Numerical study on lateral buckling of fully bonded sandwich pipes

Sandwich pipes (SP) are promising subsea pipelines for deep-water applications. Thus, their lateral buckling response is a significant design aspect. The temperature field of SP denotes the load in lateral buckling analysis, and it is calculated using the heat transfer differential equation in this study. A general temperature field formula is proposed for an arbitrary multilayer SP, and this formula is verified by finite element models. Another finite element model based on the fiber shell element is then constructed to investigate the lateral buckling response of SP. They are validated by existing experimental and numerical results. The evolution of the lateral buckling profiles and of stress distribution are studied in consideration of nonlinear pipe-soil interaction and nonlinear material constitutive law. Moreover, the influence of initial imperfections and pipe-soil interaction on lateral buckling response is examined. Finally, a formula is approximated for a SP with a half-wave sinusoidal imperfection profile on the basis of dimensionless analysis and numerical results. This formula is convenient for engineering applications.     

Loss of stability of thin, elastic, strongly convex shells of revolution with initial imperfections, subjected to uniform pressure. A probabilistic approach

This paper presents an attempt to evaluate theoretically the influence of initial geometric imperfections in the shell surface on the value of the upper critical load of a strictly convex shell of revolution which is subjected to uniform pressure. Pogorelov's geometric method for nonlinear stability problems of thin shells is applied to obtain an analytical formula for the upper critical load, dependent on the initial imperfections. A probabilistic solution of the problem is presented. As a result, the stochastic influence of the initial deviations in the shell surface on the probability density function of the critical load and on the shell reliability are estimated and presented graphically. An example is given for an ellipsoidal shell of revolution.     

Der Einfluss von Imperfektionen in dünnwandigen geschweißten Rechteckquerschnitten unter Druckbeanspruchung

On imperfections in thin‐walled welded rectangular hollow section compressive members. This contribution presents the results of a research project analysing some aspects of stability failure of thin‐walled RHS compression members that are likely to exhibit combined global and local buckling. In particular the influence of various imperfections, namely residual stresses due to weld‐ing and local as well as global geometrical defects, on the load‐carrying capacity is subject to detailed experimental and numerical investigations. The insight into the structural behaviour leads to recommendations for standardized imperfections that should be used in the context of the numerical modelling of class‐4 square and rectangular hollow section members subjected to compression.     

The shape of circumferential weld-induced imperfections in thin-walled steel silos and tanks

The strength of thin-walled cylindrical shell structures is highly dependent on the nature and magnitude of imperfections. Most importantly, circumferential imperfections have been reported to have an especially detrimental effect on the buckling resistance of these shells under axial load. Due to the manufacturing techniques commonly used during the erection of steel silos and tanks, specific types of imperfections are introduced into these structures, among them circumferential weld-induced imperfections between strakes of steel plates. The shape of such a localised circumferential imperfection has been shown to have a great influence on the degree of strength loss of thin-walled cylindrical shell structures. The results of a survey of imperfections in an existing silo at a location in Port Kembla, Australia in combination with linear elastic shell bending theory was used to develop and calibrate a shape function which accurately describes the geometric features of circumferential weld imperfections. The proposed shape function is the first function to combine shell theory with actual field imperfection measurements. It is a continuous function and incorporates all the necessary features to represent the geometry of a circumferential weld-induced imperfection. It was found that after filtering out the effects of overall imperfections three parameters governed the shape of the surveyed imperfections: the depth, the wavelength and the roundness.     

Axially compressed cylindrical shells with local settlement

The design of cylindrical metal silos and tanks is often controlled by considerations of buckling under axial compression. Whilst the effects of geometric imperfections on the buckling strength have been extensively explored, few studies have explored the effects of defects in the boundary conditions and the effects of residual stresses have received even less attention.This paper investigates the initiation and development of imperfections caused by local differential settlement at the supported base and their effect on the elastic buckling of a thin cylindrical shell under axial compression. The shells were treated as initially perfect with perfect support, but developing geometric imperfections and residual stresses as a consequence of local displacement at the supported edge and with residual stresses consistent with the induced geometric imperfections.The results raise interesting questions concerning the criteria of failure and appropriate tolerance measurements for constructed cylindrical shells.     

The influence of the fabrication process on the buckling of thin-walled steel box sections

Steel box sections are usually fabricated from flat plates which are welded at the corners. The welding process can introduce residual stresses and geometric imperfections into the sections which can influence their strength. For some thin-walled sections, large periodic geometric imperfections have been observed in manufactured sections. Subsequent investigations have indicated that the imperfections are in fact buckling deformations i.e. the box section has buckled due to welding residual stresses prior to any application of external load. The welding procedure and the behaviour of the box sections under load has been modelled using a finite element analysis that accounts for both geometric and material non-linearities. Tests have been carried out on box sections with a range of width to thickness ratios for the plate elements. Modelling has been shown to give good correlation with the test results. The conditions for buckling to take place as a result of the welding process have been established. A design method has been proposed.     

Calculation of guyed masts in accordance with EN 1993-3-1 standard taking into account mast shaft geometrical imperfections

Selected problems concerning designing of guyed masts with lattice shaft in accordance with the “EN 1993-3-1: Design of steel structures. Part 3-1: Towers, masts and chimneys-Towers and masts” European standard have been described in this paper. The method of application of the mast shaft geometrical imperfections in calculations has been discussed. Based on the performed comparative analysis of a certain mast, the influence of such imperfections on the ultimate values of internal forces in the mast shaft has been demonstrated.     

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.     

Sensitivity assessment of steel members under compression

The objective of the paper is to analyse the influence of initial imperfections on the behaviour of a steel member under compression. The influence of the variability of initial imperfections on the variability of the load-carrying capacity studied has been calculated by sensitivity analysis. The advantages of Sobol’s sensitivity analysis and the most important properties of Sobol’s sensitivity indices are described. The Sobol’s first order sensitivity indices are evaluated in dependence on the nondimensional slenderness. The Sobol’s sensitivity indices are supplemented with a lucid elaboration based on the Monte Carlo method. Material and geometrical characteristics of a steel member IPE 220 were considered to be random quantities the histograms of which were obtained from experiments. Imperfections that have a dominant influence on the load-carrying capacity are identified.     

Residual stresses in cold-rolled stainless steel hollow sections

Stainless steel exhibits a pronounced response to cold-work and heat input. As a result, the behaviour of structural stainless steel sections, as influenced by strength, ductility and residual stress presence, is sensitive to the precise means by which the sections are produced. This paper explores the presence and influence of residual stresses in cold-rolled stainless steel box sections using experimental and numerical techniques. In previous studies, residual stress magnitudes have been inferred from surface strain measurements and an assumed through-thickness stress distribution. In the present study, through-thickness residual stresses in cold-rolled stainless steel box sections have been measured directly by means of X-ray diffraction and their effect on structural behaviour has been carefully assessed through detailed non-linear numerical modelling. Geometric imperfections, flat and corner material properties and the average compressive response of stainless steel box sections were also examined experimentally and the results have been fully reported. From the X-ray diffraction measurements, it was concluded that the influence of through-thickness (bending) residual stresses in cold-rolled stainless steel box sections could be effectively represented by a rectangular stress block distribution. The developed ABAQUS numerical models included features such as non-linear material stress-strain characteristics, initial geometric imperfections, residual stresses (membrane and bending) and enhanced strength corner properties. The residual stresses, together with the corresponding plastic strains, were included in the FE models by means of the SIGINI and HARDINI Fortran subroutines. Of the two residual stress components, the bending residual stresses were found to be larger in magnitude and of greater (often positive) influence on the structural behaviour of thin-walled cold-formed stainless steel sections.     

Nonlinear in-plane behavior of circular steel arches with hollow circular cross-section

In this work the nonlinear in-plane behavior of circular arches with hollow circular cross-section is investigated. The influence of a number of design parameters, such as the boundary conditions, the rise-to-span ratio, and the included angle on the strength is presented. Moreover, the effect of other behavior factors, such as the geometrical and material nonlinearities and the initial imperfections, is investigated. A criterion for the prediction of the type of nonlinear behavior of arches is given, and a formula for the determination of the nonlinear buckling load is proposed. It is found that the effect of initial imperfections on the strength depends largely on the arch slenderness and the imperfection magnitude in the case of shallow arches. When arches are deep this dependence becomes less significant. The effect of geometrical nonlinearity depends significantly on the shallowness and the slenderness of the arches. Stocky arches are less influenced by the rise-to-span ratio than slender ones. The effect of boundary conditions depends significantly on the shallowness of arches and the arch slenderness. The reduction of strength is larger in slender arches than in stocky ones.     

Neue Prüftechniken anstelle schweißtechnischer Reparaturen

New testing technologies instead of welding repairs. The present report concerning the topic “New testing technologies instead of welding repairs” describes possible solutions of testing non‐penetrated welded joints using ultrasonic testing. The types of solutions presented all have the same objective – to measure the actual magnitude of defects. Here, it should be stated that it is not true that the exact magnitude of imperfections may be measured by usual ultrasonic testing. The conventional ultrasonic measuring techniques are suitable for detecting imperfections. The determination of the actual magnitudes is not possible directly, but the comparison with artificial reflectors such as side drilled holes or disk shaped reflectors. The types of solution presented do not serve to compete with complex ultrasonic systems with sophisticated software. On the contrary – it has been tried to realise solutions suitable for practice with the least possible expenditure.     

扣件式模板支架初始缺陷分类及缺陷敏感度分析

针对扣件式钢管模板支撑体系坍塌事故频发的现状,分析初始缺陷对架体承载能力的影响及计算方法。按照初始缺陷的性质,将扣件式钢管模板支架常见缺陷分为力学缺陷、材料缺陷、搭设参数偏差和初始几何缺陷共4大类。根据某真型实验架体建立有限元模型,分别计算架体承载能力对4类初始缺陷的敏感程度。针对较为敏感的初始缺陷,提出通过在现行规范承载力验算公式中加入修正参数来考虑材料初始缺陷的方法,以提高扣件式钢管模板支架极限承载能力计算的精度。     

Experiments on dented cylindrical shells under peripheral pressure

In spite of numerous papers in the literature on the buckling behavior of cylindrical shell structures, the effect of local large imperfections caused by physical contacts has not been exhaustively examined yet. To this end, this paper reports on an experimental program on the buckling and post-buckling response of thin cylindrical shells with local dent imperfections under uniform external pressure. The results of this study can be used in practical structures with similar geometric features, i.e. D/t ratio.     

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.     

Old and new solutions for contact splices in columns

Compression forces in a splice can be transferred by contact. Accordingly additional imperfections can be noticed and have to be accounted for. If a contact splice is placed inside the length of a column these initial additional imperfections will have an influence on the buckling behaviour and thus the load carrying capacity of the column. Report on theoretical investigations on the member behaviour and on the design of a splice and its fastenings is given. Also full scale tests on different types of splices are referred to. The test results are compared to ultimate load calculations and respective design methods are proposed. Especially for contact splices in columns arranged directly one on top of the other the stability behaviour for a splice at midspan is examined and leads to a special buckling curve.     

Semi-empirical design of complex metal beams by buckling analysis

Structural elements with complex geometries, boundary conditions and load patterns cannot be designed against buckling using empirical formulae because of uncertain elastic buckling moments or unknown buckling effective lengths, which are basic parameters for these equations. This article proposes a shell finite element procedure for buckling design of metal beams of complex configurations with codified initial imperfections assumed in the Perry–Robertson formula. The advantage of the proposed method lies in the use of elastic buckling moment with empirical design formulae for determination of design moment capacity of a beam; thereby eliminating the uncertainty of modelling initial imperfections. More importantly, the moment modification factor and assumption of effective length can be avoided because all second-order and yield effects have been considered in the computer model. Numerical examples demonstrate that the simplified method has a high level of accuracy, versatility and flexibility for the design of complex beams.     

锈蚀箱梁极限强度试验中板变形量的分析

根据垂直弯曲荷载下3个锈蚀箱梁板的压应力试验结果,分析初始和倒塌后的板变形量。研究初始缺陷和腐蚀对倒塌后最终变形的影响,得出不同的荷载响应、初始缺陷和板高厚比之间的关系。分析初始缺陷、板高厚比和倒塌后最终变形,建立高厚比准则以计算倒塌后变形。     

Effect of imperfections on numerical simulation of instability behaviour of cold-formed steel members

The paper analyses the influence of imperfections on the behaviour of cold-formed steel members. Special attention is paid on the characterisation and codification of imperfections for non-linear FEM simulation. Based on the ECBL approach [2] and using an advanced non-linear inelastic analysis, the erosion of theoretical buckling strength, due to geometrical imperfections, in single and coupled instability modes is evaluated.     

Analysis of plate deflections during ultimate strength experiments of corroded box girders

The objective of this work is to analyze the initial and post-collapse plate deflections based on measurement records of the experiments of three corroded box girders subjected to pure vertical bending loading inducing a compressive stress on deck. The effect of initial imperfections and corrosion degradation on the final post-collapse deformation shape has been investigated and a relationship between different loading responses, shape of initial imperfections and plate slenderness has been derived. Analyzing initial imperfections, plate slenderness and final post-collapse deformations, a slenderness criterion has been established to predict the post-collapse deformation shape.