Analytical Method for thin-walled members in general bending and torsion

The classical theory of thin-walled members has been applied extensively in practice. Since the theory was based on the assumption of no shear deformation, it is unable to reflect some of the important phenomena such as shear lag in structures.In mixed variational principles, both stresses and displacements are taken as variables, and they create equal possibilities to yield good results both in stresses and in displacement. Based on a mixed variational principle and introducing the co-ordinate functions in the cross-section, a mixed variational method has been presented.¹ Following this method, the method of solution for thin-walled members of open cross-sections in general bending and torsion is derived in this paper. This method is more general than the classical one and can be applied to members with rows of openings. It can also be applied to problems involving tension, bending and torsion actions, and simple analytical solutions in closed form can be obtained. Both warping and shear lag phenomena can be dealt with.     

Non-uniform torsion of stiffened open thin-walled members of steel structures

A general solution is derived, from distributional differential equations of equilibrium, for thin-walled structural members that are non-uniformly torsioned continuous, or situated in a Winkler rotational-elastic medium, with constant open cross-sections, stiffened with transversal ribs along their length. The equations were solved for a general case by means of the Laplace transform. Solutions were obtained in the form of closed generalized functions, holding good — for both non-uniform torsion displacements and internal forces and their influence lines — along the entire length of the bars. The effect of ribbing (diaphragms and closed ribs) on constrained torsion displacements and internal forces and on the respective influence lines is assessed for single-span and continuous I-section structural members.The results of non-uniform torsion tests carried out on I-bars stiffened along their length with battens or closed ribs (Fig. 12), in order to verify the theoretical models of the stiffened members (particularly with battens), are discussed. The test results confirmed the poor effectiveness of stiffeners in the form of battens directly joining the flanges of I-section members (Fig. 12(a)), due to the deformation of the flanges. The deformation can easily be eliminated by modifying the battens so that they join the flanges to the web (Fig. 12(b)). Tests showed that, by using the modified battens, one can effectively stiffen open thin-walled members. The effectiveness of the stiffening that is obtained is similar to that of stiffeners in the form of closed ribs.     

预应力混凝土双向受弯构件的优化设计

本文以新规范为依据,把受拉区与受压区张拉控制应力作为两个设计变量．以构件的造价最小为目标函数,考虑了九个约束条件,编制了优化程序,采用了Powell法对预应力混凝土双向受弯构件进行了优化设计,并给出了比较实例。     

Plastic mechanisms database for thin-walled cold-formed steel members in compression and bending

Short members of thin-walled cold-formed (TWCF) steel sections, in compression and bending, fail by forming local plastic mechanisms. Taking into account the localised buckling pattern, the collapse of slender members, due to the interaction between local and overall buckling modes, is always characterised by local plastic mechanism failure mode. Based on these two observations, the ultimate strength in interactive buckling of these members can be regarded as an interaction between localised plastic mode and overall elastic one.The yield line mechanism method has been widely used to predict the sectional strength (e.g. local) of thin-walled cold-formed steel members that involve failure mode characterized by local collapse mechanisms. This method can be also used to study post-collapse behaviour and to evaluate the load-carrying capacity, ductility and energy absorption.This paper is based on previous studies and some latest investigations of authors, as well as the literature collected data. It represents an attempt to make an inventory, classify and range geometrical and analytical models for the local-plastic mechanisms aiming to characterize the ultimate capacity of some of the most used cold-formed steel sections in structural applications.     

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。     

SRC弯扭构件的非线性有限元分析

以6根实腹式型钢混凝土梁弯扭试验研究为基础,利用有限元软件ABAQUS进行数值模拟分析。数值模拟得到的扭矩-扭率曲线以及极限扭矩与试验结果吻合良好,验证了所建模型分析型钢混凝土梁弯扭全过程数值模拟方法的可行性,进而探讨了不同因素对构件极限扭矩的影响规律。结果表明,试件极限扭矩随着弯扭比的增大而减小,随着配箍率、配钢率的增大而提高。     

A more accurate evaluation of buckling loads of thin-walled members in torsion and torsion-bending

The objective of this paper is to present a more accurate evaluation of torsional and torsional-flexural buckling loads of thin-walled members. Numerical examples, which exhibit the accuracy of the formulae obtained in the buckling analysis of thin-walled members, are given.     

Coupled instability of thin-walled members under combined bending moment, axial and shear force

In this paper we analyse the behaviour of thin-walled steel members with an I-shaped cross-section, in the presence of phenomena of coupled instability as overall-local type and combined state of stress of bending moment, axial and shear force. The analysis has been made by the ‘column model method’ and it has been used for bending moment-curvature-axial force diagrams, modified by the presence of local instability for web buckling of steel beams.

The previous analysis allows one to define interaction diagrams M_Imax−λ−N, which can be used to check the steel members in relation to the overall slenderness and the local slenderness of the web panel.     

A non-linear theory for the behaviour of thin-walled sections subject to combined bending and torsion

Thin-walled steel sections are extensively used in modern building either as purlins or as sheeting rails. Comparatively little is known about the effects of position and orientation with respect to the shear centre of the loading on the stability of such sections. The governing differential equations for the non-linear elastic behaviour of thin-walled sections subject to combined bending and torsion are developed in the paper. They include the non-linear contribution resulting from the movement of the point of application of the load. This is shown to have a significant influence on the behaviour of the member when the loads are inclined to the principal axes, as in the case of an asymmetrical section subject to gravity loading. Furthermore, it is shown that load resultants which pass through the shear centre but which are inclined to the principal axes of the section do not produce pure bending. They induce torsional moments in the section which are not accounted for in traditional theories. A finite-difference method is used to solve the equations, and the validity of the theory is assessed by comparing the results with those obtained from experiment.     

腹板开孔冷弯薄壁C型钢纯弯构件直接强度法研究

直接强度法(DSM)是冷弯薄壁型钢稳定设计的主要方法,这种方法对腹板未开孔构件设计可行性强,但是对于腹板开孔构件的适用性还不得而知。选取一定参数的纯弯开孔构件进行了有限元分析,分析表明:纯弯构件发生畸变屈曲的DSM公式在孔高比为0.2,0.4,0.6和0.8下均需要进行修正,并给出了修正公式。     

不同截面形式高强冷弯薄壁槽钢构件受弯承载力试验研究

对36个屈服强度为550 MPa的高强冷弯薄壁槽钢受弯试件进行静力试验研究,考虑了加劲形式和卷边形式对试件受弯性能的影响,其中加劲形式分为无加劲、翼缘中间V形加劲和翼缘及腹板中间V形加劲3种,卷边形式分为直卷边、斜卷边和复杂卷边3种。试验结果表明：加劲形式和卷边形式是影响试件受弯承载力和屈曲模式的重要因素;与无加劲形式相比,采用板件中间V形加劲有效减小了板件宽厚比,试件受弯承载力提高了30%~70%;同种加劲形式下,短（直、斜）卷边试件受弯承载力提高幅度最大,复杂卷边试件提高幅度次之,长（直、斜）卷边试件提高幅度最小;试验过程中试件发生了局部屈曲、畸变屈曲与局部和畸变相关屈曲。对试验进行了有限元模拟,模拟结果与试验结果吻合较好。     

Strength and stability criteria for thin-walled stainless steel circular hollow section members under bending

A series of tests consisting of various cross-section geometries were performed on structural stainless steel circular hollow sections (CHS) subjected to bending. The test program comprised a total of eight tests on CHS in two grades of stainless steel, namely 304 and Duplex 2205. For each grade four sections, each with a different slenderness, were tested, in order to cover a range of structural responses. Measurements of overall geometric imperfections and material properties were conducted. The test strengths are compared with the strengths predicted using the American, Australian and European specifications for cold-formed stainless steel structures. In the light of the test results and code recommendations, strength and cross-section classification criteria for stainless steel circular hollow section members in bending are examined.     

腹板开孔冷弯薄壁C型钢纯弯构件抗弯承载力研究

为了研究腹板开孔对冷弯薄壁C型钢抗弯承载力的影响,选取不同孔洞尺寸和不同孔洞数目的冷弯薄壁C型钢受弯构件进行了有限元分析,结果表明:当此类构件发生畸变屈曲失稳模式时,构件抗弯承载力随孔洞高度的增加呈现降低的趋势,但随孔洞数目的增加变化不大。     

钢筋混凝土U形薄壁梁弯-剪-扭复合受力性能试验研究

U形薄壁混凝土梁主要用于城市轨道交通工程,受弯-剪-扭复合作用。本文通过试验研究了一根大尺寸钢筋混凝土U形薄壁梁在弯-剪-扭复合作用下的力学性能,包括裂缝的发展与分布、钢筋应变分布以及破坏形态等。试验结果表明：弯-剪-扭复合作用下的U形薄壁混凝土梁呈现明显的空间受力特征,表现为裂缝和钢筋应变在两侧腹板上显著差异分布,同时,腹板内外侧斜裂缝以及箍筋应变的分布也存在明显差异;加载过程中纵筋应变在跨中和支座沿截面高度方向的分布基本符合平截面假定,纵筋应变沿梁跨近似线性分布;弯-剪-扭复合作用下钢筋混凝土U形薄壁梁出现了受弯矩和翘曲弯矩影响的延性弯曲破坏,且破坏仅发生在加载侧腹板,而非加载侧腹板处于相对低应力状态。     

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.     

General analysis of asymmetric thin-walled members

This paper presents the closed-form solution for the deflection and stresses of an asymmetric thin-walled member. The method is based on the assumption that the cross-section can deform out of plane when warping and shear-lag effects are significant. The out-of-plane deformation is represented by a linear warping function plus a truncated series of complete eigenfunctions. The differential equations are derived by using the principle of Minimum Potential Energy and solved by a symbolic manipulator. An example is used to illustrate the application of the method and the use of the closed-form solutions obtained. Results of the example are compared to the results of a finite element analysis and other approximate models. The comparison indicates that the maximum error of the proposed method is within 0·1% of the value obtained by the finite element method in lateral displacement and 0·2% in axial displacement.     

Elastic flexural-torsional buckling of thin-walled cantilevers

Previous studies by the authors revealed that the two representative theories with slight differences between, widely used in investigating the flexural-torsional buckling of thin-walled beams, have led to two different solutions in well-known literature for assessing critical loads of simply supported beams of monosymmetric cross section. With these two solutions, significant differences in critical loads may be found for these monosymmetric beams. Based on the classical variational principle for buckling analyses, a new theory on the flexural-torsional buckling of thin-walled members was proposed by the authors. In this paper, this new theory as well as the other two typical theories is employed to investigate the flexural-torsional buckling of cantilevers.This paper first gives a brief review and a careful comparative study on the flexural-torsional buckling of thin-walled cantilevers employing three different buckling theories. Differences between these theories are demonstrated with investigations on buckling of cantilevers under pure bending and two typical transverse loads. Explicit solutions, capable of considering variations of beam length and loading position along the vertical axis of cross section, are presented for predicting the critical loads of doubly symmetric cantilevers under two typical transverse loads. Advantages of presented solutions, such as good accuracy and ease of use, are exploited through the comparisons of critical results with those from existing solutions and finite element analyses.     

受扭构件非线性分析

以薄膜元模型为基础，考虑混凝土的“软化效应”，对钢筋混凝土受扭构件进行非线性分析，模拟构件受力的全过程，并对构件的承载力和变形进行了计算，理论分析结果与试验结果吻合较好。     

双向受弯型钢梁设计技巧

分析了现采用的双向受弯工字型钢梁设计方法的不足,通过研究双向受弯工字型钢梁的受力,提出了一种简单实用的设计双向受弯工字型钢梁的方法,以推广双向受弯型钢梁。     

Structural analysis of assemblages of thin-walled members

A matrix method for the analysis of structural systems composed of thin-walled members is presented. The matrix displacement analysis includes the effects of thin-walled non-uniform torsion theory, cross-section asymmetry, eccentric restraint as well as joint types peculiar to thin-walled members. The method is used for a prediction of the elastic behaviour of a set of representative test frames. The test frames were pitched-roof portals constructed from channel sections bent about their major-axis and supported by eccentric restraints simulating purlins and girts.