带轴力混凝土截面弯矩-曲率计算解析

确定塑性铰塑性转动能力大小是超静定结构弹塑性分析的关键内容.混凝土开裂应力释放、钢筋屈服、轴力和弯矩等许多因素影响了截面塑性转动能力.借鉴承载能力极限状态所有可能的应变图,构造弯矩-曲率计算的应变图.以解析方式分析和计算混凝土矩形截面轴力、弯矩、应变和曲率,一次计算可以便捷地得到所有结果,避免了迭代和收敛困难.引入合力...     

塑性应变极限状态下I形和矩形管截面变形分析

通常在钢结构弹塑性设计中会假设大多数受压横截面中具有"全塑性铰"。基于平衡条件提出的用于计算塑性极限状态下结构内力的公式,不能计算出这种极限状态下各种内力组合下结构的整体变形。针对矩形管截面和双轴对称I形截面的弹塑性分析提出一个简单模型。该模型考虑了横截面塑性应变极限状态下的结构整体变形(轴向变形和弯曲曲率)与相应内力(轴力和弯矩)的关系。利用这个模型可以对横截面延性进行真实的评估。     

绕弱轴弯曲钢框架单元的非弹性二阶分析

框架单元常受绕横截面弱轴的弯矩作用,如空间框架单元、绕弱轴屈曲的压杆等。在某些组合截面柱中,绕弱轴方向的弯矩最大。建立简化模型,研究受轴压且绕弱轴弯曲时钢框架单元的二阶非弹性性能。建立了受轴压且绕弱轴弯曲时工字钢、H型钢的塑性强度公式及切线模量经验公式。切线模量公式可用于计算切线刚度,进而求得内部恢复力。这些公式可用于分析钢构件,并考虑欧洲规范ECCS中提到的残余应力,借助有限元程序,采用这些公式,分析平面框架的非弹性二阶性能。与纤维模型相比,新建立的模型的相关性更好。结果表明:新模型准确度高,能节约大量迭代计算时间,     

高强钢焊接箱形柱力学性能研究(Ⅱ)：二阶非弹性分析

高强钢的焊接残余应力分布和普通钢材的有较大差异,现有的切线模量和刚度退化函数不适合用于高强钢焊接箱形截面的二阶非弹性分析。而精炼塑性铰模型通过切线模量和刚度退化函数可合理考虑残余应力的影响和塑性渐进发展,达到与塑性区模型相近的精度。基于此,提出适合高强钢焊接箱形截面的二阶非弹性分析方法。通过稳定函数考虑单元二阶效应,基于杆端部转动引起的构件弯曲及其导致的轴向应变,考虑弯曲效应。在精炼塑性铰模型中,采用高强钢焊接箱形截面的残余应力统一分布模型,通过截面分析法构建不同强度等级的焊接箱形截面切线模量计算公式。同时,分析轴力和弯矩共同作用下的渐进屈服对箱形截面刚度退化的影响,从而建立可模拟截面塑性发展的刚度退化函数。结合塑性铰的产生与发展对平衡微分方程解的影响,建立梁柱单元的弹塑性刚度矩阵。结果表明,所提出的二阶非弹性分析方法可准确分析高强钢焊接箱形截面轴压构件的力学性能,可应用于高强钢框架结构设计,为二阶非弹性分析方法的工程应用提供参考。     

钢截面弹塑性分析的迭代法

对钢截面的弹塑性分析应用非线性方程组求解的牛顿-拉夫逊法,给出荷载-变形计算的一种正算算法,即任意给定一组轴力-弯矩,由迭代得到截面形心应变-曲率。基于截面纤维模型,采用平衡法推导截面刚度矩阵和计算截面承载力,为边缘屈服判断提供了方便,适用于各种形状和双向受力的截面。参考有限元程序设计方法,给出模块化的迭代流程,具有良好的通用性。给出手算算例,分别采用解析法和迭代法计算,结果吻合。     

钢框架弹塑性静动力反应的非线性分析模型

本文基于弹塑性铰概念提出了一种按杆系进行钢框架弹塑性静力和动力反应计算的非线性分析模型。该模型能考虑Bauschinger效应、应变强化效应和强度退化效应的影响,且能描述钢杆件在任意状态下真实弹塑性刚度的连续性变化过程。免除了双分量模型的计算刚度在杆件的不同状态下发生突变的缺陷,大大简化了钢框架弹塑性静力和动力分析计算。试验分析表明,本文的分析模型是可靠的,且具有较高的仿真精度。     

基于刚体准则的空间框架弹塑性非线性分析方法

基于刚体准则,采用二阶改进塑性铰模型,构建了空间弹塑性梁单元及其弹塑性刚度矩阵,建立了高效简洁的非线性增量迭代方法,可有效分析截面屈服产生的有限转动、二阶效应等柔性空间钢框架结构材料与几何非线性耦合效应。对于受初始力平衡的单元,随着单元的刚体转动与移动,其初始平衡力在当前状态下应保持大小不变,仅方向随单元做刚体转动,而实际结构的变形可以视为较大的刚体位移与较小的自然变形(弹性或非弹性)的组合。将此刚体准则植入增量迭代法,在预测阶段采用通过了刚体运动检验的弹塑性矩阵,从而合理确定迭代初始方向;在修正阶段使用刚体准则计算单元结点力,保证了计算精度。对三个典型柔性框架结构所做分析表明,本文方法能够准确预测结构的极限承载力值与塑性铰发展过程。对于空间框架结构,每根杆件仅需划分一个单元,极大提高了计算效率、降低了计算成本。与塑性区法、纤维元法以及考虑截面翘曲的修正切线刚度法等相比,本文提出的方法具有物理概念明确、单元划分少、刚度矩阵简单、分析过程简洁、计算精度与效率高等显著特点,适于工程应用。     

直接分析法中的二阶弹塑性分析

直接分析设计法,是一种通过在数值模型上更加精确地表征结构真实形态,采用非线性分析来获取结构的响应,不需要计算长度法进行构件受压稳定承载力验算的先进方法。该方法对数值计算提出了更高的要求,需要考虑几何非线性和材料非线性。因此,亟需针对直接分析设计法相关的基础理论展开研究。本文主要探讨适用于直接分析法的二阶弹塑性分析,介绍了一种基于柔度法的高性能梁柱单元(FBMI)。该单元采用力的平衡关系作为形函数,具有较高的精度。同时,该单元不仅能考虑轴力和弯矩的相互作用,且在单元推导过程中直接使用函数表征构件的几何初始缺陷,满足规范的相关要求。运用基于纤维截面技术的塑性区法,能够显式地考虑钢构件残余应力的影响,较为精细地模拟构件沿截面方向和沿构件方向的屈服过程。     

任意形状钢筋混凝土薄壁截面双轴压弯恢复力分析

将任意形状钢筋混凝土薄壁截面划分成适当数目的薄壁直边，通过建立薄壁边截面的面内弯矩及轴力与相应变形之间的切线刚度关系合成了整个截面的双轴压弯恢复力模型。该模型可作为钢筋混凝土高层及高耸结构空间弹塑性地震反应分析的本构关系。     

基于二阶梁柱单元的精细塑性铰算法

采用精细塑性铰法考虑残余应力和逐步塑性,并引入弓形效应来提高计算精度,同时基于截面组合法建立的工字形或H形截面的屈服面方程进行严格推导,提出一种单元恢复力迭代算法,减少了半理论半经验公式的使用。此外,所采用的梁柱单元还可以考虑梁构件剪切变形和几何初始缺陷的影响。相比之前的方法,该方法能在进行塑性铰分析的同时,在单元的轴力表达式中考虑二阶效应,更全面地考虑非线性因素影响。最后,通过两个经典算例的对比,证明了该方法具有高效率和高精度的特点。     

Material yielding by both axial and bending spring stiffness at elevated temperature

Material yielding is typically modeled either by plastic zone or plastic hinge methods under the context of geometric and material nonlinear finite element methods. In fire analysis of steel structures, the plastic zone method is widely used, but it requires extensively more computational efforts. The objective of this paper is to develop the nonlinear material model allowing for interaction of both axial force and bending moment, which relies on the plastic hinge method to achieve numerical efficiency and reduce computational effort. The biggest advantage of the plastic-hinge approach is its computational efficiency and easy verification by the design code formulae of the axial force-moment interaction yield criterion for beam-column members. Further, the method is reliable and robust when used in analysis of practical and large structures. In order to allow for the effect of catenary action, axial thermal expansion is considered in the axial restraint equations. The yield function for material yielding incorporated in the stiffness formulation, which allows for both axial force and bending moment effects, is more accurate and rational to predict the behaviour of the frames under fire. In the present fire analysis, the mechanical properties at elevated temperatures follow mainly the Eurocode 3 [Design of steel structures, Part 1.2: Structural fire design. European Committee for Standisation; 2003]. Example of a tension member at a steady state heating condition is modeled to verify the proposed spring formulation and to compare with results by others. The behaviour of a heated member in a highly redundant structure is also studied by the present approach.     

Combined MVP failure criterion for steel cross-sections

This study determines failure criterion for steel member cross-sections, subjected to combined bending moment M, shear force V, and axial force P (MVP). The principle of maximum plastic strain energy is employed to develop the strain-stress relationship for plastic flow, and the expression for the MVP yield surface of the cross-section. A linear distribution of shear strain over the cross-section is assumed. The influence of plastic deformation on bending moment, shear force and axial force, at full yield of the cross-section, is investigated. Results predicted by the derived MVP failure surface, are compared with those obtained by other studies in the literature. The derived MVP yield surface can serve as a basis to identify the failure of steel members, such as during seismic or progressive-failure analysis of building frameworks.     

Inelastic second order analysis of steel frame elements flexed about minor axis

Frame elements may be subjected to significant bending moments about cross-sectional minor axis such as space frame elements and struts that buckle about minor axes. In some cases such as columns with compound cross-sections, the major bending moment acts about minor axes of cross-sectional components. The present paper proposes a simplified model for predicting the second order inelastic behavior of steel frame elements under axial compression force and bending moment about minor axis. New formulae are proposed to describe the plastic strength surface for steel I- and H-shaped cross-sections under axial force and bending moment about minor axis. Moreover, empirical formulae are developed to predict the tangent modulus for those cross-sections. The tangent modulus formulae are extended to evaluate the secant stiffness that is used for internal force recovery. The formulae are derived for steel sections considering the residual stresses as recommended by the European Convention for Construction Steelwork (ECCS). A finite element program is prepared to predict the inelastic second order behavior of plane frames using the derived formulae. The derived model exhibits good correlations when compared with the fiber model results. The analysis results indicate that the new model is accurate, furthermore it saves a lot of calculation time that may be consumed by iterations on the cross-sectional level.     

交错桁架结构体系的极限承载力及其影响因素分析

本文基于非线性连续介质力学理论和内力屈服面塑性流动理论,推导出计算交错桁架结构体系极限承载力的二阶弹塑性刚度方程。在该刚度方程的构造中不仅考虑了单元截面上的轴力、剪力、弯矩、扭矩以及结构剪切变形的影响,还考虑了杆端塑性铰处内力之间的相互影响。数值计算表明本文方法具有良好的计算精度。最后,本文还在此基础上就结构高宽比、荷载偏心、柱子截面形式和平面桁架的形式等因素对交错桁架结构极限承载力的影响进行了探讨,结果表明当交错桁架结构体系达到其极限承载力时,杆件的塑性铰主要集中分布在下部楼层,设计时建议适当加大下部楼层的杆件截面,以保证结构具有足够的极限承载力。此外,在偏心荷载作用下,柱子截面形状对结构极限承载力的影响较大,其工形截面的影响要比箱形截面更为显著。     

方钢管混凝土压弯构件截面非线性分析

构件截面非线性分析是进行结构抗震性能分析的重要基础,针对方钢管混凝土构件中钢管的三向受力特点,提出了一种适于计算方钢管混凝土压弯构件弯矩-曲率骨架曲线的钢材本构模型,模型中考虑了钢材的环向拉力作用;并应用提出的钢材模型和已有的混凝土模型编制了纤维模型数值计算程序;分析了含钢率、轴压比、混凝土强度和钢材强度对方钢管混凝土压弯构件截面弯矩-曲率曲线的影响。通过对构件屈服弯矩、极限弯矩的分析,提出了一种方钢管混凝土压弯构件的三线性骨架曲线,该曲线可用于工程中方钢管混凝土框架结构的动力学分析。     

Analytical formulation for the deformations of I-shapes and RHS at the plastic strain ultimate limit state

The development of “full plastic hinges” in the most stressed cross-sections is a common hypothesis considered in the elastic-plastic design of steel structures. The equations for the internal forces at the plastic limit state are then based on equilibrium conditions only, and they do not allow the global deformations corresponding to each combination of internal forces at this ultimate limit state to be estimated.This paper presents a simplified analytical model for the elastic-plastic analysis of rectangular hollow sections and bisymmetrical I-sections bent about their strong axis. This model states the relations between the global deformations (axial deformation and bending curvature) and the corresponding internal forces (axial force and bending moment) at the cross-section plastic strain ultimate limit state. It allows a realistic evaluation of the cross-section ductility, based on a relevant strain limitation at the most strained cross-section fibres.     

受负弯矩和压缩作用的组合梁的性能和设计

调查了受负弯矩和轴向压缩共同作用下钢-混凝土组合梁结构的性能。在这项研究中,对6个承受负弯矩作用的足尺寸的组合梁同时进行压缩。轴向压缩的等级由低到高变化。根据试验,构建并标定一个非线性有限元模型来对试验结果进行验证。该模型能够对试验所用梁的非线性响应和最终破坏模式做出预测。所构建的有限元模型对一些常在实际中使用的组合梁可进行一系列参数分析。分析发现,当压缩荷载作用于组合截面时,组合梁的负弯矩承载能力明显降低,钢梁的局部屈曲更显著,影响了截面的延展性。基于截面平衡的刚塑性分析可以合理地预测组合截面的复合强度,因此可适当地使用于设计原理中。在负弯矩区钢梁腹板处使用纵向加劲肋可消除腹板屈曲,并增加组合截面的转动能力。根据试验结果和有限元分析提出一个可应用于工程实践中的简化设计模型。     

Behaviour and design of composite beams subjected to negative bending and compression

This paper investigates the behaviour of steel–concrete composite beams subjected to the combined effects of negative bending and axial compression. For this study, six full-scale tests were conducted on composite beams subjected to negative moment while compression was applied simultaneously. The level of the applied axial compression varied from low to high. Following the tests, a nonlinear finite element model was developed and calibrated against the experimental results. The model was found to be capable of predicting the nonlinear response and the ultimate failure modes of the tested beams. The developed finite element model was further used to carry out a series of parametric analyses on a range of composite sections commonly used in practice. It was found that, when a compressive load acts in the composite section, the negative moment capacity of a composite beam is significantly reduced and local buckling in the steel beam is more pronounced, compromising the ductility of the section. Rigid plastic analysis based on sectional equilibrium can reasonably predict the combined strength of a composite section and, thus, can be used conservatively in the design practice. Detailing with longitudinal stiffeners in the web of the steel beam in the regions of negative bending eliminate web buckling and increase the rotational capacity of the composite section. Based on the experimental outcomes and the finite element analyses a simplified design model is proposed for use in engineering practice.