Made available in DSpace on 2016-06-02T20:02:57Z (GMT). No. of bitstreams: 1 6458.pdf: 5523001 bytes, checksum: 13a03e09a64c7737467c2e1eee8e86bc (MD5) Previous issue date: 2014-10-17 / The dissertation presents a proposal for teaching the content of fractions to a 7th grade classroom of basic education, based on a concrete didactical material, Fraction Case , and the Bar Model inspired in Singapore Mathematics, focused on the conceptual understanding along with basic operation skills. The motivation to this work was the recognition of great difficulty in learning with understanding of rational numbers, shown by the students of basic education across the grades. The learning of rational numbers is of fundamental importance to the accomplishment of the mathematics curriculum of basic education. We adopted the Fraction Case and the Bar Model because they actually offer the possibility of visualizing concrete representation of ideas that underline the subject of fractions. The proposed activities were inspired by the didactical ideas and activities in Baldin & Malagutti (2006), and they aim at the understanding of the concept of equivalent fractions together with the basic operations of addition, subtraction, multiplication and division of fractions, starting from the perspective of the part-whole relationship. We bring out the outcome resulted from the application of activities in three classrooms of 7th grade students of a private school of city of Bauru. / Apresentamos neste trabalho uma proposta de ensino do conteúdo de frações para uma turma de 7º ano, baseada na utilização de um material concreto intitulado Estojo das frações e do Modelo de Barras da Matemática de Singapura, e centrada na consolidação dos conceitos e das operações básicas. A realização deste trabalho foi motivada por uma constatação da enorme dificuldade de aprendizagem e compreensão dos números racionais apresentada por alunos de diversas séries do ensino fundamental. A aprendizagem dos números racionais é de fundamental importância para o desenvolvimento do conteúdo curricular da matemática do ensino fundamental. O Estojo de frações e o Modelo de Barras foram utilizados, pois oferecem a possibilidade de visualizar concretamente os conceitos relacionados ao tema de frações. As atividades propostas foram baseadas nas ideias didáticas e atividades do material de Baldin e Malagutti (2006), e buscam a compreensão do significado de frações equivalentes e das operações de adição, subtração, multiplicação e divisão de frações a partir do significado parte-todo. Trazemos também os resultados obtidos a partir da aplicação dessa proposta com três turmas de 7º ano de uma escola particular de Bauru.

The aim of this Diploma thesis is focused on a design of the road bridge between Brodzany and Partizanske municipality, spaned the Valley. The design is processed in three preliminary designs. Selected variant is a continuos girder box with inclined walls, post-tensioned by bonded cables. Structural analysis includes the influences of construction by TDA method. The sctructure is assessed for temporary and permanent states. Design and check were carried out according to EC.

En utgångspunkt för denna studie har varit att flera svenska elever har svårigheter att lösa matematiska textuppgifter. I ett försök att utveckla elevers förmågor att lösa matematiska textuppgifter har Singaporemetoden blivit allt mer populär. I Singaporemetoden används blockmodellen för att visualisera textuppgifter. Syftet med följande uppsats är att, utifrån ett sociokulturellt perspektiv, synliggöra hur fem lärare uppfattar att blockmodellen kan stötta elever i att utveckla problemlösningsförmågan när de löser textuppgifter. Uppsatsen syftar även till att synliggöra vilka erfarenheter lärarna har av att arbeta med blockmodellen i matematikundervisningen för årskurserna 1–6. Studien utgår från en kvalitativ metod där syftet besvaras genom fem enskilda semistrukturerade intervjuer med grundlärare som undervisar utifrån blockmodellen i matematikämnet. Studien har utgångspunkt i Vygotskijs sociokulturella teori och har inspirerats av en tematisk metodanalys. Resultatet visar att lärare uppfattar att det finns såväl fördelar som nackdelar med att använda blockmodellen i matematikundervisningen. Lärarna uppfattar att blockmodellen främst är stöttande genom att modellen strukturerar textuppgifter och stödjer elever och lärare att ta sig an textuppgifter. Med stöd av blockmodellen visualiseras dessutom matematiska områden och elever ges möjlighet att utveckla matematisk förståelse. Modellen kan även hjälpa lärare att skapa samtalssituationer för att låta elever utvecklas i den proximala utvecklingszonen. I samtalen får elever möjlighet att utveckla problemlösnings-, begrepps-, resonemangs- och kommunikationsförmåga. Resultatet visar även att främsta utmaningen är att modellen innehåller många steg som kräver att rita och skriva vilket inte passar för alla elever. Blockmodellen ger dessutom upphov till utmaningar när det gäller att differentiera undervisningen, eftersom arbetet oftast sker gemensamt med uppgifter på en specifik svårighetsgrad. Slutsatsen är att blockmodellen kan stötta elever i att utveckla problemlösningsförmågan i textuppgifter i kombination med lärarens kompetens. / The premise for this study has been that swedish upper primary- and lower secondary pupils have been shown to have difficulties in solving textual tasks in mathematics. In an attempt to develop pupils’ abilities in solving these textual tasks, the Singapore model has become increasingly popular. The Singapore model utilizes what is known as the bar model, which is used to visualize the text within these tasks. The purpose of this study is to highlight how five teachers perceive that the bar model can support pupils in developing problem-solving skills in textual tasks, from a socio-cultural perspective. The study also aims to highlight the experiences the teachers have gained from working with the bar model in mathematics teaching for grades 1-6. The study's purpose has been answered through five individual, qualitative and semi-structured interviews, with primary teachers who teach mathematics with the support of the the bar model. The study uses Vygotskij’s sociocultural theory and has been further inspired by a thematic method analysis to present and understand the results. The results show that teachers perceive both advantages and disadvantages in using the bar model in mathematics teaching. The teachers expressed that the bar model is primarily supportive in that the model structures textual tasks and supports pupils and teachers when approaching textual tasks. With the support of the bar model, abstract areas are also visualized and the pupils gain an increased mathematical understanding. The model can also contribute to creating conversational situations in order for pupils to develop in regards to the proximal development zone. In these conversations, pupils are given the opportunity to develop problem-solving, conceptual, reasoning and communicational skills. The results also show that the main challenge is that the model contains many elements that require drawing and writing, which are not suitable for all pupils. The bar model also gives rise to challenges in regard to differentiating the teaching, since the work usually takes place jointly with tasks at a specific degree of difficulty. The conclusion is that the bar model can support pupils in developing problem-solving skills in textual tasks in combination with teacher competence.

In this thesis, the possibility of detection of fault location in the cable distribution systems by using traveling waves due to fault and circuit breaker operations is investigated. Waveforms originated from both actions and fault steady state are separately analyzed. During such switching actions, high frequency variations which are absent in the steady state conditions, take place. In order to simulate high frequency changes properly, system elements are modeled accordingly. In other words, frequency dependent models are introduced, and they are used in Electro-Magnetic Transients Program (EMTP). Since the characteristics of waveforms are different for separately analyzed portions, different fault locating algorithms with their limitations are introduced.

Made available in DSpace on 2016-06-02T20:02:57Z (GMT). No. of bitstreams: 1 6507.pdf: 2675622 bytes, checksum: 1fa2e1a89f27433883070d1a6ede575e (MD5) Previous issue date: 2014-10-17 / The difficulties in learning and teaching of algebra can be detected in the school cycle 4 (8th and 9th grades) of the Elementary School II and throughout High School, such difficulties being present in all Brazilian schools. These difficulties arise from an institutional failure, in others words, in the transition from arithmetic to algebra, in the phase of pre-algebra which occurs at cycle 3 ( 6th and 7th grades) of the Elementary School II. When this transition is unsatisfactory this compromises the subsequent studies making the students feel not motivated in learning the content of algebra. Therefore, in this research project we planned and executed 6 (six) activities based on the methodology of Problem Solving based on the phases proposed by George Polya, along with the methodology of the Bar Model from Singapore Mathematics. The activities were carried out in seventh grade classrooms of Elementary School II of Instituto Educacional Estilo , Campinas, SP. The results of this dissertation suggests to teachers of Elementary School II didactical sequences of activities that they can use and enjoy in classroom practices, so that they can improve also their teaching and learning, contributing to the development of the students. With the objective of achieving a satisfactory transition from arithmetic to algebra, the activities were developed and based on problems solving, and then analyzed critically using the Problem Solving steps. After 6 (six) activities, we applied a diagnostic evaluation in order to analyze the results and to check if the activities contributed to a meaningful learning of algebra. The dissertation presents a theoretical study about teaching and learning algebra as well as a study on the methodologies of Problem Solving in classroom practice and Bar Model from Singapore Mathematics. / As dificuldades na aprendizagem e no ensino da álgebra podem ser constatadas no ciclo 4 (8º Ano e 9º Ano) do Ensino Fundamental II e também em todo o Ensino Médio, tais dificuldades estão presentes em todas as escolas brasileiras. Essas dificuldades são decorrentes de uma falha na introdução, ou seja, na transição da aritmética para a álgebra, a pré-álgebra que ocorre no final do ciclo 3 (6º Ano e 7º Ano) do Ensino Fundamental II, já que feita de maneira não satisfatória pode comprometer as aulas seguintes fazendo com que os alunos se sintam desmotivados a aprenderem o conteúdo de álgebra. Deste modo foram planejadas e executadas 6 (seis) atividades utilizando a metodologia de Resolução de Problemas seguindo as etapas de George Polya, juntamente com a metodologia do Modelo de Barras segundo a Filosofia da Matemática de Singapura. As atividades foram aplicadas em duas turmas do sétimo ano do Ensino Fundamental II, no colégio Instituto Educacional Estilo, Campinas, SP. O trabalho desenvolvido nesta dissertação proporciona aos professores do Ensino Fundamental II e Ensino Médio uma sequência didática, que podem utilizar e aproveitar em suas aulas de forma que possam também melhorar em suas práticas de ensino e aprendizagens, de maneira a contribuir para o desenvolvimento de seus alunos. Com o objetivo de realizar uma transição satisfatória da aritmética para álgebra, as atividades foram elaboradas e baseadas na resolução de problemas, e depois analisadas criticamente por meio das etapas de resolução. Após as 6 (seis) atividades, aplicamos uma avaliação diagnóstica de forma a analisar os resultados para verificar se as atividades contribuíram com significado para uma aprendizagem da álgebra. O trabalho apresenta um estudo teórico sobre o ensino e aprendizagem da álgebra e também apresenta um estudo sobre as metodologias desenvolvidas no trabalho, Resolução de Problemas e Modelo de Barras segundo a Filosofia da Matemática de Singapura.

My diploma thesis deals with design of the bridge number 202 on expressway in Slovakia. The bridge leads across the road number I50 (between Trenčín and Bánovce nad Bebravou) and railway number 130 (between Trenčín and Chynorany). For each course there is a separate super-structure. Only left super-structure is considered for the work. The box girder with four spans is chosen from three variations. This bridge is designed according to limit states, construction´s influence on design is taking into consideration. Structural model of construction is made as a spatial bar model. Structural analysis, well arranged drawings and visualization are elaborated in this thesis too.

The subject of this bachelo r’s thesis is the design a new supporting bridge construction in Prešovský kraj, district Levoča the territory of Slovak Republic. This object is located on the highway D 26,5/120, at kilometer 13,499 795 and communication of third class – 131-00 bridges. The objective is the design of a perpendicular four-span construction, which is proposed in three variants. The first variant is a chamber girder with inclined walls from post-tensioned concrete height 2,480 m. The second variant is composed of two beamed cross-section and the third variant is composed of one beamed cross-section. For detailed assessment the first variant was chosen with a length of bridging of 166,000 m. The calculation of load effects is done by software Scia Engineer and compared with a manual calculation according to current standards. This bridge is designed according to limit states, construction´s influence on design is taking into consideration. Structural analysis, well arranged drawings and visualization are elaborated in this thesis too.

In my thesis, I created a study of plan curved cable stayed pedestrian bridge. As the main construction material is used prestressed concrete. Suspenders and railing are made from steel. The footbridge has a length of 130,00 meters and a width of 3,70 meters. The plan shape of the structure is composed of two oposite arches. Bridge deck is made of box girder. The bridge deck is single-side suspended on two concrete pylons with a height of 39,00 m. Pylons are supported by suspender.

The development of renewable energies and the desired independence from fossil energy sources are essential for security of supply. Wind energy turbines already account for the largest share of electricity generation in Germany. As part of modular precast concepts for wind turbine towers, vertical joints now divide the segments into even smaller components. This significantly reduces transport costs and installation time. The load-bearing behaviour of these segmented concrete towers is very complex due to the horizontal and vertical joints and the resulting restrained cross-sectional deformations. In the case of thin-walled half-shell segments now used in modern wind turbine towers, cross-sectional distortion and warping can significantly reduce the load-bearing capacity. Even under pure torsional loading, there is a decrease in the horizontal joint load capacity compared to conventional thin-walled circular rings. However, there are currently no design approaches for this new construction, as the structural behaviour is neither fully understood nor reliably modeled. This cumulative dissertation deals with the modeling of the torsional behaviour of segmented concrete towers for wind turbines based on the warping theory of thin-walled bars. Transferring the complex mechanical relationships into an understandable and comprehensible bar model allows differentiated evaluation approaches. In the case of segmented concrete towers, this leads to the long-term realization of even more innovative, higher and safer tower concepts. With this calculation approach, the practical engineer always remains in control of his or her own actions. Accordingly, the results can be used as a basis for evaluation without much need for interpretation, e.g. to assess the effect of restrained sectional warping on the distribution of normal stresses. The successive derivation of an engineering approach is presented using mechanical modeling concepts and non-linear numerical investigations as well as further (experimental) investigations. This provides the basis for future validation with carefully conducted tests on actual concrete segments. The core of the dissertation consists of four peer-reviewed papers that have already been published in scientifically proven journals (Structural Concrete and Engineering Structures). The framework story begins by explaining the scientific classification and relevance of the topic. The current state of the art is the basis for deriving research gaps and objectives, as well as a framework of hypotheses to be evaluated. Subsequently, the four papers are placed in the overall context of modeling the torsional behaviour of segmented concrete towers. Paper [A] deals with experimental investigations, analysis and evaluation of the joint behaviour of modular towers in large-scale tests. The gain of knowledge about the uneven distribution of forces in the horizontal joints also has a significant influence on the design models of the half-shell structure. Papers [B] and [C] present an engineering approach to determine the torsional behaviour of segmented concrete towers based on the warping theory of thin-walled bars. This calculation approach includes two methods for evaluating the internal forces of a half-shell pair and the associated stress calculation. A practical analysis method using an analogy to higher order beam theory is introduced to overcome the difficulties of numerical calculation by the finite element method. In this way, the load-bearing behaviour can be described as accurately as possible and the decisive influencing parameters can be isolated. Paper [D] presents the further development and the numerical and analytical validation of the engineering model for the entire tower structure. The influence of the adjacent segments on the torsional behaviour of the assembled half-shell tower is implemented in the model approach. This is based on analytical modeling using spring systems and extensive numerical investigations. Additional studies relate to the surface condition of ground concrete segments, the preliminary investigations on aluminium segments, the initial preliminary considerations on a coherent test design and the effects of multiple vertically divided segments. Finally, the findings are summarized and the overall result of the research is described by evaluating the hypotheses. In addition, the most important perspectives for future research and transfer achievements are pointed out. The presentation of the overall results of this dissertation impressively shows that the successive extension of the model approach leads to a more precise and differentiated isolation of the influencing variables. This improves the realistic representation of the torsional behaviour of assembled half-shells based on the warping theory of thin-walled bars, taking the application limits into account. However, the simplicity and applicability of the engineering model are not compromised by the continuous development. The analytically proven and numerically validated dependence on the slenderness ratio of the segments results in a better understanding of the load transfer in the modular precast structure. A much simplified internal force calculation can be used as the basis for the reinforced concrete design by applying the analogy to the tension rod under bending stress. The division of the load components provides a better understanding of the force flow of the modular structure. Accordingly, the combination of the tension rod analogy, the load redistribution principle and the modified deformation approach, taking the adjacent segments into account, allow the user to isolate and evaluate the influencing parameters of the torsional behaviour with little effort. Finally, in addition to model approaches and detailed numerical simulations, accompanying experimental investigations are required, and this dissertation provides the basis for a coherent and well-conceived experimental program. / Der Ausbau der erneuerbaren Energien und die angestrebte Unabhängigkeit von fossilen Energieträgern sind für die Versorgungssicherheit unerlässlich. Den größten Anteil an der Stromerzeugung haben in Deutschland schon heute die Windenergieanlagen. Im Rahmen modularer Fertigteilkonzepte für Türme von Windenergieanlagen teilen mittlerweile Vertikalfugen die Segmente in immer kleinere Komponenten. Auf diese Weise können die Transportkosten und der Montageaufwand erheblich reduziert werden. Das Tragverhalten dieser segmentierten Betontürme ist aufgrund der horizontalen und vertikalen Fugen sowie der daraus resultierenden behinderten Querschnittsverformungen sehr komplex. Bei dünnwandigen Halbschalensegmenten, die inzwischen im modernen Turmbau für Windenergieanlagen eingesetzt werden, können Querschnittsverzerrungen und -verwölbungen die Tragfähigkeit erheblich beeinträchtigen. Bereits bei einer reinen Torsionsbelastung ist im Vergleich zu konventionellen dünnwandigen Kreisringen eine Abnahme der horizontalen Fugentragfähigkeit zu erkennen. Es existieren zurzeit jedoch noch keine Bemessungsansätze für die neuartige Konstruktion, da weder das Strukturverhalten vollständig verstanden ist, noch verlässlich modelliert werden kann. Diese kumulative Dissertation befasst sich daher mit der Modellierung des Torsionstragverhaltens von segmentierten Betontürmen für Windenergieanlagen auf Basis der Wölbtheorie dünnwandiger Stäbe. Ziel ist die realitätsnahe Abbildung des Torsionstragverhaltens der hybriden Turmkonstruktion durch die sukzessive Entwicklung eines Ingenieurmodells. Die Übertragung der komplexen mechanischen Zusammenhänge in ein verständliches Stabmodell ermöglicht differenzierte Bewertungsansätze. Dies führt im Anwendungsfall der segmentierten Betontürme langfristig zur Realisierung noch innovativerer, höherer und sicherer Turmkonzepte. Mit diesem Berechnungsansatz behalten die in der Praxis tätigen Ingenieur:innen stets die Kontrolle über das eigene Handeln. Die Ergebnisse können ohne besonderen Interpretationsbedarf als Bewertungsgrundlage verwendet werden, um z. B. die Auswirkungen des Phänomens der behinderten Querschnittsverwölbung auf die Verteilung der Normalspannungen zu beurteilen. Ausgehend von mechanischen Modellvorstellungen und nichtlinearen numerischen Untersuchungen sowie weiteren (experimentellen) Untersuchungen wird daher die sukzessive Herleitung eines ingenieurmäßigen Ansatzes vorgestellt. Dieser dient als Grundlage für die zukünftige Validierung im Zuge sorgfältig durchzuführender Versuche an Betonsegmenten. Den Kern der Dissertation bilden vier begutachtete Fachartikel, die bereits in wissenschaftlich anerkannten Fachzeitschriften (Structural Concrete und Engineering Structures) veröffentlicht wurden. Die Rahmenhandlung erläutert zu Beginn die wissenschaftliche Einordnung und Relevanz der Thematik. Der aktuelle Stand der Technik ist die Grundlage für die Ableitung von Forschungslücken und Zielsetzungen sowie eines zu evaluierenden Hypothesengerüsts. Darauf aufbauend erfolgt die Einordnung der vier Fachbeiträge in den Gesamtkontext der Modellierung des Torsionsverhaltens segmentierter Betontürme. Der Artikel [A] befasst sich mit experimentellen Untersuchungen und der Analyse und Bewertung des Fugentragverhaltens modularer Türme in Großversuchen. Die gewonnenen Erkenntnisse über die ungleichmäßige Kraftverteilung in den Horizontalfugen haben auch einen erheblichen Einfluss auf die Bemessungsmodelle der Halbschalenkonstruktion. In den Artikeln [B] und [C] wird ein ingenieurmäßiger Ansatz zur Ermittlung des Torsionsverhaltens von segmentierten Betontürmen vorgestellt, der auf der Wölbtheorie dünnwandiger Stäbe basiert. Dieser Berechnungsansatz beinhaltet zwei Methoden zur Ermittlung der inneren Schnittgrößen eines Halbschalenpaares und der zugehörigen Spannungsberechnung. Es wird eine praktikable Analysemethode in Analogie zur Balkentheorie höherer Ordnung eingeführt, um die Schwierigkeiten bei der numerischen Berechnung mit der Finiten Elemente Methode zu bewältigen. Damit kann das Tragverhalten möglichst genau beschrieben und die maßgeblichen Einflussparameter isoliert werden. In Artikel [D] wird die Weiterentwicklung sowie die numerische und analytische Validierung des Ingenieurmodells für die gesamte Turmstruktur vorgestellt. Der Einfluss der Nachbarsegmente auf das Torsionsverhalten des zusammengesetzten Halbschalenturms wird in den Modellansatz implementiert. Dies erfolgt auf der Grundlage analytischer Modellvorstellungen unter der Verwendung von Federsystemen und umfangreicher numerischer Untersuchungen. Ergänzende Betrachtungen umfassen die Oberflächenbeschaffenheit der geschliffenen Betonsegmente, die Voruntersuchungen an Aluminiumsegmenten, die ersten Vorüberlegungen zu einem kohärenten Versuchskonzept und die Auswirkungen von mehrfach vertikal geteilten Segmenten. Abschließend werden die gewonnenen Erkenntnisse zusammengefasst und das übergreifende Gesamtergebnis der Forschung wird über die Bewertung der Hypothesen beschrieben. Darüber hinaus werden die wichtigsten Perspektiven für zukünftige Forschungs- und Transferleistungen aufgezeigt. Die Darstellung des Gesamtergebnisses dieser Dissertation zeigt eindrucksvoll, dass die sukzessive Erweiterung des Modellansatzes zu einer genaueren und differenzierteren Isolierung der Einflussgrößen führt. Dies verbessert unter Berücksichtigung der Anwendungsgrenzen die realitätsnahe Abbildung des Torsionsverhaltens zusammengesetzter Halbschalen auf Basis der Wölbtheorie dünnwandiger Stäbe. Die kontinuierliche Weiterentwicklung geht nicht zulasten der Einfachheit und Anwendbarkeit des Ingenieurmodells. Dementsprechend führt die analytisch nachgewiesene und numerisch validierte Abhängigkeit vom Schlankheitsgrad der Segmente zu einem besseren Verständnis der Lastabtragung in der modularen Fertigteilstruktur. Die Anwendung der Analogie zum biegebeanspruchten Zugstab ermöglicht eine wesentlich vereinfachte Schnittgrößenermittlung als Grundlage für die Stahlbetonbemessung. Ein besseres Verständnis des Kraftflusses in der modularen Konstruktion wird durch die Aufteilung der Lastkomponenten erreicht. Die Zusammenführung der Ansätze aus Zugstabanalogie, Lastumverteilungsprinzip und modifiziertem Verformungsansatz unter Berücksichtigung der Nachbarsegmente ermöglichen es den Anwender:innen, die Einflussparameter des Torsionsverhaltens ohne großen Aufwand zu isolieren und zu bewerten. Schließlich sind neben den Modellansätzen und detaillierten numerischen Betrachtungen auch begleitende experimentelle Untersuchungen erforderlich, wobei diese Dissertation die Grundlage für ein schlüssiges und durchdachtes Versuchsprogramm darstellt.

The diploma thesis describes the design and assessment of steel structure of the roofing of the military museum in Králíky. The supporting structure of hall is 40.00 meters span. The total layout are 55.93 x 72.04 m, building height 11.43 m, 16.11 m pylon height. Main construction material is steel, grade S355, secondary constructions are made from steel grade S235, rods are made from steel grade S460. I did optimization of steel structure and chose the best option. For this option I made detailed structural analysis. It is prepared by static analysis of the main load-bearing parts of the structure, including joints and details. The supporting structure of hall consists in the transverse direction from the curved spatial lattice structure made of steel circular tubes which hang on rods on a sloped pylon. Part of the report is open-air roofing.