地铁隧道开挖引起临近地下管线竖向位移及内力分析

基于Winkler弹性地基梁理论,分析地下管线在地铁开挖作用下的受力情况,推导考虑硬化地基扩散作用因素影响的地下管线位移表达式、转角表达式、弯矩表达式和剪力表达式,并定量分析地下管线变形与地基扩散角、埋深等因素间的关系。理论分析表明:地下管线的最大位移在沉陷区的中间,最大弯矩和最大剪力发生在沉陷区的边缘;地基扩散角与管线的埋深对管线的最大沉降量有较大影响。分析结果为工程实践中确定管线的加固位置提供了理论依据。     

基于地基反力与沉降非线性关系的地基梁研究

基于实验测量的地基反力与地基梁沉降关系数据,分别将地基和梁之间的作用力与梁的挠度拟合成线性关系和三次多项式关系,推导出非线性弹性地基梁的有限差分法基本理论方程式,并用MATLAB软件编程解出数值解。算例计算对非线性弹性地基梁和经典线弹性Winkler地基梁的挠度、转角、剪力和弯矩结果进行了对比,结果表明二者的相对误差可达到10%~30%,因此在实际工程中应尽量考虑地基反力与沉降的非线性关系。     

考虑地基水平摩阻的Winkler地基Timoshenko梁分析

考虑地基水平摩阻的影响,建立Winkler地基上Timoshenko深梁的平衡方程,导出微分方程的初参数解和传递矩阵法,利用初参数解建立有限元列式和单元内均布荷载、集中力、集中力偶等非结点荷载的等效公式。当地基水平劲度系数为0时,地基退化为传统的Winkler地基,当梁的抗剪劲度无穷大时,Timoshenko梁退化为Euler梁,该模型是一种较为通用的模型。利用传递矩阵法和有限元法分析在均布荷载和集中力共同作用下的两端自由Timoshenko梁及在集中力、集中力偶和分布荷载共同作用下的二端自由阶梯梁弯曲问题,讨论Winkler地基、双参数地基、考虑水平摩阻的Winkler地基梁的挠度、转角、剪力、弯矩变化。算例结果表明:传递矩阵法结果与有限元结果完全一致,可相互验证其正确性,有限元精度不依赖于单元划分密度,水平摩阻对弹性地基梁有较大影响。     

地基不均匀沉降时埋地管涵纵向力学模型探讨

地基不均匀沉降是影响埋地管涵纵向力学性状的主要因素之一。针对Winkler地基模型的缺陷,采用Pasternak双参数地基模型建立了较为合理的考虑地基差异沉降的埋地管涵纵向力学模型,得到了沉陷区埋地管涵的挠曲线表达式,进而对埋地管涵的纵向力学性状要素进行分析,表明管涵结构的挠度、转角、弯矩、剪力均在差异沉降处有突变,且各要素受不均匀沉降的影响范围有限。     

锁脚锚管受力分析的双参数弹性地基梁模型

 针对Winkler地基梁模型的固有缺陷,将能够反映地基连续性的Pasternak双参数地基梁模型引入到锁脚锚管–钢拱架的联合承载分析中,考虑锁脚锚管与钢拱架之间的变形协调与荷载传递,采用结构力学和弹性地基梁理论推导锁脚锚管挠度、剪力、弯矩和地基反力的解析表达式。分别通过算例和工程实例考察不同地基基床系数和剪切刚度对锁脚锚管力学行为的影响规律,并与Winkler地基梁模型进行比较。结果表明：基床系数越小,2种模型计算所得锁脚锚管剪力、弯矩以及地基反力等的差异越明显;由双参数模型所得的地基反力数值较大,而且分布范围更小,主要集中在锁脚锚管端部附近区域;由双参数模型所得的隧道下沉量要小于Winkler模型的计算值。给出了适当减小锁脚锚管长度,并增大其直径的建议。研究成果可为软弱围岩隧道支护设计提供理论参考。     

基于参变量变分原理的地基梁位移非线性分析

提出一种分析地基梁非线性位移的新方法。首先采用分段线性函数对非线性的基底压力(p) -基底沉降(s)关系曲线进行拟合,通过引入控制变量,得到p-s曲线统一表达式。根据地基梁模型能量泛函,结合参变量变分原理和分段线性地基模型中的互补条件,导得一个标准的线性互补模型。该模型可用较为成熟的规划算法进行求解,使地基梁位移非线性求解问题转化为一个标准的数学问题。在对该法的合理性进行验证后,详细推导了集中荷载作用下地基梁位移的非线性求解方程,并对其进行求解。在此基础上,对线性与非线性计算的差异及影响非线性计算结果的因数进行分析,得到如下主要结论：考虑非线性影响时,地基梁位移曲线不均匀沉降增大,地基梁内力增大;随着p-s曲线非线性程度增加以及p-s曲线上进入非线性段临界压力值的减小,非线性影响越明显;荷载大小及梁与地基的相对刚度均会影响地基梁位移分布形式。     

局部均布荷载作用下软土盾构隧道结构分析

通过对集中荷载作用下弹性地基梁挠曲曲线函数进行积分,推出局部均布荷载作用下软土盾构隧道结构简化为弹性地基梁进行纵向结构分析时的挠度、转角、弯矩、剪力及地基反力的解析表达式,并对上海典型地质条件下的盾构隧道结构进行计算,得出其隧道结构纵向各个位置挠度、转角、弯距、剪力及地基反力的值,对局部均布荷载作用下软土盾构隧道结构纵向设计具有指导意义。     

半空间体上无限长轨道梁作用集中力的Fourier变换解

从弹性力学半空间问题的Boussinesq解出发,建立无限长梁的弯曲微分方程与半空间体上表面的位移表达式,对两个方程进行Fourier变换联合求解,然后通过Fourier逆变换求得半空间体的支承反力与梁的位移表达式。通过理论解与有限元分析比较,求得Fourier变换解中的待定系数C=γ+e≈3.295 5。分析发现,半无限空间上的梁的特征长度是开四次方的量。最后提出梁下承压应力计算的等效计算长度,用于下部半空间材料的强度计算。所得到的梁的弯矩和剪力公式,可用于轨道梁的强度计算。     

局部线性分布荷载作用下软土盾构隧道解析解

通过对集中荷载作用下弹性地基梁挠曲曲线函数进行积分,推出局部线性分布荷载作用下软土盾构隧道结构简化为弹性地基梁进行纵向结构分析时挠度、转角、弯矩及剪力的解析表达式;并对上海地铁2号线的盾构隧道结构进行计算,得出其隧道结构纵向各个位置挠度、转角、弯矩及剪力的值,对局部线性分布荷载作用下软土盾构隧道结构纵向设计具有重要意义。     

弹性地基上矩形水池的计算及用表

本文对Winkler弹性地基上的矩形水池底板,用量纲分析和有限元计算的方法,提出了弯矩、刚度、传递系数和板边反力的计算用表,并提出了将其用于空间整体弯矩分配法进行弹性地基上矩形水池内力计算的实用方法。     

Semi-empirical design of complex metal beams by buckling analysis

Structural elements with complex geometries, boundary conditions and load patterns cannot be designed against buckling using empirical formulae because of uncertain elastic buckling moments or unknown buckling effective lengths, which are basic parameters for these equations. This article proposes a shell finite element procedure for buckling design of metal beams of complex configurations with codified initial imperfections assumed in the Perry–Robertson formula. The advantage of the proposed method lies in the use of elastic buckling moment with empirical design formulae for determination of design moment capacity of a beam; thereby eliminating the uncertainty of modelling initial imperfections. More importantly, the moment modification factor and assumption of effective length can be avoided because all second-order and yield effects have been considered in the computer model. Numerical examples demonstrate that the simplified method has a high level of accuracy, versatility and flexibility for the design of complex beams.     

General analysis and application to redundant arches under static loading

The aim of this paper is to define an exact formulation of a curved beam finite element for static analysis. The basic equations are combined in the coupled fundamental system in terms of radial displacement v, tangential displacement u and rotation ϕ. An original procedure for solving the fundamental system of equations is used. A finite element formulation based on shape functions that satisfy the homogeneous form of the fundamental system of differential equations is developed. The effects of bending moment, axial extension and transverse shear are taken into account. The exact elastic solution renders the element obtained free of shear and membrane locking.An efficient numerical procedure is presented for determining the pressure curve in the case of circular arches under static loading and arbitrary bonding conditions. The solution obtained is applicable to the analysis of both thin and thick curved beams.Several examples of arches with various loading and boundary conditions are investigated to illustrate the validity and the accuracy of the method. Finally, the effect of the arch rise on the structural response is pointed out.     

Behavior of steel-concrete composite cantilever beams with web openings under negative moment

The effect of web openings on the mechanical behavior of composite beams under negative moment was studied through monotonically loading tests. Nonlinear finite element method based analysis was also conducted for cantilever composite beams. The test and the finite element analysis results indicated that the initial cracking loads of composite beams with web opening are lower than that without web opening. The first crack initiated from the concrete slab on the top of the opening. The beams with web opening failed due to shear failure of concrete slab upon the opening. It was also found that the load carrying capacity of beam decreases with the increase of the moment-to-shear ratio at the central line of the opening and the mechanical behavior of beam can be improved significantly by applying stiffening steel plates around the opening. To quantify the reduction of load carrying capacity, a method for calculating the load carrying capacity of beams with web openings under negative moment was derived with consideration of the interaction between moment and shear. Good consistency was obtained between the proposed method, the finite element method and the test results.     

基于Wieghardt地基桩基稳定性分析

基于Wieghardt地基模型,考虑剪力对桩受力的影响,采用梁的弯曲微分方程,利用梁单元间的位移、转角、弯矩和剪力协调条件,桩的整体平衡条件,建立了不计桩侧摩阻力时两端铰支完全埋入土桩的微分方程,并给出了基桩屈曲临界荷载。利用本文解答分析了地基基床系数对基桩屈曲荷载的影响。结果表明,考虑桩侧有明显土体约束计算的桩屈曲荷载明显大于没有考虑侧向约束桩的屈曲荷载,说明桩侧约束对桩的稳定性具有重要影响;并且基桩屈曲临界荷载随地基基床系数a,b增大而减小;对于细长桩,纯弯曲状态时的屈曲荷载小于考虑剪切变形时的屈曲荷载,实际计算中应采用纯弯曲变形时的屈曲荷载。     

考虑水平摩阻力的弹性地基梁非线性分析

基于传统文克尔弹性地基梁理论,考虑梁土间的摩阻效应、梁的纵横向变形耦合及变形的几何非线性,建立出相应的弹性地基梁挠曲变形控制微分方程。引入Galerkin法,导出了对称荷载作用下有限长梁的挠曲变形、转角、剪力及弯矩的非线性解析解。在此基础上,分析探讨了外加荷载、地基梁刚度、梁与土体之间的水平摩阻力、竖向地基反力系数等因素对地基梁位移及内力的影响。分析结果表明:水平摩阻力并不影响地基梁位移及内力的整体变化发展趋势,但将导致地基梁位移及内力值的降低,且水平摩阻力越大,其对地基梁位移及内力的影响也就越大,此外,当地基梁抗弯刚度越大,水平摩阻力对梁位移及内力的影响反而越小。     

钢-玻璃组合梁平面内受力性能及计算方法研究

目前国内外对钢-玻璃组合梁结构的受力模式及承载力研究不足,对5个钢-玻璃组合梁试件进行了平面内受力性能试验,并基于多线性和线性材料本构模型进行了有限元分析。研究了采用钢化夹层（胶）玻璃腹板和单片钢化玻璃腹板组合梁的剪压破坏模式及纯弯曲破坏模式,两种破坏模式的区别在于纯弯曲破坏始于梁底弯矩最大部位,而剪压破坏在局部受压及剪跨区域发生。采用我国JGJ 102—2003中关于平面内玻璃肋受弯计算公式分析了组合梁承载力,基于塑性铰线方法提出了该类组合梁承载力的理论计算公式。研究结果表明：剪压破坏时钢化夹层（胶）玻璃腹板随着荷载增大而呈现明显的界面孔隙,相比同厚度的单片钢化玻璃腹板,夹层（胶）玻璃腹板能提高组合梁的弯曲变形能力。增加腹板玻璃厚度和胶结强度均可提高组合梁的承载力,且前者的贡献更为明显,对于后者,剪压破坏和纯弯曲破坏分别取决于结构胶的压缩模量和剪切模量。考虑了胶结部分受拉刚度贡献的有效截面系数能更好预测组合梁的纯弯曲破坏承载力,而提出基于塑性铰线机制的计算方法能更好预测组合梁的剪压破坏承载力。     

Exact solutions for thin-walled open-section composite beams with arbitrary lamination subjected to torsional moment

The exact solutions for torsional analysis of thin-walled open-section composite beams with arbitrary lamination subjected to torsional moment are presented for the first time. For this, a general thin-walled composite beam theory with arbitrary lamination is developed by introducing Vlasov's assumption and the equilibrium equations and the force–deformation relations are derived from the energy principle. Applying the displacement state vector consisting of 14 displacement parameters and the nodal displacements at both ends of the beam, the displacement functions are derived exactly. Then, the exact stiffness matrix for torsional analysis is determined using the force–deformation relations. As a special case, the closed-form solutions for symmetrically laminated composite beams with various boundary conditions are derived. Finally, the finite element procedure based on Hermitian interpolation polynomial is developed. To demonstrate the validity and the accuracy of this study, the numerical solutions are presented and compared with the closed-form solutions and the finite element results using the Hermitian beam elements and ABAQUS's shell elements.     

Effects of partial shear connection on the behavior of semi-continuous composite beams

In this paper, the effects of partial shear connection on the behavior of semi-continuous composite beams were studied numerically using two-dimensional finite element model with plane stress elements. The finite element model takes into account the nonlinearity of the different materials involved. For the shear connectors, a non-linear (shear-slip) relation, drawn from the push-out tests, was used. The accuracy of the proposed finite element model was verified against test results available in the literature. A simplified method to predict load capacity and deflection of the semi-continuous composite beams was also proposed. Based on the results obtained from the finite element analysis, the concept of partial shear connection in the hogging moment regions can be accepted provided that the shear connectors are sufficiently ductile.     

焊接箱形截面梁抗震性能影响因素研究

为考察板件宽厚比对焊接箱形截面梁抗震性能的影响,对中国、美国、日本和欧洲的钢结构设计标准中的相关规定进行了比较,结果表明各国规范对于梁板件宽厚比限值的规定总体上具有较好的一致性。采用钢材循环加载本构,建立了多尺度非线性有限元计算模型。提出了刚性竖杆 箱形梁加载方式,模拟水平地震、重力荷载与轴向压力对箱形截面框架梁的作用。有限元分析结果表明,在设计常用的板件宽厚比范围内,箱形截面梁的弹性屈曲荷载均显著高于其屈服荷载。在水平往复荷载作用下,随着板件宽厚比减小,箱形截面梁极限变形角与延性系数随之增大,抗弯刚度降低速率变缓,塑性耗能能力显著增强。当满足一级抗震宽厚比要求时,焊接箱形截面梁的梁端截面转角约为1/30。承受轴压作用时梁刚度退化很快,变形能力减弱。当轴压比不大于0.2、满足一级抗震宽厚比要求时,梁端截面转角约为1/50。跨高比对梁承载力影响不大,但变形能力可以大幅度提高。横向荷载对梁抗震性能的影响显著,随着静载比（重力荷载代表值与屈服弯矩之比）增大,骨架曲线逐渐发生平移,抗弯刚度降低,耗能性能减弱。当地震弯矩与静力弯矩方向相同时,箱形截面梁承载力显著降低,静载比0.8时极限变形角可减小约50%;当地震弯矩与静力弯矩方向相反时,梁虽然承载力稍有提高,但极限变形角略有减小。