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。     

轴力与双向弯矩作用下方钢管焊接球节点的承载力与实用计算方法研究

国家游泳中心“水立方”结构中采用了连接方钢管、且承受轴力与弯矩共同作用的焊接空心球节点。文献[1]系统研究了方钢管焊接球节点在轴力与单向弯矩作用下的承载能力并建立了实用计算方法。本文进一步对轴力与双向弯矩作用下的这类节点进行深入研究。对轴力与双向等弯矩共同作用的节点,通过有限元分析、试验研究以及简化理论解三条途径,系统研究其受力性能,并提出节点承载力的实用计算方法。而对双向任意弯矩作用的情况,提出了对单向弯矩及双向等弯矩两种情况进行线性插值的简化计算方法。     

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.     

Plastic interaction relations for elliptical hollow sections

Interaction expressions are developed for steel elliptical hollow sections (EHS) subjected to combinations of axial force, biaxial bending moments and torsion. The formulation is based on the lower bound theorem of plasticity and the maximum distortional energy density yield criterion. The interaction expressions developed consist of a set of elliptical integrals which are cast in a dimensionless form and numerically evaluated to obtain a grid of internal force combinations lying on the yield surface sought. A series of trial functions are fitted to the grid of internal force combinations and a simplified and conservative interaction equation is selected. The interaction relation relates axial force, biaxial bending and twisting moment combinations for EHS sections of common geometries. Its applicability for conducting the cross-sectional interaction check in structural steel design problems is illustrated through a practical example.     

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.     

方钢管焊接空心球节点的承载力与实用计算方法研究

国家游泳中心“水立方”采用了一种新型的多面体空间刚架结构,杆件形式包括圆钢管、方钢管和矩形钢管,节点则主要采用焊接空心球节点。本文系统研究在轴力、弯矩及两者共同作用下方钢管焊接空心球节点的受力性能与承载能力。建立了采用理想弹塑性应力-应变关系、Mises屈服准则,同时考虑几何非线性的有限元分析模型,并对承受轴力、弯矩及两者共同作用的方钢管焊接球节点进行了大量的有限元参数分析。对轴力和弯矩共同作用的焊接球节点,其轴力-弯矩相关关系与节点的几何参数(包括空心球的球径、壁厚及钢管边长)无关。对若干典型节点进行了试验研究,直观了解节点的受力性能和破坏机理,并验证了有限元模型的正确性。还推导了基于冲切面剪应力破坏模型的节点承载力简化理论解,从而得到节点承载力计算公式的基本形式。最后,综合简化理论解、有限元分析和试验研究的结果,建立了轴力、弯矩及两者共同作用下方钢管焊接球节点承载力的实用计算公式,其中,对轴力和弯矩共同作     

考虑局部屈曲影响的H形钢构件在双向压弯作用下的滞回性能研究

由于地震作用是多维的,结构构件在地震作用下将会受到双向弯矩作用,而构件在一个主轴方向的屈服或屈曲会给构件在另一主轴方向的各项性能带来退化。针对H形截面钢构件,设计了一种由万向铰与三个跟动装置组成的三维加载系统,对11个不同宽厚比、轴压比和加载方向组配下的大宽厚比H形截面钢构件进行了双向压弯的滞回试验研究,考察了其破坏模态、滞回曲线及耗能能力等滞回性能。采用ABAQUS软件建立了有限元模型,采用试验结果进行了校核。最后基于试验和有限元分析结果,分析了扭转效应对试件的影响特性。研究结果表明,板件的局部屈曲和塑性变形的相关作用是影响试件滞回响应的重要因素,而影响效果主要取决于板材宽厚比、轴压比和加载方向的耦合作用;扭转效应对所设计的试件影响较小。     

矩形钢管焊接空心球节点承载能力的简化理论解与实用计算方法研究

国家游泳中心“水立方”的新型多面体空间刚架结构采用配合矩形钢管、且承受轴力与弯矩共同作用的焊接空心球节点,目前规范对该类节点的设计方法尚属空白。在有限元分析和试验研究的基础上,进一步研究轴力、弯矩及两者共同作用下矩形钢管焊接空心球节点的承载能力及设计方法。首先推导基于冲切面剪应力破坏模型的节点承载力简化理论解,从而得到节点承载力计算公式的基本形式。在此基础上,利用有限元分析和试验结果,建立了轴力、单向弯矩以及两者共同作用下节点承载力的实用计算公式。对双向任意弯矩作用的情况,提出了基于线性插值的简化计算方法。成果可供实际工程设计采用,也可供相关规程修订时参考。     

Plastic interaction relations for semi-elliptical hollow sections

General plastic interaction relationships are developed for semi-elliptical hollow structural sections subjected to general combinations of normal force, twisting moments and biaxial bending moments. The lower bound theorem of plasticity is employed to obtain the fully plastic resistance of the section in conjunction with the maximum distortional energy density criterion.     

椭圆中空截面的塑性交互作用

建立了计算轴压、双轴弯矩和扭转组合作用下的椭圆中空钢截面的交互作用公式。公式基于塑性下限定理和最大畸变能密度屈服准则而建立。交互作用公式中包括一系列无量纲的椭圆积分,并可以预测屈服曲面上的内力组合。为计算内力组合选用了一系列测试公式和简化的交互作用公式。交互作用包括普通尺寸EHS截面的轴力、双轴弯矩和扭矩的组合内力。最后采用实例验证了这个公式在计算钢结构横截面交互作用中的有效性。     

Behaviour and design of restrained steel column in fire, Part 3: Practical design method

This paper presents a practical design method for calculating the buckling and failure temperatures of restrained steel column under axial load or combined axial load and bending moment based on the results of extensive numerical parametric studies. Design equations for unrestrained columns in fire are adopted to calculate the buckling temperature of a restrained column by including the additional compression axial force due to restraint thermal elongation. The cross-section yield axial strength-plastic bending moment interaction curve is employed when calculating the failure temperature of restrained column. Results from the proposed method are compared with ABAQUS simulation for different cases. For the restrained column under axial load only, the buckling and failure temperatures calculated by the simplified method agree well with predictions by ABAQUS. For the restrained column under combined axial force and bending moment with realistic parameters, the buckling and failure temperatures predicted by the proposed method also agree well with ABAQUS predictions.     

半椭圆形中空截面的塑性交互关系

为半椭圆形中空建筑截面在普通的受力组合(力、扭矩和双轴弯曲)作用下提出了一个通用塑性交互关系。利用塑性下限理论和最大扭曲能量密度准则得出截面完全塑性抵抗能力。研究得到的计算关系是通用的,且为无量纲的,可用于极限状态设计。开发一个用于解决相互关系参数形式的迭代图表,并且归纳了一个许用应力组合表。提出符合表中内力组合的一系列测试函数和两个简化、保守的交互方程式。交互关系将轴力、双轴弯曲和扭转弯曲的组合与半椭圆形中空截面的几何特性联系起来。通过几个实际例子,验证了所提出的交互方程式的适用性。     

矩形钢管混凝土受弯构件材料本构关系与失效判据研究

为了正确评估矩形钢管混凝土(CFST)受弯构件的承载力,提出钢管和核心混凝土材料本构关系的修正模型,建立CFST受弯构件的承载力失效判据。首先,考虑受拉区钢管双轴受拉有利应力状态及受压区钢管双轴拉压不利应力状态,并基于矩形CFST轴压短柱试验数据库,通过回归分析建立约束混凝土峰值应力表达式,在此基础上建立矩形钢管混凝土材料本构关系的修正模型。其次,基于构件承载能力极限状态,并合理考虑受拉区钢管的应变强化段,提出矩形CFST受弯构件的承载力失效判据。最后依据纤维模型法和试验数据库对比分析CFST受弯构件的不同材料本构关系和失效判据的精度及适用性。结果表明,所建立的CFST构件材料本构关系和承载力失效判据能够更加准确地反映矩形CFST构件的抗弯能力,具有更高的计算精度和广泛的适用性。     

Investigation of FRP strengthened circular columns under biaxial bending

This paper presents the analysis and design of cylindrical reinforced concrete (RC) columns confined with fiber reinforced polymer (FRP) composites. The columns studied are under combined axial loads and biaxial bending moments. The fiber method modeling (FMM) together with finite element analysis (FEA) are adopted to investigate the behavior of such columns. The procedure finds the inclination and depth of the neutral axis that satisfy the equilibrium conditions. Moreover, the proposed analysis is capable of solving slender columns under biaxial bending through a developed computer program. The finite element derivation of a general stiffness matrix that accounts for the loss of symmetry of the cross-section due to material nonlinearity and biaxial moments is presented herein. The derivation starts from the principle of virtual work and develops an updated Lagrangian procedure for geometric nonlinear analysis. It should be noted that the stiffness for an elastic-plastic cross-section is a function of the current state and the past history of the strain of the column section as well as the stress-strain relations for each of concrete, steel and the fibers used. Therefore the cross-section is partitioned into a number of small elemental areas and a step-by-step application of the force-deformation equilibrium equation is applied. Interaction diagrams for columns under uniaxial bending are plotted and compared with experimental results conducted in the literature review. Moreover, contour lines for columns under biaxial bending are plotted. A parametric study was carried out to investigate the effect of various parameters on the strength of the column. The parameters include unconfined concrete strength, type of FRP used, thickness of FRP and the column height to the cross-sectional diameter (H/D) ratio. The developed diagrams provide the designer with an easy and reliable way to analyze and design such columns.     

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.     

A numerical method to design reinforced concrete sections subjected to axial forces and biaxial bending based on ultimate strain limits

A new iterative algorithm to design the steel reinforcement of concrete sections subjected to axial forces and biaxial bending is presented in this paper. The algorithm allows for the extrapolation of the ultimate strain limits, traditionally implemented in uniaxial bending theory, to biaxial bending cases. The new algorithm iterates a system of equations presenting high efficiency and becoming useful for any arbitrary-shaped cross section, including multicellular hollow sections. The new approach is compared with experimental results, obtaining good agreement.     

钢筋砼双向拉弯构件正截面承载力计算及研究

编制了钢筋砼双向拉弯构件的正截面承载力计算的计算机程序,可用于各类型截面的计算。并用此程序对矩形截面、等肢Ｌ形截面、Ｔ形截面和十形截面在双向拉弯作用下的Ｎ－Ｍ相关曲线、等轴力下的 Ｍｘ－ Ｍｙ相关曲线进行了分析研究。     

方形截面钢管混凝土双向压弯构件承载力理论分析和简化计算

在合理确定钢和混凝土应力－应变关系模型基础上,采用数值方法对方形截面钢管混凝土（以下简称方钢管混凝土）双向弯曲和双向压弯构件的荷载－变形全过程关系进行了分析,理论计算结果与试验结果吻合良好,并基于大量参数分析结果,提出该类构件承载力简化计算公式,可供工程设计参考．     

承受轴向、弯曲、剪切和扭曲组合荷载的钢筋混凝土和预应力混凝土的三维数值模型

提出了钢筋混凝土和预应力混凝土承受组合荷载下的分析模型，荷载包括轴力、双向弯矩、扭矩和双向剪力。所提出的模型基于Timoshenko梁理论的简单动力假设，保持了任意截面尺寸情况下的三维框架的形状。框架的控制截面被细分为一维，二维和三维材料响应。钢筋混凝土和预应力混凝土构建的材料模型遵循用切线刚度公式表示的改进压缩场理论的基本假设。     

Elastic, full plastic and lateral torsional buckling analysis of steel single-angle section beams subjected to biaxial bending

Flexural strength limits of steel single-angle section beams should be calculated based on the full plastic moment capacities, local buckling resistance and lateral torsional buckling capacities of the angle sections. The angle section beams are generally under the effect of external loads applied along the direction of geometrical axes parallel to their legs, so that they cause simultaneous biaxial bending about both principal axes. The behavior of angle sections under biaxial bending is complicated. The stress distribution of the critical points of the section cannot be easily determined since all specific points need to be checked. Furthermore, the design specifications require the consideration of the full plastic moment capacities of angle sections. This brings up the question of determining the required increase in first yield moment in order to attain full plastic moment capacities. Since single-angle section beams are thin walled slender structural members, they cannot be designed only according to their elastic and plastic moment capacities. Lateral torsional buckling and local buckling cases need to be considered in determining nominal design moments. In this study, the bending moment about the minor principal axis is assumed to be less than or equal to the moment about the major principal axis. Under that condition the first yield moment capacities, the interaction diagrams between first yield and full plastic moment capacities and critical lateral torsional buckling moments are calculated. These values are obtained by means of dimensionless coefficients, and design procedures have been given for the case of biaxial bending for single-angle section beams taking LRFD [LRFD Load and resistance factor design of single-angle members. Chicago (IL): American Institute of Steel Construction; 2000] rules into account.