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。     

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.     

An inelastic model for low cycle fatigue prediction in steel braces

This paper presents a nonlinear inelastic cyclic model to predict the effect of low cycle fatigue on the behavior of steel brace elements. This brace element is assumed as a beam-column element with pinned ends and a plastic hinge at mid-span. The kinematic hardening rule, based on the concept of a yielding surface in the theory of plasticity, together with the tangent modulus of elasticity, have been taken into account. Furthermore, a simplification of the linear cumulative damage theory is used to represent the low cycle fatigue deterioration of the brace element during the inelastic cyclic behavior. In the presented method, as an expansion of physical model theory, the governing yield function of the plastic behavior of the brace element is transformed mathematically by different factors. Then the yield surface which is defined in resultant stresses space, is changed and diminished by separately altering the axial load and bending moment terms of the yield function in each step of loading history to manifest low cycle fatigue deterioration. Comparison of the results of the proposed model with two existing experimental results has shown that this model was capable of predicting the low cycle fatigue of brace elements, and in one example, the rupture point of the brace element was predicted well by the model. It is advised that the model should be further expanded to more precisely include the effect of local buckling and distortion of brace elements with different cross-sectional geometries at the plastic hinge.     

轴力和双向弯曲下工字钢承载力

确定钢横断面抵抗力的塑性准则常基于一些基本假设,例如,取决于内力和截面形状相互作用的塑性铰的发展,因此,需要对每种截面形式提出相应的特定方程。该文提出新的相互作用准则分析轴力或双向弯曲下工字钢的弹性和塑性极限状态(不包括屈曲现象)。首先,针对一些特殊的内力组合(例如:单向弯矩-轴力组合和双向弯矩),给出相应的塑性相互作用准则。这二种情况都给出了精确的计算公式(包含采用该研究假设的框架),将所有塑性相互作用准则与EC3中相应的塑性准则进行比较。然后,提出适用于轴力和双向弯曲共同作用时的简化且总的准则。新的简化的塑性准则及EC3中采用的相应的塑性准则与精确的数值解相比较,结果显示,简易塑性准则的计算结果较为精确。对EC3提出改进建议。     

Resistance of steel I-sections under axial force and biaxial bending

The plastic criteria for the verification of steel cross-sections resistance are usually based on some basic hypotheses such as the development of plastic hinges, which depend on the interaction between the internal forces and the cross-section shape; therefore, specific equations are required for each type of cross-section.This paper presents new alternative interaction criteria for the analysis of steel I-sections subjected to an axial force and biaxial bending moments, at the elastic or the plastic limit states (as long as buckling phenomena are not involved).The plastic interaction criteria are presented, in a first step, for some particular combinations of the internal forces, such as axial loading with bending about a main axis, and biaxial bending without axial loading. In these cases, they are given by exact equations (within the frame of the hypotheses adopted in this study). All these plastic interaction criteria are compared with the corresponding plastic criteria adopted in the Eurocode 3 (EC3).Afterwards, a simplified global criterion is proposed for the simultaneous combination of an axial force and bending moments about both the main axes of inertia. This new simplified plastic criterion and the corresponding plastic criterion adopted in the EC3 are compared with the exact solution, obtained by a mixed numerical and analytical integration procedure. This comparison shows that this simplified criterion usually leads to results closer to the exact solutions. Some suggestions are then presented to improve the results given by the EC3.     

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.     

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.     

自复位方钢管混凝土框架-薄钢板剪力墙结构的水平边缘构件受力分析

基于薄钢板剪力墙在目标位移下充分屈服并形成拉力带,对绕梁腹板销轴转动的自复位方钢管混凝土框架-薄钢板剪力墙结构的水平边缘构件（中梁和顶梁）进行受力分析。分别对水平边缘构件在钢绞线预应力和薄钢板剪力墙拉力带作用下的受力进行分析,推导了钢绞线在目标位移下的拉伸预应力计算公式;基于薄钢板剪力墙极限破坏形态,研究了薄钢板剪力墙拉力带产生的水平边缘构件端部的轴力和剪力;提出了水平边缘构件的弯矩、剪力及轴力计算公式,明确了水平边缘构件的内力分布。结果表明:水平边缘构件内力公式计算值与有限元分析值吻合较好,可为水平边缘构件的设计提供参考。     

A computer method for nonlinear inelastic analysis of 3D semi-rigid steel frameworks

This paper presents an efficient computer method for inelastic and large deflection analysis of steel space frames with non-linear flexible joint connections, based on the most refined type of second order inelastic analysis, the plastic zone analysis. The method employs modeling of structures with only one element per member, which reduces the number of degree of freedom involved and the computational time. Gradual yielding of cross-sections is modeled using the nonlinear inelastic force strain relationships, and then using the flexibility approach the elasto-plastic tangent stiffness matrix and equivalent nodal loads vector of 3-D beam-column element is developed. The method ensures also that the plastic bending moment is nowhere exceeded once a full plastified section develops. A zero-length rotational spring element is used for incorporating the connection flexibility into the element tangent stiffness matrix and equivalent nodal forces. The combined effects of material, geometric and connection behaviour nonlinearity sources are simulated into an object oriented computer program automatically. This program was used to study the ultimate response of several steel frames, which have been studied previously by other researchers. The example of computations and the comparisons made have proved the robustness, accuracy and time saving of the proposed analysis method.     

Analysis of equal leg single-angle section beams subjected to biaxial bending and constant axial compressive force

Single-angle section beams are generally loaded parallel to their geometrical axes and their cross-sections are not symmetrical to their principal axes. Even equal leg angle beams have only one symmetrical axis. Many types of loading cause biaxial bending and axial forces in these members. Since single-angle section beams are slender members, they also need to be analyzed in terms of flexural buckling, lateral torsional buckling and local buckling effects. In this study, a calculation procedure is presented to analyze the nominal loads of equal leg angle section beams loaded vertically to the axis of the beam. It is assumed that the axial force is composed of a constant compressive force. The constant axial force is only taken into consideration for the uniform compressive stress and the second-degree effects caused in the cross-section. Thus only the biaxial bending moments remain. The first yield, full plastic and critical lateral torsional buckling moments for biaxial bending are calculated with respect to the slenderness of the beam and the axial force. The nominal design force on the cross-section is calculated according to the load and resistance factor design rules. The analysis proposed for the constant axial load can also be used for other axial forces, by using an iterative calculation procedure.     

Lateral–torsional buckling of cold-formed channel sections subject to combined compression and bending

This paper presents an analytical study of the flexural buckling and lateral–torsional buckling of cold-formed steel channel section beams subject to combined compression and bending about their major and minor axes. For channel section beams a bending about the minor axis creates a non-symmetric pre-buckling stress distribution, which has a significant influence on the lateral–torsional buckling of the beams. This kind of feature has not been discussed in the existing literature. The focus of this present study is the interaction between the compression load and the bending moments about the major and minor axes. It has been found that for a section subject to combined compression and the major-axis bending the bending moment will decrease the critical compression load, although the critical value of the largest compressive stress in the section actually increases with the applied bending moment. However, for a section subject to combined compression and the minor-axis bending the effect of the bending moment on the critical compression load depends on the direction of bending applied. For bending that creates a compressive stress in the lips the bending moment will reduce the critical compression load. However, for bending that creates a compressive stress in the web the bending moment has almost no influence on the critical compression load.     

钢管杆中刚性法兰的有限元分析

研究了钢管杆中刚性法兰的力学性能,应用ANSYS进行了非线性数值模拟,重点讨论了单元的选择、螺栓预紧力的模拟、弯矩的加载及接触分析中相关参数的设置问题。分析比较了法兰板厚度、主管厚度及肋板厚度对螺栓受力的影响。有限元分析结果表明刚性法兰节点中的螺栓在受力过程中明显弯曲。最后提出了计算螺栓轴力的新的旋转轴位置,可供实际工程应用参考。     

木结构钢板螺栓连接节点承载力计算分析及试验研究

为便于木结构工程设计,提出了钢板螺栓连接承载力计算式,并提出了受弯螺栓连接节点承载力上限和下限的计算方法。设计制作了钢填板螺栓连接节点试件,并进行了复合受力节点承载力试验研究。试验结果表明,各受力工况下试验节点的承载力平均值均介于所计算的承载力上、下限之间,且基本等于所计算的承载力上、下限的平均值。从而验证了所提出的钢板螺栓连接承载力计算式和连接节点承载力计算方法的正确性和适用性,为设计提供了可靠依据。     

Lateral buckling strengths of cold-formed Z-section beams

This paper is concerned with the inelastic lateral buckling strengths of cold-formed Z-section (CFZ) beams. The point symmetry of the cross-section of a CFZ beam introduces characteristics that are not encountered in a doubly symmetric I-beam. Firstly, the effective section rotates after yielding, so that a CFZ beam under in-plane bending about the geometrical major principal axis is subjected to bending moments about the effective minor axis and bimoments. Secondly, the minor axis bending and warping strain distributions and therefore the lateral inelastic buckling behaviour and strengths of CFZ beams are related to the twist rotation and minor axis displacement directions. The stress–strain curves, residual stresses, initial imperfections, and lipped flanges of CFZ beams are all different to those of hot-rolled I-beams. This paper develops a realistic finite element model for the analysis of CFZ beams and uses it to investigate the elastic lateral-distortional buckling, inelastic behaviour, and strengths of CFZ beams with residual stresses and initial imperfections. The results of the study are used to develop improved design rules which are suitable for CFZ beams. The effects of moment distribution and load height on the lateral buckling strengths are also studied.     

Inelastic behaviour and design of slender I-sections in minor axis bending

Slender steel sections in bending are generally designed by taking the maximum moment as the yield moment. The assumption for the ultimate condition is thus the point at which first yield is reached in the section. Certain types of slender sections, however, have shown significant post-elastic behaviour in attainment of the ultimate moment. Experiments on I-sections in minor axis bending have shown this to be the case, where significant plastic stress distributions are attained in the tension flanges after the compression flanges have locally buckled. Current international steel specifications are unduly conservative when estimating the bending strength of these sections as the yield moment. This paper quantifies this conservatism and presents inelastic design methods whereby the post-elastic strength may be captured. Design equations are proposed for Australian, American and European hot-rolled and cold-formed steel specifications.     

不等截面三肢格构式钢管混凝土柱的换算长细比计算

根据弹性稳定理论,同时考虑弯矩和剪力对结构临界荷载的影响,推导了不等截面三肢格构式钢管混凝土柱的换算长细比,并进行了适当的简化,可供工程设计人员参考。     

Tangent moduli of hot-rolled I-shaped axial members considering various residual stress distributions

This paper presents an equation for the effective tangent moduli for steel axial members of hot-rolled I-shaped section subjected to various residual stress distributions. Because of the existence of residual stresses, the cross section yields gradually even when the member is subjected to uniform axial stresses. In the elasto-plastic stage, the structural response can be easily traced using rational tangent modulus of the member. In this study, the equations for rational tangent moduli for hot-rolled I-shaped steel members in the elasto-plastic stage were derived based on the general principle of force-equilibrium. For practical purpose, the equations for the tangent modulus were presented for conventional patterns of the residual stress distribution of hot-rolled I-shaped steel members. Through a series of material nonlinear analyses for steel axial members modeled by shell elements, the derived equations were numerically verified, and the presented equations were compared with the CRC tangent modulus equation, the most frequently used equation so far. The comparative study shows that the presented equations are extremely effective for accurately analyzing elasto-plastic behavior of the axially loaded members in a simple manner without using complex shell element models.     

Behavior and resistance of beam-column structural elements

Most of the structural elements in a steel structure are subjected to bending moment and axial force simultaneously. In some elements, one of the two components is relatively small compared to the other. Yet, the smaller component cannot be ignored due to the interactive behavior of the two components. Therefore, it is not adequate to design the beam-column element as a beam or a column by ignoring one of the two load components even if the ignored component is relatively small.Most of the design codes use empirical interaction equations that are based on semi-experimental semi-analytical results. Most of the design formulae adopted by the design codes do not explicitly account for the geometrical imperfection.This research aims at investigating the buckling behavior of steel beam-column elements for the sake of developing an analytical model to calculate their ultimate resistance under axial compression and bending moment. The analytical model will be based on Perry-type formulation, and it will account for the effect of initial imperfection. The model will be validated by comparing its results with those obtained by the Finite Element Non-Linear Elasto-Plastic analysis using ANSYS 5.4 program.Finally, a simple but rational design method based on the model, will be introduced. This method can be applied using a simple mathematical expression or charts and tables. The results of the developed design method will be compared with the design method of the international codes of practice for design of steel structures. On light of these comparisons, design recommendations are introduced.     

截面轴力与弯矩屈服面在钢框架动力弹塑性分析中的应用

为了在现行规范下考虑轴力与弯矩的相互作用,并兼顾计算精度与计算效率,研究了截面屈服面在钢框架动力弹塑性分析中的新应用。首先选用截面组合思想构建轴力与弯矩的屈服面。接着,基于经典塑性理论建立截面恢复力模型,并给出了截面状态确定方法。然后阐述了基于力的梁柱单元状态确定过程及其对截面恢复力模型的调用。最后采用alpha-OS积分算法,对一个四层两跨钢框架开展了动力弹塑性分析。结果表明：截面轴力弯矩屈服面能很好地考虑轴力存在及变化对截面弯矩承载力的影响,基于屈服面的恢复力模型在计算精度上远高于塑性铰模型并逼近纤维模型,在效率上远高于纤维模型,可以用于钢框架的动力结构弹塑性分析。