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。     

空间钢框架结构的弹塑性稳定

本文根据Giberson弹塑性梁单元模型和总势能最小值原理,导出了空间受力杆单元的二阶弹塑性切线刚度矩阵,并建立了空间钢框架结构的二阶弹塑性分析亢法。空间受力杆和缩尺空间框架模型的试验结果不仅验证了本文理论分析方法的正确性,而且反映空间结构的一些受力特性。     

基于拟力法的纤维梁有限元非线性分析方法

以拟力法中的弹塑性分解思路和纤维梁理论为基础,将梁单元的截面变形分解为弹性变形和塑性变形,并引入塑性自由度,在材料层面建立了基于拟力法的纤维梁有限元非线性分析方法。该方法可以保持结构整体刚度矩阵不变,其非线性状态通过局部塑性矩阵加以体现,在迭代计算时避免了结构整体刚度矩阵的实时更新与分解,且塑性矩阵相比于结构整体刚度矩阵规模小,提高了计算效率。通过数值算例,将文中方法与采用有限元软件ABAQUS的分析结果进行对比,两者吻合较好,证明了该方法的有效性。     

Implementation of advanced analysis method for steel-framed structures under fire conditions

This paper is concerned with the development of an advanced analysis numerical tool capable of estimating the inelastic large-displacement behaviour of plane steel-framed structures under fire conditions. A non-linear transient heat transfer analysis is performed on the basis of the finite element method (FEM), following the main guidelines proposed by the European Code for steel structures under fire conditions. The computational analysis program is used to assess the structural load-bearing functions and to estimate the structural behaviour and the corresponding time-resistance period. The original refined plastic hinge method is extended for fire design analysis considering both tangent modulus model and inelastic stiffness degradation concepts in the developed computational program. A tangent modulus model is developed for the European column buckling-curve for fire condition. A gradual inelastic surface is proposed as a function of the temperature and the loading combination. The results obtained are compared with those from an FEM computational program and those from the Eurocode simplified design recommendations. The benefits of using steel ductility in the current design of fire-unprotected structures are outlined.     

基于连接单元法的半刚性钢框架计算

采用连接单元法,考虑连接柔性的影响,推导出半刚性框架梁柱的刚度矩阵及半刚性梁的固端弯矩.经试算,该方法可用于半刚性框架内力分析.     

翼缘削弱型节点空间钢框架在低周反复荷载

为研究翼缘削弱型节点空间钢框架在低周反复荷载作用下的抗震性能,采用有限元分析软件ABAQUS对普通节点和翼缘削弱型节点的空间钢框架模型进行有限元模拟,对2种钢框架模型的破坏形式、承载力、滞回性能、耗能能力、强度及刚度退化性能等进行了对比分析。结果表明:翼缘削弱型节点可使梁端塑性铰外移至梁端翼缘削弱处,避免梁端焊缝处应力集中导致脆性破坏;翼缘削弱型节点等效粘滞阻尼系数与普通节点空间钢框架相比有明显的提高,进入屈服阶段后由于应力重分布,其刚度及承载力退化速度较普通节点空间钢框架慢,翼缘削弱型节点钢框架具有梁铰延性破坏机制,抗震性能较好。     

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。     

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,     

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.     

Application of linear structural analysis program for steel frame ultimate limit state analysis

This paper describes the feasibility of applying a modified linear structure analysis computer program in the ultimate limit state design of unbraced steel frames. The elastic–plastic hinge zone concept and the linear elastic structural analysis computer program SAP90, are used to simplify the nonlinear steel frame structural analysis model. Most steel structures are designed by plastic theory, called ‘ultimate limit state design’. In practice, most steel structure analysis is performed by linear elastic computer programs that do not take into account either inelastic behavior or calculation of the ultimate strength. Herein, a modified analysis approach is presented and its design implications discussed. The results obtained from the modified approach are provided and compared with both experimental data and the inelastic structural analysis computer program DRAIN‐2DX with respect to the ultimate strengths and the lateral displacements of unbraced steel frames. Copyright © 1999 John Wiley & Sons, Ltd.     

无支撑半刚性连接钢框架的简化分析

用变刚度的螺旋弹簧模拟梁柱节点半刚性连接的弯曲特性 ,建立了半刚性连接钢框架梁单元的刚度矩阵。通过分别引入横梁修正线刚度和修正转动刚度 ,将等效代替框架法和无剪力分配法推广应用于无支撑半刚性连接钢框架的结构分析 ,其计算十分简便     

空间钢框架结构的改进塑性区模型

为探讨三维结构的高等分析方法 ,给出了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所建立的严格三维梁柱单元切线刚度方程 ,并提出了基于三维单元改进塑性区模型的双重非线性刚度方程。在方程中考虑了轴向位移、弯曲位移和扭转位移的耦合效应 ,使用包括几何与材料双重非线性的数值算例来验证本文方法和计算机程序的可行性、有效性与精确度。利用该程序 ,每个构件只需一个单元即可准确预测三维结构的极限承载力与失稳模态 ,可提高结构非线性空间性能的分析效率。     

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.     

钢结构的弹塑性大位移研究分析

为了探讨钢结构的高等分析和设计方法，本文作者应用泛函的最小势能原理，将经典的梁柱理论与非线性有限元法相结合，提出一种钢结构弹塑性大位移研究分析的简化单元模式和计算方法。它考虑了结构大位移、轴力的P-Delta效应、残余应力、轴力使杆件截面极限弯矩的变化、截面刚度退化和塑性区长度等非线性因素的综合影响。通过一个典型钢框架的非线性全过程分析，说明了该法的实际应用。算例表明，本文方法是可靠的，可供工程设计人员参考。     

Practical second-order inelastic analysis for three-dimensional steel frames subjected to distributed load

A practical second-order inelastic analysis of three-dimensional steel frames subjected to distributed load is developed. This analysis realistically assesses both strength and behavior of a structural system and its component members in a direct manner. To capture second-order effects associated with P−δ and P−Δ, stability functions are used to minimize modeling and solution time. The Column Research Council (CRC) tangent modulus concept is used to account for gradual yielding due to residual stresses. A softening plastic hinge model is used to represent the degradation from elastic to zero stiffness associated with development of a hinge. In proposed analysis, a member has two elements and three nodal points. A plastic hinge location can be captured in analysis as the internal nodal point traces the maximum moment location at each load step. Maximum moments and load–displacements predicted by the proposed analysis compare well with those given by other approaches.     

考虑节点域变形效应的空间支撑钢框架结构二阶弹塑性分析

详细推导了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所建立的严格三维梁柱单元虚功增量方程和切线刚度方程, 该方程包含了轴向、剪切、双向弯曲与扭转及其各耦合效应。提出的三维单元简化塑性区模型可模拟塑性扩展。建立了考虑支撑效应的节点域剪切变形模型, 该模型可更真实地反映节点域的变形影响。使用包括几何、材料非线性和节点域变形影响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: 利用该程序, 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。该程序可用于三维结构的非线性全过程分析, 为建立高层钢结构的高等分析方法奠定了基础。     

New method of inelastic buckling analysis for steel frames

In general, the concept of bifurcation stability cannot be used to evaluate the critical load of typical steel frames that have geometric imperfections and primary bending moment due to transverse loads. These cases require a plastic zone or plastic hinge analysis based on the concept of limit-load stability instead. However, such analyses require large computation times and complicated theories that are unsuitable for practical designs. The present paper proposes a new method of inelastic buckling analysis in order to determine the critical load of steel frames. This inelastic analysis is based on the concept of modified bifurcation stability using a tangent modulus approach and the column strength curve. Criteria for an iterative eigenvalue analysis are proposed in order to consider the primary bending moment as well as the axial force by using the interaction equation for beam-column members. The validity and applicability of the proposed inelastic buckling analysis were evaluated alongside elastic buckling analysis and refined plastic hinge analysis. Simple columns with geometric imperfections and a four-story plane frame were analyzed as benchmark problems. The results show that the proposed inelastic buckling analysis suitably evaluates the critical load and failure modes of steel frames, and can be a good alternative for the evaluation of critical load in the design of steel frames.     

半刚性钢框架优化设计研究

推导了考虑连接柔性和几何非线性的局部坐标下的单元刚度矩阵,并对半刚性连接单元的固端力进行了修正;其次,采用增量加载法,给出了考虑连接柔性、框架的几何非线性和单元内力与连接之间耦合效应的半刚性钢框架结构分析计算机流程;按照GB50017-2003《钢结构设计规范》和实际施工的要求,建立了考虑构件和连接最小费用问题的半刚性钢框架优化数学模型;然后,在遗传算法和半刚性钢框架结构分析流程的基础上,给出了半刚性钢框架优化设计步骤;根据算例,对半刚性钢框架优化设计做了初步的探讨。     

柔性连接钢框架稳定分析的计算长度

根据钢框架柱稳定设计的计算长度概念,以部分框架为计算单元,用变刚度的螺旋弹簧模拟梁柱节点连接的柔性,通过引入柔性连接刚度修正系数,建立了无侧移和有侧移柔性连接钢框架柱计算长度系数修正公式,其形式与我国钢结构设计规范(GB17—88)规定的计算长度稳定方程完全相同,可供工程设计人员使用.     

Implications of using refined plastic hinge analysis for load and resistance factor design

A plastic hinge analysis based on a two-surface stiffness degradation model is outlined for second-order inelastic analysis of steel structures. The analysis approach is based on refinements to the elastic-plastic hinge method and allows for a smooth transition from initial yielding to the full yielding of cross-sections in a beam-column element. This analysis method shows a good representation of the inelastic structural response compared to the conventional elastic-plastic hinge analysis, and it is efficient for use in the analysis design of large-scale structures. Design implications, recommendations and case studies for use of refined plastic hinge analysis for direct frame design considering semirigid connection effects are presented.