Dynamic analysis method of steel-concrete composite beams based on equivalent single layer theory
SUN Qikai1,3, ZHANG Nan1,3, ZHANG Bing4, LIU Xiao1,3, CHENG Zenong1, TAO Xiaoyan2,3
1.School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China;
2.Railway Engineering Research Institute, China Academy of Railway Sciences Co., Ltd., Beijing 100081, China;
3.State Key Lab for Track Technology of High-Speed Railway, Beijing 100081, China;
4.Urban Rail Transit Design and Research Institute, China Railway Engineering Consulting Group Co., Ltd.， Beijing 100055, China
Abstract：Here, based on Reddy’s higher-order beam theory and bond slip theory, an equivalent single-layer theoretical finite element model for dynamic analysis of steel-concrete composite beam was proposed considering effects of shear slip between concrete slab and steel beam and shear deformation of each sub-beam.Axial displacement of steel-concrete composite beam was assumed to be a third-order function along beam height so as to more accurately simulate parabolic curve change of shear stress.The advantage of this calculation model was considering in advance the shear continuity between sub-beams and the condition of no shear stress on beam’s upper and lower surfaces in the constructed high-order displacement field of steel-concrete composite beam to make the equivalent single-layer displacement field function exclude the first-order derivative of beam transverse displacement, thus only C0 continuous interpolation function was needed in finite element calculation.Finally, by comparing with the numerical results in published papers, the rationality, applicable range and calculation accuracy of the proposed model were illustrated.The results showed that the equivalent single-layer theory can be used to analyze natural vibration characteristics of steel-concrete composite beam with higher calculation accuracy; the larger the ratio of height to span, the more obvious the advantage of the model.
孙琪凯，张楠，张冰，刘潇，程泽农，陶晓燕. 基于等效单层理论的钢-混组合梁动力分析方法[J]. 振动与冲击, 2021, 40(17): 92-98.
SUN Qikai, ZHANG Nan, ZHANG Bing, LIU Xiao, CHENG Zenong, TAO Xiaoyan. Dynamic analysis method of steel-concrete composite beams based on equivalent single layer theory. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(17): 92-98.
［1］聂建国，余志武．钢-混凝土组合梁在我国的研究及应用［J］．土木工程学报，1999，32(2)：3-8．
NIE Jianguo, YU Zhiwu.Research and practice of composite steel-concrete beams in China［J］．China Civil Engineering Journal, 1999, 32(2): 3-8.
［2］朱力，聂建国，季文玉.钢-混凝土组合箱型梁的滑移和剪力滞效应［J］.工程力学，2016, 33(9): 49-68.
ZHU Li, NIE Jianguo, JI Wenyu.Slip and shear-lag effects of steel-concrete composite box beam ［J］.Engineering Mechanics, 2016, 33(9): 49-68.
［3］NEWMARK N M, SIESS C P, VIEST I M.Test and analysis of composite beams with incomplete interaction［J］.Proceedings of the Society for Experimental Stress Analysis, 1951, 9(1): 75-92.
［4］GIRHAMMAR U A, PAN D H.Dynamic analysis of composite members with interlayer slip［J］.International Journal of Solids and Structures, 1993, 30(6): 797-823.
［5］GIRHAMMAR U A, PAN D H, GUSTAFSSON A.Exact dynamic analysis of composite beams with partial interaction［J］.International Journal of Mechanical Sciences, 2009, 51(8): 565-582.
［6］HUANG C W, SU Y H.Dynamic characteristics of partial composite beams［J］.International Journal of Structural Stability and Dynamics, 2008, 8(4): 665-685.
［7］侯忠明，夏禾，王元清，等.钢-混凝土组合梁动力折减系数研究［J］.振动与冲击，2015，34(4)：74-81.
HOU Zhongming, XIA He, WANG Yuanqing, et al.Dynamic redution coefficients for a steel-concrete composite beam［J］.Journal of Vibration and Shock, 2015, 34(4): 74-81.
［8］杨骁，李晓伟，汪德江.界面掀起和轴力对组合梁动力弯曲特性的影响［J］.振动与冲击，2016，35(8)：124-137.
YANG Xiao, LI Xiaowei, WANG Dejiang.Influences of the interfacial uplift and axial load on dynamic bending characteristics of composite beams［J］.Journal of Vibration and Shock, 2016, 35(8): 124-137.
［9］XU R, WU Y.Static dynamic and buckling analysis of partial interaction composite members using Timoshenko’s beam theory［J］.International Journal of Mechanical Sciences, 2007, 49(10): 1139-1155.
［10］XU R, WANG G.Variational principle of partial-interaction composite beams using Timoshenko’s beam theory［J］.International Journal of Mechanical Sciences, 2012, 60(1): 72-83.
［11］NGUYEN Q H, HJIAJ M, GROGNEC P L.Analytical approach for free vibration analysis of two-layer Timoshenko beams with interlayer slip［J］.Journal of Sound and Vibration, 2012, 331(12): 2949-2961.
［12］SCHNABL S, SAJE M, TURK G, Planinc I.Locking-free two-layer Timoshenko beam element with interlayer slip［J］.Finite Elements in Analysis and Design, 2007, 43(9): 705-714.
［13］李晓伟，何光辉.Timoshenko组合梁动力特性与瞬态响应的求积元分析［J］.振动与冲击，2018，37(18)：257-265.
LI Xiaowei, HE Guanghui.Quadrature element analysis on dynamic characteristics and transient responses of Timoshenko composite beams［J］.Journal of Vibration and Shock, 2018, 37(18): 257-265.
［14］REDDY J N.A simple higher-order theory for laminated composite plates［J］.Journal of Applied Mechanics, 1984, 51(1984): 745-752.
［15］KANT T, OWEN D R J, ZIENKIEWICZ O C.A refined higher-order C0 plate bending element［J］.Computers and Structures, 1982, 15(2): 177-183.
［16］KANT T, GUPTA A.A finite element model for a higher-order shear-deformable beam theory［J］.Journal of Sound and Vibration, 1988, 125(2): 193-202.
［17］HE G H, YANG X.Dynamic analysis of two-layer composite beams with partial interaction using a higher order beam theory［J］.International Journal of Mechanical Sciences, 2015, 90: 102-112.
［18］HE G H, WANG D J, YANG X.Analytical solutions for free vibration and buckling of composite beams using a higher order beam theory［J］.Acta Mechanica Solida Sinica, 2016, 29(3): 300-315.
［19］FU C, YANG X.Dynamic analysis of partial-interaction Kant composite beams by weak-form quadrature element method［J］.Archive of Applied Mechanics, 2018, 88(1): 2179-2198.
［20］CHAKRABARTI A, SHEIKH A H, GRIFFITH M, et al.Analysis of composite beams with partial shear interactions using a higher order beam theory［J］.Engineering Structures, 2012, 36: 283-291.
［21］CHAKRABARTI A, SHEIKH A H, GRIFFITH M, et al.Dynamic response of composite beams with partial shear interaction using a higher-order beam theory［J］.Journal of Structural Engineering, 2013, 139(1): 47-56.
［22］周旺保，蒋丽忠，余志武，等.考虑剪力滞和滑移效应的钢-混凝土连续组合箱梁自振特性［J］.中国公路学报，2013，26(5)：88-94.
ZHOU Wangbao, JIANG Lizhong, YU Zhiwu, et al.Free vibration characteristics of steel-concrete composite continuous box girder considering shear lag and slip［J］.China Journal of Highway and Transport, 2013, 26(5): 88-94.
［23］陈玉骥，罗旗帜.钢-混凝土组合梁考虑剪力滞和滑移的一阶自振频率［J］.烟台大学学报(自然科学与工程版)，2015，28(1)：49-69.
CHEN Yuji, LUO Qizhi.First order natural vibration frequency for steel-concrete composite beams considering influence of shear lags and slips［J］.Journal of Yantai University (Natural Science and Engineering Edition), 2015, 28(1): 49-69.
［24］苏庆田，薛智波，李晨翔，等.组合梁钢与混凝土界面连接效应的精细化计算［J］.同济大学学报（自然科学版），2016，44(12)：1803-1809.
SU Qingtian, XUE Zhibo, LI Chenxiang, et al.Refined calculation of steel-concrete interface connection in composite girders［J］.Journal of Tongji University (Natural Science), 2016，44(12)：1803-1809.
［25］ATAEI A, ZEYNALIAN M, YAZDI Y.Cyclic behaviour of bolted shear connectors in steel-concrete composite beams［J］.Journal of Constructional Steel Research,2019,161:328-340.
［26］ZHAO Y, ZHOU X H, YANG Y L, et al.Shear behavior of a novel cold-formed U-shaped steel and concrete composite beam［J］.Engineering Structures, 2019, 200: 109745.［27］WANG Y H, YU J, LIU J P, et al.Experimental study on assembled monolithic steel-prestressed concrete composite beam in negative moment ［J］.Engineering Structures,2019,180:494-509.
［28］BATHE K J.Finite element procedures［M］.Englewood Cliffs, NJ: Prentice Hall, 1996.
