Reliability analysis of thin-walled cylindrical shells

The subject of the article is the verification of the reliability of thin-walled rotationally symmetric cylindrical shells, using probabilistic approaches. Internal forces and stress of the shell are analysed assuming a membrane action. Material and geometric characteristics of the steel shell are considered as random variables. The reliability index is evaluated using the Latin Hypercube Sampling method. The results of the reliability analysis are derived in a general form, so that they may be useful for assessing the reliability of tanks and pipes

Geometry functions for edge cracks in steel bridge under three- and four- point bending with various span

Fatigue cracks are found during the regular structural inspections. To precisely describe/suggest propagation of fatigue cracks throughout structure and it’s designed service life, the knowledge of geometry functions describing the stress situation in front of the crack tip for relative crack lengths are important. The cracks usually propagate/initiated from the edge or the surface of the structural element, where the maximum value of applied load is achieved. The theoretical model of fatigue crack propagation is based on linear fracture mechanics (Paris law). Steel structural elements are subjected to various bending load (three-, four- point bending and pure bending etc.). The geometry functions for the edge cracks are calculated for various span according to real steel bridge elements and appropriate polynomial functions independent on the distance are proposed for three- and four- point bending load

Global sensitivity analysis in stability problems of steel frame structures

Slender steel frame structures are characterised by a number of imperfections which may reduce their load carrying capacity drastically. This article studies the effects of these imperfections on the load carrying capacity of a single storey steel plane frame using global sensitivity analysis and geometrically nonlinear (second-order) elastic finite element analysis. Imperfections are considered as random variables. Statistical load carrying capacities needed for the evaluation of sensitivity analysis are processed using classical statistical methods upon the emulation of Latin Hyper­cube Sampling simulation methods. The main interaction effects of random imperfections on the load carrying capac­ity are identified using global sensitivity analysis. It is illustrated that the effects of imperfections on the load carrying capacity varies dramatically depending on the height of the columns and the boundary conditions of the end conditions of the columns

Influence of partial safety factors on design reliability of steel structures ‐ probability and fuzzy probability assessments

The paper is aimed at the analysis of the influence of partial safety factors on the reliability of designing steel members. The reliability assessment of a steel member is based on extensive experimental research on real material and geometric characteristics evaluated by samples obtained from frequently manufactured products. Material and geometric characteristics are random variables represented by histograms during the probabilistic assessment of reliability. The random variability of structural dimensions and of material characteristics does not present the only source of uncertainty present during design according to standards. The reliability of steel structures design is also dependent on the partial safety factor values, which are specified by the design standards. Partial safety factors are basic indicators, which determine structural dimensions in relation to loading. The probabilistic assessment of reliability is performed as a parametric study in the first part of the numerical analysis. The probability of failure is analysed in dependence on values of partial safety factors of material, permanent loading and long time variable loading. Partial safety factors are considered as fuzzy numbers with triangular membership functions in the second part of the numerical analysis. Membership functions of failure probability are evaluated using the general extension principle. The most important results are then summarised and additional applications of the verifications of limit states design criteria are described. Dalinių saugos koeficientų įtaka plieno konstrukcijų projektiniam patikimimui – tikimybės ir fuzi tikimybės įvertinimas Santrauka Straipsnyje nagrinėjama dalinių saugos koeficientų įtaka patikimumui projektuojant plieninius elementus. Plieninio elemento patikimumo įvertinimas remiasi realios medžiagos ir geometrinių charakteristikų išsamiais dažniausiai gaminamų produktų eksperimentiniais tyrimais. Medžiaga ir geometriniai parametrai yra atsitiktiniai dydžiai, charakterizuojami histogramomis įvertinant patikimumą. Atsitiktinė konstrukcijos dimensijų ir medžiagos parametrų variacija veikiama ne vienintele stochastiškumo priežastimi projektuojant pagal standartus. Patikimumas projektuojant plienines konstrukcijas priklauso nuo dalinių saugos koeficientų, parenkamų remiantis projektavimo standartais. Daliniai saugos koeficientai yra indikatoriai, lemiantys apkrautos konstrukcijos dimensijas. Pirmuoju konstrukcijos analizės etapu jos patikimumas nustatomas parametriškai. Suirimo tikimybė analizuojama atsižvelgiant į dalinius saugos veiksnius, skirtus medžiagai, nuolatinėms ir ilgalaikėms apkrovoms. Daliniai saugos koeficientai išreiškiami trikampėmis narystės funkcijomis, naudojamomis antrame konstrukcijos analizės etape. Suirimo tikimybės narystės funkcijos nustatomos naudojant bendrąjį išskleidimo principą. Pateikiami pagrindiniai rezultatai, apibendrinimai ir taikymas norint patikrinti projektinius ribinių būvių kriterijus. First Published Online: 14 Oct 2010 Reikšminiai žodžiai: plienas, konstrukcija, patikimumas, atsitiktinis dydis, fuzi analizė, netikslumas, modeliavima

Reliability analysis of the lateral torsional buckling resistance and the ultimate limit state of steel beams with random imperfections

The paper deals with the analysis of reliability of a hot-rolled steel IPE-beam designed according to Eurocodes. A beam at its ultimate limit state is considered. The load acting on the beam consists of permanent and long-term single variation actions. The beam is loaded with end bending moments about the major principal axis. The beam is susceptible to lateral torsional buckling between the end supports. Reliability of the beam is assessed using probabilistic analysis based on the Monte Carlo method. Failure probability is a function of the random variability of the loadcarrying capacity and the random variability of load effects. The variability of the load-carrying capacity is influenced by the variability of initial imperfections. Imperfections are considered according to experimental research. Numerical studies showed that the failure probability is significantly misaligned. High values of failure probability were obtained for slender beams, for beams loaded only by permanent load action, and for beams loaded only by long-term single variation load. In further studies the values of partial safety factors of load and resistance were calibrated so that the failure probability had a target value of 7.2E–5. Relatively high values of partial safety factors were obtained especially for beams with high slenderness

Elastic Lateral-Torsional Buckling of Simply Supported Hot-Rolled Steel I-Beams with Random Imperfections

The paper deals with the problem of lateral beam buckling of simply supported hot-rolled I-beams under major axis bending. The bending stability problem is analysed by consideration the minor axis bending and torsion equations. Both perfect straight beams and beams with initial imperfections are considered. The mathematical solutions are derived, based on a non-linear stability model. The attention is paid to virtual computer experiments of beams with initial random imperfections. Realizations of initial imperfections are simulated, applying the numerical simulation method Latin Hypercube Sampling.The paper deals with the problem of lateral beam buckling of simply supported hot-rolled I-beams under major axis bending. The bending stability problem is analysed by consideration the minor axis bending and torsion equations. Both perfect straight beams and beams with initial imperfections are considered. The mathematical solutions are derived, based on a non-linear stability model. The attention is paid to virtual computer experiments of beams with initial random imperfections. Realizations of initial imperfections are simulated, applying the numerical simulation method Latin Hypercube Sampling

Quantile-oriented global sensitivity analysis of design resistance

The article investigates the application of a new type of global quantile-oriented sensitivity analysis (called QSA in the article) and contrasts it with established Sobol’ sensitivity analysis (SSA). Comparison of QSA of the resistance design value (0.1 percentile) with SSA is performed on an example of the analysis of the resistance of a steel IPN 200 beam, which is subjected to lateral-torsional buckling. The resistance is approximated using higher order polynomial metamodels created from advanced non-linear FE models. The main, higher order and total effects are calculated using the Latin Hypercube Sampling method. Noticeable differences between the two methods are found, with QSA apparently revealing higher sensitivity of the resistance design value to random input second and higher order interactions (compared to SSA). SSA cannot identify certain reliability aspects of structural design as comprehensively as QSA, particularly in relation to higher order interactions effects of input imperfections. In order to better understand the reasons for the differences between QSA and SSA, two simple examples are presented, where QSA (median) and SSA show a general agreement in the calculation of certain sensitivity indices

Application of uncertainty analysis to stability problems of steel-concrete structural members

The paper deals with the fuzzy analysis of the ultimate limit state of a steel strut with an encased web in compression. The first part of the paper lists presumptions required for the determination of the theoretical load carrying capacity for the column. Stresses in the concrete and steel sections are determined according to the principles of elasticity. The ultimate limit state is given as the limit stress attained in the most stressed section of either the steel or concrete section. A general extended principle, which takes into account the epistemic uncertainty of input parameters, was utilized for the conducted analysis. Neapibrėžtumo analizės taikymas plienbetonio konstrukcinių elementų stabilumo uždaviniuose Santrauka Straipsnyje nagrinėjamas plienbetonio konstrukcinių elementų stipris remiantis fuzzy analize. Pirmoje straipsnio dalyje aprašomos prielaidos, reikalingos teoriniam kolonos laikomosios galios nustatymui. Itempiai plieniniuose ir betoniniuose skerspjūviuose nustatomi pagal tamprumo teorijos principus. Ribinis pavojingiausio pjūvio būvis pasiekiamas tada, kai įtempiai pasiekia ribinių įtempių reikšmes plieno apvalkale arba betono užpilde. Analizei buvo pasitelktas išplėstinis principas, kuris įvertina pradinių parametrų „epistematinį“ neapibrėžtuma. First Published Online: 16 May 2013 Reikšminiai žodžiai: plienas, betonas, konstrukcija, projektavimas, tvirtumas, fuzzy, yda

Material and geometrical characteristics of structural steels based on statistical analysis of metallurgical products

The experimental research results of material and geometrical characteristics of Czech steel are given in the presented paper. Measurements are carried out for the yield strength of plates made of steel grade S355. The values measured are used to compute axial resistances which are compared with the resistance resulting from standard (nominal) values. In this paper, there was used a statistical information for evaluating the results of strength measurements on a series of plates and hot‐rolled profiles under tension to determine the adequate partial γM0 safety factor. Santrauka Straipsnyje pateikti Čekijos plienų mechaninių ir geometrinių charakteristikų eksperimentinių tyrimų rezultatai. Atlikti S355 klasės plieno plokštės takumo stiprio matavimai. Nustatytos reikšmės naudojamos ašiniam stipriui apskaičiuoti, o gauti rezultatai palyginti su standartinėmis (nominaliosiomis) vertėmis. Plieno plokščių ir karštai valcuotų profilių tempiamojo stiprio matavimo rezultatams įvertinti pasitelkta statistinė informacija. Įvertintas dalinio patikimumo koeficiento γM0 adekvatumas. First Published Online: 14 Oct 2010 Reikšminiai žodžiai: medžiaga, plienas, takumo stipris, patikimumas, konstrukcija, projektavimas, atsitiktinis dydis