Research on stress calculation method for main beam of plain steel gate in deepwater delivery structure[J]. Journal of Hydroelectric Engineering, 2010, 29(3):170-176. (in Chinese) [10] 舒小娟, 钟新谷, 沈明燕, 等. 统筹考虑全截面剪切变形能的单剪滞位移参数的薄壁箱梁剪力滞计算方法[J]. 土木工程学报, 2016, 49(6):32-37. SHU X J, ZHONG X G, SHEN M Y, et al. Calculation method with single shear-lag displacement parameter for the shear lag of thin-wall box girders considering the shear deformation energy of whole section[J]. China Civil Engineering Journal, 2016, 49(6):32-37. (in Chinese) [11] 蔺鹏臻, 周世军. 基于剪切变形规律的箱梁剪力滞效应研究[J]. 铁道学报, 2011, 33(4):100-104. LIN P Z, ZHOU S J. Analysis on shear-lag effect of box girders based on flange-slab shear deformation law[J]. Journal of the China Railway Society, 2011, 33(4):100-104. (in Chinese) [12] 韦成龙, 曾庆元, 刘小燕. 薄壁箱梁剪力滞分析的多参数翘曲位移函数及其有限元法[J]. 铁道学报, 2000, 22(5):60-64. WEI C L, ZENG Q Y, LIU X Y. Warping displacement function and finite element method for calculation of shear lag effect in box girder[J]. Journal of the China Railway Society, 2000, 22(5):60-64. (in Chinese) [13] 张元海, 白昕, 林丽霞. 箱形梁剪力滞效应的改进分析方法研究[J]. 土木工程学报, 2012, 45(11):153-158. ZHANG Y H, BAI X, LIN L X. An improved approach for analyzing shear lag effect of box girders[J]. China Civil Engineering Journal, 2012, 45(11):153-158. (in Chinese) [14] 张元海, 胡玉茹, 林丽霞. 基于修正翘曲位移模式的薄壁箱梁剪力滞效应分析[J]. 土木工程学报, 2015, 48(6):44-50. ZHANG Y H, HU Y R, LIN L X. Analysis on shear lag effect of thin-walled box girders based on a modified warping displacement mode[J]. China Civil Engineering Journal, 2015, 48(6):44-50. (in Chinese) [15] 王修信. 面板剪滞有效宽度的二维弹性理论解答[J]. 宁波大学学报(理工版), 1991, 4(1):57-67. WANG X X. Exact solution of deck-plate effective width by plane elasticity theory[J]. Journal of Ningbo University (Natural Science & Engineering), 1991, 4(1):57-67. (in Chinese) [16] 何余良, 项贻强, 李少俊, 等. 基于不同抛物线翘曲函数组合箱梁剪力滞[J]. 浙江大学学报(工学版), 2014, 48(11):1933-1940, 1961. HE Y L, XIANG Y Q, LI S J, et al. Analysis on shear-lag effect of composite girders based on different parabolic warping displacement function[J]. Journal of Zhejiang University (Engineering Science), 2014, 48(11):1933-1940, 1961. (in Chinese) [17] 刘寒冰, 秦绪喜, 焦玉玲, 等. 悬臂T梁剪力滞现象的圣维南解析解[J]. 吉林大学学报(工学版), 2009, 39(3):691-696. LIU H B, QIN X X, JIAO Y L, et al. Analytic solutions of Saint-Venant problem in shear lag effect of T cantilever beam[J]. Journal of Jilin University (Engineering and Technology Edition), 2009, 39(3):691-696. (in Chinese) [18] 甘亚南, 周广春. 薄壁箱梁纵向剪滞翘曲函数精度选择的研究[J]. 工程力学, 2008, 25(6):100-106. GAN Y N, ZHOU G C. An approach for precision selection of longitudinal shear lag warping displacement function of thin-walled box girders[J]. Engineering Mechanics, 2008, 25(6):100-106. (in Chinese) [19] 肖军, 李小珍, 刘德军, 等. 不同位移函数对箱梁剪力滞效应的影响[J]. 中国公路学报, 2016, 29(9):90-96. XIAO J, LI X Z, LIU D J, et al. Influence of different displacement functions on shear lag effect of box girders[J]. China Journal of Highway and Transport, 2016, 29(9):90-96. (in Chinese) [20] 钱寅泉, 倪元增. 箱梁剪力滞计算的翘曲函数法[J]. 铁道学报, 1990, 12(2):57-70. QIAN Y Q, NI Y Z. Warping displacement function for calculation of shear lag effect in box girder[J]. Journal of the China Railway Society, 1990, 21(2):57-70. (in Chinese) [21] 张永健, 黄平明. 考虑剪力滞效应的简支箱梁自振特性[J]. 建筑科学与工程学报, 2005, 22(2):40-42. ZHANG Y J, HUANG P M. Free vibration characteristics of simply supported box girder with effect of shear lag[J]. Journal of Architecture and Civil Engineering, 2005, 22(2):40-42. (in Chinese) [22] 冀伟, 刘世忠. 波形钢腹板简支箱梁竖向频率的影响因素分析[J]. 振动、测试与诊断, 2013, 33(6):1039-1043. JI W, LIU S Z. Influencing factors of vertical frequency of the box beam with corrugated steel webs[J]. Journal of Vibration, Measurement & Diagnosis, 2013, 33(6):1039-1043. (in Chinese) [23] 中华人民共和国住房和城乡建设部. 钢结构设计标准:GB 50017-2017[S]. 北京:中国建筑工业出版社, 2018. Ministry of Housing and Urban-Rural Development of the People's Republic of China. Standard for design of steel structures:GB 50017-2017[S]. Beijing:China Architecture and Building Press, 2018. (in Chinese) [24] 吴思远, 王正中, 曹炜林, 等. 深孔钢闸门组合截面主梁应力计算方法[J]. 北京工业大学学报, 2018, 44(1):97-103. WU S Y, WANG Z Z, CAO W L, et al. Calculation of stress for composite walled main beam of deep-hole sluice gate[J]. Journal of Beijing University of Technology, 2018, 44(1):97-103. (in Chinese) [25] 舒小娟, 钟新谷, 沈明燕, 等. 基于剪切变形的矩形梁剪力滞求解方法[J]. 计算力学学报, 2015, 32(4):518-522. SHU X J, ZHONG X G, SHEN M Y, et al. Calculation method for shear lag of rectangular section beam based on the shear deformation[J]. Chinese Journal of Computational Mechanics, 2015, 32(4):518-522. (in Chinese) [26] 韩西, 李磊, 钟厉, 等. MTMD参数设计控制拱桥竖向振动方法研究[J]. 振动与冲击, 2008, 27(3):104-107, 135. HAN X, LI L, ZHONG L, et al. Study on parameters of MTMD for controlling vertical vibration of archbridge[J]. Journal of Vibration and Shock, 2008, 27(3):104-107, 135. (in Chinese) [27] 王正中, 朱军祚, 谌磊, 等. 集中力作用下深梁弯剪耦合变形应力计算方法[J]. 工程力学, 2008, 25(4):115-120. WANG Z Z, ZHU J Z, CHEN L, et al. The stress calculation method for deep beams with shear-bending coupling distortion under concentrated load[J]. Engineering Mechanics, 2008, 25(4):115-120. (in Chinese)
2019, Vol. 59 
