Torsional buckling behaviour of stiffened cylinders under combined loading

In this study cylindrical boundary conditions for finite element analysis are formulated that allow torsional displacement and buckling of a sector of a cylinder of half axial height, and of a circumferential arc angle that will divide into 360°. Finite element tests are carried out on un-stiffened elastic cylinders to verify the method of analysis against classical elastic torsional buckling theory.Elastic–plastic limit point finite element tests are carried out on ring and stringer stiffened and stringer stiffened cylinders to investigate the effects of stiffeners on post-buckling behaviour in torsion.A stringer stiffened cylinder is subjected to many combinations of axial force and surface pressure in the elastic range of response and then tested to failure in torsion to investigate the effects of axial and surface pressure loads on the resistance to plastic collapse in torsion.     

Non-linear finite element analysis of axially restrained steel beams at elevated temperatures in a fire

A method is presented for the analysis of the non-linear structural behavior of axially restrained steel beams at elevated temperatures, which employs the axis arc-length and section rotation of the deformed beam as basic variables. The novelty of the proposed formulation is an inclusion of a balance function that measures the error of the equilibrium between the internal- and external-forces in a cross-section of the beam. This strategy can easily deal with the geometric non-linearity and elasto-plasticity of steel at elevated temperatures. Each node for representing the section of the beam has two degrees of freedom in the proposed method. It is more computationally economical than the traditional beam element, which has three degrees of freedom. An example beam is studied to verify the proposed method. Parameters including the load ratio, axial restraint stiffness ratio, transversal and longitudinal temperature gradient, are studied. The middle-span’s deflection, axial force and moment, along with the strain and stress distributions across the section, are calculated at elevated temperatures. The comparison with results from the finite element method employing shell elements shows that the method presented here is precise.     

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.     

Impact response of rectangular and square stiffened plates supported on two opposite edges

Experimental drop weight impact tests have been performed to examine the dynamic response of small-scale stiffened plates struck laterally by a mass with a spherical indenter. The laboratory results are compared with numerical simulations. The plates stiffened with a flat bar or L profile are supported at two opposite edges and impacted at different velocities and locations along the span. The impact scenarios could represent incidents in marine structures, such as load actions due to dropped objects on decks. The experiments are conducted using a fully instrumented impact testing machine. The obtained force–displacement responses show a good agreement with the simulations performed by the LS-DYNA finite element solver. The finite element model includes defining the experimental boundary conditions so as to simulate small axial displacements of the specimen at the supports. This representation can be used to analyze the structural crashworthiness of similar marine structures under collision scenarios. The strain hardening of the material is defined using experimental data of quasi-static tension tests and the strain rate sensitivity is evaluated using standard coefficients of the Cowper–Symonds constitutive model. The results show that the plastic response of the specimens is highly sensitive to the amount of restraint provided at the supports. Furthermore, it is found that in most of the specimens the contribution of the stiffeners to the impact response is insignificant, since the ends of the stiffener are free at the unsupported edges and the specimens experience small axial displacements at the supports.     

Behavior of axially-and-rotationally restrained concrete columns with ‘+’-shaped cross section and subjected to fire

Most of the previous investigations studied the structural behavior of concrete columns with ‘+’-shaped cross section at room temperature, but the behavior of such columns during a fire and the effect of boundary conditions on the mechanical properties of the heated columns have seldom been examined. In this paper, the influence of axial-and-rotational restraint on the behavior of heated concrete columns with ‘+’-shaped cross section is investigated. A self-developed finite element program RCSSCF is applied in this study. The development of column internal forces as well as deflections at the mid-height of concrete columns are discussed. Simulation results show that: (1) axial restraint can induce significant additional axial forces in concrete columns with ‘+’-shaped cross section and subjected to fire, and the additional axial forces in strongly restrained concrete columns during a fire can reach approximately 65–70% of the axial forces in columns at room temperature; (2) the fire resistance of concrete columns without rotational restraint decreases significantly with an increase of load eccentricity ratio, but that with rotational restraint is influenced lightly by load eccentricity ratio; and (3) for columns with different non-zero rotational restraint ratios, the internal axial forces, and the internal moments and deflections at the mid-height of these columns appear to follow common trends.     

Inelastic buckling and strengths of steel I-section arches with central torsional restraints

The elastic flexural–torsional buckling behaviour of arches with a central elastic torsional restraint has been reported elsewhere by the authors, and it was found that a central elastic torsional restraint restricts the buckling shape of an elastic arch and increases its elastic buckling resistance. However, both the inelastic buckling and strength of arches with a central elastic torsional restraint have hitherto not been investigated. It is not known whether the threshold stiffness for elastic buckling can be applied to arches which buckle inelastically, nor is it known how to determine the strength of steel arches with a central elastic torsional restraint. This paper modifies a finite element model for the nonlinear inelastic flexural–torsional analysis of steel I-section arches by including the effects of elastic restraints, and uses it to investigate the influence of central elastic torsional restraints on the inelastic flexural–torsional buckling and strength of steel I-section arches. It is found that a central elastic torsional restraint increases the strength of steel arches, but that the increase in strength decreases as the modified slenderness of the arches decreases. The threshold value of the stiffness of a central elastic torsional restraint at which the inelastic strength of an arch is equal to that of the corresponding arch with a rigid restraint is related to both the modified slenderness and included angle of the arch. For an arch with a low modified slenderness and with a small included angle which buckles inelastically, the threshold restraint stiffness is much smaller than that for an arch which buckles elastically. Design formulae for the strengths of steel I-section arches in uniform bending and in uniform compression with a central elastic torsional restraint are proposed. Comparisons with finite element results show that the proposed formulae provide good predictions for the strength of thin-walled steel I-section arches with a central elastic torsional restraint.     

压弯扭复合荷载作用下钢管约束钢筋混凝土柱的承载力及弯扭相关关系研究

以4个钢管约束钢筋混凝土柱(STRC)在弯扭和压弯扭复合荷载作用下的试验研究为基础,采用有限元软件ABAQUS建立了钢管约束钢筋混凝土柱的有限元模型,分别模拟试件在弯扭以及压弯扭复合荷载作用下的破坏模式和承载能力,与试验结果进行对比,验证了有限元模型的正确性。通过有限元模型参数化分析,研究钢管强度、钢管厚度、截面尺寸、混凝土强度、纵筋直径与屈服强度、箍筋直径与屈服强度以及轴力等因素对复合荷载作用下承载力的影响。研究结果表明,钢管厚度、截面尺寸、纵筋的直径与屈服强度以及轴压力是影响复合荷载作用下承载力的主要因素。当圆形截面STRC柱的轴压力达到0.3N_u(N_u为柱轴压承载力)或方形截面STRC柱的轴压力达到0.5N_u时,柱的承载力达到最大。在不同因素的影响下,相同荷载作用下钢管约束钢筋混凝土柱的受弯承载力和受扭承载力之间的相关关系基本一致。     

Coupled flexural–torsional dynamic stiffness matrix of an elastically supported axially loaded beam with shear resistant in‐fill

The dynamic stiffness matrix of an axially loaded elastically supported uniform beam with doubly asymmetric cross‐section that exhibits coupling between flexural and torsional motions is developed and subsequently used to investigate its free vibration characteristics. The beam comprises a thin‐walled outer section that encloses, and works compositely with, a core of shear resistant in‐fill material. The outer layer provides flexure, warping and Saint–Venant rigidity, while the inner layer provides both Saint–Venant and shear rigidity. A three‐parameter Winkler model is used to describe the distributed elastic support. Hamilton's principle is used to derive the partial differential equations governing the free vibration of the beam, together with the associated natural boundary conditions. This gives rise to three coupled equations that are subsequently combined into a single, 12th order, ordinary differential equation. Throughout the process, the uniform distribution of mass in the member is accounted for exactly and thus necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick–Williams algorithm, which enables the required natural frequencies to be converged upon to any required accuracy with the certain knowledge that none have been missed. Finally, in order to verify the accuracy of the presented theory, the numerical solutions are given and compared with the results that are available in the literature and finite element solutions using abaqus software. Copyright © 2014 John Wiley & Sons, Ltd.     

双向加劲钢板剪力墙在纯剪作用下的弹性稳定性研究

在前人研究基础上,通过施加多道具有抗扭刚度的竖向槽钢加劲肋,然后再加1道没有抗扭刚度的横向板条加劲肋,对双面双向加劲的钢板剪力墙进行大量有限元弹性屈曲分析,最后提出钢板剪力墙弹性屈曲临界剪切应力和加劲肋门槛刚度的计算公式。数值计算结果表明:公式具有良好的精度,并且偏安全;影响加劲肋门槛刚度的关键因素是钢板剪力墙小区格宽高比、竖肋数目以及横竖肋板厚比。     

钢筋混凝土双向偏心受压矩形截面直接设计方法

基于破坏曲面的等轴力相关曲线 ,提出了钢筋混凝土双向偏心受压矩形截面直接设计方法。有限元分析和数学回归表明等轴力相关曲线方程可靠 ,根据该方程 ,可把钢筋混凝土双向偏心受压矩形截面配筋设计转化为单向偏心受压矩形截面配筋设计。从算例中可看出 ,方法简单、实用、可靠 ,可供设计时参考。     

Coupled static and dynamic buckling of thin walled beam by spline finite element

For the coupled static and dynamic buckling of thin walled beam subjected to various forces, such as axial force, uniform bending moment, and bending moment due to concentrated and distributed lateral forces, the spline finite element method is employed to obtain the dynamic stiffness matrix. Second order effects of the axial force and moment are considered. A doubly symmetric cantilever beam with uniform cross-section is investigated. Extensive static and dynamic interaction diagrams are plotted. The effects of warping rigidity, torsional rigidity, axial tension and compression on moment buckling, moment on axial buckling compression, higher buckling modes are discussed in detail. The spline finite element method is proved to be very efficient for the present problem and many interaction diagrams can be plotted easily. Some new results are presented. The methodology is based on finite element formulation and therefore it can be easily extended to analyze structural frames.     

Experimental study on seismic behavior of concrete filled steel tube columns under pure torsion and compression–torsion cyclic load

Based on the quasi-static test on eight CFST columns subjected to pure torsion and compression–torsion cyclic load, the torsion behavior of CFST columns with various section types, steel ratios and axial load levels was studied. The test results showed that the hysteretic curves of CFST columns under pure torsion and low compression–torsion cyclic load are very plump, which indicate that CFST columns have good seismic capacity. The unloading stiffness of CFST columns was equal to the initial elastic stiffness. The torsion capacity of CFST columns could be improved by the low compressive load, and the ductility was also good. But the torsion capacity of CFST columns would be reduced by the high compressive load. When CFST columns subjected to pure torsion, spiral diagonal compressive struts will be created in the in-filled concrete, and the axial components of the diagonal compressive force of the in-filled concrete was equal to the axial tensile force of the steel tube in order to satisfy the axial load equilibrium condition on the section, so the axial strain will be produced in the steel tube. The shear strain has good linear relationship with the rotation angle of the section when CFST columns subjected to pure torsion and compression–torsion combined action. Based on the test results and literatures available, the torsion mechanism of CFST columns was preliminarily analyzed.     

再论弹性约束杆挠度影响系数及稳定性计算

弹性约束杆之临界力和变形不仅与杆截面特性相关，还取决于约束条件。本文结合起重机设计规范（GB3811-83），在文献已讨论的两端弹性约束杆基础上，再就一端自由另一端弹性约束的悬臂柱之临界力和找度影响系数进行分析。     

薄壁复合箱型梁的弯曲-扭转屈曲分析

对一轴心受压薄壁复合构件的屈曲进行研究。提出一个广义的分析模型,可用于分析轴心受压薄壁复合箱型梁的弯曲、扭转以及弯扭屈曲作用。此模型基于经典层压理论,考虑了任意层压堆积规律,结构的弯曲和扭转模式的耦合问题,如非对称以及对称和各种边界条件。采用一个基于位移的一维有限元模型来预测薄壁复合钢筋的临界荷载和随后的屈曲模式。从总势能的平稳值原则中推导出屈曲控制方程。轴心受压薄壁复合件的数值计算结果可用于估测纤维角、各向异性和边界条件对临界屈曲荷载和复合件模态的影响。     

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.     

Effect of Heating and Cooling on Axially Restrained RC Columns with Special-Shaped Cross Section

This paper describes the performance of 12 axially restrained RC columns (four for each type of cross section, i.e., +-, T- and L-shaped cross section) under fire conditions that were recently finished in South China University of Technology. The main objective of the paper is to investigate the effect of axial restraint on RC columns during both expanding and contracting phases. The RC columns were all initially concentrically loaded and subjected to ISO834 standard fire on all sides. Axial restraints were imposed at the top of the columns to simulate the restraining effect of the rest of the whole frame. Different degrees of axial restraint were obtained by varying the length of the restraining beam. The boundary conditions of the columns were considered as fixed–fixed for all tests. It is found that restrained RC columns behave quite differently to isolated ones. No typical ‘runaway’ failure of isolated RC columns was observed in the fire test. Finally, the finite element software, SAFIR, is employed to conduct a numerical analysis of the tests.     

双钢板-混凝土组合剪力墙压弯承载力数值模型及简化计算公式

基于双钢板-混凝土组合剪力墙构件材料的单轴本构关系,研发了分析组合剪力墙压弯性能的弹塑性数值模型,对构件的弯矩-曲率曲线以及压弯相关关系曲线进行分析,并对压弯承载力进行计算,该模型计算结果与有限元分析结果、试验结果吻合良好。基于该模型对组合剪力墙中部墙体承担弯矩比例进行统计,结果表明,组合剪力墙中部墙体在受弯过程中承担比例较大,设计中不可忽略。对组合剪力墙压弯承载力进行数值计算和参数分析,研究了极限状态下影响压弯承载力关键因素,并基于关键参数提出计算该类组合剪力墙极限状态压弯承载力的简化计算公式,将该简化公式计算结果与数值结果进行对比,并与文献中组合剪力墙试验进行对比验证,计算精度较高,该公式可用于双钢板-组合剪力墙压弯承载力设计。     

多弹性扭转支承开口薄壁杆的扭转屈曲

研究了截面形心和剪切中心重合的多弹性扭转支承开口薄壁杆在轴向压力作用下的扭转屈曲,把作用在开口薄壁杆上的弹性扭转支承去掉,代之以相应的未知扭矩,采用Laplace变换推导出了其扭转变形的位移函数,并求得了多弹性扭转支承开口薄壁杆在轴向压力作用下扭转的屈曲特征方程。     

Quadruply coupled linear free vibrations of thin-walled beams with a generic open section

The coupled vibration of thin-walled beams with a generic open section induced by the boundary conditions is investigated using the finite element method. If the axial displacement of the pin end is restrained at another point rather than the centroid of the asymmetric cross section, the axial vibration, two bending vibrations, and torsional vibration may be all coupled. The element developed here has two nodes with seven degrees of freedom per node. The shear center axis is chosen to be the reference axis and the element nodes are chosen to be located at the shear centers of the end cross sections of the beam element. Different sets of element nodal degrees of freedom corresponding to different pin ends are considered here. The relation between element matrices referred to different sets of element nodal degrees of freedom is derived.

Numerical examples are presented to demonstrate the accuracy of the proposed method and to investigate the effects of different pin ends on the coupled vibrations of the thin-wall beam.     

考虑柱底纵筋滑移的纤维模型及框架地震反应分析

基于材料本构关系的纤维模型能有效模拟柱在变轴力与双向弯矩耦合作用下的非线性反应,但常规的纤维模型分析方法忽略了纵筋滑移。在纤维模型基础上,采取在非线性梁柱单元端部附加零长度截面单元的方法以模拟杆端纵筋滑移的影响。以钢筋混凝土柱为例,将弯曲转角、滑移引起的固端转角等模拟结果分别与柱在低周反复荷载作用下的试验数据进行对比,校准了该模型化方法。考察了6层钢筋混凝土平面框架的非线性地震反应,研究了底层柱根纵筋滑移对框架整体和局部反应的影响。结果表明,模拟分析的纵筋滑移规律与柱的试验结果相符较好。底层柱根纵筋滑移有增大框架整体非线性地震反应的趋势,并将改变底层柱非线性变形的组成方式,减小其柱端塑性铰区的非线性弯曲变形。