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。     

直接分析设计法中的受压构件等效初始缺陷研究

在GB 50017—2017《钢结构设计标准》中，仅对考虑材料弹性阶段的直接分析设计法中的构件初始缺陷取值作出了规定，对考虑材料弹塑性发展的直接分析设计法中未给出构件初始缺陷取值的具体数值。为此，基于钢结构塑性稳定理论，利用轴心受压构件稳定系数反向推导其等效初始缺陷，包括初始几何缺陷和残余应力。根据不同的截面类型和钢材牌号，给出受压构件不同的等效初始缺陷，使直接分析设计方法能够真正地应用于实际工程中。利用直接分析设计软件NIDA，建立带有初始缺陷的弯曲单元，模拟受压构件的等效初始缺陷，得到构件的稳定承载力系数，并与轴压构件稳定系数φ进行对比分析，验证了构件等效初始缺陷取值的正确性。     

钢结构直接分析法在设计软件中的应用

钢结构设计中的直接分析法在结构力学模型中引入整体和杆件初始缺陷,在分析过程中考虑P-Δ和P-δ效应,并以求取的内力作为校核构件的依据,该方法具有概念清晰等优点。对比了常用设计软件的直接分析法应用方式,并基于SAP2000软件提供的OAPI接口,开发了可快速施加杆件初始缺陷的插件,并通过多个案例探讨了直接分析法的应用要点。通过对超静定结构进行弹塑性全过程分析,得到了结构的承载力设计值与承载力极限值,获得了结构系统杆件失稳→塑性开展→卸载的全过程响应。同时分别采用传统的一阶弹性分析法与直接分析法,求取结构达到承载力设计值时杆件内力分布,对比了两种方法求得内力的差异,并分析了产生差异的原因。所采用的编译方法和技术途径可为直接分析法在SAP2000等有限元软件中的应用提供参考。     

半刚性钢框架的直接分析方法理论研究

介绍了一种针对半刚性连接钢框架的直接分析法,该方法可以同时考虑结构和构件的初始缺陷、几何非线性(包括P-Δ,P-δ效应)、材料非线性以及半刚性连接(支座)对结构受力性能的影响。建立了可同时考虑初始缺陷、半刚性连接以及塑性铰的弯曲稳定函数单元(CSF单元),推导了CSF单元的二阶单元刚度矩阵,并扩展为三维单元刚度矩阵。采用弹簧单元对半刚性连接和塑性铰单元的非线性行为进行了模拟,确定了塑性铰出现的判断准则以及弹簧刚度的取值,定义了结构破坏准则。利用NIDA程序对3组半刚性连接框架结构进行了直接分析,并与试验结果进行了对比。对比分析表明:利用NIDA程序得到的结果与试验结果吻合较好,验证了直接分析法对半刚性连接钢框架进行结构分析的有效性和可靠性。     

钢结构几何缺陷的直接分析方法

本文介绍了结构几何缺陷的几种处理方法，导出了一种显式的缺陷分析模型，将构件初始缺陷直接引入到单元位移插值函数中，可以同时考虑缺陷以及单元横向荷载引起的二阶效应。分析表明对于构件数较少且缺陷敏感型结构，局部缺陷的影响显著；而对于构件数较多的复杂结构系统，局部缺陷的影响是局部的。给出的几个数值算例表明了本文模型的高效性和准确性，计算结果可直接用于设计，而无需进行构件验算和长度系数的计算。     

薄壁钢构件非线性稳定问题的曲壳有限单元法

笔者将薄壁钢构件作为柱形薄壳组合结构,导出了分析薄壁钢构件各类非线性稳定问题的曲壳有限单元法。对于过去种种板壳有限单元法分析梁柱构件时很难解决的一些问题,本文分别导出了一些特殊方法给予了有效的处理。本文方法适用于具有任意截面形式和任意边界条件的薄壁钢构件弹塑性整体稳定问题的分析,以及薄壁构件的整体稳定-局部稳定相互作用问题的分析。分析时,可计入任意形式的初始缺陷的影响,可以考虑任意形式的加载方式以及弹塑性区域内的加卸载现象。经比较,证明本文方法具有极高的精度。     

直接分析法在连续倒塌中的应用

结构连续性倒塌分析中的核心问题主要有材料非线性、初始缺陷、动力效应和悬链线效应。结构的抗连续性倒塌性能设计验算主要采用构件拆除法,将关键竖向承载力构件拆除后检验结构的响应。结构整体分析可采用线性静力分析、非线性静力分析和非线性动力分析三种方法。采用基于非线性静力分析的直接分析法,在分析中直接考虑对结构响应有影响的因素,如材料非线性、初始几何缺陷、残余应力、节点连接刚度等,以整个结构体系为对象进行抗连续性倒塌分析。基于NIDA软件,通过一个算例体现了GSA和UFC规范中的构件拆除法的设计过程,并与传统的线性静力分析结果作比较。     

考虑整体和构件几何缺陷的隐式框架-支撑结构动力弹塑性二阶效应分析

通过对ETABS软件进行二次开发,给出《钢结构设计标准》(GB 50017—2017)直接分析设计法在ETABS软件中的实现方式。在此基础上,以山东某高层住宅项目采用的隐式框架-支撑结构体系为例,采用考虑结构整体初始几何缺陷和构件初始缺陷的动力弹塑性分析方法,分析该结构在大震作用下的动力响应和两种缺陷对结构抗震性能的影响。分析结果表明:罕遇地震作用下,有无考虑缺陷和二阶效应时得到的结构最大层间位移角均未超过1/50限值,支撑起到了第一道抗震防线的作用,框架柱保持弹性,满足"强框架,弱支撑"的设计要求。考虑缺陷和二阶效应会使结构最大层间位移角有所增加,根据结构二阶效应系数和延性系数可近似估算二阶效应对最大层间位移角的放大系数;对于高延性结构,在进行动力弹塑性分析时,应考虑缺陷和二阶效应对结构抗震性能的影响。     

运用NIDA进行钢框架结构二阶直接分析

文章提出了运用二阶直接分析法对钢框架结构进行分析,同时考虑P-A-δ效应以及结构和构件的初始缺陷对钢框架的影响,避免了考虑计算长度问题和单独检查每根构件的稳定性.结构和构件的强度和稳定性可以简单地通过构件截面进行检验.算例表明,这种设计方法较传统线性分析法和计算长度法更加准确和有效.     

莱钢产轧制H型钢构件受力性能的理论与试验研究(Ⅳ)H型钢构件轴心受力性能的理论分析

对国产轧制H型钢截面构件进行了轴心受压承载力的理论研究。通过有限元方法 ,对国产轧制H型钢轴心受压构件的极限承载力进行了弹塑性和几何非线性的有限单元法理论分析 ,同时考虑了热轧型钢的残余应力和构件的初始缺陷。计算了 114根国产轧制H型钢轴心受压构件的极限承载力 ,得出国产轧制H型钢轴心受压构件极限承载力的主要公式。提出了便于设计人员应用的轴心受压修正公式。     

Parametric study and design approach of off‐center bracing systems

This paper presents an effective approach for the seismic design of off‐center bracing systems (OBSs). The nonlinear behavior of an OBS can be specified by evaluation of two yielding stages representing tensile yielding of different bracings. This can be achieved when stiffness of the corner brace member is deliberately considered less enough to act as a fuse‐like component. An accurate two‐dimensional finite element modeling for the geometric and material nonlinearity of such systems considering buckling behavior of the brace members is developed. Through an extensive parametric study, the optimal ratios of the influential parameters of OBS are obtained, and their effects on the nonlinear performance of OBS are evaluated. Next, a number of design graphs for determining the trilinear behavior model of different types of the OBS are presented. The aforementioned diagrams are included of non‐dimensional force and stiffness parameters that can be used for other frames with the same properties. Then, by extracting an equivalent bilinear model from the trilinear approximated behavior, an effective design algorithm based on the calculation of system's ductility under desired earthquake is presented, and finally, applicability of the proposed design approach is well demonstrated through an example problem.     

河南艺术中心大剧院钢屋盖基于延性的性能化设计研究

河南艺术中心大剧院是屋盖为平面钢管相贯桁架、下部由三个钢筋混凝土结构单元组成的复杂结构体系。进行了基于延性的结构抗震设计研究,对整体结构进行小震、中震反应谱分析及大震弹塑性时程分析,对结构自振特性、构件应力比、结构位移、塑性铰分布与损坏程度等进行了深入的量化分析。研究了结构整体大变形失稳破坏极限状态下的体系强屈比和体系延性,并确立了关键节点不屈服的性能设计目标,对整体结构进行了考虑几何非线性、材料弹塑性、初始几何缺陷的荷载-位移全过程屈曲稳定分析,并完成了相关结构构件与节点的设计。实现了基于延性的抗震安全及体系稳定安全的双重设计目标。     

Nonlinear analysis of 3-D steel frames

In this paper, a nonlinear analysis of three-dimensional steel frames is developed. This analysis accounts for material and geometric nonlinearities. The material nonlinearity considers the gradual yielding associated with member forces. The geometric nonlinearity includes the second-order effects associated with P-δ and P-Δ. The material nonlinearity at a section is considered using the concept of the P–M hinge consisting of many fibers. The geometric nonlinearity is considered by the use of stability functions. The modified incremental displacement method is used as the solution technique. The load–displacement relationships predicted by the proposed analysis compare well with those given by other approaches.     

Advanced analysis of hybrid steel and concrete frames: Part 2: Refined plastic hinge and advanced analysis

Robust geometric and material nonlinear analysis of buildings under ultimate loads is a key to success of advanced analysis, performance-based seismic design and progressive collapse analysis. This is the second part of two companion papers about the advanced analysis of hybrid steel and concrete frames allowing for various effects such as initial imperfections, gradual cracking effect and geometrical and material nonlinearities. Besides the use of Pointwise–Equilibrium–Polynomial (PEP) element allowing for initial imperfections and the P–Δ–δ effects by one element per member, the plastic hinge approach is refined for modelling of material yielding. In order to assess the sectional strength, the cross-section analysis technique described in the companion paper is utilized in this paper for analysis of steel reinforced concrete (RC) and steel-concrete composite (SCC) sections. Cracking in concrete component, which has significant influence on structural deformation and internal force distribution, is considered by using the Branson's model combined with the concrete cracking fracture surface. The distinct feature of the proposed method is that it integrates the accurate cross-sectional analysis technique to the refined lumped plasticity approach such that a feasible and reliable solution can be obtained. Members with previous experimental results and a portal frame are studied and compared for validation of the proposed method.     

空间支撑钢框架结构的三重非线性分析

为了探讨三维结构的高等分析方法,本文将有限单元法与梁柱法相结合,建立了空间支撑钢框架结构的三重非线性分析方法,该法综合考虑了几何、材料和连接非线性效应。文中基于非线性连续介质力学理论和考虑剪切效应的稳定插值函数建立的严格三维梁柱单元刚度矩阵,包含了轴向、剪切、双向弯曲与扭转及其各耦合效应。三维单元简化塑性区模型可模拟塑性扩展,利用单元两端抗转弹簧和考虑支撑效应的节点域剪切变形模型来模拟连接非线性。使用包括几何、材料和连接非线性的数值算例来检验本文方法和所编计算机程序的可行性、有效性与精确度。算例表明,利用本文方法,每个构件只需一个单元即可准确预测三维结构的极限荷载与失稳模态,可提高结构非线性空间性能的分析效率。     

单层肋环型椭圆穹顶网壳整体稳定性分析

大跨网壳结构具有高度的几何非线性,结构设计一般由整体稳定性控制.本文以北京某单层肋环型椭圆穹顶网壳工程为背景,利用非线性有限元计算方法,对其整体稳定性进行了线性特征值屈曲、弹性屈曲以及弹塑性屈曲三方面的分析,并求得了它们的极限荷载.同时,还考察了钢材的屈服强度以及初始缺陷对极限荷载的影响,并将数值计算结果与拟壳法所得的设计临界荷载进行了比较,得出的结论对实际工程具有一定参考价值.     

Nonlinear inelastic response history analysis of steel frame structures using plastic-zone method

A beam–column element formulation and solution procedure for nonlinear inelastic analysis of planar steel frame structures under dynamic loadings is presented. The spread of plasticity is considered by tracing the uniaxial stress–strain relationship of each fiber on the cross section of sub-elements. An elastic perfectly-plastic material model with linear strain hardening is employed for deriving a nonlinear elemental stiffness matrix, which directly takes into account geometric nonlinearity and gradual yielding. A solution procedure based on the combination of the Hilber–Hughes–Taylor method and the Newton–Raphson method is proposed for solving nonlinear equations of motion. The nonlinear inelastic time-history responses predicted by the proposed program compare well with those given by the commercial finite element package known as ABAQUS. Shaking table tests of a two-story steel frame were carried out with an aim to clarify the inelastic behavior of the frame subjected to earthquakes generated by the proposed program. A more practical analysis method for seismic design can be developed by comparing it with the presented frames for verification.     

Q690钢焊接H形截面轴压柱整体稳定性能研究及设计方法

该文旨在研究Q690高强钢焊接H形轴压柱的整体稳定性能,并给出适合该类型构件的一阶弹性设计建议。为此,对Q690焊接H形试件进行残余应力试验研究和轴压试验研究,基于试验结果,给出残余应力分布模型;并分析该类型试件的失稳形态和整体稳定性能。同时,使用直接分析法建立数值模型,并对其进行验证。该数值模型采用PEP单元(Pointwise-Equilibrating-Polynomial Element)来模拟构件的几何初始缺陷,采用塑性纤维铰方法结合截面屈服面(该屈服面考虑了残余应力效应)来反映关键截面的屈服影响。最终,采用该直接分析法对Q690焊接H形轴压构件进行了参数分析。基于参数分析结果,给出该类型轴压试件的一阶弹性设计建议。     

Nonlinear inelastic analysis of space frames

In this paper, a fiber beam-column element which considers both geometric and material nonlinearities is presented. The geometric nonlinearities are captured using stability functions obtained from the exact stability solution of a beam-column subjected to axial force and bending moments. The material nonlinearities are included by tracing the uniaxial stress-strain relationship of each fiber on the cross sections. The nonlinear equilibrium equations are solved using an incremental iterative scheme based on the generalized displacement control method. Using only one element per member in structure modeling, the nonlinear responses predicted by the proposed element compare well with those given by commercial finite element packages and other available results. Numerical examples are presented to verify the accuracy and efficiency of the proposed element.