Konsistente geometrische Ersatzimperfektionen für den numerisch gestützten Beulsicherheitsnachweis axial gedrückter Schalen

Consistent equivalent geometric imperfections for the numerical buckling strength verification of axially compressed shells. A geometrically and materially nonlinear analysis with imperfections included (GMNIA) is the most sophisticated and perspective the most accurate method of a numerical buckling strength verification of steel shell structures. By this way, equivalent geometric imperfections, which have to cover the influence of all deviations from the nominal dates of the resistance parameters, are fundamental. The problems resulting from this aim are discussed in the paper. The Eurocode gives hints regarding the application of equivalent imperfections and makes statements about their amplitudes, which are to be adopted. It is shown, that the current regulation doesn't cover all relevant parameters with respect to the load bearing capacity. This way, inconsistencies between numerically and experimentally determined buckling resistances arise for several geometries. Modifications are suggested for the basic buckling case of the axially compressed shell to succeed in consistent equivalent geometric imperfections.     

Die neuen Stabilitätsnachweise im Stahlbau nach Eurocode 3

New assessment rules for stability of steel‐structures in Eurocode3. Steel structures are light‐weight structures with great advantages for aesthetics and sustainability. However these advantages have to be compensated by accounting for more stability rules. In Eurocode 3 – Part 1 “Design of steel structures – Basic rules and rules for buildings” various stability rules for bar‐structures, plated structures and shell structures are given that comprise either rules for equivalent geometrical imperfections for second order analysis or formulas for member verifications with imperfections being implemented. This report deals in particular with the consistency of rules for imperfections and formulas for member resistance. Such a consistency exists for flexural buckling verifications, but it is not eo ipso evident for lateral torsional buckling verifications for beams subject to bending, combined compression and bending and combined compression and biaxial bending. To clarify the situation this paper gives the background and a technical guidance for using the “general method” in Eurocode 3 – Part1–1, so that flexural buckling, lateral torsional buckling and any combination for these under any in plane and out of plane loading with any boundary conditions can be easily assessed. The “general method” is checked in view of sufficient reliability according to EN 1990 – Annex D. Comparisons are also given with the results of alternative rules in Eurocode 3 – Part1–1 intended to be used for special cases.     

Numerische Beulsicherheitsnachweise bei Schalenbeulfällen mit überkritischen Tragreserven

Numerical buckling strength verification of shell buckling cases with postcritical load carrying reserves. At many buckling endangered shell structures, the experimental data are not sufficient to assess the load carrying capacity. Therefore, the Eurocode EN 1993‐1‐6 provides the alternative of a numerical buckling strength verification. In this code, the first instability load is assumed to be decisive for the assessment of the load bearing capacity. The problem of local instabilities and postcritical load bearing reserves is only mentioned by the way but not sufficiently regulated for practice. The problems resulting from this restriction of the definition of failure are discussed in the contribution. Proposals for overcoming the deficiencies are submitted.     

Stählerne Kamine mit abgestufter Wanddicke – Tragverhalten und Bemessung

Steel chimneys with stepwise changing wall thickness – structural behaviour and design. Firstly, the results of analyses of the load bearing behaviour of slender wind loaded cylindrical shells with stepwise changing wall thickness are presented. Special attention is turned on the differences of the stress resultants from the beam theory at the one hand and from the one segment shell with constant wall thickness on the other hand. From it, conclusions for design are drawn. The several possibilities of numerical buckling strength verification given in the Eurocode still contain partly substantial problems, which limit their application. Therefore, proposals on the approximation of the internal forces of two segment shells are presented, which make possible the buckling strength verification by stress design in a safe manner.     

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.     

Buckling strength verification of cantilevered cylindrical shells subjected to transverse load using Eurocode 3

At present, there are only a few studies concerning the application of different types of buckling strength verification according to Eurocode 3 at combined loading. Besides the stress design as classical hand calculation method of checking cylindrical steel shells against buckling failure, the new Eurocode 3 also offers two global numerical analyses at different modelling levels. The linear buckling analysis (LBA) combined with a materially nonlinear but geometrically linear analysis (MNA) is the simpler concept from the perspective of the modelling and calculation effort. The more sophisticated method is a geometrically and materially nonlinear analysis of the imperfect structure (GMNIA). This paper presents the application of both numerical concepts to the cantilevered shell subject to a transverse load at the free edge. The results are compared to those from stress design. There are specific features at both types of numerical analysis: As the determination of the plastic reference resistance and the buckling parameters is the main focus at MNA/LBA, the choice of proper equivalent geometric imperfections demands special diligence at GMNIA. The presented analyses show that the GMNIA concept in connection with consistent equivalent geometric imperfections may lead to a safe and economic design of cylinders subject to combined loading. At the particular load case the MNA/LBA concept currently suffers from the lack of proper regulations concerning the determination of the overall buckling reduction factor.     

Zum Beulverhalten kaltgeformter und geschweißter Rechteckhohlprofile aus hochfestem Stahl

Local Buckling Behaviour of Cold‐formed and Welded Rectangular Hollow Sections made from Extra High Strength Steel (EHSS). New structural steels, such as (liquid) quenched and tempered (QT) steels, with extra high strength, good toughness and weldability have been developed in Europe in recent years and are included in Eurocode 3 Part 1‐12 for strengths up to S 700. However, extra high strength steels (EHSS) with a yield strength of 1100 N/mm² so far have not been taken into account in the present version of Eurocode 3 due to insufficient knowledge on their buckling behaviour and fatigue strength and lack of associated experimental data. In this article results of experimental and numerical investigations concerning the local buckling behaviour of cold‐formed and welded hollow sections made of EHSS are summarised. The investigations have been carried out within the scope of an European research project. Results have been used to check the applicability of existing design rules for local buckling to EHSS. As a consequence the scope of Eurocode 3, Part 1.12 could be expanded to cover stability rules also for such steels.     

Interaction formulae for members subjected to bending and axial compression in EUROCODE 3—the Method 2 approach

The final version of EN1993-1-1, EUROCODE 3 [EN1993-1-1. Eurocode 3. Design of steel structures, general rules and rules for buildings. 2005] for Steel Structures provides two alternatives for the buckling check of members subjected to axial compression and bending by interaction formulae, which are called there Method 1 and Method 2. This paper presents the characteristics, the background and the use of Method 2. The analogous presentation of Method 1 has already been given in [Boissonnade N, Jaspart J-P, Muzeau J-P, Villette M. New Interaction formulae for beam-columns in Eurocode 3. The French-Belgian approach. Journal of Constructional Steel Research 2004;60;421-31].The Method 2 formulae have been derived on the basis of the general format of the interaction concept of existing codes, e.g. the ENV-rules; however with advanced numerical background and consistent classification of the buckling modes. In this respect new improved interaction factors were developed from a wide scope of numerical simulations and the concept of the formulae was focussed distinctly on describing the modes of in-plane and out-of-plane buckling for members susceptible to fail either in flexural buckling or in lateral-torsional buckling. As result two sets of formulae are provided, which each cover a clear scope of physical member behaviour. Hereby, the specific effects of intermediate lateral restraints—as often found in steel structures—have also been included.The Method 2 formulae aim at providing buckling rules with compact simplified interaction factors and transparent application for standard cases.     

Zur Vereinheitlichung der Stabilitätsregeln im Eurocode 3

Unified stability rules in Eurocode 3. During the conversion of the ENV‐Eurocode 3 to the EN‐Eurocodes 3 the stability rules for beams‐columns (flexural and lateral torsional buckling), for built up members (plate buckling) and for shell structures (shell buckling) could be harmonized in using a common method with reduction factors ρ from buckling curves that can be determined with a global slenderness depending on the structural system and its loading conditions. This procedure and its justification according to EN 1990 Annex D – Design assisted by testing – which is used to determine the partial factors from tests is presented. The procedure allows to assess structures and structural members that so far were not accessible to simple numerical verifications.     

Design rules for out-of-plane stability of roller bent steel arches with FEM

This paper describes a numerical investigation into the out-of-plane buckling behavior of freestanding roller bent steel arches. As roller bent arches have structural imperfections which differ considerably from those of hot-rolled or welded sections, specific attention is paid to their inclusion in the numerical model. Sensitivity analyses are performed to assess the influence of the imperfections due to roller bending on the out-of-plane buckling response. The accuracy of the finite element model is checked by comparing the results with earlier performed experiments as presented in a related paper. The finite element model is able to replicate the structural behavior displayed by the experiments with good accuracy. A database is created with elastic–plastic buckling loads for a large number of freestanding roller bent arches. The numerical data is analyzed and presented in a so-called imperfection parameter diagram from which imperfection parameter curves are derived. The imperfection parameter curves are substituted into the European column curve formulation, leaving the original column curve formulation unaffected but extending its applicability to the out-of-plane buckling response of roller bent arches. The column curve with proposed imperfection parameter expressions can be used to check the out-of-plane buckling response of a roller bent steel arch with known non-dimensional slenderness.     

Iterative Fourier decomposition of imperfection measurements at non-uniformly distributed sampling points

Buckling of cylindrical shells subject to axial compression is acutely sensitive to the form and amplitude of geometric imperfections present in the structure. As a result, many attempts have been made to measure geometric imperfections in cylindrical shells both in laboratory specimens and less frequently in full-scale structures. The imperfections are generally interpreted using the well-known method of Fourier decomposition, so that the different components of imperfections can be more easily related to structural features such as positions of welds and their effects on buckling strength better understood. A common situation in imperfection measurements on full-scale shell structures is that some parts of the structure are not accessible, due to the presence of accessories such as service ladders and pipes. As a result, a measurement grid with non-uniform intervals is generally employed in imperfection surveys on full-scale structures. This paper first shows that when results from such surveys are interpreted using the traditional Fourier decomposition method, the resulting Fourier series cannot provide an accurate representation of the discrete measurement data due to the non-uniform distribution of sampling points. The paper then presents an iterative Fourier decomposition method which overcomes this problem. The theoretical background of the proposed method is detailed, followed by a numerical demonstration of the effectiveness of the method.     

Local buckling of steel equal angle members with normal and high strengths

Steel angle sections have been widely accepted with the development of steel structures, and such members made by high strength steel (HSS) sections are also increasingly used in buildings and bridges, and especially in transmission towers and long span trusses. Compared to normal strength steels, HSS exhibits different mechanical properties, which can cause different local buckling behavior. A finite element analysis (FEA) was performed in this paper to investigate the local buckling of steel equal angle members with different strengths under axial compression, where the residual stresses and the initial geometric imperfections of specimens were accurately described. Through this work, the relationship of the ultimate local buckling stress of steel equal angle members under axial compression as a function of steel strength and width-to-thickness ratio was established. By comparing the FEA results with the international design specifications (ANSI/AISC 360-10 and Eurocode 3), a modified design formula was developed and corresponding design suggestions were proposed, to take into account the effects of steel strength.     

The conception of quasi-collapse-affine imperfections: A new approach to unfavourable imperfections of thin-walled shell structures

Despite of the intensive research effort of the last decades there are considerable gaps of knowledge concerning the imperfection sensitivity of steel shell structures, even with regard to the basic buckling cases. It is explained in the presented paper why the most unfavourable imperfection pattern does not exist for shell structures but only different unfavourable patterns depending on the imperfection amplitude. This amplitude-depending pattern cannot be determined with certainty because of the substantial influence of the material non-linearity and because of the numerous post-buckling paths which cross each other. However, the method of quasi-collapse-affine imperfections allows a reasonable approximation to the most unfavourable imperfection pattern. The basic thoughts of this concept are presented. The application of the concept to slender wind-loaded shells illustrates its capability.     

Numerical analysis of slender elliptical concrete filled columns under axial compression

This paper presents a non-linear finite element model (FEM) used to predict the behaviour of slender concrete filled steel tubular (CFST) columns with elliptical hollow sections subjected to axial compression. The accuracy of the FEM was validated by comparing the numerical prediction against experimental observation of eighteen elliptical CFST columns which carefully chosen to represent typical sectional sizes and member slenderness. The adaptability to apply the current design rules provided in Eurocode 4 for circular and rectangular CFST columns to elliptical CFST columns were discussed. A parametric study is carried out with various section sizes, lengths and concrete strength in order to cover a wider range of member cross-sections and slenderness which is currently used in practices to examine the important structural behaviour and design parameters, such as column imperfection, non-dimension slenderness and buckling reduction factor, etc. It is concluded that the design rules given in Eurocode 4 for circular and rectangular CFST columns may be adopted to calculate the axial buckling load of elliptical CFST columns although using the imperfection of length/300 specified in the Eurocode 4 might be over-conservative for elliptical CFST columns with lower non-dimensional slenderness.     

An experimental study of ultimate compressive strength of transversely stiffened aluminium panels

An experimental investigation was carried out to determine the ultimate strength of welded stiffened aluminium panels in alloy 6082 T6 subjected to in-plane compressive loads normal to the directions of the stiffeners. This load case is not treated in the European standard for aluminium structures, Eurocode 9. A total of 21 panel specimens with various side aspect ratios and both open and closed stiffener sections were tested in a purpose made test rig. Great care was taken to ensure the rig gave very precise boundary conditions. The panels were manufactured by metal inert gas arc welding and friction stir welding. An extensive measurement program was carried out to determine the distribution of material strength and initial geometric imperfections. Small imperfection amplitudes were found. Tensile tests revealed variation in material properties, but the strength values were on average higher than the values stated in Eurocode 9. The panels failed by two different deformation modes; global flexural buckling and local buckling of the plate elements between the stiffeners.     

Gemeinsame Grundlagen von Methode 1 (wirksame Breiten) und Methode 2 (Beulspannungsbegrenzung) beim Plattenbeulnachweis nach Eurocode 3 – Teil 1‐5

Demonstration of the common basis of method1 (effective width approach) and method2 (stress limit approach) for the plate‐buckling assessment of built‐up steel components according to Eurocode 3 – Part 1‐5. Eurocode 3 – Part 1‐5 gives two methods for the plate buckling verification of built up members: method 1 with an effective width approach and method 2 with a stress limit approach. These methods have a common basis in the form of a bilinear stress‐strain diagram with a “plastic plateau”, the level of which is determined by the buckling strength of the plate element considered. The integration of the plate buckling strengths of all its plated elements give the resistance of the full cross‐section in analogy to plastic design of cross‐sections. The mobilization of the strength reserves of plated elements stronger than others by this integration effects a modification of the stress fields initially determined by elastic design in the weaker plate elements. This modification leads to an increase of shear stresses and a decrease of longitudinal stresses following the interaction curve for plate buckling strengths. This modification is also the cause for the shape of the interaction formula for the cross‐sectional resistances for plate buckling. Method 2 therefore provides two levels of resistance, one without the mobilisation of strength reserves suitable for serviceability limit checks, the other with mobilisation of strength reserves applicable to ultimate limit state verifications. Method 2 with mobilizing strength reserves can be also expanded to cover the plate‐buckling of stiffened plates. Though so far no design code with an explicite rule for this case exists, the reassessment of various plated bridge structures using different criteria for the size of admissible yield zones demonstrates that such an expansion of the method would be consistent with the results of the traditional plate buckling design according to DASt‐Ri 012.     

高强度钢材轴心受压钢柱整体稳定性能的缺陷影响研究

为研究高强度钢材轴心受压构件的整体稳定受力性能,了解构件的几何初始缺陷和截面残余应力对其屈曲强度和失稳变形的影响,以及与普通强度钢材轴压杆相比高强度钢材柱的整体稳定性能对缺陷敏感性的变化,采用有限元方法进行数值模拟计算,通过变换几何初始缺陷系数、残余应力数值大小和钢材强度等参数,对计算结果进行对比分析。研究结果表明,随着钢材强度的提高,高强度钢材轴压杆的整体屈曲强度对初始缺陷的敏感性明显降低,特别是对残余应力分布的敏感性;此外,初始缺陷的影响还与构件的长细比有直接关系。研究工作进一步揭示了高强度钢材轴压柱整体稳定性能的特点和优势。     

Class 4 stainless steel I beams subjected to fire

Structural elements composed of Class 4 sections are common in stainless steel buildings structures. These thin walled profiles are more susceptible to the occurrence of local buckling. Additionally, in beams the lateral-torsional buckling is also a common failure mode. These instability phenomena are intensified at high temperatures. This work has the main objective of presenting a numerical study on the fire behavior of beams with Class 4 stainless steel sections when subjected to pure bending and high temperatures. The influence of several parameters, as geometrical imperfections and residual stresses, on the ultimate load will be evaluated and comparisons between the numerical results and the Eurocode 3 rules will also be made.     

A numerical imperfection sensitivity study of cold-formed thin-walled tubular steel columns at uniform elevated temperatures

A numerical study is carried out on cold-formed rectangular hollow section columns to evaluate the sensitivity of column failure strength to initial imperfections, stress–strain relationships and to assess the existing design methods. It is shown that the magnitude of initial local buckling imperfection has a significant effect on the ultimate strength of short columns where failure is predominantly local buckling. Its effect on long columns is relatively small. Similarly the magnitude of initial global imperfection has more influence on the ultimate strength of a long column, whose failure is governed by global buckling, than on short columns, where local buckling controls. The shape of the stress–strain relationship of cold-formed steel will have noticeable effect on the column failure load. Current design methods, for high temperatures in ENV1993-1-2 and for ambient temperature in ENV1993-1-3, can provide a valid basis of calculation but modification will be necessary, depending on the exact model of stress–strain relationship of cold-formed steel at elevated temperatures.     

Normativer Hintergrund für den Entwurf und die Berechnung von Krankonstruktionen

Normative background for the design of crane structures. For the design of crane structures the CEN Technical Specification CEN/TS 13001‐3‐1: 2005 has been prepared in CEN/TC 147. This Technical Specification refers to EN 1990 – Eurocode: “Basis of Structural Design” and to EN 1993‐1‐1: Eurocode 3: “Design of steel structures”, Part 1‐1: “General rules and rules for buildings”, however there are significant deviations from the Eurocode‐rules. Examples for such deviations are the rules for the choice of material to avoid brittle fracture and the detail classes for the fatigue strengths of various details. Also CEN/TC 13001‐3‐1 does not yet contain design rules for plate buckling. This contribution shows examples for such deviations which possibly are based on different approaches to the experimental background of rules. A standardized approach is given in EN 1990 that specifies how to determine characteristic values of resistances from tests and recommended values for partial factors for the Eurocodes. For plate buckling the design methods given in EN 1993‐1‐5 and the reliability background of these rules are explained.