Showing papers in "Thin-walled Structures in 2002"

New extruded multi-cell aluminum profile for maximum crash energy absorption and weight efficiency

Abstract: New types of trigger and multi-cell profiles with four square elements at the corner are developed. In terms of the crash energy absorption and weight efficiency, the new multi-cell structure shows dramatic improvements over the conventional square box column. The optimization process with the target of maximizing the specific energy absorption has been successfully carried out, and the example of design process is provided. In the optimization process, the problem of stable progressive folding is also addressed. The analytical solution for calculating the mean crushing force of new multi-cell profiles is derived showing good agreement with the numerical results. Finally, the advantage of the new design over the conventional single or multi-cell profiles is discussed.

Second-order generalised beam theory for arbitrary orthotropic materials

Abstract: This paper presents the formulation of a Generalised Beam Theory (GBT) developed to analyse the structural behaviour of composite thin-walled members made of laminated plates and displaying arbitrary orthotropy. The main concepts and procedures involved in the available isotropic first-order GBT are revisited and adapted/modified to account for the specific aspects related to the member orthotropy. In particular, the orthotropic GBT fundamental equilibrium equations and corresponding boundary conditions are derived and their terms are physically interpreted, i.e., associated with the member mechanical properties. Moreover, different laminated plate material behaviours are dealt with and their influence on the GBT equations is investigated. Finally, in order to clarify the concepts involved in the formulated GBT and illustrate its application and capabilities, a thin-walled orthotropic beam is analysed and the results obtained are thoroughly discussed.

Strength and ductility of concrete filled double skin (SHS inner and SHS outer) tubes

Abstract: This paper describes a series of compression and bending tests carried out on concrete filled double skin tubes (CFDST). Theoretical models developed to predict the ultimate strength of CFDST stub columns and beams are also described. Both outer and inner tubes were cold-formed C450 (450 MPa nominal yield stress) square hollow sections (SHS). Four different section sizes were chosen for the outer tubes with a width-to-thickness ratio ranging from 16.7 to 25.0. One section size was chosen for the inner tube which had a width-to-thickness ratio of 20. It was found that there is an increase in ductility for CFDST both in compression and bending when compared to empty single skin tubes. It was also shown there was good agreement between theoretical and experimental results.

Tests on concrete filled double-skin (CHS outer and SHS inner) composite short columns under axial compression

Abstract: This paper presents stub columns tests on concrete-filled double skin sandwich tubes (CFDT) constructed using cold-formed steel tubes. The annulus is filled with micro high-strength concrete having compressive cylinder strength of 64 MPa. The outer skin is made of circular hollow sections (CHS), while the inner skin is made of square hollow sections (SHS). Eight different section sizes were used for the outer skin with diameter-to-thickness ratio ranging from 19 to 55. Three section sizes were chosen for the inner skin with width-to-thickness ratio in the range of 20 to 26. The CFDT construction was found to have significant increase in strength, ductility and energy absorption over the outer jacket. A simplified formula is derived to determine the compressive capacity of CFDT and compared against the current design rules. The proposed formula was found in good agreement with experimental results. This paper also verifies the yield slenderness limit (λey) of 82 specified in AS 4100 for cold-formed CHS stub columns.

Future directions and challenges in shell stability analysis

Abstract: Recent advances in structural analysis and design technology for buckling-critical shell structures are discussed. These advances include a hierarchical analysis strategy that includes analyses that range from classical analysis methods to high-fidelity nonlinear finite element analysis methods, reliability based design methods, the development of imperfection data bases, and the identification of traditional and nontraditional initial imperfections for composite shell structures. When used judiciously, these advances provide the basis for a viable alternative to the traditional and conservative lower-bound design philosophy of the 1960s. These advances also help answer the question of why, after so many years of concentrated research effort to understand the behavior of buckling-critical thin-walled shells, one has not been able to improve on this conservative lower- bound design philosophy in the past.

Stability of circular cylindrical steel shells under combined loading

Abstract: Circular cylindrical shells made of steel are used in a large variety of civil engineering structures, e.g. in off-shore platforms, chimneys, silos, tanks, pipelines, bridge arches or wind turbine towers. They are often subjected to combined loading inducing membrane compressive and/or shear stress states which endanger the local structural stability (shell buckling). A comprehensive experimental and numerical investigation of cylindrical shells under combined loading has been performed which yielded a deeper insight into the real buckling behaviour under combined loading . Beyond that, it provided rules how to simulate numerically the realistic buckling behaviour by means of substitute geometric imperfections. A comparison with existing design codes for interactive shell buckling reveals significant shortcomings. A proposal for improved design rules is put forward.

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

Abstract: 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.

A simplified method for elastic large deflection analysis of plates and stiffened panels due to local buckling

Abstract: A computational model for analysis of local buckling and postbuckling of stiffened panels is derived. The model provides a tool that is more accurate than existing design codes, and more efficient than nonlinear finite element methods. Any combination of biaxial in-plane compression or tension, shear, and lateral pressure may be analysed. Deflections are assumed in the form of trigonometric function series. The deformations are coupled such that continuity of rotation between the plate and the stiffener web is ensured, as well as longitudinal continuity of displacement. The response history is traced using energy principles and perturbation theory. The procedure is semi-analytical in the sense that all energy formulations are derived analytically, while a numerical method is used for solving the resulting set of equations, and for incrementation of the solution. The stress in certain critical points are checked using the von Mises yield criterion, and the onset of yielding is taken as an estimate of ultimate strength for design purposes.

Free vibrations of simply-supported piezoelectric adaptive plates: An exact sandwich formulation

Abstract: An exact two-dimensional analytical solution is proposed for the free-vibration analysis of simply-supported piezoelectric adaptive plates. It is based on an original sandwich formulation that considers layerwise first-order shear-deformation theory and quadratic non-uniform electric potential, with no assumptions on electric field and displacement components. Thus, the electric-charge conservation equation is exactly satisfied and the induced potential, hence the electromechanical coupling, is correctly represented. Also, two-dimensional electromechanical equations of motion and generalized piezoelectric constitutive equations, corresponding to introduced stress and electric displacement resultants, are derived and presented for the first time. The proposed approach was numerically validated through modal analysis of several hybrid plates with graphite-epoxy cross-ply substrates and embedded or surface-bonded piezoelectric layers. Compared to available uncoupled and coupled (exact) three-dimensional elasticity (Navier and state space) and finite-element (layerwise and mixed equivalent single-layer/layerwise) solutions, the obtained results were the closest to the exact coupled three-dimensional ones, making the present approach very reliable.

Plastic mechanism analysis of concrete-filled double-skin (SHS inner and SHS outer) stub columns

Abstract: A plastic mechanism to predict the collapse behaviour of concrete-filled double-skin stub columns is developed and analysed in this paper. Both outer and inner tubes are square hollow sections (SHS). In the analysis, the inner tube is treated the same way as that used in previous research on empty SHS stub columns. New mechanism models are developed for the outer tubes. The effect of local buckling in the outer tube is also studied. The concrete model adopted in this paper considers the effect of confinement of the concrete induced by the double skin tubes. It also considers the strength degradation of concrete for large deformation analysis. It has been found that the effect of local buckling on the collapse curve of the outer tube can be ignored. The concrete model including confinement and strength degradation should be used in order to simulate the collapse behaviour, especially for thin outer tubes. Good agreement was achieved between the plastic mechanism analysis and experimental results.

Buckling strength of the cylindrical shell and tank subjected to axially compressive loads

Abstract: This paper aims to develop practical design equations and charts estimating the buckling strength of the cylindrical shell and tank subjected to axially compressive loads. Both geometrically perfect and imperfect shells and tanks are studied. Numerical analysis is used to evaluate buckling strength. The modeling method, appropriate element type and necessary number of elements to use in numerical analysis are recommended. According to the results of the parametric study of the perfect shell, the buckling strength decreases significantly as the diameter-to-thickness ratio increases, while it decreases slightly as the height-to-diameter ratio increases. These results are different from those in the case of columns. The buckling strength of the perfect tank placed on an extremely soft foundation and a stiff foundation increases by up to 1.6% and 5.6%, respectively, compared with that of the perfect shell. The buckling strength of the shell and tank decreases significantly as the amplitude of initial geometric imperfection increases. Convenient and sufficiently accurate design equations and charts used for estimating buckling strength are provided.

Deflections of inflatable fabric panels at high pressure

Abstract: Inflatable structures made of modem textile materials with important mechanical characteristics can be inflated at high pressure (up to a several hundreds of kPa). They can be used as strong building elements thanks to their mechanical strength. The aim of the paper is to present experimental and analytical studies on the behaviour of inflated fabric panels at high pressure and submitted to bending loads. It is shown that inflatable structures cannot be viewed as ordinary plates or beams, because their deformation pattern is quite different. Experiments show that their behaviour depends on the applied load, the inflation pressure, and the constitutive law of the fabrics. Equilibrium equations are written in the deformed state to take into account the influence of geometrical stiffness and the following forces. A Timoshenko's beam theory must be used because sections of the panels do not satisfy the usual Bernoulli's beam theory. A new inflatable beam theory is developed. Wrinkling loads are derived from equilibrium equations. Deflections satisfy the fact that the compliance of the inflatable panel is the sum of the beam compliance and of the yarn compliance. Comparisons between the results of our modelling and experimental results are shown and prove the accuracy of this theory on the mechanical strength of inflatable structures at high pressure.

The suitability of round clinching tools for high strength structural steel

Abstract: The use of light gauge steel framing is increasing rapidly. New methods for joining frames are being sought. One of the most promising methods is clinching. Clinching has been used for almost 20 years. There has been much research into the method, the tools, suitable materials and applications. Few articles have been published concerning clinching of high strength structural steels, which are currently the most relevant materials for house construction. This study included 11 different clinching methods. In total, 469 test pieces were produced. Despite the high strength of the materials, all the clinching methods that were examined could be used satisfactorily. The most significant result was that a round tool is appropriate for all the materials tested. In fact, in comparison with results obtained using other types of tool, when the methods were ranked by maximum shear load capacity, the round design appeared in the top three classes seven times out of nine.

Energy absorption in splitting square metal tubes

Abstract: This paper presents an investigation into the energy absorbing behaviour of axially splitting square metal tubes. Tubes 50 mm square with a variable thickness were pushed slowly against rigid pyramid shaped dies, which had various semi-angles. By pre-cutting 5 mm long slits at the four corners, the tube splits along the corners and curls outward with a certain radius at a constant force. In this energy dissipating system, there are three components: tearing energy, plastic deformation energy and frictional energy. Theoretical analysis of the three energy components is presented. Curl radius is also studied in detail. Good agreement between experiments and theory is obtained. The results show that tubes which both split and curl may be used as efficient, long stroke energy absorbing devices.

Lateral post-buckling analysis of thin-walled open section beams

Abstract: Thin-walled beams with open sections are studied using a nonlinear model. This model is developed in the context of large displacements and small deformations, by accounting for bending-bending and bending-torsion couplings. The warping and shortening effects are considered in the torsion equilibrium equation. The governing coupled equilibrium equations obtained from Galerkin’s method are solved by a Newton–Raphson iterative process. It is established that the buckling loads are highly dependent on the pre-buckling deformations of the beam. The bifurcated branches are unstable and strongly influenced by shortening effects. Some comparisons are presented with the solutions commonly used in linear stability, like in the standard European steel code (Eurocode 3). The regular solutions appear to be very conservative, especially for I sections with large flanges.

Residual strength of concrete-filled RHS columns after exposure to the ISO-834 standard fire

Abstract: The residual strength of a composite column may be used to assess the potential damage caused by fire and help to establish an approach to calculate the structural fire protection for minimum post-fire repair. The behavior of six rectangular hollow structural steel (RHS) columns filled with concrete, with or without fire protection, after exposure to the ISO-834 standard fire (ISO 834, 1975), subjected to axial or eccentric loads have been experimentally investigated and the results presented in this paper. Comparisons are made with predicted column strengths using the existing codes such as LRFD-AISC-1994, AIJ-1997, EC4-1996 and GJB4142-2000. It was found, in general, that the loss of the strength of the specimens without protections was significantly greater than that of columns with fire protection. A mechanics model is developed in this paper for concrete-filled RHS columns after exposure to the ISO-834 Standard Fire (ISO 834, 1975), and is a development of the analysis used for ambient condition (Han et al., 2001). The predicted load versus mid-span deflection relationship for the composite columns is in good agreement with test results. Based on the theoretical model, influence of the changing strength of the materials, fire duration time, sectional dimensions, steel ratio, load eccentricity ratio, depth-to-width ratio and slenderness ratio on the residual strength index (RSI) is discussed. It was found that, in general, the slenderness ratio, sectional dimensions and the fire duration time have a significant influence on the residual strength index (RSI). However, the steel ratio, the depth-to-width ratio, the load eccentricity ratio and the strength of the materials have a moderate influence on RSI. Finally, formulas suitable for incorporation into a building code, for the calculation of the residual strength of the concrete-filled RHS columns after exposure to ISO-834 standard fire is developed based on the parametric analysis results.

A new stiffened plate element for the analysis of arbitrary plates

Abstract: In spite of the large number of finite elements developed so far, most of these lack in generality, and are found to be inadequate and inefficient in some way or other, when it comes to analyzing plates of arbitrary geometrical configurations. So far the isoparametric element has been the most successful among available elements because of its ability to model a curved boundary successfully. However, the shear-locking problem inherent in the isoparametric element makes it unsuitable for analyzing thin plates of arbitrary shapes. Though research has been conducted using reduced integration and stabilization to overcome the problem, the formulations either do not converge to the correct solution in the thin-plate limit or they make the stiffness matrix a singular one. In this paper, a four-noded stiffened plate element is developed. This has the advantages and elegance of an isoparametric element in modelling arbitrary shaped plates, but without the disadvantage of shear-locking phenomena. Though this element is a high-order element, only the usual degrees of freedom have been considered, and performance is superior to that of the low-order ones. The stiffened plate element has the feature of accommodating the arbitrary shape of the plate geometry, and the stiffener modelling has been done in a general manner, with the stiffener lying anywhere with arbitrary orientation, and not necessarily following the nodal lines. The new element has been successfully used for the static, free vibration and stability analyses of arbitrary bare and stiffened plates. The results are found to agree quite satisfactorily with those of previous investigators.

Mushrooming of circular tubes under dynamic axial loading

Abstract: Extensive studies on axial crushing of cylindrical shells have been carried out due to their wide applications for crashworthiness. Most of the studies have been conducted under static and low speed impact conditions to predict the deforming mechanism, resulting in typical progressive buckling and dynamic plastic buckling, from which the energy absorption capacity of the structural component can be predicted. Though the effect of the strain rate, inertia and stress wave propagation can all be considered to determine the dynamic buckling modes, the present study concentrates on a different mechanism under higher energy impact, where mushrooming, or thickening of the shell wall is observed. Both experimental study and finite element (FE) simulations were carried out. It was found that mushrooming is an important feature under high speed impact but experimental results show that the high impact energy leads to dynamic tensile fracture in the mushroomed regions and the lack of suitable models for dynamic fracture in FE codes hinders a full understanding of the problem.

Finite element modelling of plate girders with web openings

Abstract: This paper is concerned with a finite element model to predict the behaviour and ultimate load of plate girders with web openings. The finite element package ABAQUS is used to model the plate girders with web openings. Accuracy of the model is assessed by applying it to plate girders tested earlier by other researchers. Comparison of analytical results with the available experimental results for yielding patterns, ultimate load values and load–deflection relationships show good agreement between the finite element and experimental results thus validating the accuracy of the proposed model. The proposed finite element method was extended to carry out a parametric study. The study covered parameters such as web slenderness and flange stiffness.

Ultimate strength formulations for stiffened panels under combined axial load, in-plane bending and lateral pressure: a benchmark study

Abstract: This paper develops advanced, yet design-oriented ultimate strength expressions for stiffened panels subject to combined axial load, in-plane bending and lateral pressure. The collapse patterns of a stiffened panel are classified into six groups. It is considered that the collapse of the stiffened panel occurs at the lowest value among the various ultimate loads calculated for each of the collapse patterns. The panel ultimate strengths for all potential collapse modes are calculated separately, and are then compared to find the minimum value which is then taken to correspond to the real panel ultimate strength. The post-weld initial imperfections (initial deflection and residual stress) are included in the developed panel ultimate strength formulations as parameters of influence. The validity of the developed formula is confirmed by comparing with the mechanical collapse tests and nonlinear FEA. A comparison of the present method is also made with theoretical solutions from the Det Norske Veritas classification society design guideline. Important insights developed are summarized.

Buckling of thin plates and members - and early work on rectangular tubes

Abstract: A brief examination of some of the research on the post-buckling elastic and plastic behaviour of plates and plate structures is outlined. This field is so wide ranging that only a very superficial examination of the early research has been carried out, and the writer has concentrated on some specific aspects of the general field of study. A very limited examination of some of the early research on rectangular cross-section tubes is also given.

Buckling behavior of cold-formed zed-purlins partially restrained by steel sheeting

Abstract: This paper presents a study on the buckling behaviour of purlin-sheeting systems under wind uplift loading. The restraint provided by the sheeting to the purlin is modeled by using two springs representing the translational and rotational restraints. The analysis is performed using finite strip methods in which the pre-buckling stress is calculated based on the same model used for the buckling analysis rather than taken as the ‘pure bending’ stress. The results obtained from this study show that, for both local and distortional buckling, the restraints have significant influence on the critical loads through their influence on the pre-buckling stress rather than directly on the buckling modes. While for lateral-torsional buckling, the influence of the restraints on the critical loads is mainly due to their influence on the buckling modes rather than the pre-buckling stress.

Vibration of cross-ply laminated composite plates subjected to initial in-plane stresses

Abstract: Natural frequencies, modal displacements and stresses of cross-ply laminated composite plates subjected to initial in-plane stresses are analyzed by taking into account the effects of higher-order deformations and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for rectangular laminates is derived through Hamilton’s principle. Several sets of truncated approximate theories can be derived to solve the eigenvalue problems of a simply supported laminated plate. After examining the convergence properties of the lowest natural frequency, only the numerical results for M=5, which are considered to be sufficient with respect to the accuracy of solutions, are presented. Numerical results are compared with those of the published existing three-dimensional theory and FEM solutions. The modal displacement and stress distributions in the thickness direction are plotted in figures. The buckling stresses can be obtained in terms of the natural frequencies of the laminates without initial in-plane stresses.

Parametric instability of edge cracked plates

Abstract: The presented paper deals with the parametric instability behavior of a simply supported rectangular plate with a crack emanating from one edge, subjected to in-plane compressive periodic edge loading. The problem is reduced to computing the free vibration frequencies and the corresponding mode shapes and substituting them into an integral equation based formula, which leads to a compact matrix form. Once the components of this matrix are found, the rest of the computation, i.e., establishing regions of instability, buckling loads and modified frequencies, is straightforward and fast. Several plates, each with a different dimension and crack length size are analyzed using this approach. The comparison of results with those of finite element models is found to be in close agreement.

Discontinuity effects at cone-cone axisymmetric shell junctions

Abstract: In this paper, the problem of a conical shell axisymmetrically intersecting another conical shell, such that the vertices of the cones lie on opposite sides of the plane of intersection, is considered, and associated discontinuity effects quantified for arbitrary loading and geometric parameters of the intersecting cones. The ensuing very practical closed-form results are based on the one-term asymptotic-series solution for the axisymmetric bending of a non-shallow conical shell, and are intended for use in the quick evaluation of stresses and deformations in double-cone pressure vessels, as well as liquid-retaining vessels with intersecting conical portions. As an example of the application of the developed formulation, the stress distribution in a large liquid-filled elevated rhombic tank is evaluated. The stresses obtained on the basis of the closed-form analytical approach developed in the paper are shown to be in good agreement with those obtained from a finite-element analysis, confirming the reliability of the presented formulation.

Large-scale cooling towers as part of an efficient and cleaner energy generating technology

Abstract: The present paper will outline the main aspects of the design and construction of cooling towers in Germany in the last decade. As part of electricity generating power plants, cooling towers play a significant role for the availability of reliable energy supplies, in a manner compatible with environmental requirements. They definitely belong to the largest and thinnest concrete structures at present. Because of the combined action of wind, thermal and moisture effects, special care has to be taken with regard to fatigue, cracking and corrosion to ensure an adequate level of safety and durability. Such a design strategy has been employed for the world’s tallest cooling tower at the Niederaussem power plant in Germany, with an overall height of 200 m and thickness values of 22–24 cm. Special considerations included the realistic non-axisymmetric distribution of soil characteristics, wind action due to interference effects (as determined by wind-tunnel tests), optimisation of the shell shape to improve structural and dynamic behaviour, injection of the cleaned flue-gas into the cooling tower, and the use of high-performance concrete (85 MPa) to improve shell resistance against acid attack by the cleaned flue-gas. The paper will present some results of an actual research project on this problem, which was conducted at the University of Wuppertal, to explore the use of high-performance concrete on design, stability and durability of cooling tower shells.

Two-way bending behavior of profiled steel sheet dry board composite panel system

Abstract: This paper describes the structural behavior, analysis, and testing of a structural system known as the profiled steel sheeting dry board (PSSDB) system when applied as two-way floor panels subjected to out-of-plane loading. The system consists of profiled steel sheeting connected to dry boards by self-drilling, self-tapping screws. Analytical models employing the finite element method have been proposed to analyze the panel. This involved two types of modeling: first, the isotropic model, and secondly, the orthotropic equivalent model representing the geometrically orthotropic profiled steel sheeting. It is the simpler latter approach which is of main interest. However, comparison of theoretical to experimental results shows that the isotropic model is more accurate, within reasonable agreement with discrepancies ranging from 2.8% to 12.8%. The ‘orthotropic model’, on the other hand, shows a bigger discrepancy of more than 30%. This indicates that there is a need for improving further the orthotropic model as described in this paper. However, for practical design purposes, the orthotropic model is acceptable since it is more conservative in predicting deflection values of the two-way PSSDB panel. The orthotropic model is preferred over the isotropic model because it is less tedious, requiring less computer memory and computational time, and is more practical for design purposes.

Parametric stress distribution in shell-of- revolution sludge digesters of parabolic ogival form

Abstract: Egg-shaped sludge digesters have become popular in relatively recent times owing to their superior functional performance and lower maintenance costs in comparison with conventional cylindrical digesters. These innovative structures are usually constructed as thin shells of revolution in concrete, designed to withstand principally the hydrostatic pressure loading from the contained liquid. As regards the precise shape of the egg shell, a number of mathematical shell surfaces may be envisaged, and the stress distribution will very much depend on the chosen form. In this paper, it is desired to explore the possible adoption of the parabolic ogival shell as a sludge digester. The stress distribution in such a shell is expressed in terms of a single governing parameter ξ, greatly facilitating the investigation. For various values of ξ covering the most practical range for egg-shaped digester shells, recommendations are made regarding the positioning of supports. Taking into account maximisation of tank capacity, minimisation of peak stress resultants in the shell, and ease of prestressing, the best range of ξ for parabolic ogival digester shells is identified. The overall conclusion is that from a structural and functional point of view, the parabolic ogival profile is suitable for adoption in the design of egg-shaped concrete sludge-digester shells.

Inelastic behavior of orthotropic steel deck stiffened by U-shaped stiffeners

Abstract: Owing to its high strength and stiffness, the orthotropic steel deck system has been widely used in the construction of long-span steel bridges. However, due to esthetic and economic considerations, slender types of orthotropic bridge have become very popular in recent years. Consequently, the stability of the orthotropic steel deck system under traffic load becomes more critical. Although the instability problem of the orthotropic steel deck system due to flexural compressive stress has been recognized for years, current bridge design specifications do not clearly specify the criteria to prevent local buckling of the orthotropic deck system. Most previous studies on orthotropic steel deck systems were focused on the out-of-plane behavior of the steel deck, and limited study has been carried out on the in-plane compressive behavior of the orthotropic steel deck system. There is a lack of knowledge on the inelastic behavior of the orthotropic steel deck system under flexural compressive stress. In this study, the inelastic behavior of 30 full-scale orthotropic steel deck specimens was examined. According to this study, it is found that the current design practice may lead to local buckling of the deck system. Based on this study, criteria are proposed for the requirement of compact and non-compact sections. Design guidelines for the inelastic ultimate strength of the steel deck system are also suggested.

Optimization of open cross section of the thin-walled beam with flat web and circular flange

Abstract: This paper is devoted to cold-formed thin-walled beams with open cross section. The beam cross section is optimized for a fixed cross section area under strength and stability constraints. Optimal geometrical parameters of the cross section are determined with regard to maximal and safe bending moment. The strength condition is a classical condition applied to the theory of beams for assumed allowable stress. The stability condition serves also as a classical condition for lateral buckling, taking the warping torsion into account. Moreover, the thin-walled beams have been analyzed, for which the shear center, i.e. the main pole, is located in the centroid of the cross section. Results of the numerical analysis are given. Figures present examples of optimal cross sections of the thin-walled beams.