斜交钢—混凝土组合箱梁空间有限元分析

【作者】 伍亮；

【导师】 余志武；

【作者基本信息】 中南大学 ， 结构工程， 2007， 硕士

【摘要】 本文基于连续介质力学、薄壁结构力学理论以及有限元理论，对斜交组合箱梁进行了深入的理论分析和研究，建立了分析斜交组合箱梁的空间位移模型，提出了分析斜交组合箱梁的斜交板梁段单元法，编制了用于斜交组合箱梁分析的有限元计算程序，进行了主要设计参数分析，得到了斜交组合箱梁的刚度和变形性能随斜交角、剪力连接度等参数的变化规律。主要的研究成果如下：(1)提出了斜交组合箱型梁空间位移场的计算方法：假设箱梁项底板与腹板的连接点为刚性结点，各板块中任意点的位移为3个方向的线位移。建立正、斜交坐标系的转换关系，采用斜交坐标系描述单元的位移。各板段连接线上任意点的位移用Hermite函数插值，假定各板段的面内位移沿其宽度方向线性变化，以描述各板段面内位移；沿与斜支承边平行的箱梁横截面切取单位长度的横截面框架进行分析，用框架角点位移的插值函数描述面外位移。(2)按板面内变形和板面外挠曲计算斜交箱梁单元弹性应变能，考虑了拉压、弯曲、扭转等各项应变能，无须分项计算。并利用最小势能原理和“对号入座法则”建立斜交组合箱梁“板梁段有限元法”的有限元列式。(3)根据本文的理论分析和方法，编制了斜交组合箱梁有限元分析程序SCBG，可用于分析正交组合箱梁、单一材料斜交箱梁和斜交组合箱梁结构的线性静力分析。(4)利用本文提出的考虑滑移影响的斜交组合箱梁空间分析理论和计算程序，对斜交组合箱梁结构进行了主要设计参数分析，得到了斜交角、剪力连接度等参数对箱梁的挠度、扭转、滑移的影响规律，对斜交组合箱梁的设计具有一定的参考价值。更多还原

【Abstract】 Based on the mechanics of continuous medium, mechanics of thin-walled structure and the finite element analysis, the overall service behavior of skew steel-concrete composite box girders are analyzed. A spacial displacements model for skew composite box girder is built, a skew slab-beam segment element method for skew composite box girder is present, a finite element calculating program for skew composite box girder is compiled, some analysis about primary design parameters are done, and the laws of stiffness and deformation with different parameters such as skew angle, degrees of shear connection and etc are obtained.The main contents are listed as follows:(1) A calculation method of the special displacement model of skew composite box girder is presented. Regard joints of apical plate, soleplate and web plate as rigid, displacements of any point in all plates are 3-dimensions linear displacements. A formulation of transformation between the orthogonal coordinate and the skew coordinate is presented, then taking the skew coordinate to describe displacements of element. In order to obtain displacements of any point in the plane of slab segment, it is assumed that the special displacements of any point in the joint line between slab segments can be described by Hermite interpolation functions and those two displacements in the plane of slab segment are linear in the transverse direction. In order to use Hermite interpolation functions to describe the displacement of any point off the slab plane, a transverse unit-length frame is cut longitudinally form the skew box girder segment.(4) A method is presented for calculating the elastic strain energies of skew box girder element in accordance with deformation in the inner slab plane and the bending off the slab plane, which including the strain energies from flexure, tensile and compressive, torsion etc.On the basis of principle of total potential energy with stationary value and ’set-in-right-position’ rule, a finite element method for slab beam segment of skew composite box girder is presented.(5) According to the theory and method presented by this thesis, a finite element analysis program for skew composite box girder, which can be applied to linear statics analysis of orthogonal box girder, unitary material box girder and skew composite box girder, is compiled.(6) By design parameters analysis on some skew composite box girders with different skew angel and degrees of skear connection, which simulated with the skew slab-beam segment element method and analysis program, the laws of deflection, torsion and slippage with different parameters are obtained. It is some reference for design of skew composite box girders.更多还原