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。     

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.     

Analytical formulation of the elastic-plastic behaviour of bi-symmetrical steel shapes

This paper presents the analytical relationships of a non-linear model for the in-plane elastic-plastic analysis of bi-symmetrical steel shapes bent about one of their main axes. The basic variables are the cross-section global deformations, from which it is possible to evaluate the internal loads and the cross-section stiffness matrix components by means of simple expressions. Furthermore, the values of stresses and strains at any point of the cross-section may be determined, knowing the values of the internal loads, in the elastic and elastic-plastic domains. The effects of progressive yielding spreading, as well as those of material strain-hardening, are taken into account in the evaluation of the cross-section resistance capacity in the elastic-plastic domain. This analytical model represents an efficient, simple and accurate alternative to the elastic-plastic models based on numerical methods.     

Elastic-plastic analysis of internally pressurized torispherical shells

The constitutive equation for an elastic-plastic material model was derived using the von Mises yield criterion and assuming isotropic strain hardening. A layered finite element permitting geometrically linear and geometrically nonlinear elastic-plastic analysis of thin shell structures is presented. The effect of linear strain hardening on the size of plastic regions and the distribution of internal forces in an internally pressurized torispherical shell was analyzed. At sufficiently high pressures a significant difference in the distribution of internal forces was observed between elastic, perfectly plastic and strain hardening material. The effect of the size of plastic regions on the difference in the magnitude of internal forces obtained by geometrically linear and geometrically nonlinear computations of the torispherical shell was studied. An increase in the size of the plastic region was found to produce greater differences in the computation of meridional bending moments than in the computation of hoop stress resultants.     

体外预应力混凝土连续梁弯曲性能试验研究

为了研究体外预应力混凝土连续梁的弯曲性能、极限受力状态及内力重分布规律,以施工方法和体内外预应力筋配比为参数,对1根整体式(体内外配筋)和2根节段式(体内外配筋和全体外配筋)体外预应力混凝土连续梁进行了模型试验。通过试验数据分析,得到了模型梁挠度、混凝土应变、体外预应力筋应力与有效高度随荷载变化规律,以及混凝土裂缝发展与分布情况。结果表明:整体式梁的混凝土极限压应变和挠度最大、延性较好但体外预应力筋有效高度减少最大,节段式体内外预应力梁的体外预应力筋极限应力最大,节段式全体外预应力梁的混凝土极限压应变和挠度最小、延性较差、体外预应力筋极限应力及有效高度减少也最小。节段式梁的裂缝主要集中在接缝位置、无斜裂缝,接缝位置的塑性变形使内力重分布更充分。整体式梁内力重分布的区域集中而节段式全体外预应力梁的范围较大,各梁控制截面弯矩增、减幅值不超过10%。     

Ermittlung der Grenztragfähigkeit von Mehrschraubenverbindungen bei Normalkraft‐Biegemoment‐Interaktion

Determination of the ultimate bearing capacity of multi‐bolt connections with normal force – bending moment – interaction. This paper will present a general design method for single or multi‐bolt connections of beams with arbitrary thin‐walled cross sections, suitable for application in computer programs. The design method is based on the classical strain iteration algorithm for the determination of the stress distribution in cross sections. In this case, the ultimate capacity of bolted connections will be obtained using an iterative numerical determination of the elastic‐plastic stress distribution in the connection elements. The numerical method will be derived in two steps – the first step is the numerical determination of the stress distribution in the connection for a given combination of internal forces and the next step is the determination of the ultimate bearing capacity of the connection. Furthermore, an analytical design method for a multi‐bolt tube connection will be derived. Finally, results of numerical and analytical calculations will be compared with corresponding test results.     

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。     

A 3D numerical model for reinforced and prestressed concrete elements subjected to combined axial, bending, shear and torsion loading

This paper presents a model for the analysis of reinforced and prestressed concrete frame elements under combined loading conditions, including axial force, biaxial bending, torsion and biaxial shear force. The proposed model is based on the simple kinematic assumptions of the Timoshenko beam theory and holds for curved three dimensional frame elements with arbitrary cross-section geometry. The control sections of the frame element are subdivided into regions with 1D, 2D and 3D material response. The constitutive material model for reinforced and prestressed concrete follows the basic assumptions of the Modified Compression Field Theory with a tangent-stiffness formulation. The validity of the model is established by comparing its results with several well-known tests from the literature. These simulations include a variety of load combinations under bending, shear and torsion. The analytical results show excellent agreement with experimental data regarding the ultimate strength of the specimen and the local strain response from initiation of cracking to ultimate load.     

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.     

Some specific aspects of elastic-plastic behaviour of profiled steel sheeting and decking

The non-linear behaviour of continuous sheeting and decking is greatly influenced by the complexity of the moment-rotation relationship in the region over the internal support. The rotation of the hinge created in this region modifies the deflexion and also causes the redistribution of moments and forces. Eurocode 3, Part 1.3, allows the use of plastic deformation in a global analysis for ultimate states, provided that the relationship between the support moment and the corresponding hinge rotation is obtained by testing. The ultimate limit state is defined as that which is created when plastic hinges occur at the support and also in the span. However, in order to ease the difficulties in calculation, some simplifying assumptions are adopted. The aim of this paper is to examine if these assumptions ensure sufficient accuracy in different practical conditions, and, in conclusion, to propose improvements to the assumptions.     

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。     

钢管塔塔柱与腹杆插板连接点的弹性受力分析

本文根据薄壁圆柱壳的有矩理论推导了塔柱在节点板造成的横向弯矩作用下的内力和变形公式 ,计算并比较了 4种截面的塔柱在轴力和附加横向弯矩共同作用下的内力 ,同时 ,讨论了该横向弯矩造成的局部应力对塔柱的影响 ,并比较了不同节点板尺寸和塔柱中最大复合应力的关系。     

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.     

The internal force relationship of rectangular and I-section for bi-linear hardening material with limit strain

Based on bilinear stress-strain constitutive law σ = f (ε), the elastic to fully plastic analysis of bending of rectangular-section and bi-symmetrical I-section beams with the influence of axial load is presented for hardening material with limit strain. The variation of the applied bending moment with the axial force for the fully elastic, elastic-plastic, and fully plastic conditions is given in analytical form. The Internal force relationship of the elastic limit is the same for both hardening and non-hardening material and independent of the geometry of the beam section. However, for the elastic-plastic and plastic limits, the relationships are dependent of the hardening parameter β _q, limit strain ε _lim and the geometry of the beam section for neutral axis (N.A) inside the cross section. When N.A outside the cross section, the relationships are dependent of hardening parameter β _q and limit strain ε _lim but independent of the geometry of the beam section. The results given by the analytical expressions reduce to the ones for non-hardening material are in good agreement with the existing results.     

高温下钢筋混凝土框架的内力重分布研究

通过钢筋混凝土框架的火灾全过程分析,初步探讨高温下钢筋混凝土框架的内力重分布规律。推导建立了高温下钢筋混凝土的简化梁单元模型,编制了钢筋混凝土框架高温反应的全过程分析程序,程序的正确性得到了其他学者试验结果的验证。选取1榀单层3跨的钢筋混凝土框架,针对不同梁柱线刚度比和不同柱子轴压比的情况分别进行了该框架的高温反应分析,考察了部分控制截面的内力重分布规律。研究结果表明,高温下框架结构产生剧烈的内力重分布,其中框架梁的轴力和梁端弯矩变化尤为剧烈,成为影响框架结构其他控制截面内力变化的主要因素之一;随着梁柱线刚度比和柱子轴压比增大,框架梁的轴向压力逐渐加大。在结构层次上开展钢筋混凝土框架的耐火研究,可更为全面科学地把握不同构件的最不利受力状况。     

交错桁架结构体系的空间二阶弹塑性全过程分析

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。该方法在刚度方程的构造中考虑了单元轴力、剪力、弯矩、扭矩以及结构剪切变形的影响,并在塑性铰处考虑了内力之间的相互影响。算例分析表明本文方法具有良好的计算精度。     

基于能量原理的压力型锚杆数值模拟计算

根据能量原理,推导了压力型锚杆的轴力与位移计算式。其中锚固体与周围土层的黏结力计算采用弹塑性剪切位移模型,并考虑因位移过大而发生土层卸荷的情况。提出了最小势能原理在压力型锚杆问题中的应用方法,并给出了能量方程的程序求解流程。最后通过算例分析了压力型锚杆在各级荷载下的轴力、位移以及剪应力分布情况,进一步讨论了压力型锚杆的荷载–位移曲线,计算了压力型锚杆极限锚固长度。得出的结论：①压力型锚杆在大部分荷载下都处于弹性工作阶段,一旦进入塑性状态,就表明即将达到承载力极限;②考虑土层卸荷情况的锚固体能量传递理论可以解释压力型锚杆极限锚固长度的存在。     

钢筋增强超高韧性水泥基复合材料约束梁耐火性能试验研究

对3个钢筋混凝土（RC）约束梁试件和3个钢筋增强超高韧性水泥基复合材料（RECC）约束梁试件进行了升降温全过程耐火性能试验，研究了升降温全过程中梁端约束、受火时间等参数对梁试件高温下变形和内力的影响，比较了RECC约束梁和RC约束梁高温下的温度场分布、变形和内力。研究结果表明：RECC约束梁的截面测点温度低于RC约束梁，在相同的条件下，RECC约束梁的跨中挠度和梁端弯矩均小于RC约束梁；升温时间为60min的RECC约束梁轴向变形峰值比RC约束梁低25%，RECC约束梁轴力比RC约束梁低18%，升温时间为120min的RECC约束梁和RC约束梁轴向变形和轴力峰值比较接近；梁试件的反弯点位置在整个升降温过程中不断变化，在降温到某一时刻反弯点会基本消失。     

考虑P-⊿效应的筒体结构弯-扭分析

本文提出了一个筒体结构在任意荷载作用下的弯-扭分析方法。视P-⊿效应为虚拟节点荷载,同时考虑弯曲、剪切、轴向拉压三种变形,导出结构各个部分之间的相互联系,逐层传递求出结构的变形和内力。