Current procedures for estimating effective length factors for web-tapered members rely heavily on the use of charts and graphs. This makes them difficult to implement using a computer. In addition, they are often based on unrealistic assumptions. In cases where these assumptions are not satisfied, design errors may result. This investigation proposes a modification to an effective length factor expression developed by Lui (1992). This modification allows the expression to be applied to web-tapered members with good accuracy. A derivation of the proposed expression is presented, and the results obtained by applying the expression to a range of frames are compared to the results obtained from second-order finite element analyses. Calculations involved in using the expression are presented. / Master of Science

Dentro da prática de verificação e projeto de estruturas metálicas, o cálculo de instabilidade exerce papel importante, já que o aço, por sua elevada resistência, incentiva o uso de colunas significativamente esbeltas. É comum na verificação da instabilidade de pórticos metálicos de andares múltiplos a utilização do conhecido fator K, que define, para a coluna, um comprimento efetivo. Tal fator é usualmente obtido em ábacos construídos a partir de duas hipóteses distintas para o mecanismo de instabilidade: a de flambagem por deslocamento lateral do andar e a de flambagem com esse deslocamento impedido. Essa divisão, e os modelos usualmente utilizados para tratá-la, se mostram incompletos para o caso de pórticos que se distanciem das hipóteses simplificadoras adotadas, e podem induzir a confusões e mal-entendido no uso do fator K. Neste trabalho, serão mostrados modelos alternativos para a determinação desse fator, buscando-se maior generalidade, assim como tentativas de esclarecer algumas possíveis ambiguidades no seu uso; além disso, esses modelos serão aplicados a alguns exemplos particulares. Como complemento ao trabalho, foi criado um programa de computador para determinar deslocamentos e esforços em segunda ordem para esse tipo de edificação, assim como ábacos alternativos. Os resultados obtidos nos exemplos serão contrastados com os fornecidos pelo programa e pelos ábacos. / In the practice of analysis and design of steel structures, instability calculations is a very important feature, since steel, for its high strength, motivates the use of significantly slender columns. It is usual in the analysis of multi-storey steel plane frames, the use of the K factor, that defines, for a column, an effective length. Such factor is usually obtained from nomograms, based on two different hypothesis for the instability mode: one with a side-way mode and the other with no lateral displacements. That division, and the models usually used to deal with, are incomplete to treat frames for which behaviour go away from the adopted hypothesis and simplifications, and they can induce to confusions and misunderstanding in the use of the K factor. In this work, alternative models will be shown for the determination of the K factor, looking for a larger generality, as well as attempting to clear ambiguities in its use; a series of examples will be then presented as applications of the models. As a complement, a computer program was created to determine first and second order nodal displacements and member forces, as well alternative nomograms; the results obtained from the models will be contrasted with those obtained from the program and the nomograms.

Baigiamajame magistro darbe atliekama plieninių neskėtrių arkinių tiltų pastovumo plokštumoje analizė. Pirmajame skyriuje apžvelgiami pavienių gniuždomųjų strypų, arkų ir arkinių tiltų pastovumo tikrinimo metodai, pateikiamos projektavimo normos ir jų taikymo sritys. Antrajame skyriuje pateikiamas analiziniais ir skaitiniais metodais apskaičiuotų pavienių strypų ir arkų pastovumo parametrų palyginimas. Konstrukcijų pastovumo analizei atlikti naudojamas programinis paketas „Sofistik“. Skaičiuojant pastovumo parametrus vertinama arkos geometrinė apybrėža, apkrovimo pobūdis, lenkiamasis standis, aukščio ir tarpatramio santykis. Nustatomi racionalūs arkos geometriniai parametrai. Trečiajame skyriuje nagrinėjami dvimačiai neskėtrių arkinių tiltų modeliai. Vertinama tinklelio pakabų skaičiaus ir išdėstymo įtaka pastovumui. Palyginami neskėtrių arkinių tiltų stabilumo analizės rezultatai. Pateikiamos išvados ir rekomendacijos. Darbą sudaro: įvadas, trys skyriai, bendrosios išvados ir rekomendacijos, literatūros sąrašas, priedai. Darbo apimtis – 96 puslapiai, 66 paveikslai, 26 lentelės, 32 bibliografiniai šaltiniai. / The master thesis is carried out for in plane stability analysis of tied steel arch bridges. In first chapter overview of the individual compression bars, arches and arch bridges stability testing methods is presented. The first chapter also provides design standards and their application areas. The whole structural stability analysis was performed using “Sofistik” finite element software. Using software two dimensional models of arches and arch bridges were made. Second chapter concludes comparison of analytical and numerical stability analysis of single arches. Stability parameter and effective length factor was calculated according to arch geometric outlines, load type, bending stiffness, height and span ratio. The third chapter consists of stability analysis of two dimensional arch bridge models. Different suspension cable grids were used in order to compare and evaluate stability analysis results. Comparison of stability factors of various versions of arch bridges was made. Conclusions and recommendations are presented in the final chapter. The work contains: introduction, three chapters, conclusions and recommendations, references and appendices. The whole work consists of – 96 pages, 66 figures, 26 tables, 32 references.

Dentro da prática de verificação e projeto de estruturas metálicas, o cálculo de instabilidade exerce papel importante, já que o aço, por sua elevada resistência, incentiva o uso de colunas significativamente esbeltas. É comum na verificação da instabilidade de pórticos metálicos de andares múltiplos a utilização do conhecido fator K, que define, para a coluna, um comprimento efetivo. Tal fator é usualmente obtido em ábacos construídos a partir de duas hipóteses distintas para o mecanismo de instabilidade: a de flambagem por deslocamento lateral do andar e a de flambagem com esse deslocamento impedido. Essa divisão, e os modelos usualmente utilizados para tratá-la, se mostram incompletos para o caso de pórticos que se distanciem das hipóteses simplificadoras adotadas, e podem induzir a confusões e mal-entendido no uso do fator K. Neste trabalho, serão mostrados modelos alternativos para a determinação desse fator, buscando-se maior generalidade, assim como tentativas de esclarecer algumas possíveis ambiguidades no seu uso; além disso, esses modelos serão aplicados a alguns exemplos particulares. Como complemento ao trabalho, foi criado um programa de computador para determinar deslocamentos e esforços em segunda ordem para esse tipo de edificação, assim como ábacos alternativos. Os resultados obtidos nos exemplos serão contrastados com os fornecidos pelo programa e pelos ábacos. / In the practice of analysis and design of steel structures, instability calculations is a very important feature, since steel, for its high strength, motivates the use of significantly slender columns. It is usual in the analysis of multi-storey steel plane frames, the use of the K factor, that defines, for a column, an effective length. Such factor is usually obtained from nomograms, based on two different hypothesis for the instability mode: one with a side-way mode and the other with no lateral displacements. That division, and the models usually used to deal with, are incomplete to treat frames for which behaviour go away from the adopted hypothesis and simplifications, and they can induce to confusions and misunderstanding in the use of the K factor. In this work, alternative models will be shown for the determination of the K factor, looking for a larger generality, as well as attempting to clear ambiguities in its use; a series of examples will be then presented as applications of the models. As a complement, a computer program was created to determine first and second order nodal displacements and member forces, as well alternative nomograms; the results obtained from the models will be contrasted with those obtained from the program and the nomograms.

Στην παρούσα διδακτορική διατριβή, με βάση την ηλεκτρομαγνητική θεωρία,παρουσιάζεται μία μεθοδολογία για τη μοντελοποίηση πολύθυρων κεραιών κατά την κατάσταση εκπομπής και λήψης τους, δύο στοχαστικές μεθοδολογίες για την αξιολόγησή τους κατά τη λειτουργία τους σε συστήματα διαφορισμού λήψης και μία στοχαστική μεθοδολογία για την περίπτωση που αυτές λειτουργούν σε συστήματα πολλαπλών εισόδων πολλαπλών εξόδων.Οι πολύθυρες κεραίες μοντελοποιούνται στις καταστάσεις εκπομπής και λήψης τους χρησιμοποιώντας είτε τον πίνακα διανυσμάτων ενεργών μηκών ή τον πίνακα αποτελεσματικών ενεργών μηκών. Ο πρώτος τρόπος είναι προσαρμοσμένος για ανάλυση με Ζ-παραμέτρους ενώ ο δεύτερος για ανάλυση με S-παραμέτρους.Η αξιολόγηση των πολύθυρων κεραιών κατα τη λειτουργία τους σε συστήματα διαφορισμού επιτυγχάνεται είτε με τη μέθοδο του πίνακα συνδιασποράς ή με μία υβριδική στοχαστική-ηλεκτρομαγνητική μεθοδολογία. Η πρώτη μεθοδολογία έχει χρησιμοποιηθεί αρκετά στη διεθνή βιβλιογραφία, ενώ η δεύτερη προτείνεται στην παρούσα διατριβή. Και οι δύο μέθοδοι λαμβάνουν υπόψη τους τόσο τις χαρακτηριστικές ιδιότητες των κεραιών όσο και τις ιδιότητες του περιβάλλοντος διάδοσης.Η αξιολόγηση των πολύθυρων κεραιών κατα τη λειτουργία τους σε συστήματα πολλαπλών εισόδων πολλαπλών εξόδων επιτυγχάνεται χρησιμοποιώντας μία γενική μεθοδολογία που βασίζεται σε βασικές αρχές ηλεκτρομαγνητισμού και κυκλωματικής ανάλυσης. Η συγκεκριμένη μεθοδολογία είναι προσαρμοσμένη για ανάλυση με S- παραμέτρους αλλά μπορεί να επεκταθεί και για ανάλυση με Ζ-παραμέτρους. Παρουσιάζεται, επιπλέον, η εφαρμογή της μεθοδολογίας σε κεραίες οι οποίες έχουν κοινό κέντρο φάσης. / Ιn this thesis a method for modeling multi-port antenna structures at both their transmitting and receiving operational modes and methods for their performance evaluation when operating in diversity and MIMO systems is demonstrated under the perspective of electromagnetics combined with stochastic analysis. The method for modeling multi-port antenna structures at both their transmitting and receiving operational modes is achieved using either the effective length matrix or the realized effective length matrix. The former way is convenient for Z-parameter analysis while the latter for S-parameter analysis. Two stochastic methodologies for the performance evaluation of diversity systems are presented. The first one is based on the covariance matrix of the received signals and has been used by many researchers worldwide. The second one, which has been developed in this thesis, combines electromagnetic modeling of multi-port antennas’ the reception mode with a stochastic model. A stochastic methodology for the performance evaluation of MIMO systems is also presented. The methodology has been developed in this thesis in order to be used for Sparameter analysis. Moreover this methodology is applied to model multiport antenna systems with common phase center.

Este trabalho trata das principais filosofias de verificação de pilares à flexão composta em pórticos de aço assim como das normas que as recomendam. São discutidas as metodologias baseadas em comprimentos efetivos de flambagem, forças horizontais fictícias e análise avançada. É proposta uma metodologia de análise avançada utilizando elementos finitos de casca, que incorpora os efeitos das tensões residuais, imperfeições geométricas e não-linearidades geométricas e do material. São apresentados, ao final do trabalho, exemplos para comparação das diversas metodologias discutidas ao longo do texto. / This work discusses the main philosophies used to verify columns subjected to bending and compression in steel frames as well as the standards which recommend them. The effective length and notional loads approaches and the advanced analysis concept are discussed too. It is proposed a methodology of advanced analysis based on shell finite elements that accounts for the effects of residual stresses, geometric imperfections and geometric and material non-linearity. It is presented, at the end of the text, samples for the comparison of the several methodologies discussed throughout this work.

For steel structures, stability is a very important concept since many steel structures are governed by stability limit states. Therefore, stability of a structure should be assessed carefully considering all parameters that affect the stability of the structure. The most important of these parameters can be listed as geometric imperfections, member inelasticity and connection rigidity. Geometric imperfections and member inelasticity are taken into account with the stability method used in the design. At this point, the stability methods gain importance. The Direct Analysis Method, the default stability method in 2010 AISC Specification, is a new, more transparent and more straightforward method, which captures the real structure behavior better than Effective Length Method. In this thesis, a study has been conducted on the semi-rigid steel frames to compare Direct Analysis Method and Effective Length Method and to investigate the effect of flexible connections to stability. Four frames are designed for different connection rigidities with stability methods existing in the 2010 AISC Specification: Direct Analysis Method and Effective Length Method. At the end,conclusions are drawn about the comparison of these two stability methods and the effect of semi-rigid connections to stability.

Este trabalho trata das principais filosofias de verificação de pilares à flexão composta em pórticos de aço assim como das normas que as recomendam. São discutidas as metodologias baseadas em comprimentos efetivos de flambagem, forças horizontais fictícias e análise avançada. É proposta uma metodologia de análise avançada utilizando elementos finitos de casca, que incorpora os efeitos das tensões residuais, imperfeições geométricas e não-linearidades geométricas e do material. São apresentados, ao final do trabalho, exemplos para comparação das diversas metodologias discutidas ao longo do texto. / This work discusses the main philosophies used to verify columns subjected to bending and compression in steel frames as well as the standards which recommend them. The effective length and notional loads approaches and the advanced analysis concept are discussed too. It is proposed a methodology of advanced analysis based on shell finite elements that accounts for the effects of residual stresses, geometric imperfections and geometric and material non-linearity. It is presented, at the end of the text, samples for the comparison of the several methodologies discussed throughout this work.

Thesis (MScEng (Civil Engineering))--Stellenbosch University, 2008. / The Southern African Institute of Steel Construction expressed concern with regard to the unit definition of the effective length factor, K, stipulated for compressive elements of parallel chord trusses in Clause 15 of SANS 10162-1:2005 - Limit state design of hot-rolled steelwork. The simplified method for truss design specified in the code assumes all compression members are pin-connected, which allows for greater design simplicity and reduces the amount of code interpretation required by the designer. In addition to this, Clause 15 requires the additional reduction in resistance of the first web compression members by a factor of 0.85. However, this approach may be considered overly conservative and in current design practice the effective length factor is often reduced to less than 1.0. This research investigates the effective length factor of web compression members in parallel chord trusses, by means of investigative structural analyses of representative trusses using ANGELINE and Prokon analytical programs, and by designing, constructing and testing six representative trusses, using current design practices. A comparative study of a number of different countries’ codified approaches to truss design is also included. The structural analyses revealed that in-plane buckling of the web compression members was the consistent mode of failure, however at a much greater applied load than the design load determined according to SANS 10162-1:2005. Contrary to the expected mode of failure, all six tests performed on the representative trusses exhibited elastic out-of-plane buckling, or strongaxis buckling, of the web compression members, but still at a much greater applied load than the design load. The unexpected out-of-plane buckling of the web members is due to the inplane stiffness of the end connections used. In order to stay true to current design practice, gusset plates and longitudinal welds were used to join the web members to the chords. The stiffness of the gusset plates therefore significantly reduced the effective length of the web compression members in-plane, but did not reduce the effective length out-of-plane. Despite the unanticipated behaviour of the tests performed, certain conclusions can still be drawn from the results. The unit definition of the effective length factor for in-plane buckling of web compression members is too conservative and a K factor of 0.8 is recommended. In addition to this an effective length factor for out-plane-buckling of web compression members of 1.1 is recommended for trusses with welded connections. The necessity of the reduction in resistance of 0.85 of the first web compression members requires further investigation. The most important conclusion to be drawn is that out-of-plane buckling of web compression members can be the dominant failure mode, which is not taken into consideration in current design practice.

Esse trabalho apresenta um estudo comparativo entre métodos simplificados para avaliação da estabilidade de pórticos planos de aço. Aspectos relacionados à classificação das estruturas de aço quanto à deslocabilidade e sistema de contraventamento são apresentados e discutidos. O tradicional procedimento do comprimento efetivo de flambagem, ainda presente em algumas normas, é confrontado com métodos que empregam forças horizontais fictícias para contabilizar os efeitos desestabilizantes, tais como imperfeições geométricas iniciais e tensões residuais. Uma análise numérica avançada via MEF que permite a modelagem explícita dos efeitos que contribuem para a instabilidade de pórticos é empregada como referência na comparação dos resultados. É avaliada a resposta de pilares isolados, edifícios industriais e de múltiplos andares. Os métodos que empregam forças horizontais fictícias foram considerados adequados, pois além de eliminar o cálculo do comprimento efetivo de flambagem, apresentaram resultados mais consistentes em relação à análise avançada. / Two strategies for assessing steel frame stability and beam-column design are studied and compared. Some aspects related to bracing system and sway or non-sway classification are also discussed. The traditional procedure based on effective lengths are compared with some approaches based on notional loads, which propose a set of notional horizontal loads for account stability effects such as initial geometric imperfections and residual stresses. The results are compared with an advanced analysis using FEM, which consists in an explicit modeling of stability effects. Some industrial and multistory frames are studied and the results show that the notional load based procedures are accurate. These procedures are also practical because the need for effective length factors is eliminated.