普通荷载作用下的薄壁构件截面屈曲分析

分析了普通加载条件下薄壁构件截面的屈曲性能。使用半解析有限条法进行分析。结论主要适用于均布荷载作用下的截面,如均布压力、均布弯矩和均布荷载,都施加在截面的剪力中心。在普通荷载作用条件下,首先采用线性分析得到截面的纵向应力。刚度矩阵也采用标准的表达形式。每一个有限单元条带都分割成单元,并对这些单元上的纵向应力进行记载。每一个单元都是一个完整的个体,最后将其全部汇总,便可得到带状的几何矩阵。     

Inelastic local buckling of curved plates with or without thickness-tapered sections using finite strip method

This paper addresses the inelastic local buckling of the curved plates using finite strip method in which buckling modes and displacements of the curved plate are calculated using sinusoidal shape functions in the longitudinal direction and polynomial functions in the transverse direction. A virtual work formulation is employed to establish the stiffness and stability matrices of the curved plate whilst the governing equations are then solved using a matrix eigenvalue problem. The accuracy and efficiency of the proposed finite strip model is verified with finite element model using ABAQUS as well as the results reported elsewhere while a good agreement is achieved. In order to illustrate the proposed model, a comprehensive parametric study is performed on the steel and aluminium curved plates in which the effects of curvature, the length of the curved plate as well as circumferential boundary conditions on the critical buckling stress are investigated. The developed finite strip method is also used to determine the buckling loads of the curved plates with thickness-tapered sections as well as critical stresses of the aluminium cylindrical sectors that are subjected to uniform longitudinal stresses.     

Zur Ermittlung der Beton‐ und Stahlspannungen

On the Determination of Concrete and Steel Stresses The limitation of concrete and steel stresses is required in DIN 1045‐1 [1] as well as in EC 2 [2]. A general procedure of their determination is reported for reinforced concrete sections subjected to bending and longitudinal force. Finally tables for usual practical cases are presented.     

Buckling analysis of thin-walled sections under localised loading using the semi-analytical finite strip method

Thin-walled sections under localised loading may lead to web crippling of the sections. This paper develops the Semi-Analytical Finite Strip Method (SAFSM) for thin-walled sections subject to localised loading to investigate web crippling phenomena. The method is benchmarked against analytical solutions, Finite Element Method (FEM) solutions, as well as Spline Finite Strip Method (SFSM) solutions. The paper summarises the SAFSM theory then applies it to the buckling of plates, and channel sections under localised loading. Multiple series terms in the longitudinal direction are used to compute the pre-buckling stresses in the plates and sections, and to perform the buckling analyses using these stresses. Solution convergence with increasing numbers of series terms is provided in the paper. The more localised the loading and buckling mode, the more series terms are required for accurate solutions. The loading cases of Interior One Flange (IOF) and Interior Two Flange (ITF) are investigated in this paper using simply supported boundary conditions.     

Stress components in the foundation bed of a semi-infinitely long strip subjected to a uniform vertical loading

All six stress components in the foundation bed of a semi-infinitely long strip situated on the surface of an elastic half space and subjected to a uniform vertical load are found as a result of solution of the three-dimensional problem. The distribution of these stresses in the foundation at the end of the strip, and also a certain distance from its is investigated, and the expediency of their consideration demonstrated in solving certain design problems. Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 3, pp. 2–5, May–June, 1999.     

Elastic buckling analysis of ideal thin-walled structures under combined loading using a finite strip method

The details of an application of the finite strip method to the elastic buckling analysis of thin-walled structures with various boundary conditions and subjected to single or combined loadings of longitudinal compression, transverse compression, bending and shear are presented. The presence of shear loading is accounted for by modifying the displacement functions which are commonly used in cases when shear is absent. A program based on the finite strip method was used to obtain the elastic buckling stress, buckling plot and buckling mode of thin-walled structures and some of these results are presented.     

单箱双室箱梁对称弯曲时的局部扭转效应

为研究单箱双室箱梁在对称竖向荷载作用下的受力特征,基于横截面的荷载等效原理与荷载分解,分析了单箱双室箱梁对称弯曲时的局部扭转效应。基于截面的剪力流平衡和箱室受力分解,得到了局部扭转的等效荷载及应力计算式。通过与有机玻璃模型试验和有限元模拟结果的对比,验证了局部扭转效应计算式的正确性,并获得了单箱双室简支箱梁的局部扭转效应下的应力分布规律。研究表明,单箱双室箱梁在仅中腹板作用竖向荷载及两边腹板作用相等竖向荷载时,均存在纵向弯曲和局部扭转的组合变形模式。局部扭转由约束扭转、畸变和横向弯曲效应组成,在截面引起纵向应力和横向应力。局部扭转效应的理论计算结果与模型试验和板壳有限元分析结果吻合良好,表明基于截面剪力流等效的局部扭转荷载求解方法对双室箱梁是适用的;单箱双室箱梁的局部扭转效应在荷载作用点附近截面最为突出,截面上、下缘纵向应力和横向应力以中腹板为拐点呈折线分布,其应力分布和大小与荷载在横截面上作用的部位紧密关联;对算例箱梁,局部扭转效应产生的纵向应力可达初等梁弯曲应力的25%。     

钢-混凝土组合梁扭转的组合作用分析

在试验及理论分析的基础上,对开口截面钢-混凝土组合梁在扭转中的组合作用进行研究。组合梁在扭转中,即使是纯扭作用下,截面上仍存在组合作用,分析时不能忽略混凝土翼板和钢梁间的相互约束作用,否则会低估组合梁的抗扭能力。钢梁自身的抗扭作用很小,钢梁对组合梁扭转的贡献在于,它向混凝土翼板提供了纵向约束。在钢筋混凝土变角软化桁架模型(RA-STM)的基础上,通过引入平截面假定,以考虑组合梁扭转中的组合作用,建立适于分析开口截面钢-混凝土组合弯扭性能的三维桁架模型:在弯扭作用下,组合梁截面各单元分别处于一维应力状态(体系1)和二维应力状态(体系2),体系1用来抵抗由弯矩和扭矩引起的截面纵向应力,体系2用来抵抗由扭矩引起的截面剪应力,两者通过截面的纵向应变协调和内力平衡条件联系起来。所分析内容充分满足平衡条件、变形协调条件和材料本构方程。计算结果与试验结果吻合良好。此外还简要评价了现有的组合梁极限扭矩计算公式的不足。     

开口截面钢-混凝土组合梁弯扭性能非线性分析

在钢筋混凝土变角软化桁架模型的基础上,提出了适于分析开口截面钢-混凝土组合梁弯扭性能的三维桁架模型。在弯扭作用下,组合梁截面各单元分别处于一维应力状态(体系1)和二维应力状态(体系2),体系1用来抵抗由弯矩和扭矩引起的截面纵向应力,体系2用来抵抗由扭矩引起的截面剪应力,两者通过截面的纵向应变协调和内力平衡条件联系起来。分析充分满足平衡条件、变形协调条件和材料本构方程。通过对部分试件的计算验证,结果表明该模型不仅可以用于预测组合梁的极限强度,而且为混凝土翼板开裂后组合梁全过程分析,提供了有效途径。     

Theoretical elastoplastic buckling of stringer stiffened cylindrical shells

A linear analysis method is offered to predict the theoretical elastoplastic buckling of stringer stiffened cylindrical shells subjected to longitudinal loading. Welding residual stresses are taken into account in the calculation, but effects of geometrical imperfections and pre-buckling displacements are ignored.The examples analysed show a good correlation between the analytical results and those obtained experimentally with stocky models of moderate geometrical imperfections.     

A finite strip analysis of locally buckled plate structures subject to nonuniform compression

The post-local-buckling behaviour of thin plate structures is governed by the mode of loading which can be either one of prescribed load eccentricity or displacement pattern of end sections. A finite strip approach to the analysis of post-local-buckling behaviour under either mode of loading is presented. A particularly simple initial postbuckling analysis based on the perturbation technique is discussed in detail. Examples are presented to illustrate the convergence of the solution and contrast the behaviour of the structure under the two modes of loading. In particular it is demonstrated that a channel-section strut is stiffer and attains a higher collapse load under uniform end shortening that when loaded through the centroid of the cross-section.     

在应力梯度下边缘加劲板的试验和设计

薄钢板结构有3种典型类型:非加劲(无边缘加劲板),加劲(有充足边缘的加劲板)和部分加劲(有部分边缘加劲板)。当被用于冷弯薄壁型钢时,在承受均匀压力和应力梯度下,钢板可能发生弹性屈曲,有6种可能的荷载组合条件。除了应力梯度作用下的部分加劲构件,对所有类型的钢板都进行了试验研究并提出了设计公式。阐述了当部分加劲板的加劲单元尺寸从零到足够产生加劲作用时,在应力梯度作用下部分加劲板的试验情况。研究了单一加劲和复合加劲的边缘加劲类型。利用有效宽度概念,提出了部分加劲构件在应力梯度作用下的设计公式。在此基础上提出了适用于所有构件在任意荷载条件下的有效宽度公式。     

Experimental investigation on longitudinal residual stresses for cold-formed thick-walled square hollow sections

This paper presents the experimental study on cold-formed thick-walled square hollow sections with thickness greater than 6 mm. Square hollow sections are formed using two different forming processes of a “direct square” way and an “indirect way from circular to square”. Two test methods of the hole-drilling method and the X-ray diffraction method are used to measure the magnitudes and distributions of longitudinal residual stresses. The magnitudes and distributions of longitudinal residual stresses along the section perimeter as well as along the section thickness are obtained in this study. It is shown that the longitudinal residual stresses are in tension at outer surface and in compression at inner surface, and present nonlinear distributions, which seems like “sine” curve along the section thickness. Furthermore, the effects of forming process and cross-section geometry on the magnitudes and distributions of longitudinal residual stresses for cold-formed thick-walled square hollow sections are discussed. At last, two distribution patterns have been proposed for the square hollow sections formed using two different forming processes, respectively.     

厚壁矩形中空截面冷弯型钢纵向残余应力试验研究

对壁厚超过6mm的厚壁矩形中空截面冷弯型钢进行试验研究。矩形中空截面采用两种成型方法:直接法(直接形成矩形)和间接法(先形成圆形,再转换成矩形)。采用两种方法(钻孔法和X射线衍射法)计算纵向残余应力的大小和分布。研究了沿截面周长方向和厚度方向的纵向残余应力的大小和分布。结果显示,沿厚度方向的纵向残余应力在外表面为拉力,内表面为压力,表现出类似于正弦曲线的非线性特性。此外,讨论了厚壁矩形中空截面冷弯型钢的成型过程和截面几何尺寸对残余应力的大小和分布的影响。最后,针对厚壁矩形中空截面冷弯型钢两种不同成型过程,分别给出相应的残余应力分布情况。     

Buckling analysis of thin-walled cold-formed steel structural members using complex finite strip method

In this paper, a generalised complex finite strip method is proposed for buckling analysis of thin-walled cold-formed steel structures. The main advantage of this method over the ordinary finite strip method is that it can handle the shear effects due to the use of complex functions. In addition, distortional buckling as well as all other buckling modes of cold-formed steel sections like local and global modes can be investigated by the suggested complex finite strip method. A combination of general loading including bending, compression, shear and transverse compression forces is considered in the analytical model. For validation purposes, the results are compared with those obtained by the Generalized Beam Theory analysis. In order to illustrate the capabilities of complex finite strip method in modelling the buckling behavior of cold-formed steel structures, a number of case studies with different applications are presented. The studies are on both stiffened and unstiffened cold-formed steel members.     

爆炸作用下地下直墙拱结构动荷载分布规律试验研究

为研究集中装药爆炸条件下地下直墙拱结构被覆段的荷载分布规律,通过野外抗爆模型试验测试土中自由场应力以及拱结构表面各点荷载的应力时程曲线。采用数据拟合与归一化方法,得到拱结构横断面及纵断面的荷载峰值分布规律包络图,并将测试结果与理论方法、数值手段的研究结果进行对比验证。结果表明,地下拱结构承受的动荷载与理论方法、数值手段得到的基本规律一致,呈类三角形分布。根据荷载分布情况,结合荷载作用面积的等效原理,提出局部动载的简化计算公式,给出地下拱结构抗化爆的荷载计算步骤。     

Untersuchungen zur Längssteifigkeit von Stahlstützen mit kastenförmigem Querschnitt

Experimental tests and theoretical analyses of longitudinal stiffness of closed cross‐sections steel columns. In structures made of thin‐walled elements it is of great importance to establish how the compressed elements change their stiffness while loading increases. Nonuniform change of longitudinal stiffness induces change of force and stress redistribution. More ductile elements take less loading and more stiff, tensed, ones are being overloaded. Columns with closed cross‐sections, box cross‐sections and hollow circular cross‐sections need to be distinguished from steel elements with longitudinal stiffness decreasing while loading increases. Shortening of column working in elastic‐plastic phase comes from material compression, cross‐section walls buckling and increased displacement of column as a whole. Imperfections that depend on fabrication process of cross‐section have a great influence on stiffness variation of an element. It can be designated, among other factors, from the equilibrium paths of tested elements. Those equilibrium paths, up to the limit point, were obtained by applying incremental method of numerical integration of equilibrium equations assuming initial displacements and residual stresses of column's walls and initial displacements of column's axes. Some numerical analyses were calculated using FEA software LUSAS. All theoretical analyses were verified by experimental tests carried out by the authors with full scale elements: box cross‐section columns – length 5280 mm, cold‐formed welded cross‐section columns – length 2000 mm. The research results and analyses by others were also used.     

Shear buckling of thin-walled channel sections

The elastic buckling stresses of channel sections with and without lips and subject to shear forces parallel with the web are determined, where computational modelling of the thin-walled steel sections is implemented by means of a spline finite strip analysis. Both unlipped and lipped channels are studied, where the main variables are flange width, different boundary conditions and shear flow distribution. The channel sections are also analysed at different lengths, to investigate the effect of length/width ratio on the critical shear buckling stresses. Comparisons between cases and with classical solutions are included in this paper.     

广义位移的有限条法及其在高层建筑结构分析中的应用

本文提出了广义位移的有限条方法,用于分析物理特性沿高度突变的高层建筑构。该法消除了经典有限条方法分析此类结构的缺陷,即截面应力在刚度突变处不连续,致使靠近突变截面一定范围内的应力收敛到不正确的结果。本文对这种非均匀的高层建筑平面结构在T-300微型机上进行了实例分析,算例包括实体剪力墙、联肢墙、框剪结构。此法同样适用于分析均匀高层结构。     

筒中筒结构弯扭耦联简化分析

本文在文献[1]、[2]的基础上,讨论了筒中筒结构的弯扭耦联问题,得到了结构弯扭耦联问题的闭合解,并给出三种典型荷载下的位移、内力计算公式。文中提出的求解内外简之间相互作用力的方法,避免了复杂的解耦困难,有广泛的适用性,无论对于较精确的空间有限元法、有限条法或其他简化计算,只要符合楼板平面内刚度无穷大,出平面刚度忽略不计的基本假定,都是有效的。只要求出各自的柔度矩阵,按本法求得内外筒之间的相互作用力后,即可利用现有程序对内外筒分别进行计算。