多因素影响下钢-混连续组合梁的挠度计算分析
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摘要
为精确计算钢-混凝土连续组合梁的挠度,在综合考虑钢梁与混凝土板之间的滑移效应及组合梁剪切变形影响的基础上,运用能量变分法推导出了钢-混凝土组合梁挠度计算的平衡微分方程,并给出了相对应的边界条件.通过引入均布荷载作用下钢-混凝土两跨连续组合梁的边界条件,求得了考虑滑移效应和剪切变形效应下组合梁的挠度计算公式,并对计算公式的正确性进行了验证.对钢-混凝土连续组合梁挠度做进一步分析表明:滑移效应会降低钢-混凝土连续组合梁的刚度,使组合梁产生附加挠度,并且会在中支点处引起梁负弯矩的增加,对混凝土板的受力产生不利影响.层间滑移位移随剪力连接件抗剪刚度的增大而减小,当剪力连接件抗剪刚度小于1200MPa时,层间滑移效应产生的附加挠度较大,对总挠度的影响也较大,应当考虑滑移效应对组合梁挠度的影响;当剪力连接件抗剪刚度大于1200MPa时,层间滑移效应产生的附加挠度较小,对总挠度的影响也较小,可以忽略滑移效应对组合梁挠度的影响.
To calculate the deflection of steel-concrete continuous composite girder accurately,the equilibrium differential equations and the corresponding boundary conditions for calculating the deflection of steel-concrete composite girder were derived by using the energy variational method. The influence of shear deformation of composite girder and the slip effect between steel girder and concrete slab were considered. By introducing the boundary conditions of two-span continuous steel-concrete composite girder under uniformly distributed load, the deflection calculation formula of the steel-concrete continuous composite girder was obtained.The correctness of the deflection calculation formula was also verified. A further analysis of the deflection of steel-concrete continuous composite beams shows that the slip effect reduces the stiffness of steel-concrete continuous composite girder,causes additional deflection,and increases the negative bending moment of the girder at the middle fulcrum,which adversely affects the stress of the concrete slabs.Slip displacement between layers decreases with the increase of shear stiffness of shear connectors.When the shear stiffness of shear connectors is less than 1200 MPa,the additional deflection caused by slip effect is larger,and the influence on the total deflection is greater.The influence of slip effect on the deflection of the composite girder should be considered.However,when the shear stiffness of shear connectors is greater than 1200 MPa,the additional deflection caused by slip effect is small and the influence on the total deflection is small.The influence of slip effect on the deflection of the composite girder can be ignored.
To calculate the deflection of steel-concrete continuous composite girder accurately,the equilibrium differential equations and the corresponding boundary conditions for calculating the deflection of steel-concrete composite girder were derived by using the energy variational method. The influence of shear deformation of composite girder and the slip effect between steel girder and concrete slab were considered. By introducing the boundary conditions of two-span continuous steel-concrete composite girder under uniformly distributed load, the deflection calculation formula of the steel-concrete continuous composite girder was obtained.The correctness of the deflection calculation formula was also verified. A further analysis of the deflection of steel-concrete continuous composite beams shows that the slip effect reduces the stiffness of steel-concrete continuous composite girder,causes additional deflection,and increases the negative bending moment of the girder at the middle fulcrum,which adversely affects the stress of the concrete slabs.Slip displacement between layers decreases with the increase of shear stiffness of shear connectors.When the shear stiffness of shear connectors is less than 1200 MPa,the additional deflection caused by slip effect is larger,and the influence on the total deflection is greater.The influence of slip effect on the deflection of the composite girder should be considered.However,when the shear stiffness of shear connectors is greater than 1200 MPa,the additional deflection caused by slip effect is small and the influence on the total deflection is small.The influence of slip effect on the deflection of the composite girder can be ignored.
引文
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[18]QUEIROZ F D,VELLASCO P C G S,NETHERCOT D A. Finite element modeling of composite beams with full and partial shear connection[J].Journal of Constructional Steel Research,2007,63(4):505—521.
[2]WANG S H,TONG G,ZHANG L.Reduced stiffness of composite beams considering slip and shear deformation of steel[J].Journal of Constructional Steel Research,2017,131:19—29.
[3]DEZI L,TARANTINO A M.Creep in composite continuous beams.Ⅱ:parametric study[J]. Journal of Structural Engineering,1993,119(7):2112—2133.
[4]NIE J G,CAI C S. Steel-concrete composite beams considering shear slip effects[J].Journal of Structural Engineering,2003,129(4):495—506.
[5]NGUYEN Q H,HJIAJ M. Nonlinear time-dependent behavior of composite steel-concrete beams[J]. Journal of Structural Engineering,2016,142(5):04015175.
[6]肖岩,彭罗文,KUNNATH S.组合梁考虑滑移效应的理论分析[J].湖南大学学报(自然科学版),2017,44(1):77—86.XIAO Y,PENG L W,KUNNATH S.Analysis of composite beams with interlayer slip[J]. Journal of Hunan University(Natural Sciences),2017,44(1):77—86.(In Chinese)
[7]NGUYEN Q H,HJIAJ M,UY B. Time-dependent analysis of composite beams with continuous shear connection based on a space-exact stiffness matrix[J].Engineering Structures,2010,32(9):2902—2911.
[8]JOAO B M,SOUSA J. Exact finite elements for multilayered composite beam-columns with partial interaction[J].Computers and Structures,2013,123(4):48—57.
[9]UDDIN M A,SHEIKH A H,BROWN D,et al. A higher order model for inelastic response of composite beams with interfacial slip using a dissipation based arc-length method[J].Engineering Structures,2017,139:120—134.
[10]周凌宇,余志武,蒋丽忠.钢-混凝土组合梁界面滑移剪切变形的双重效应分析[J].工程力学,2005,22(2):104-109.ZHOU L Y,YU Z W,JIANG L Z.Analysis of composite beams of steel and concrete with slip and shear deformation[J].Engineering Mechanics,2005,22(2):104—109.(In Chinese)
[11]聂建国,李法雄.钢-混凝土组合板的弹性弯曲及稳定性分析[J].工程力学,2009,26(10):59—66.NIE J G,LI F X.Elastic bending and stability of steel-concrete composite plate[J].Engineering Mechanics,2009,26(10):59—66.(In Chinese)
[12]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—58.ZHU L,NIE J G,JI W Y. Slip and shear-lag effects of steelconcrete composite box beam[J]. Engineering Mechanics,2016,33(9):49—58.(In Chinese)
[13]苗林,陈德伟.考虑层间滑移效应的组合梁解析计算[J].同济大学学报(自然科学版),2011,39(8):1113—1119.MIAO L,CHEN D W. Closed-form solution of composite beam considering interfacial slip effects[J].Journal of Tongji University(Natural Science),2011,39(8):1113—1119.(In Chinese)
[14]聂建国,沈聚敏,袁彦声.钢-混凝土简支组合梁变形计算的一般公式[J].工程力学,1994,11(1):21—27.NIE J G,SHEN J M,YUAN Y S.A general formula for predicting the deflection of simply supported composite steel-concrete beams with the consideration of slip effect[J].Engineering Mechanics,1994,11(1):21—27.(In Chinese)
[15]CHIOREAN C G,BURU S M.Practical nonlinear inelastic analysis method of composite steel-concrete beams with partial composite action[J].Engineering Structures,2017,134:74—106.
[16]BERTAGNOLI G,GINO D,MARTINELLI E.A simplified method for predicting early-age stresses in slabs of steel-concrete composite beams in partial interaction[j].Engineering Structures,2017,140:286—297.
[17]孙飞飞,李国强.考虑滑移、剪力滞后和剪切变形的钢-混凝土组合梁解析解[J].工程力学,2005,22(2):96-103.SUN F F,LI G Q. A closed-form solution for steel-concrete composite beams with slip,shear lag and shear deformation[J].Engineering Mechanics,2005,22(2):96—103.(In Chinese)
[18]QUEIROZ F D,VELLASCO P C G S,NETHERCOT D A. Finite element modeling of composite beams with full and partial shear connection[J].Journal of Constructional Steel Research,2007,63(4):505—521.