Buckling and strength characteristics of some CFRP stiffened curved panels

This paper describes the initial and post-buckling behaviour of CFRP stringer-stiffened curved panels. The panels are of 500-mm radius, 2-mm thickness and have either three or four blade stringers. Initial buckling loads were calculated using the finite strip code VIPASA within the design optimisation program PASCO. An unstiffened, externally supported panel is also considered.Stringer stiffening gave higher buckling loads than external supports. The initial buckling behaviour was influenced by geometric imperfections, and methods of modelling these with PASCO are discussed. The imperfections caused scatter in buckling load, but there was minimal scatter in failure load, despite the presence of impact damage in some cases. The failure loads were about 50% higher than the buckling loads.     

Quadrilateral shear panel

Various models of structures and structural elements use an assembly of stringers and shear panels. The normal forces in the stringers can vary linearly and the membrane panels have constant shear. Often, these shear panels can be just rectangular but sometimes shear panels with a non-rectangular shape need to be used. In this paper a mathematical formulation is presented for a linear–elastic shear panel with a quadrilateral shape. The panel stiffness matrix is derived by the discrete element method, which yields a simple and efficient computational formulation. Comparison with finite element computations shows that the stiffness matrix is sufficiently accurate for engineering design.     

Elasto-plastic model for analysis of influence of imperfections on stiffness of fully anchored light-frame timber shear walls

In order to stabilize timber-framed buildings against lateral loads, the diaphragm action of roofs, floors and walls is often used. This paper deals with the influence of imperfections such as gaps and uplift on the stiffness and the horizontal displacement of fully anchored shear walls. The significance of analyzing the effects of imperfections is evident when evaluating the stiffness of shear walls; tests of walls show that the horizontal displacement is underestimated in calculations using the stiffness of sheathing-to-framing joints as obtained from experiments. Also, in real structures where hold-downs are used, the influence of gaps and uplift should be included in order to obtain realistic displacements in the serviceability limit state. The analytical model is based on ideal plastic behavior of the mechanical sheathing-to-timber joints with stresses parallel to the perimeter of the frame and on linear elastic behavior for stresses perpendicular to the bottom rail. Using this elasto-plastic model, the equations for the stiffness and the deflection versus the number of segments in the wall are derived. The fully anchored condition for the shear walls is simulated by applying a diagonal load to the shear wall. Three types of imperfections are evaluated: Walls with gaps at all studs, a gap only at the trailing stud, and gaps at all studs, except at the trailing stud. It is shown that the effect of imperfections on the stiffness of the wall in the initial stage is considerable. Depending on the distribution of the gaps and the number of segments included in the shear wall, the displacement of the shear wall is increased several times compared to that of a fully anchored wall diaphragm with no gaps; e.g. for a single segment wall more than four times. However, for walls with more than six segments the effect of imperfections can be neglected. Finally, the theoretical model is experimentally verified.     

竖向荷载下纵向柱列交叉支撑刚度要求

从保证柱列纵向稳定性的角度,对竖向荷载作用下交叉支撑的刚度要求进行研究.介绍无初始几何缺陷的单、双层纵向柱列支撑体系的抗侧刚度要求;根据实际框架中的各种初始几何缺陷,考虑竖向荷载的P-△与P-δ二阶效应,利用有限元程序ANSYS对承受竖向荷载作用的单、双层纵向柱列支撑体系进行受力分析,据此确定用于设计的竖向荷载作用下单...     

Shear resistance of longitudinally stiffened panels—Part 1: Tests and numerical analysis of imperfections

This paper deals with the results of four full-scale tests, numerical simulation of tests and initial geometric imperfection analysis for longitudinally stiffened panels in shear. The tests examine the influence of varying position and bending stiffness of one trapezoidal longitudinal stiffener on the panel shear resistance and its buckling behaviour. The stiffeners were designed such as to obtain both global and local buckling shapes. Numerical simulations (FEA), based on the test girder geometry, the measured initial geometric imperfections and elastic-plastic material characteristic from the tensile tests, demonstrate a very good agreement with the tests. The initial geometric imperfection study on different verified numerical models shows a limited sensitivity of the panel shear capacity to any kind of imperfection shape variation with amplitude at the allowable fabrication tolerances. Finally, the paper offers some ideas for modelling geometric imperfections with regard to the design or research demands.     

Influence of initial imperfection on the behaviour of extended bolted end-plate connections for portal frames

Initial imperfection in bolted end-plate connections is mainly induced by residual deformation of welding. Three typical initial imperfections, namely V-shape, C-shape and W-shape are identified in terms of the geometrical imperfection shapes for extended bolted end-plate connections based on a field study. Seven specimens of extended bolted end-plate connection, among which six specimens with V-shape initial imperfection and one without imperfection in the end-plates were tested, and the influence of the initial imperfection of the end-plate on the behaviour of the connections was investigated. Test results show that initial rotation stiffness of extended bolted end-plate joints decreases with increase of initial imperfection in the end-plate, however, the strength of the end-plate joints is only affected slightly by the imperfection. Besides, the thicker the end-plate is, the more reduction in the initial rotation stiffness relatively. Further parametric study on 14 extended bolted end-plate connections with three typical shapes of imperfections were conducted based on the finite element analysis. Among the three types of initial imperfection, the V-shape has the least influence, and the C-shape has the biggest influence on the initial rotation stiffness of the extended bolted end-plate joints. For initial geometrical imperfection in a V-shape, its influence on behaviour of extended bolted end-plate connections is negligible as far as the imperfection is limited to the criterion, giving H/300. The influence of initial imperfection in a W-shape on rotation stiffness should be acceptable if the initial imperfection is limited to the criterion. In the case of a C-shape initial imperfection in the end-plate, its influence on the rotation stiffness would be substantial; even it satisfies the requirement of the imperfection limit. The results of the study should be applicable to the bolted end-plate connections, whether flushed or extended end-plate beam to column joints in structural frames.     

双层纵向柱列支撑的设计要求

支撑体系的作用是保证柱列的几何不变性和减少柱子计算长度。本文从柱列整体稳定性出发,对双层纵向支撑体系的强度和刚度设计要求进行了研究,分别得到了横系杆完全刚性、交叉支撑完全刚性以及支撑构件有限刚度情况下,对支撑的门槛刚度要求;考虑实际柱列的初始缺陷,确定最不利初始缺陷组合情况下,使柱列极限承载力达到计算长度减半的欧拉荷载所需要的支撑的强度设计要求。     

Numerical study of built-up double-Z members in bending and compression

The use of the finite element method (FEM) for the design of composed, thin-walled, structural steel members is considered. The bolted double-Z frame member is an interesting and economical engineering solution, already used in practice [1]. However, the European recommendations for the design of steel structures do not consider built-up members from cold-formed steel profiles. Finite element analysis is used to capture the various buckling effects that shape the response of slender thin-walled members. From the finite element model, the importance of initial imperfections and stiffness of connections is identified. The experimentally validated model predictions show that a non-linear finite element analysis can predict the member behaviour, in terms of failure mode and ultimate load, yield line pattern, overall stiffness and local strain in the cold-formed profiles. To obtain a good prediction, overall and localised initial imperfections should be considered and included in the analysis.     

非完全支撑的框架结构的稳定性

设置了支撑架的框架结构,当支撑刚度还不足以使框架柱可按无侧移框架确定计算长度时,如何确定框架柱的计算长度问题,本文对此进行了研究,提出了计算公式.本文还提出了使框架柱可按无侧移计算稳定性的支撑门槛刚度.适当考虑结构初始缺陷和侧向荷载的影响后,此刚度可作为确定框架柱计算长度时区分有侧移和无侧移框架的合理标准.     

Investigation of geometric imperfections and joint stiffness of support scaffold systems

This paper describes the findings from various site measurements of geometric imperfections of support scaffold systems, also known as falsework in industry. The measurements consist of out-of-straightness of the standards (uprights), out-of-plumb of the frame and loading eccentricity between the timber bearer and the U-head screw jack. The measurements were taken from different support scaffold construction sites before the pouring of concrete, representing actual initial geometric imperfections and loading eccentricity encountered in practice. The paper also reports the results of support scaffold joint tests. The tests were performed on randomly chosen used components to investigate the joint stiffness for rotations about vertical and horizontal axes. Tests were performed for various joint configurations (two-way, three-way, and four-way connections), bending axes, and loading directions. The statistical analysis of the data is presented in the paper for practical application in modelling and probabilistic assessment of support scaffold systems.     

On the effective stiffness of slender steel sections for deflection calculations

The paper is concerned with the reduced stiffness of slender (Class 4) cross-sections due to the increased in-plane deformability of buckled panels. The main purpose is to underline that the effective width for stiffness is not the same as that for strength on principle, and to give a theoretical evaluation of this fact. The analysis is carried out using an analytical large deflection solution based on reasonable assumptions with account taken of the initial imperfections. The results show that the theoretical effective width for stiffness is always larger than that for strength, and therefore, as a rule, a separate design equation should be provided. In this context, a new, Winter-type expression is proposed. On this basis, an extension of the effective-width concept for stiffness is suggested. The conclusions drawn are of practical interest especially in the case of design limited by deflections.     

Combined axial and pressure buckling of end supported shells of revolution

A reduced stiffness theoretical analysis of the imperfection sensitive elastic buckling for end supported shells of revolution is extended to the case of arbitrary combinations of axial and radial pressure loading. Depending upon the shell and loading parameters, the potential reductions in load capacity due to imperfections are shown to involve two distinct forms of post-buckling loss of stiffness. Lower bounds in each of these regimes are provided by appropriate reduced stiffness models, and shown by comparisons with available test data to be reliable even for relatively perfect test models. By attributing reductions in load carrying capacity to weakened end support conditions, it is suggested that past interpretations of these tests may have underestimated the deleterious effects of initial imperfections.     

An equivalent stiffness approach for modelling the behaviour of compression members according to Eurocode 3

The development of design procedures based on inelastic advanced analysis is a key consideration for future steel design codes. In advanced analysis the effect of imperfections has to be modelled in such a way that the incremental analysis fully captures this effect in the process of moment redistribution. In modelling the influence of imperfections on the behaviour of individual members of real structures, different approaches have been used to globally represent this effect in the overall analysis of structural systems. They are referred to as the initial bow imperfection approach or as the equivalent transverse load approach. When using the abovementioned approaches in analysis of multiple member structural systems, the designer is required to arrange the directions of bow imperfections or equivalent transverse loads in such a way that the imperfection arrangement leads to the least constrained solution, i.e. the lowest ultimate load predicted from all possible sets of member initial imperfection arrangements. Since there is still ongoing research on the development of simple application rules ensuring that the designer obtains a unique solution when choosing a certain set of member initial imperfections, there is at the same time interest in the development of alternative approaches to modelling the influence of member imperfections on the behaviour of structural systems. This paper provides the necessary background information as well as describes the formulation and modelling techniques used in the development of a new approach to modelling the influence of imperfections on the stability behaviour of structural components and systems. This new approach, called hereafter an equivalent stiffness approach, has an advantage over the previously described approaches since an imperfect member is treated as a hypothetically straight element, flexural and axial stiffnesses of which at each load level are predicted in a continuous fashion dependent upon the actual force and deformation states. This type of modelling does not require any explicit modelling of equivalent geometric imperfections or equivalent forces and their directions in advanced analysis; therefore also it does not require any buckling mode assessment. Moreover, the effects of strain hardening and section class may conveniently be included in modelling. Finally, European buckling curves are used to estimate the values of parameters of the developed model that can be immediately used in advanced analysis conducted according to Eurocode 3.     

Flexural strength of tubular flange girders

A tubular flange girder is an I-shaped steel girder with either rectangular or round tubes as flanges. A tubular flange girder has a much larger torsional stiffness than a conventional I-shaped plate girder of similar weight, which results in a much larger lateral-torsional buckling strength. Finite element (FE) models of tubular flange girders with hollow tubes (HTFGs) are developed in this paper, considering material inelasticity, instability, initial geometric imperfections, and residual stresses. A parametric study is performed using the FE models to study the effects of stiffeners, geometric imperfections, residual stresses, cross section dimensions, and bending moment distribution on the lateral-torsional buckling flexural strength of HTFGs. These analytical results are used to evaluate formulas for determining the flexural strength of HTFGs.     

Sensitivity analysis of stability problems of steel plane frames

The objective of the paper is to analyse the influence of initial imperfections on the load-carrying capacity of a single storey steel plane frame comprised of two columns loaded in compression. The influence of the variance of initial imperfections on the variance of the load-carrying capacity was calculated by means of Sobol’ sensitivity analysis. Monte Carlo based procedures were used for computing full sets of first order and second order sensitivity indices of the model. The geometrical nonlinear finite element solution, which provides numerical results per run, was employed. The mutual dependence of sensitivity indices and column non-dimensional slenderness is analysed. The derivation of the statistical characteristics of system imperfections of the initial inclination of columns is described in the introduction of the present work. Material and geometrical characteristics of hot-rolled IPE members were considered to be random quantities with histograms obtained from experiments. The Sobol sensitivity analysis is used to identify the crucial input random imperfections and their higher order interaction effects.     

Ultimate strength of stiffened plates with a square opening under axial and out-of-plane loads

The high strength to weight ratio and high stiffness to weight ratio of stiffened plates find wide application in aircraft structures, ship structures, offshore oil platforms and lock gates. The strength and stability of stiffened plates is highly influenced by openings and initial imperfections. The main objective is to study the behaviour of stiffened steel plates with openings up to collapse and to trace the post-peak behaviour under axial and out-of-plane loads. Four stiffened steel plates with a square opening were fabricated for testing. Angle sections were used as stiffeners. Imperfections in the plate, stiffener and overall imperfection of the whole panel were measured. All fabricated panels were tested to failure. A finite element (FE) model was developed for the analysis of stiffened plates with initial imperfections and validated with the test results. Parametric studies were conducted using the developed FE model, and interaction curves and equations were developed for the design of stiffened plates with initial imperfections and openings. The interactive effect for stiffened panels with a square opening was found to be linear, with proportional reduction of the ultimate axial load carrying capacity due to the constant out-of-plane load.     

华能大厦单层柱面网壳的设计及分析

以某低矢跨比的单层柱面网壳分析与设计为例,分析该网壳在各种荷载作用下的受力特点;讨论网壳支承刚度对网壳的受力影响;介绍网壳的设计和节点构造方法;并着重研究网壳的整体稳定性。得出：低矢跨比单层柱面网壳的整体稳定对支承刚度和初始几何缺陷较敏感;考虑塑性影响后,低矢跨比柱面网壳的稳定承载力相对弹性稳定承载力有大幅度降低;不同...     

Influence of geometric imperfections on the load capacity of orthotropic stiffened and composite shells of revolution with arbitrary meridians and boundary conditions

A stiffness matrix for an element of a shell of revolution has been derived, considering arbitrary load distributions and initial geometric imperfections. This element-stiffness matrix is based on the transfer-matrix method and describes the whole section of a shell of revolution between two rings in modal coordinates (a so-called super-element). The modal coordinates here are circumferential Fourier members, thus reducing the partial differential equations to ordinary ones.

Several stability analyses investigating the sensitivity of composite shells to different geometric imperfection shapes were carried out. The influence of the load distribution and boundary conditions in combination with geometric imperfections was analysed by different modellings of a hypothetical Jupe Avant shell of the ARIANE 5 rocket.     

Stability and initial post-buckling behaviour of frame system with vertical bracings

Steel halls are assembled of plane thin-walled frames stiffened with vertical bracings consisting of two crossed rods in order to fulfil requirements concerning stability and stiffness of horizontal loads. In the paper, using stationary conditions of the total potential energy, a stability analysis and initial post-buckling behaviour of the construction are investigated. The hall construction is modelled by rigid plane frames, elastically connected on upper ends with the roof and in one or more spans with vertical bracings. It has been proved that the obtained bifurcation point is unsymmetrical and unstable, indicating that a reduction of the critical loads is possible due to some geometrical and loading imperfections.     

Global buckling and the interaction of initial imperfections of columns subjected to conservative loading

This paper deals with the problem of global instability of slender systems with imperfections. The inaccuracies in the systems are modelled assuming an initial curvature and the introduction of the eccentricity of an external load. Systems loaded by Euler’s load or by a force directed towards the positive pole are considered. The problem is formulated on the basis of an energetic method. Analysis of the global imperfections is carried out. The results of analytical, numerical and experimental research concerning the mutual relations between the introduced imperfections and their influence on the system behaviour are presented.