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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Ökologische Belastungsgrenzen - Aktualisierung und Präzisierung der Erfassung von ökologischen Belastungsgrenzen und ihrer Überschreitungen im Freistaat Sachsen – Fortschreibung der Critical Loads/Level- Untersuchungen bis 2006

Schlutow, Angela, Scheuschner, Thomas 12 May 2009 (has links) (PDF)
Mit dem Critical Loads/Levels-Konzept wurde ein europäischer Ansatz verwirklicht, der einerseits die Notwendigkeit zur Verminderung des Eintrags von Luftschadstoffen verdeutlicht, andererseits die Beurteilung des Erfolgs von Luftreinhaltemaßnahmen erlaubt. Im vorliegenden Heft werden für Sachsen die Überschreitungen der ökologischen Belastungsgrenzen hinsichtlich des Säure- und Stickstoffeintrages für die Rezeptoren Wald und naturnahe waldfreie Ökosysteme dargestellt. Diese liegen für den Zeitraum 1990 - 2006 im Landesplanungsmaßstab (1:200.000) vor. Danach sind viele sächsische Ökosysteme einer ernst zu nehmenden kritischen Belastung insbesondere durch oxidierte und reduzierte Stickstoffverbindungen aus der Atmosphäre ausgesetzt. Das vorliegende Heft richtet sich insbesondere an Institutionen, die an Planungen im Landes-, Regional- und lokalen Maßstab beteiligt sind, aber auch an Naturschutzverbände, Eigentümer und Nutzer des Waldes sowie Forschungseinrichtungen und die interessierte Öffentlichkeit.
2

Ökologische Belastungsgrenzen - Aktualisierung und Präzisierung der Erfassung von ökologischen Belastungsgrenzen und ihrer Überschreitungen im Freistaat Sachsen – Fortschreibung der Critical Loads/Level- Untersuchungen bis 2006

Schlutow, Angela, Scheuschner, Thomas 12 May 2009 (has links)
Mit dem Critical Loads/Levels-Konzept wurde ein europäischer Ansatz verwirklicht, der einerseits die Notwendigkeit zur Verminderung des Eintrags von Luftschadstoffen verdeutlicht, andererseits die Beurteilung des Erfolgs von Luftreinhaltemaßnahmen erlaubt. Im vorliegenden Heft werden für Sachsen die Überschreitungen der ökologischen Belastungsgrenzen hinsichtlich des Säure- und Stickstoffeintrages für die Rezeptoren Wald und naturnahe waldfreie Ökosysteme dargestellt. Diese liegen für den Zeitraum 1990 - 2006 im Landesplanungsmaßstab (1:200.000) vor. Danach sind viele sächsische Ökosysteme einer ernst zu nehmenden kritischen Belastung insbesondere durch oxidierte und reduzierte Stickstoffverbindungen aus der Atmosphäre ausgesetzt. Das vorliegende Heft richtet sich insbesondere an Institutionen, die an Planungen im Landes-, Regional- und lokalen Maßstab beteiligt sind, aber auch an Naturschutzverbände, Eigentümer und Nutzer des Waldes sowie Forschungseinrichtungen und die interessierte Öffentlichkeit.
3

Multi-Agent Systems in Microgrids: Design and Implementation

Feroze, Hassan 21 September 2009 (has links)
The security and resiliency of electric power supply to serve critical facilities are of high importance in today's world. Instead of building large electric power grids and high capacity transmission lines, an intelligent microgrid (or smart grid) can be considered as a promising power supply alternative. In recent years, multi-agent systems have been proposed to provide intelligent energy control and management systems in microgrids. Multi-agent systems offer their inherent benefits of flexibility, extensibility, autonomy, reduced maintenance and more. The implementation of a control network based on multi-agent systems that is capable of making intelligent decisions on behalf of the user has become an area of intense research. Many previous works have proposed multi-agent system architectures that deal with buying and selling of energy within a microgrid and algorithms for auction systems. The others proposed frameworks for multi-agent systems that could be further developed for real life control of microgrid systems. However, most proposed methods ignore the process of sharing energy resources among multiple distinct sets of prioritized loads. It is important to study a scenario that emphasizes on supporting critical loads during outages based on the user's preferences and limited capacity. The situation becomes further appealing when an excess DER capacity after supplying critical loads is allocated to support non-critical loads that belong to multiple users. The previous works also ignore the study of dynamic interactions between the agents and the physical systems. It is important to study the interaction and time delay when an agent issues a control signal to control a physical device in a microgrid and when the command is executed. Agents must be able to respond to the information sensed from the external environment quickly enough to manage the microgrid in a timely fashion. The ability of agents to disconnect the microgrid during emergencies should also be studied. These issues are identified as knowledge gaps that are of focus in this thesis. The objective of this research is to design, develop and implement a multi-agent system that enables real-time management of a microgrid. These include securing critical loads and supporting non-critical loads belonging to various owners with the distributed energy resource that has limited capacity during outages. The system under study consists of physical (microgrid) and cyber elements (multi-agent system). The cyber part or the multi-agent system is of primary focus of this work. The microgrid simulation has been implemented in Matlab/Simulink. It is a simplified distribution circuit that consists of one distributed energy resources (DER), loads and the main grid power supply. For the multi-agent system implementation, various open source agent building toolkits are compared to identify the most suitable agent toolkit for implementation in the proposed multi-agent system. The agent architecture is then designed by dividing overall goal of the system into several smaller tasks and assigning them to each agent. The implementation of multi-agent system was completed by identifying Roles (Role Modeling) and Responsibilities (Social and Domain Responsibilities) of agents in the system, and modeling the Knowledge (Facts), rules and ontology for the agents. Finally, both microgrid simulation and multi-agent system are connected together via TCP/IP using external java programming and a third party TCP server in the Matlab/Simulink environment. In summary, the multi-agent system is designed, developed and implemented in several simulation test cases. It is expected that this work will provide an insight into the design and development of a multi-agent system, as well as serving as a basis for practical implementation of an agent-based technology in a microgrid environment. Furthermore, the work also contributes to new design schemes to increase multi-agent system's intelligence. In particular, these include control algorithms for intelligently managing the limited supply from a DER during emergencies to secure critical loads, and at the same time supporting non-critical loads when the users need the most. / Master of Science
4

Nitrogen, parasites and plants : key interactions in boreal forest ecosystems

Strengbom, Joachim January 2002 (has links)
In the work described in this thesis I studied how increases in nitrogen (N) inputs may affect plant community structure in boreal forest understorey vegetation. These phenomena were investigated in N fertilization experiments and along a national N deposition gradient. After five years of N additions, large changes in understorey vegetation composition were observed in the fertilization study. In plots that received 50 kg N ha'1 year"1 (N2), the abundance of the dominant species, Vaccinium myrtillus, decreased on average by 32 %. No decrease was observed in control plots during the same period. In contrast, the grass Deschampsia flexuosa responded positively to increased N input, being on average more than five times as abundant in the N2 treatments as in controls. Also an increase was seen in the incidence of disease caused by the parasitic fungus Valdensia heterodoxa on leaves of V. myrtillus following N additions. The parasite was on average nearly twice as abundant in N2 plots than in control plots. This could be explained by increased N concentrations in host plant tissue. Disease incidence also increased following experimental additions of glutamine to leaf surfaces of V. myrtillus, suggesting a causal connection between plant N concentration and performance of the fungus. The parasite also played a key role in the observed changes in understorey species composition. D. flexuosa was more abundant in patches in which V. myrtillus was severely affected by V heterodoxa. This suggests that V heterodoxa mediates the increased abundance of D. flexuosa following increased N additions. The fungus mediates changes in the composition of understorey vegetation mainly by increasing light availability via premature leaf loss of V. myrtillus. The incidence of disease due to the parasite was on average higher in large than in smaller N-treated plots, indicating that the response to N fertilization is spatially scale dependent. This shows that using small plot sizes in experiments that simulate changed environmental conditions may be problematic, as important interactions may be underestimated. Comparison of the occurrence of understorey species between regions with different rates of N deposition revealed that the occurrence of the two dwarf shrubs V. myrtillus and V. vitis- idaea was lower in regions with high N deposition compared to regions with low deposition. The opposite pattern was found for V heterodoxa. This is consistent with expectations from N fertilization experiments. For D. flexuosa no differences in occurrence were found between the different regions investigated. The effects on vegetation and mycorrhizal fungi observed following N additions were also found to be long lasting. Nine years after termination of the fertilization, no signs of recovery were detected, and nearly 50 years after termination characteristic signs of N fertilization were found among bryophytes and mycorrhizal fungi. This suggests that the time needed for re-establishment of the original biota following N-induced changes may be substantial. / <p>Diss. (sammanfattning) Umeå : Umeå universitet, 2002, härtill 5 uppsatser</p> / digitalisering@umu
5

Prédiction de la sensibilité biogéochimique et écologique des écosystèmes forestiers français aux dépôts atmosphériques azotés dans un contexte de changement global / Predicting french forest ecosystems biogeochemical and ecological sensitivity to atmospheric nitrogen deposition in a context of global change

Rizzetto, Simon 24 October 2017 (has links)
Depuis des décennies, les dépôts atmosphériques azotés sont connus pour agir de manière sévère sur le fonctionnement des écosystèmes forestiers. Ils influent en effet la biogéochimie du sol, l’équilibre des éléments nutritifs et, en conséquence, la croissance des espèces végétales, la biodiversité végétale de sous-étage et plus globalement la santé des forêts. Dans le cadre de la convention internationale de Genève visant à limiter la pollution atmosphérique transfrontalière à longue distance, le concept de « Charges Critiques », défini à la fin des années 1980, a été retenu comme outil permettant d’évaluer la sensibilité d’un écosystème aux contaminants. Il permet d’estimer la quantité maximale de polluants atmosphériques acceptable par l’écosystème avant apparition de conséquences néfastes à son fonctionnement. De plus, en raison de l’impact des changements globaux sur les processus biogéochimiques régissant le fonctionnement des écosystèmes, l’influence des dépôts atmosphériques et du changement climatique doit être considéré de manière simultanée pour évaluer l’évolution de l’état des écosystèmes au cours du temps. Dès lors l’enjeu majeur est de pouvoir prédire l’effet combiné de ces facteurs sur les écosystèmes forestiers français. C’est l’objectif de ce travail de thèse. Des modèles dynamiques couplés biogéochimiques – écologiques, tels que les modèles ForSAFE-VEG ou PROPS, ou écologiques (basés sur la base de données EcoPlant) ont été développés ou adaptés à ces fins, et appliqués à différentes échelles locale, régionale et nationale, selon différents scénarios de dépôts et climatiques. L’application et la calibration du modèle couplé ForSAFE-VEG sur des placettes forestières permanentes du réseau RENECOFOR ont permis de prédire l’évolution de la composition biogéochimique de la solution du sol et en cascade de la composition floristique de trois sites, sous différents scénarios de dépôts atmosphériques et de changement climatique. Les principales évolutions des sites sont liées à leurs caractéristiques stationnelles. Si le changement climatique joue un rôle prédominant sur la réponse des espèces, les écosystèmes oligotrophes restent sensibles aux dépôts de N. A court terme, l’effet combiné des dépôts et du changement climatique sur le long terme est modulé par les effets de la gestion forestière. L’extrapolation du modèle couplé à plus large échelle nécessite une continuité dans la disponibilité des données d’entrée et de calibration de la réponse des espèces. Les données et scénarios de changement climatiques ont été complétés et actualisés à l’aide du modèle SAFRAN et des nouveaux scénarios RCP régionalisés. La calibration de la réponse des espèces végétales à l’échelle de la France a été réalisée à partir des mesures de la base de données phytoécologiques EcoPlant, par le développement de modèles de distribution d’espèces (SDM), en intégrant simultanément des variables climatiques, édaphiques, d’énergie et de nutrition. Le couplage entre le modèle ForSAFE et les SDM assure une modélisation robuste à l’échelle du territoire de la réponse des écosystèmes forestiers dans le temps, calibrée pour les conditions pédoclimatiques françaises. La modélisation des charges critiques d’acidité, d’eutrophisation et de biodiversité sur l’ensemble des sites RENECOFOR et la totalité des écosystèmes forestiers français montre des sensibilités variées aux dépôts de soufre et d’azote en fonction des écosystèmes, avec parmi les plus sensibles les Landes, la Sologne et le Massif Central. Des indices de qualité des habitats (HSi) ont été calculés à l’échelle de tous les écosystèmes par le modèle PROPS et les SDM. La sélection des espèces représentatives reste primordiale car elle conditionne la valeur finale de HSi. Ce paramètre est l’un des plus sensibles à prendre en compte dans la modélisation. Il est à mettre en relation avec les objectifs de protection des écosystèmes voulus par les gestionnaires. / For decades, it has been known that atmospheric nitrogen depositions have a severe impact on the operations of forest ecosystems. Indeed, they affect the soil biogeochemistry, the balance of the nutritive elements and consequently the plant species growth, the biodiversity of the understory vegetation and more globally the forest health. As part of the Geneva Agreement to limit the long-range transboundary air pollution, the concept of "critical loads", defined towards the end of the 1980s, was adopted as a tool to enable the assessment of the sensitivity of the ecosystems to contaminants. It can be used to estimate the maximal amount of atmospheric contaminants which can be accepted by the ecosystem before significant harmful effects on specified sensitive biological indicators appear. In addition, because of the impact of global warming on biogeochemical processes regulating the functioning of ecosystems, the influence of atmospheric depositions and climate change must be considered simultaneously to evaluate the evolution of ecosystem conditions over time. Since then, the major issue has been to be able to predict the combined effect of these factors on the French forest ecosystems. This is the aim of this PhD work. Coupled dynamic biochemical-ecological models, such as ForSAFE-VEG or PROPS models, or ecological (based on EcoPlant database) were developed or adapted for this purpose and applied to different local, regional and national scales against different deposition and climatic scenarios. The application and calibration of the coupled model ForSAFE-VEG on permanent forest plots from the RENECOFOR network enabled prediction of the evolution of the soil solution biogeochemical composition, as well as monitoring of the floristic composition of three sites, under different scenarios of atmospheric deposition and climate change. The principal site evolutions are related to their stational characteristics. If the climate change plays a primary role on a species’ response, the oligotrophic ecosystems remain sensitive to nitrogen depositions. On a short term basis, the combined effect of the deposits and long term climate change is modulated by forest management. The extrapolation of the coupled model on a larger scale requires continuity in the availability of input data and calibration of the species’ response. The data and climate changes scenarios were completed and updated with the SAFRAN model and new regionalised RCP scenarios. The calibration of the response of plant species throughout France was carried out using measurements of the phytoecological database EcoPlant, via development of species distribution models (SDM). The coupling between ForSAFE and the SDM ensures a robust global modelling of the forest ecosystems’ response over time, calibrated for the French pedoclimatic conditions. The modelling of the acidic, eutrophication and biodiversity critical loads, on all the RENECOFOR sites and French forest ecosystems, shows the various sensitivities to sulphur and nitrogen depositions depending on the ecosystem. Ecosystems located in the Landes, Sologne and Massif Central appear to be amongst the most sensitive ones. The Habitats Suitability Index (HSI) was calculated throughout all the ecosystems via PROPS models and the SDM. The selection of representative species remains pivotal as the final HSI value is conditional, depending on this factor. This parameter is one of the most sensitive factors to take into account with the model. It must be linked with forest managers' objectives for the protection of the ecosystems.
6

Buckling of End-Bearing Retaining Walls in Clay

Jansson, Fredrik, Nilsson, Nils January 2018 (has links)
The design of back-anchored retaining walls in Sweden has traditionally not included global elastic instability of the retaining wall as a possible failure mode. Eurocode 3 part 5 (SS-EN 1993-5) requires design of steel structural members for retaining walls to assess the risk of buckling if the normal force exceeds 4 % of the critical buckling load of the retaining wall. The geological conditions in Eastern Sweden are characterized by the intersection of very hard Precambrian rock and very soft Holocene clays. Thus often ground anchors anchored in rock at a 30-50 degree angle to the vertical plane are used to support retaining walls, resulting in a very high utilization of the ground anchor and a significant normal force in the retaining wall. The threshold value for buckling risk is consequently frequently exceeded and the specific failure mode, of global buckling, is often limiting the use of the structural members in practical design. The buckling load can either be calculated using Euler’s second or third buckling mode, or by modelling the soil-structure interaction by a suitable model. Since no such model is specified in the code, the aim of this thesis was to develop a model which takes into account the stabilizing effect of the soil for the calculation of the buckling force and to model the soil-structure interaction with a beam-spring model connected to Winkler springs. The model simulations show that the soil has a significant influence on the critical load, especially when the retaining wall base is driven to depths greater than 2 meters below excavation depth. The model simulations suggest that higher utilization, with up to 4 times greater critical load, of the steel members is possible for some specific cases and an idealized design factor is also elaborated. / Dimensioneringen av bakåtförankrade spontväggar har traditionellt sett i Sverige inte tagit hänsyn till risken för global knäckning. I och med införandet av Eurokod 3 kapitel 5 (SS-EN 1993-5) som styrande dokument vid dimensionering av sponter måste risken för knäckning nu mera beaktas när normalkraften överstiger 4 % av den kritiska knäckningslasten. De geologiska förhållandena i de östra delarna av Sverige, med lösa leror som täcker hårt berg, leder till att bakåtförankrade sponter med brant lutande stag ofta används. Detta leder till en hög utnyttjandegrad av ankaret och också stora normalkrafter i sponten, vilket leder till att knäckning ofta blir dimensionerande brottmod för sponten. Metoden för att beräkna knäckningslasten kan enligt SS-EN 1993-5 göras med Eulers andra eller tredje knäckningsfall eller med en modell som tar hänsyn till jordens stabiliserande effekt. Idag finns ingen sådan numerisk modell att hitta i litteraturen, varför målet med detta arbete har varit att finna en lämplig modell för att ta hänsyn till jordens inverkan vid bestämning av knäckningslasten. För att modellera samverkan mellan jorden och sponten användes en balkmodell med Winkler fjädrar. Simuleringarna visar att jorden har en signifikant inverkan på den kritiska knäckningslasten, särskilt när nedslagsdjupet är större än 2 meter. Flera simulerade geometrier har gett drygt fyra gånger högre knäcklast jämfört med den knäcklast som erhålls om SS-EN 1993-5 följs. Om jorden tas hänsyn till i dimensioneringen av en spont skulle således slankare konstruktioner kunna användas.
7

Alimentação de cargas hospitalares críticas utilizando conversores estáticos

Oliveira, Yuri Calil Loures de 12 January 2016 (has links)
Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-05-05T18:23:07Z No. of bitstreams: 1 yuricalillouresdeoliveira.pdf: 2613361 bytes, checksum: b14d216c9e91ffe085e35724d58bc704 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-06-07T15:42:11Z (GMT) No. of bitstreams: 1 yuricalillouresdeoliveira.pdf: 2613361 bytes, checksum: b14d216c9e91ffe085e35724d58bc704 (MD5) / Made available in DSpace on 2016-06-07T15:42:11Z (GMT). No. of bitstreams: 1 yuricalillouresdeoliveira.pdf: 2613361 bytes, checksum: b14d216c9e91ffe085e35724d58bc704 (MD5) Previous issue date: 2016-01-12 / CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico / Esta dissertação apresenta um estudo de estratégias de alimentação de cargas hospitalares críticas utilizando conversores estáticos de energia. As cargas hospitalares escolhidas foram os equipamentos de raio x, tomografia computadorizada e ressonância magnética, sendo comparadas as seguintes formas de integração à rede: (i) estrutura com um retificador trifásico conectado à rede e três inversores monofásicos conectados às cargas ou (ii) estrutura com três retificadores monofásicos conectados à rede e três inversores monofásicos conectados às cargas. Por questões de patente, houve dificuldade em se encontrar os circuitos de front-end das fontes de alimentação das cargas hospitalares. Logo, as mesmas foram construídas dentro do ambiente de simulação do software PSIM utilizando dados de medição obtidos na literatura. O controle dos retificadores trifásico e monofásico foi realizados utilizando duas malhas de controle em cascata, com a malha interna controlando a corrente consumida da rede e a malha externa regulando a tensão no barramento CC. Para os três inversores monofásicos de saída foram implementados os controles PI RES e PI SRF visando uma comparação quanto ao desempenho. Como forma de validar o modelo matemático do sistema e o algoritmo de controle, foram feitas simulações utilizando o software PSIM. A análise feita comprovou que os resultados de simulação se mostraram coerentes com a modelagem matemática do sistema. / This master thesis presents a study about feeding strategies of critical hospital loads through power static converters. The chosen hospital loads were the x ray equipment, the computed tomography and the magnetic resonance. The following forms of grid integration were compared: (i) structure with a three-phase rectifier connected to the network and three single-phase inverters connected to the loads or (ii) structure with three single-phase rectifiers connected to the network and three single-phase inverters connected to the loads. Due to patent issues, it was difficult to find the front-end circuits for power supplies of hospital loads. Therefore, the loads were implemented in PSIM software environment using measurement data obtained from literature. The control of three-phase and single-phase rectifiers was implemented using two cascaded control loops, with the inner loop controlling the current drawn from the network and the outer loop regulating the DC bus voltage. For the single-phase inverter, PI RES and PI SRF controls were implemented, targeting a comparison in terms of performance. In order to validate the mathematical model of the system and the control algorithm, simulations were performed using the PSIM software. The analysis showed that the simulation results were consistent with the mathematical modeling of the system.
8

[pt] ESTUDO DA FLAMBAGEM LATERAL ESTÁTICA E DINÂMICA DE VIGAS ALTAS COM USO DE ELEMENTOS FINITOS DE PLACAS / [en] STATIC AND DYNAMIC BUCKLING OF DEEP BEAMS WITH PLATE FINITE ELEMENTS

FELIPE DA SILVA BRANDAO 14 December 2020 (has links)
[pt] Este trabalho tem como objetivo principal estudar o comportamento de flambagem lateral de vigas através de modelos de elementos finitos baseados nas teorias de placas de Kirchhoff e de Mindlin–Reissner. Esses modelos foram combinados com efeitos de membrana, possibilitando a análise de cascas. Foi desenvolvido um código MATLAB para analisar cargas críticas estáticas e dinâmicas, modos de flambagem, frequências e modos de vibração de placas finas e espessas sujeitas a cargas conservativas e cargas não conservativas (também chamadas de seguidoras ou circulatórias). O programa ANSYS foi usado para validação e comparação. Para o cálculo das frequências naturais foram usadas as matrizes de massa e a matriz de rigidez. Para o cálculo da carga crítica estática com carga conservativa, implementa-se a matriz geométrica. Quando há carregamento seguidor não conservativo, é necessário adicionar uma matriz de correção de cargas que é uma matriz assimétrica, achando assim a carga crítica dinâmica, também denominada de flutter. Diferentes condições de contorno e diferentes carregamentos são aplicados em vigas e analisados os casos de flambagem lateral. Valores teóricos encontrados na literatura são comparados com os valores achados usando o método de elementos finitos. A instabilidade lateral de vigas esbeltas tem grande interesse prático, pois em alguns casos pode ocorrer o esgotamento da resistência da peça antes mesmo que seja atingido o estado limite último de flexão. Por isso, o tema flambagem lateral é mencionado em diversas normas nacionais e internacionais, tendo sido feitas algumas comparações com os resultados do programa implementado neste trabalho. / [en] The main objective of this paper is to present results on the lateral buckling of beams using finite elements based on Kirchhoff and Mindlin-Reissner Plate theories, merged with membrane elements in order to include the analysis of shells. A MATLAB code was developed to calculate static and dynamic critical loads, buckling modes, frequencies, and vibration modes of thin and thick plates subjected to conservative and non-conservative (also called follower or circulatory) loads. Mass and stiffness matrices are employed to determine natural frequencies. In the case of conservative loads, static critical loads are calculated by adding a so-called geometric matrix. However, in case of displacement-dependent applied forces, it is necessary to implement a matrix that will correct the loads, designated as load matrix. In the case of conservative forces, the load matrix is symmetric, and in the case of non-conservative forces, it is non-symmetric. In the latter case, the critical load usually will correspond to dynamic behavior designated as flutter. Different boundary conditions and loads are considered and several cases of lateral buckling are investigated. Theoretical values when found in the literature are compared with values determined by Finite Element Method (FEM). The lateral instability of slender beams is very important in practice, because in some situations it may occur prior to ultimate plastic limit state in bending. Therefore, lateral buckling is mentioned in a wide variety of national and international rules, and some comparisons with the results of the computer code developed herein are presented.

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