钢桁腹式混凝土组合箱梁的扭转效应分析

结合钢桁腹式混凝土组合箱梁的结构特点,基于薄壁箱梁扭转理论,推导出组合箱梁闭口断面的混凝土顶底板和换算钢腹板的扭转翘曲应力表达式,进而推导出组合箱梁约束扭转控制微分方程;利用初参数法求解微分方程,并分析出翘曲双力矩以及扭转翘曲正应力随梁跨的变化规律.通过有限元模拟分析,将有限元值和理论值进行比较,结果吻合良好.研究表明,翘曲双力矩在集中扭矩作用处达到最大值,并且衰减速度很快,使得该处箱梁截面的翘曲应力达到最大值,箱梁的翘曲双力矩在远离集中扭矩作用处几乎为零,翘曲正应力也几乎为零;有限元数值与理论数值的差值百分比在10％以内,说明本文建立的理论计算方法合理可行.     

薄壁杆约束扭转的单肢解析化分析方法

针对薄壁杆件约柬扭转的基本受力反应分析问题,采用与符拉索夫的经典约束扭转理论截然不同的立论途径,将自由扭转刚度视为调整因素,而将剥离了该抗力效应的薄壁杆件基本体系作为主要分析对象,推导出基于翘曲理论并考虑了自由扭转刚度影响的杆件刚度方程及结问荷载的等效措施.此外,提出了基于微段薄壁杆简化单刚的有效数值化分析方法.上述研究表明,对于钢构件等具有薄壁构型截面形式的杆件,这种单肢解析化分析方法无需进行复杂的截面特性如弯、翘曲惯矩或弯、形心坐标等的分析,力与变形的表达简洁、直接,本文的抗力性能分析和表述方式可为薄壁构件的稳定及畸变等研究提供新的思路切入点.     

基于新型广义位移的箱形梁扭转单元及应用

为了改进变截面连续箱梁桥的扭转分析理论，将截面总扭转角分解为自由翘曲扭转角和约束剪切扭转角，选取自由翘曲转角扭率作为广义位移，提出一个2节点8自由度的扭转梁段单元。从约束扭转控制微分方程出发，推导单元刚度矩阵及等效节点荷载列阵。引入应力增大系数，以反映约束扭转对初等梁应力的增大效应。数值算例验证了本文梁段单元的可靠性。最后对一个三跨变截面连续箱梁桥进行分析，结果表明，双力矩影响线与弯矩影响线较为类似，按双力矩影响线进行最不利荷载加载时最大应力值偏小；应力增大系数在集中荷载作用截面出现极值，均发生在腹板与顶板交点处；利用偏载放大系数来考虑扭转附加效应时，不宜考虑弯曲正应力较小及翘曲正应力出现极值的梁段区域。     

考虑剪切变形影响的开口薄壁梁约束扭转的扭转角分析

以开口薄壁梁约束扭转分析理论为基础,通过初参数法推导开口薄壁梁在外扭矩作用下产生的扭转角;推导了槽钢扭转剪应力不均匀系数的精确计算公式;为得到与Timoshenko梁理论类似的简化公式,探讨圣维南扭矩可以忽略时的情形,阐述了简化方法与理论解之间的误差来源,定义了剪切变形影响参数。通过具体算例分析跨度、高宽比等参数对扭转角的影响,并与符拉索夫理论、ANSYS壳单元、简化方法的计算结果进行对比。计算结果表明:当弯扭系数、高宽比恒定时,本文方法的解与符拉索夫解的最大误差从跨径为30m的16.15%到跨径为5m的89.5%;当弯扭系数、跨径恒定时,本文方法的解与符拉索夫解的最大误差从高宽比为1的6.9%到高宽比为5的62.44%;随跨径减小或高宽比增大,剪切变形不容忽略。当弯扭系数与跨径的乘积减小到一定值时可以忽略圣维南扭矩从而得到简化公式;高宽比增大,扭转剪应力不均匀系数先减小后增大。     

A NEW SPATIAL THIN-WALLED BEAM ELEMENT INCLUDING TRANSVERSE AND TORSIONAL SHEAR DEFORMATION

基于Timoshenko梁及Benscoter薄壁杆件理论,建立了考虑剪切变形、弯扭耦合以及翘曲剪应力影响的空间任意开闭口薄壁截面梁单元. 通过引入单元内部结点,对弯曲转角和翘曲角采用三节点Lagrange独立插值的方法,考虑了剪切变形和翘曲剪应力的影响并避免了横向剪切锁死问题;借助载荷作用下薄壁梁的截面运动分析,在位移和应变方程中考虑了弯扭耦合的影响. 通过数值算例将该单元的计算结果与理论解以及商用有限元软件和其他文献中的数值解进行对比和验证,结果对比表明该薄壁梁单元具有良好的精度和收敛性.     

开口厚壁截面短构件的约束扭转

为了分析开口厚壁截面短构件的约束扭转问题,采用统一分析梁模型与有限节线法,对T形和L形厚壁截面短构件约束扭转时横截面的翘曲和应力分布情况等问题进行了分析研究.算例计算结果表明:开口厚壁截面短构件存在与其横截面形心位置不一致的扭转(弯曲)中心,构件在不过扭转中心的外力作用下会产生弯扭耦合变形,其横截面将产生不均匀翘曲,横截面上的翘曲正应力和扭转剪应力均呈非线性分布.     

开口厚壁截面短构件的约束扭转1）

为了分析开口厚壁截面短构件的约束扭转问题,采用统一分析梁模型与有限节线法,对T形和L形厚壁截面短构件约束扭转时横截面的翘曲和应力分布情况等问题进行了分析研究.算例计算结果表明：开口厚壁截面短构件存在与其横截面形心位置不一致的扭转（弯曲）中心,构件在不过扭转中心的外力作用下会产生弯扭耦合变形,其横截面将产生不均匀翘曲,横截面上的翘曲正应力和扭转剪应力均呈非线性分布.     

薄壁箱梁的翘曲连续性条件

基于薄壁杆件理论,分析了薄壁箱梁弯曲剪流和约束扭转翘曲剪流计算时的翘曲连续性 条件. 从翘曲连续性条件出发,推导了薄壁箱梁约束扭转翘曲剪流的一般公式,此外,还指 出了有关文献中的错误并进行了更正. 最后对一个悬臂箱梁的约束扭转翘曲剪流进行了计算 比较.     

考虑约束扭转的薄壁梁单元刚度矩阵

推导了薄壁空间梁单元刚度矩阵 ,考虑了双向弯曲及截面约束扭转对杆件轴向变形的影响 ;计算了截面的翘曲变形 ,以及二次剪应力对翘曲变形的影响 ,可适用于任意截面 (包括开口、闭口和混合剖面 )的薄壁杆件。计算结果表明 ,考虑约束扭转的薄壁梁单元刚度矩阵有相当好的精确度 ,可以用于薄壁杆件的静动力分析。     

复合材料单闭室薄壁梁弯曲与扭转分析

本文主要讨论复合材料单闭室薄壁梁的弯曲与扭转，重点研究横向剪切和限制翘曲的影响。在复合材料薄壁梁弯曲与扭转经典分析理论的基础上，建立了一种能够考虑横向剪切和限制翘曲影响的复合材料单闭室薄壁梁弯曲与扭转分析方法。     

Torsion of closed section,orthotropic, thin-walled beams

The paper presents a theory for thin-walled, closed section, orthotropic beams which takes into account the shear deformation in restrained warping induced torque. In the derivation we developed the analytical (“exact”) solution of simply supported beams subjected to a sinusoidal load. The replacement stiffnesses which are independent of the length of the beam were determined from the exact solution by taking its Taylor series expansion with respect to the inverse of the length of the beam. The effect of restrained warping and shear deformation was investigated through numerical examples.     

The application of graph theory to the limit analysis for torsion of thin-walled bars with complex cross-sections

Graph theory is employed in this paper as a means to establish the topological model of complex thin-walled cross-sections. On this basis, the upper and lower bound theorems of the plastic limit analysis are applied to the analysis of the plastic limit shear flows on the cross-section of thin-walled bars under St. Venant torsion. Corresponding mathematical programming problems are formulated and their duality is shown. After solving the linear programming problem corresponding to the lower bound theorem, the limit torsional moment of a thin-walled cross-section can be calculated according to the shear stress distribution in the limit state. The formula for calculating the limit torsional moment is given. Furthermore, the limit state of thin-walled cross-sections under St. Venant torsion is also discussed and the concept of the limit tree is introduced. A computer program has been developed by the author. Results calculated by the program for typical complex cross-sections are given.     

St. Venant torsion of composite cylinders

Using a method first applied to some fluid dynamical two-phase flow problems [1], the authors derive expressions for the warping and stress functions describing the St. Venant torsion of some compound cylinders. The construction of the cylinder must have appropriate symmetries, and composites containing both two and four different elastic phases are considered. Effective shear moduli and torsional rigidities are defined, and some tables of numerical values given for various configurations. An analogous solution for the antiplane strain of a two-phase composite is also given.     

薄壁杆系结构的梁元分析模型

本文导出了用于薄壁杆系结构弹性分析的薄壁梁元分析模型，在空间梁元分析模型^[3]的基础上，采用了一种改进的位移模式，考察了薄壁杆件可能发生的拉压，剪切，弯曲，扭转和翘曲等各变形形式以及它们的耦合效应，得出了相应的单元形函数，同时从工程应变的定义出发，采用Taylor级数展开的方法，建立了单元的五阶近似正交变表达式，并建立了相应的薄壁单元刚度方程，从而得出了局部坐标系下单元刚度矩阵的显式，根据本文所导出的薄壁梁元分析模型，编制了相应的结构计算程序，通过算例验证了本文所推导的单元刚度矩阵，同时通过与传统空间梁元计算模型计算结果的比较，阐述了截面翘曲对薄壁杆系结构的影响。     

Non-uniform warping including the effects of torsion and shear forces. Part I: A general beam theory

This two-part contribution presents a beam theory with a non-uniform warping including the effects of torsion and shear forces, and valid for any homogeneous cross-section made of isotropic elastic material. Part I is devoted to the theoretical developments and part II discusses analytical and numerical results obtained for torsion and shear-bending of cantilever beams made of different kinds of cross-section. The theory is based on a kinematics assuming that the cross-section maintains its shape and including three independent warping parameters associated to the three warping functions corresponding to torsion and shear forces. Starting from this displacement model and using the principle of virtual work, the corresponding beam theory is derived. For this theory, closed-form results are obtained for the cross-sectional constants and the three-dimensional expressions of the normal and shear stresses. Comparison with classical beam theories is carried out and additional effects due to the non-uniformity of the warping are highlighted. In particular, the contributions of primary and secondary internal forces and the effect of the non-symmetry of the cross-section on the structural behavior of the beam are specified. Simplified versions of this theory, wherein the number of degrees of freedom is reduced, are also presented. The analytical and numerical analyzes presented in part II give responses on the quality of this non-uniform beam theory and indicate also when its simplified versions could be applied.