Análisis Comparativo De Métodos De Cálculo De Estructuras Formadas Por Barras, Considerando Efectos De Segundo Orden.”

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Análisis Comparativo De Métodos De Cálculo De Estructuras Formadas Por Barras, Considerando Efectos De Segundo Orden.” Universidad Austral de Chile Facultad de Ciencias de la Ingeniería Escuela de Ingeniería en Obras Civiles “ANÁLISIS COMPARATIVO DE MÉTODOS DE CÁLCULO DE ESTRUCTURAS FORMADAS POR BARRAS, CONSIDERANDO EFECTOS DE SEGUNDO ORDEN.” Para optar al título de: Ingeniero Civil en Obras Civiles Profesor Patrocinante Sr. Julio Lopetegui Torres Ingeniero Civil, Dr. en Ingeniería Profesores Informantes Sr. José Soto Miranda Ingeniero Civil, M. Sc. Eng. Civil Sr. Adolfo Castro Bustamante Ingeniero Civil, M. Sc. Eng. Civil ÁNGELA PATRICIA GONZÁLEZ AVILÉS VALDIVIA − CHILE 2009 i Agradecimientos A Dios por permitirme concluir esta etapa de mi vida brindándome fortaleza y protección A mis hermanos y padres Patricia y Hernán por su amor y apoyo incondicional A mi Abuela Sonia Por su preocupación y ayuda A mis pastores Maritza y Henrique por ceer siempre en mí A mis amigos por su palabras de aliento y consejo Índice general Índice general i Índice temático i Índice de anexos iii Índice de figuras iv Índice de tablas vi Índice de gráficos vi Resumen vii Summary viii Índice temático Capítulo I: Introducción 1.1. Planteamiento del problema 1 1.2. Objetivos 9 1.3. Metodología 10 Capítulo II: Métodos de análisis Elástico de segundo orden. 2.1. Conceptos generales 11 2.1.1. Inestabilidad de una barra 11 2.1.2. Pandeo elástico 13 2.1.3. Pandeo inelástico 15 2.1.4. Pandeo lateral-torsional 16 2.2. Método de la Matriz Geométrica 19 ii Capítulo III: Efectos de segundo orden considerados en las normas de diseño. 3.1. Recomendaciones del Instituto nacional del acero ICHA 24 3.2. Método de análisis de segundo orden establecido en el código AISC 27 3.2.1. Consideraciones generales 27 3.2.2. Análisis de segundo orden por un análisis elástico de primer orden amplificado. Método de amplificación de momentos 29 3.2.3. Método de análisis de segundo orden directo 32 3.3. Código Europeo, EC3 36 3.3.1. Consideraciones generales 36 3.3.2. Análisis de la estabilidad de un marco y factor de amplificación de momentos de primer orden 39 3.4. Resumen y comparaciones 42 Capítulo IV: Programas computacionales 4.1. SAP2000 44 4.1.1. Introducción 44 4.1.2. Forma cúbica deformada 46 4.1.3. Fuerzas P-Δ en los elemento pórtico 47 4.1.4. Análisis inicial P-Δ 49 4.2. PROGES 50 4.2.1. Introducción 50 4.2.2. Fundamentos teóricos de PROGES 51 Capítulo V: Estructura tipo marco plano analizada 5.1. Modelo de la estructura en Proges 57 iii 5.2. Modelo de la estructura en SAP2000 57 5.2.1. Casos de carga 57 5.2.2. Casos de análisis 58 5.2.3. Combinaciones 60 5.3. Resultados 62 Capítulo VI: Comentarios y conclusiones 6.1. Conclusiones generales 69 6.1.1 Respecto a los métodos estudiados 69 6.1.2. Respecto a las normas estudiadas 71 6.2. Aportaciones más significativas 72 6.3. Futuras líneas de investigación 74 Capítulo VII: Bibliografía 75 Índice de anexos Anexo A: Funciones de estabilidad 78 Anexo B: Análisis por el Método de la matriz geométrica 84 Anexo C: Archivos de entrada y salida de datos 95 Anexo D: Cálculo de Factores B2 y FA 119 iv Índice de figuras Figura 1.1.1. Efecto P-Δ y P-δ 2 Figura 1.1.2. Diagrama de carga-deformación 3 Figura 1.1.3. Tipos de análisis 4 Figura 1.1.4. Interacción entre el sistema estructural y los miembros que la Componen 4 Figura 2.1.1.1. Estabilidad de una barra rígida 11 Figura 2.1.1.2. Curvas carga-rotación de columnas 13 Figura 2.1.2.1. Columna Euler 13 Figura 2.1.4.1. Deformación lateral-torsional de viga en flexión 17 Figura 2.1.4.2. Deformación lateral-torsional de viga en flexión, detalle 17 Figura 2.2.1. Convención de signos 20 Figura 3.2.1.1. Efecto P-Δ y P-δ en vigas columna 28 Figura 3.2.2.1. Amplificación de momento 29 Figura 3.2.2.2. Curvatura que ocasionan los momentos aplicados en los extremos de los elementos 31 Figura 3.3.1.1. Imperfección de pórtico traslacional 38 Figura 3.3.1.2. Imperfección en el elemento 38 Figura 3.3.1.3. Esfuerzos horizontales equivalentes 39 Figura 3.3.2.1. Pórtico de edificación con las vigas unidas a los pilares en cada planta 41 Figura 4.1.1.1. Efecto P-Δ en SAP2000 45 Figura 4.1.2.1. Geometría deformada 46 Figura 4.1.4.1. Análisis no lineal estático 49 v Figura 4.2.1.1. Diagrama de flujo de programa Proges 50 Figura 4.2.2.1. Ecuaciones de estabilidad para un segmento de columna 51 Figura 5.1. Marco analizado por los tres métodos 56 Figura 5.1.1. Modelo de marco en Proges 57 Figura 5.2.1.1. Casos de carga en SAP2000 58 Figura 5.2.2.1. Caso de análisis de PP en SAP2000 58 Figura 5.2.2.2. Caso de análisis de SC en SAP2000 59 Figura 5.2.2.3. Caso de análisis de Pdelta en SAP2000 59 Figura 5.2.2.4. Especificación de efecto P-Delta 60 Figura 5.2.3.1. Datos de las propiedades del material 61 Figura 5.3.1. Fuerzas internas en cada barra 63 Figura A.1. Fuerzas alojadas en cada uno de los planos principales de la barra 78 Figura A.2. Viga columna sujeta a momentos en sus extremos 79 Figura A.3. Viga columna sujeta a momentos en sus extremos 80 Figura A.4. Gráfico de funciones de estabilidad 82 Figura A.5. Viga-columna sujeta a momentos y desplazamientos en los extremos 83 Figura B.1. Modelo de marco y condiciones de carga 84 Figura B.2. Sistema de coordenadas globales y locales considerados en método 1 84 Figura B.3. Barra 1 del marco 85 Figura B.4. Barra 2 del marco 87 Figura B.5. Barra 3 del marco 88 Figura B.6. Determinación de las fuerzas longitudinales 91 vi Figura B.7. Geometría y combinaciones de carga 92 Figura B.8. Valores del determinante de Ktotal usando la matriz geométrica 93 Figura B.9. Formas de modos de pandeo correspondientes a λ λ 93 Índice de Tablas Tabla 3.3.1.1. Imperfecciones de los elementos 39 Tabla 3.3.1.2. Factores de imperfecciones para las curvas de pandeo 39 Tabla 3.4.1. Tipos de análisis de acuerdo al origen de las fuerzas y deformación 42 Tabla 4.2.2.1. Valores de para la matriz de rigidez 53 Tabla 5.3.1. Resultados de desplazamientos y fuerzas internas de los elementos 62 Tabla 5.3.2. Valores de deformación vs carga aplicada en nudos 2 y 3 63 Tabla 5.3.3. Cálculo del factor B2 66 Tabla 5.3.4. Cálculo del factor αcr 67 Tabla B.1 Valores de deformación vs factor carga λ 94 Índice de gráficos Gráfico 5.3.1. Curvas de carga vs deformación 64 Gráfico 5.3.2. Variación porcentual de los desplazamientos obtenidos por los tres Métodos con respecto un análisis lineal. 65 Gráfico 5.3.3. Variación porcentual de desplazamientos de MG vs PROGES 65 Gráfico 5.3.4. Curva factores de amplificación (B2 y FA) vs carga 68 Gráfico B.2. Curva factores de amplificación (B2 y FA) vs carga 94 vii Resumen Con el objeto de determinar de qué forma influyen las cargas axiales sobre una estructura esbelta de acero, y dar a conocer una manera más directa de obtener los esfuerzos considerando la geometría deformada de dicha estructura, se muestran en la presente memoria los resultados obtenidos a partir de un Análisis Elástico de Segundo Orden y un Análisis Elástico de Primer Orden realizado a una estructura de acero tipo marco. Se presentan y comparan tres métodos mediante los cuales se realizan los cálculos, considerando la deformación de la estructura y los elementos que la componen sobre los cuales estarán actuando las fuerzas, representadas por el peso propio de los elementos y la sobrecarga. Se complementa lo anterior con el estudio de distintos códigos de diseño, en los cuales se plantean los tipos de análisis requeridos (sean estos lineales o no lineales) dependiendo principalmente de las condiciones de arriostramiento de una edificación, su altura y cargas impuestas sobre esta. A partir de la curva de carga vs deformación obtenida a través de cada método se concluye que para situaciones especificas de marcos no arriostrados, sometidos a cargas laterales y axiales de mediana magnitud, es conveniente realizar un análisis de segundo orden, debido a que las deformaciones pueden hacer que los esfuerzos en los elementos aumenten de manera significativa, afectando la estabilidad de la estructura, asimismo se evita comprobar la esbeltez de cada uno de sus elementos, como ocurre en el caso de realizar un Análisis Lineal, sin considerar la deformación de la estructura y sus elementos en una primera instancia. viii Summary With the intention of determining how they influence the axial loads a slim steel structure, and presenting one more a way more direct to obtain the efforts considering the deformed geometry of this structure, the results obtained from an Elastic Analysis of Second Order and an Elastic Analysis of First realised Order are in the present memory a steel type frame. Three methods appear and compare by means of which the calculations are realised, considering the deformation of the structure and the elements compose that it on which the forces will be acting, represented by the own weight of the elements and the overload.
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