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.     

Design of cold-formed steel channels with stiffened webs subjected to bending

The objectives of this study are to investigate the structural behaviour and evaluate the appropriateness of the current direct strength method on the design of cold-formed steel stiffened cross-sections subjected to bending. The stiffeners were employed to the web of plain channel and lipped channel sections to improve the flexural strength of cold-formed steel sections that are prone to local buckling and distortional buckling. An experimental investigation of simply supported beams with different stiffened channel sections has been conducted. The moment capacities and observed failure modes at ultimate loads were reported. A nonlinear finite element model was developed and verified against the test results in terms of strengths, failure modes and moment–curvature curves. The calibrated model was then adopted for an extensive parametric study to investigate the moment capacities and buckling modes of cold-formed steel beams with various geometries of stiffened sections. The strengths and failure modes of specimens obtained from experimental and numerical results were compared with design strengths predicted using the direct strength method specified in the North American Specification for cold-formed steel structures. The comparison shows that the design strengths predicted by the current direct strength method (DSM) are conservative for both local buckling and distortional buckling in this study. Hence, the DSM is modified to cover the new stiffened channel sections investigated in this study. A reliability analysis was also performed to assess the current and modified DSM.     

The computational post buckling analysis of fuselage stiffened panels loaded in compression

Fuselage panels are commonly fabricated as skin–stringer constructions, which are permitted to locally buckle under normal flight loads. The current analysis methodologies used to determine the post buckling response behaviour of stiffened panels relies on applying simplifying assumptions with semi-empirical/empirical data. Using the finite element method and employing non-linear material and geometric analysis procedures, it is possible to model the post buckling behaviour of stiffened panels without having to place the same emphases on simplifying assumptions or empirical data. Investigation of element, mesh, idealisation, imperfection and solution procedure selection has been undertaken, with results validated against mechanical tests. The research undertaken has demonstrated that using a commercial implicit code, the finite element method can be used successfully to model the post buckling behaviour of flat riveted panels. The work has generated a series of guidelines for the non-linear computational analysis of flat riveted panels subjected to uniform axial compression.     

Strength of damaged ring and orthogonally stiffened shells—Part II: T-ring and orthogonally stiffened shells

This paper is the second of two parts describing the procedure of, and results from, a series of tests on ring and orthogonally stiffened thin-walled shells. The primary purpose of the work was to investigate the collapse behaviour of the shells subjected to simulated damage and then tested under a combination of external pressure and axial compressive loading.The test specimens consisted of two five-bay cylinders stiffened with plain ring stiffeners; two three-bay cylinders stiffened with T-ring stiffeners and two three-bay orthogonally stiffened cylinders, one with twenty stringers, and the other with forty.This Part II deals with the tests on the T-ring and orthogonally stiffened shells. It is concluded from the test results that the T-ring stiffeners were much more effective than the corresponding plain-rings with regard to limiting the deformations which would result from minor impacts and practical conditions of loading. It is generally recommended that plain rings should not be used in shells which form parts of structural components potentially liable to damage from a minor collision, etc. It is also recommended that further work be done, including analysis and testing, to determine the optimum design of T-ring stiffeners to limit the effects of damage in an effective manner.     

Postbuckling analysis of stiffened cylindrical shells under combined external pressure and axial compression

A new approach is extended to investigate the buckling and postbuckling behaviour of perfect and imperfect, stringer and ring stiffened cylindrical shells of finite length subject to combined loading of external pressure and axial compression. The formulations are based on a boundary layer theory which includes the edge effect in the postbuckling analysis of a thin shell. The analysis uses a singular perturbation technique to determine the buckling loads and the postbuckling equilibrium paths. Some interaction curves for perfect and imperfect stiffened cylindrical shells are given and compared well with experimental data. The effects of initial imperfection on the interactive buckling load and postbuckling behaviour of stiffened cylindrical shells have also been discussed.     

Strength of damage ring and orthogonally stiffened shells—part I: Plain ring stiffened shells

This paper is the first of two parts describing the procedure of, and results from, a series of tests on ring and orthogonally stiffened thin-walled shells. The primary purpose of the work was to investigate the collapse behaviour of the shells subjected to simulated damage and then tested under a combination of external pressure and axial compressive loading.

The test specimens consisted of two five-bay cylinders stiffened with plain ring stiffeners; two three-bay cylinders stiffened with T-ring stiffeners and two three-bay orthogonally stiffened cylinders, one with 20 stringers, and the other with 40.

This Part I deals with the tests on the plain ring stiffened cylinders.

A major conclusion that can be drawn from the results of these few tests is that although the design of the plain rings was adequate to prevent general buckling of the undamaged shells, they were ineffective in limiting the area of initial damage when the shell was subjected to pressure loading.     

Ultimate strength of submarine pressure hulls with failure governed by inelastic buckling

The analysis of submarine pressure hull assumes great importance among structural engineers due to the complexity involved in the collapse mechanism of stiffened shell structures. In most of the cases, the failure of stiffened shell structures occurs due to elastic buckling. But for some combinations of shell-stiffener geometry and material characteristics, the structure can fail by inelastic buckling, for which the methods of analysis are meagre. In this paper, the analysis of submarine pressure hull structure in which the failure gets governed by inelastic buckling is demonstrated. Three different approaches have been employed to investigate the ultimate strength of the ring stiffened submarine pressure hull structure with inelastic buckling modes of failure. The methods used are ‘Johnson–Ostenfeld inelastic correction’, ‘imperfection method’ and ‘finite element approach’. A typical submarine shell structure has been analysed for the inelastic buckling failure using these three approaches and the results are discussed.     

高架式钢筒仓中转折连接的试验研究

用于散料储存的大型高架式钢筒仓结构通常由仓筒、锥形漏斗以及支承裙筒组成。在漏斗壁拉力水平分力的作用下 ,漏斗 -仓筒 -裙筒连接处产生相当大的周向压力 ,通常通过设置环梁以增加其强度。转折连接的主要破坏模式包括塑性破坏及环梁的弹性或塑性屈曲。国际上对这类连接的屈曲及破坏强度已有了大量的理论研究 ,并建立了基于理论的设计建议 ,但其试验研究尚属空白。本文总结了作者针对钢筒仓转折连接的稳定与强度问题近期在香港理工大学进行的一项大型试验研究项目。首先简单介绍该项目所建立的一套用于薄壳结构屈曲试验的试验装置 ,然后给出三个系列试验 (内压下的圆锥 -圆柱筒连接、散料荷载下的漏斗 -仓筒 -裙筒连接及散料荷载下的漏斗 -仓筒 -裙筒 -环梁连接 )的主要试验结果     

Study on the influence of the initial deflection and load combination on the collapse behaviour of continuous stiffened panels

Using the finite element analysis, a series stiffened panels under combined normal loads and biaxial compressions are conducted to investigate the effect of several influential factors on the ultimate limit states. Two spans/bays FE model with periodical boundary condition is adopted to consider the interaction between adjacent structural members. The initial deflections assumed as Fourier components including symmetric and asymmetric modes are used to identify the half-wave number of collapse of the local plate, which is compared with half-wave number of buckling calculated by formula. Based on the numerical results, the influences of half-wave number assumed in the equivalent initial imperfection and loads combination on the collapse behaviours of stiffened panels are discussed. It is found that lateral pressure might increase the ultimate strength of stiffened panels for the stiffener-induced failure modes. The one half-wave region of local plate influences significantly the load carrying capacity of stiffened panels.     

Buckling experiments on steel silo transition junctions: I: Experimental results

Large elevated steel silos for the storage of bulk solids generally consist of a cylindrical vessel above a conical discharge hopper supported on a cylindrical skirt. The cone–cylinder–skirt transition junction is subject to a large circumferential compressive force which is derived from the horizontal component of the meridional tension in the conical hopper, so either a ring is provided or the shell walls are locally thickened to strengthen the junction. Extensive theoretical studies have examined the buckling and collapse strengths of these junctions, leading to theoretically based design proposals. However, no previous experimental study on steel silo transition junctions has been reported due to the considerable difficulties associated with testing these thin-shell junctions at model scale. This paper presents the results of a series of tests on cone–cylinder–skirt–ring junctions in steel silos under simulated bulk solid loading. In addition to the presentation of test results including geometric imperfections and failure behavior, the determination of buckling modes and loads based on displacement measurements is examined in detail.     

A semi-analytical approach for linear and non-linear analysis of unstiffened laminated composite cylinders and cones under axial,torsion and pressure loads

A semi-analytical model for the non-linear analysis of simply supported, unstiffened laminated composite cylinders and cones using the Ritz method and the Classical Laminated Plate Theory is proposed. A matrix notation is used to formulate the problem using Donnell׳s and Sanders׳ non-linear equations. The approximation functions proposed are capable to simulate the elephant׳s foot effect, a common phenomenon and a common failure mode for cylindrical and conical structures under axial compression. Axial, torsion and pressure loads can be applied individually or combined, and solutions for linear static, linear buckling and non-linear buckling analyses are presented and verified using a commercial finite element software. The presented non-linear buckling analyses used perturbation loads to create the initial geometric imperfections, showing the capability of the method for arbitrary imperfection patterns. The linear stiffness matrices are integrated analytically and for the conical structures an approximation is proposed to overcome the non-integrable expressions.     

Numerical and experimental investigations on the compression behaviour of stiffened plates

The main objective of this paper is to present the results of the finite element method for non-linear analysis of stiffened plates subjected to axial compression load considering post-buckling behaviour up to collapse. For this purpose two series of well executed experimental data on longitudinally stiffened steel plates with and without transversal stiffeners subjected to uniform axial in-plane load carried out to study the buckling and post-buckling up to final failure have been chosen. The first series are those of Ghavami where the influences of stiffener cross-section of the type rectangular (R), L and T, their spacing and the presence of rigid transversal stiffeners have been studied. The second series of Tanaka & Endo, where the behaviour of stiffened plates having three and two flat bars for longitudinal and transversal stiffeners respectively were analysed. For the purpose a well-established commercially available Finite Element program ANSYS has been chosen. The selected element was SHELL43, which can trace the full-range, elastic-plastic behaviour of the stiffened plates. It is seen that the simulated results of FEM are in good consistency with the test results.     

Structural performance of buried prestressed concrete cylinder pipes with harnessed joints interaction using numerical modeling

Broken prestressing wire wraps are the main cause of failure in buried prestressed concrete cylinder pipes (PCCP), which form the backbone of water and wastewater infrastructure networks in North America. Advanced numerical modeling using non-linear finite elements is used to model the effect of the number and location of broken wire wraps on the structural performance of Class 125-14, 96-in. PCCP. The modeling technique used is unique in that it considers full interaction between adjacent pipes with harnessed joints, as well as combined internal and external loading with full soil–pipe interaction. Performance indicators in the various components of PCCP are monitored as internal pressure is increased. A sensitivity analysis is presented for how manipulating the severity of the damage affects the failure pressure of the pipe. The results show that the internal fluid pressure required to cause failure can be as much as 34% lower when the damage is at the barrel of the pipe, and that the internal pressure that causes yielding of the wire wraps decreases by 66% as the damage worsens from 5 to 100 wire breaks.     

Fatigue cracking in damaged cylinders subjected to cyclic compressive loading

This paper presents the results of analytical and experimental investigations of the occurrence of cracking in thin-walled structures which are damaged and subjected to axial compressive loading with cyclically varying magnitude. The experimental investigation comprised nine test specimens, namely three plain cylinders, three plain ring stiffened and three T-ring stiffened cylinders. The paper describes the method whereby damage was inflicted on the cylinders and describes test results, including strain gauge data.

The analysis was performed using a commercial finite element program which incorporated non-linearities in the strain-displacement and stress-strain relationships. The results of the analysis were found to be in good agreement with the test results, and the occurrence of cracking was noted to be dependent on the combined levels of tensile residual stresses due to the damage and to the levels of compressive stresses due to the imposed loading.     

柔性张拉构件补强下细长结构稳定性的基础性研究

为了分析膜、索等结构中柔性张拉构件在张力作用下对柱和拱的补强作用,基于静力平衡方程,在折线索上作用有集中荷载的情况下,提出虚拟弹簧刚度系数的概念并推导其计算式。在此基础上,分别得出一组和二组折线索 柱模型的屈曲控制方程,并采用非线性有限元分析进行对比。分析结果表明：有限元分析结果与理论分析结果吻合。补强效果中,折线索弹性刚度的贡献可以忽略,索张力起主要作用;随着折线索上荷载的增大,柱的屈曲荷载存在着先增后减的规律;折线索会起到类似铰接约束的作用,使得柱的屈曲模态发生迁移;与一组索补强效果相比,两组索补强下柱的屈曲荷载的最大值变化较小。最后,对曲线索 柱模型和曲线索 拱模型分别进行研究,分析结果表明,曲线索上集中荷载存在一个最优值,使得柱和拱的屈曲荷载取得最大值。     

Tests and finite element analysis of pin-ended channel columns with inclined simple edge stiffeners

This paper presents an experimental investigation and a finite element analysis on cold-formed channels with inclined simple edge stiffeners compressed between pinned ends. Compression tests of pin-ended channel columns with inclined simple edge stiffeners have not been performed till now. A total of 36 channel specimens including three different cross sections with different edge stiffener inclined angles and column lengths were tested. Detailed measurements of initial geometric imperfections and material properties of the specimens were also conducted before the above tests. Failure modes include local buckling, distortional buckling, flexural buckling and interaction among these buckling modes were observed in tests. The results indicate that inclined angle and loading position significantly affect the ultimate load-carrying capacity and failure mode of specimens. Moreover, a non-linear finite element model was developed and verified against tests. Geometric and material non-linearities were included in the model. Results from the finite element analysis agree well with experimentally ultimate loads and failure modes. However, it should be improved on prediction for certain displacement.     

Compression tests of longitudinally stiffened plates undergoing distortional buckling

This paper describes a series of compression tests performed on longitudinally stiffened plates fabricated from a mild steel plate of thickness of 4.0 mm with nominal yield stress of 235.0 MPa. The stiffened plates with longitudinal stiffeners of a range of rigidities were tested to failure. The ultimate strengths and performances of the longitudinally stiffened plates in compression undergoing distortional buckling or interaction between local and distortional buckling were investigated experimentally and theoretically. The compression tests indicated that the critical buckling mode was dependent mainly on the rigidity of the longitudinal stiffeners and the width-to-thickness ratio of the sub-panels. A noticeable interaction between local and distortional buckling was also observed for some stiffened plates. A significant post-buckling strength reserve was shown for those sections with distortional buckling and for those sections showing interaction between local and distortional buckling. A limiting strength curve for distortional buckling of longitudinally stiffened plates was studied. Simple design strength formulas in the direct strength method are proposed to account for the distortional buckling and the interaction between local and distortional buckling of longitudinally stiffened plates. The strength curves were compared with the test and FE results conducted. The adequacy of the strength curve was confirmed. A set of conclusions on the buckling behavior of longitudinally stiffened plates was drawn from the experimental studies.     

U形肋加劲板局部稳定性试验研究

U形肋加劲板是构成钢箱梁顶板、底板的主要板件,U形肋腹板与被加劲板局部失稳是其两种主要失稳破坏模式。为研究U形肋加劲板的局部稳定性能,分别设计并制作了U形肋腹板与被加劲板壁板两组局部稳定试件,并考虑U形肋腹板宽厚比、被加劲板宽厚比以及U形肋翼缘与腹板间弯曲半径变化。通过轴压试验得到了U形肋加劲板的局部失稳破坏模式、稳定承载力、应力-位移曲线以及局部稳定折减系数。试验研究表明：随着局部板件宽厚比的增大,试件由强度破坏转变为失稳破坏,且失稳破坏特征表现得越明显。当板件宽厚比不小于22.5时,宽厚比较大的板件先于其他板件失稳。U形肋腹板与翼缘之间弯曲半径增大时,U形肋腹板宽度及宽厚比变大,导致U形肋腹板稳定承载力降低。将试验结果与公路钢桥规范中的稳定系数曲线对比发现,对于钢桥规范中的稳定曲线,采用钢材屈服强度计算得到的板件稳定承载力明显小于试验值,而采用抗拉强度计算得到的板件稳定承载力接近试验值,说明采用钢桥规范计算U形肋加劲板稳定承载力,其安全系数和钢材的抗拉强度与屈服强度比值相当。     

非线性破坏准则下浅埋隧道掌子面三维被动稳定性能耗分析改进方法

 通过引入圆锥椭圆截交线计算公式,改进浅埋隧道掌子面三维被动破坏多椭圆锥体几何参数的计算方法。基于非线性破坏准则和极限分析上限法,推导浅埋隧道掌子面三维被动支护力的上限表达式,并进一步采用非线性规划程序优化计算获得了极限支护力最优上限解。通过对比分析,验证本文方法的可靠性;同时分析非线性抗剪强度参数对被动破坏极限支护力和破坏模式的影响,并绘制相应的破坏模式图。研究表明：被动破坏极限支护力与地面超载?s及地层容重?大致呈线性变化,而与非线性参数m、量纲一化的参数c0/?t及超负荷比C/D呈非线性变化;非线性参数m、量纲一化的参数c0/?t和超负荷比C/D对破坏模式影响显著,而地面超载?s对破坏模式影响则较小。研究成果为隧道掌子面稳定性分析提供一种新思路,进一步完善了隧道掌子面稳定性评价体系。     

Buckling and postbuckling of cylindrical shells with one end pinned and the other end free

Using finite element analysis, this paper examines the linear bifurcation buckling loads, and nonlinear collapse loads, of cylindrical shells with one end pinned and the other end free, under a variety of axial and pressure load combinations. The pinned end is formulated so as to provide no axial restraint. For the bifurcation analysis, loads are related back to the classical solutions for cylinder buckling loads, to explain the very low values found for this set of boundary conditions.The nonlinear analysis includes both imperfections and material plasticity. In this analysis, it is found that cylindrical shells with pinned-free boundary conditions are notably imperfection insensitive, and for a range of geometries are able to reach collapse loads significantly greater than their bifurcation load. For other geometries, collapse loads very close to the bifurcation load are found. This unusual imperfection insensitivity for a cylindrical shell is explained in terms of the large flexibility engendered by the pinned-free boundary conditions and the oval buckling mode.