1 Mecánica Estructural Profesor Rolando Salgado EstradaProfesor de Tiempo Completo Dr. Ingeniería (Estructuras) Correo-e: Celular: Thank you People of the Jury and all the audience for being here to attend my defences named Damage detection methods in bridges through vibration monitoring: Evaluation and Application. This thesis was under the supervision of Professor Paulo Cruz at the University of Minho in Guimarães, Portugal and Professor Gustavo Ayala from the National Autonomous University of México. Boca del Río, Veracruz, 7 de agosto 2012
2 Organización del Curso1 Introducción 2. Temario 3. Criterios de Evaluación 4. Trabajos 5. Bibliografía This research is divided in 5 main parts: Firstly is given a short introduction, the selected damage detection methods are evaluated under data acquired from simulation of the dynamic response of cracked bridges, Moreover, methods are also evaluated from data acquired from beam specimens tested in the laboratory. In the main part of this thesis, the methods were evaluated using the dynamic response calculated from bridges. Finally, it is drawn some conclusions and are given recommendations.
3 Perfil del alumno Calendario de clases AntecedentesIntroducción Perfil del alumno Calendario de clases Antecedentes
4 ¿Cuál es el perfil del Maestro en Ingeniería Civil (Estructuras)?Curso ¿Cuál es el perfil del Maestro en Ingeniería Civil (Estructuras)? El Maestro en Ingeniería Civil es el profesional capaz de resolver los problemas estructurales relacionados con las obras civiles, abordando dichas problemáticas en cuestión de: planeación, proyecto, construcción, supervisión, rehabilitación, gestión así como la investigación de nuevos métodos de resolver estas problemáticas y la enseñanza. Buscando en la realización de tales actividades, la seguridad de las obras de ingeniería encomendadas, su funcionalidad, buena calidad y economía. ¿Que se pretende que el alumno aprenda al aprobar el curso? We can start asking the question why damage detection in bridges is so important? Firstly because if damage can be detected in the first steps, it would be possible to plan the maintenance and rehabilitation of the bridge with more detail saving money. Moreover, the current and traditional methods to evaluate bridges are based on visual inspection which several times fail to detect inner damage or these located in not accessible places. For these reasons, the scientific community was encouraged to propose more advanced techniques to detect damage in structures. From the vast number of proposed methods proposed in the last 20 years, those based on the monitoring of the vibration parameters of the structure are considered suitable for their application to big structures like bridges. These methods compared the vibration parameters determined from two different structural conditions of the bridges. Furthermore, there are methods able to detect damage just with the information provided from the damaged vibration parameters like those based on wavelet analysis. Unfortunately, the application of the vibration based damage detection methods to bridges is not a straightforward procedure. Several problems have to be addressed. For instance, the change of the vibration parameters of the structure after some damage appeared is very small. For this reason, advanced mathematical methods have been proposed to highlight this small difference. However, there are other factors that also can provoke changes in the vibration parameters of structures like gradient of temperatures, humidity among others. Finally, we would like to say that these advanced damage detection methods have not been evaluated under the same structure and kind of damage, therefore a comparative performance evaluation cannot be done. El alumno será capaz de resolver los problemas prácticos que se encuentran en Estructuras empleando las teorías elásticas y plásticas.
5 -------- Calendario de clases Exámenes y EvaluacionesCurso Calendario de clases Exámenes y Evaluaciones 1er examen parcial Jueves 20 de septiembre del 2012 2o examen parcial Jueves 25 de octubre del 2012 Exámenes Ordinario 22 de nov. al 7 de dic. del 2012 Entrega final del proyecto Día del examen ordinario Aulas del 4/ago/2012 al 18/nov/2012 Feriados: 1 y 2 de nov. Clases en línea y asesorías Martes y Miércoles 19:00 a 19:59 hrs. After a exhaustive literature review of the most important vibration-based damage detection methods, it was determined that the most promising techniques are: Methods based on Wavelet Analysis: we can mention in this category the Continuous Wavelet Transform (CWT), the Discrete Wavelet Analysis (DWA), the Wavelet Packet Signature (WPS) and the combined method (CWT-DI) method; Furthermore, It was considered methods based on curvatures of the mode shapes, it means, its second derivative. In this category fails the curvature and the well-known Damage Index (DI) method. It was also considered methods based on changes in the stiffness matrix of the structure: the stiffness and flexibility change matrix methods are included in this category; All the before mentioned methods can detect and locate the position of the damage in the structure. (methods of level II). Into the category of those methods able to detect damage are included the change of frequency method and the Modal Assurance Criterion method and its derivatives as the Normalized Modal Difference (NMD) method.
6 Antecedentes del alumnoCurso Antecedentes del alumno Aclaración El alumno deberá tener buenos antecedentes en: Tenga presente que algunos conceptos de estas EEs se aplican en la solución de problemas en esta EE, por lo cual el alumno deberá estudiarlos por su cuenta. Análisis Estructural Introducción a la Mecánica del Medio Continuo Mecánica de Materiales Estructuras Isostáticas Lenguajes de Programación Mecánica de Suelos After a exhaustive literature review of the most important vibration-based damage detection methods, it was determined that the most promising techniques are: Methods based on Wavelet Analysis: we can mention in this category the Continuous Wavelet Transform (CWT), the Discrete Wavelet Analysis (DWA), the Wavelet Packet Signature (WPS) and the combined method (CWT-DI) method; Furthermore, It was considered methods based on curvatures of the mode shapes, it means, its second derivative. In this category fails the curvature and the well-known Damage Index (DI) method. It was also considered methods based on changes in the stiffness matrix of the structure: the stiffness and flexibility change matrix methods are included in this category; All the before mentioned methods can detect and locate the position of the damage in the structure. (methods of level II). Into the category of those methods able to detect damage are included the change of frequency method and the Modal Assurance Criterion method and its derivatives as the Normalized Modal Difference (NMD) method.
7 Programación tentativa de contenido y horas/claseTemario Programación tentativa de contenido y horas/clase
8 TEMARIO 1. Introducción (3) horas1.1 Soluciones de la Mecánica Estructural 2. Estática Estructural (Esfuerzos) (10) horas 2.1 Estados de esfuerzos en un punto y tensor de esfuerzos 2.2 Círculo de Mohr y esfuerzos principales 2.3 Ecuaciones de equilibrio 2.4 Modelos esfuerzo-deformación y deformación-tiempo 3. Cinemática Estructural (Deformaciones) (7) horas 3.1 Descripción del movimiento mediante campos vectoriales 3.2 Deformaciones volumétrica y distorsionante 3.3 Estados de deformaciones en un punto y tensor de deformaciones 3.4 Principio de conservación de cantidad de movimiento In the first part of the development of this research it was done a numerical model of a composite bridge (steel I beams with concrete deck) with the dimensions shown in the figure. The bridge was modelled as two-dimensional numerical model and the severity of damage was represented by three cases. The first one represents the undamaged condition of the bridge called as D0, the second one, an open vertical crack was introduced along all the bottom flange of the steel I beam, in the most severe damage scenario called D2, the crack grows until half of the web of the beam. The location of the damage was represented by 4 different cases in the internal and external beam each one.
9 TEMARIO 4. Modelos reológicos y relaciones constitutivas (10) horas4.2 Relaciones constitutivas. Modelos comunes 4.3 Modelos de Maxwell, Kelvin y Burgers 5. Elasticidad lineal aplicada (15) horas 5.1 Problemas fundamentales 5.2 Función de Airy 5.3 Ecuaciones de Plasticidad 6 Dinámica Estructural (10) horas 6.1 Sistema de un grado de libertad 6.2 Sistema de Múltiples grados de libertad 7 Mecánica de la Fractura (10) horas 7.1 Conceptos fundamentales 7.2 Modos de falla y aplicaciones 8 Aplicaciones (10) horas 8.1 Pandeo en columnas 8.2 Análisis dinámico de vigas agrietadas In the first part of the development of this research it was done a numerical model of a composite bridge (steel I beams with concrete deck) with the dimensions shown in the figure. The bridge was modelled as two-dimensional numerical model and the severity of damage was represented by three cases. The first one represents the undamaged condition of the bridge called as D0, the second one, an open vertical crack was introduced along all the bottom flange of the steel I beam, in the most severe damage scenario called D2, the crack grows until half of the web of the beam. The location of the damage was represented by 4 different cases in the internal and external beam each one.
10 Criterios de EvaluaciónInstrumentos de Evaluación Aclaraciones Sugerencias
11 Criterios de EvaluaciónTarea. Solución de problemas prácticos Objetivos de desempeño Criterios evaluación Excelente Muy bueno Bueno No suficiente Que el alumno comprenda las teorías para la obtención de esfuerzos en estructuras Tareas, exposicio-nes y ejer-cicios Buena preparación de la presentación, utilización de TICs, presenta ejempos resueltos, varias alternativas de solución, da una discusión de los llega a los resultados correctos sin errores numéricos. Presenta información adicional analizando el tema, proporciona sus puntos de vista y recomendaciones Buena presentación, llega a los resultados correctos sin errores numéricos graves. Proporciona sus puntos de vista y recomendaciones sobre los problemas resueltos. Presenta comentarios sobre el desarrollo del problema, pero no profundiza en el tema. Presenta errores numéricos no graves. El procedimiento es el correcto pero no llega a los resultados correctos Mala presentación escrita, no presenta comentarios sobre el desarrollo del problema, no profundiza en el tema. Presenta errores numéricos graves. El procedimiento es incorrecto, no presenta orden en la solución del problema. After a exhaustive literature review of the most important vibration-based damage detection methods, it was determined that the most promising techniques are: Methods based on Wavelet Analysis: we can mention in this category the Continuous Wavelet Transform (CWT), the Discrete Wavelet Analysis (DWA), the Wavelet Packet Signature (WPS) and the combined method (CWT-DI) method; Furthermore, It was considered methods based on curvatures of the mode shapes, it means, its second derivative. In this category fails the curvature and the well-known Damage Index (DI) method. It was also considered methods based on changes in the stiffness matrix of the structure: the stiffness and flexibility change matrix methods are included in this category; All the before mentioned methods can detect and locate the position of the damage in the structure. (methods of level II). Into the category of those methods able to detect damage are included the change of frequency method and the Modal Assurance Criterion method and its derivatives as the Normalized Modal Difference (NMD) method.
12 Criterios de Evaluación…Tarea. Resolver problemas prácticos mediante el uso de programas de cómputo. Objetivos de desempeño Criterios evaluación Excelente Muy bueno Bueno No suficiente Que el alumno sea capaz de desarrollar pro-gramas de cómputo para resolver proble-mas de mecánica estructural. Comprobar los programas de cómputo mediante tareas y ejercicios El(Los) programas de cómputo llega(n) a la solución correcta, existe una interface gráfica amigable para la introducción de datos; se presentan los resultados de forma gráfica y se muestran los resulta- dos numéricos en base de datos orde- nadas. El(Los) progra-ma(s) de cómputo llegan a la solución correcta, la pre-sentación visual de los resulta-dos es buena, pero no hay una interface visual amigable. Se muestran los resultados en base de datos ordenadas. El(Los) progra-ma(s) de cómputo llegan a la solución correcta. No hay una interface visual y los re-sultados no se muestran en forma gráfica. Los resultados se muestran en base de datos ordenadas. El(Los) programa(s) de cómputo no llegan a la solución correcta. No hay una interface visual y los resulta-dos no se muestran en forma gráfica. Los resultados no se muestran en base de datos or-denadas. After a exhaustive literature review of the most important vibration-based damage detection methods, it was determined that the most promising techniques are: Methods based on Wavelet Analysis: we can mention in this category the Continuous Wavelet Transform (CWT), the Discrete Wavelet Analysis (DWA), the Wavelet Packet Signature (WPS) and the combined method (CWT-DI) method; Furthermore, It was considered methods based on curvatures of the mode shapes, it means, its second derivative. In this category fails the curvature and the well-known Damage Index (DI) method. It was also considered methods based on changes in the stiffness matrix of the structure: the stiffness and flexibility change matrix methods are included in this category; All the before mentioned methods can detect and locate the position of the damage in the structure. (methods of level II). Into the category of those methods able to detect damage are included the change of frequency method and the Modal Assurance Criterion method and its derivatives as the Normalized Modal Difference (NMD) method.
13 Criterios de Evaluación…Tarea. Aplicar la mecánica estructural en la solución de un problema práctico Objetivos desempeño Criterios evaluación Excelente Muy bueno Bueno No suficiente Que el alumno realice, de manera independien-te, la solución dinámica de un edificio sometido a fuerzas laterales de viento considerando efectos de segundo orden de columnas. Entrega de la memoria estructura-les forma electrónica a través de la plataforma ms. Buena presentación del proyecto, redacción clara y concisa, presenta todos los puntos acordados, el alumno da conclusiones de los resultados obtenidos, no muestra errores de cálculo o de conceptos, Presenta información adicional que ayuda a complementar el trabajo. Buena presentación del proyecto, redacción clara y concisa, presenta todos los puntos acordados, da conclusiones de los resultados obteni-dos, no muestra errores de cálculo o de conceptos, Buena presenta-ción del proyecto, redacción confu-sa, presenta to-dos los puntos acordados, no se muestran conclu-siones de los re-sultados obteni-dos, muestra errores de cálculo o de con-ceptos pero no son graves. Mala presenta-ción del proyecto, redacción confusa, no presenta todos los puntos acordados, no da conclusio-nes, tiene errores de cálculo y/o de conceptos. After a exhaustive literature review of the most important vibration-based damage detection methods, it was determined that the most promising techniques are: Methods based on Wavelet Analysis: we can mention in this category the Continuous Wavelet Transform (CWT), the Discrete Wavelet Analysis (DWA), the Wavelet Packet Signature (WPS) and the combined method (CWT-DI) method; Furthermore, It was considered methods based on curvatures of the mode shapes, it means, its second derivative. In this category fails the curvature and the well-known Damage Index (DI) method. It was also considered methods based on changes in the stiffness matrix of the structure: the stiffness and flexibility change matrix methods are included in this category; All the before mentioned methods can detect and locate the position of the damage in the structure. (methods of level II). Into the category of those methods able to detect damage are included the change of frequency method and the Modal Assurance Criterion method and its derivatives as the Normalized Modal Difference (NMD) method.
14 Criterios de Evaluación finalCriterios desempeño Puntaje (%) Exámenes Parciales Responder acertadamente las preguntas y problemas planteados 15 % c/u Tareas y trabajos de investigación Redacción adecuada, respaldada con bibliografía, presentación oral fluida y clara. Problemas bien realizados con resultados correctos. 10 % Programas de cómputo Código correcto, se llega al resultado adecuado, de fácil uso, interface gráfica. 15 % Proyecto final Redacción buena, presentación excelente, resultados correctos, comentarios, su-gerencias, puntos de vista,. Cumple con todos los puntos establecidos. 25 % Examen ordinario 20 % TOTAL 100 % La participación en clase también se evalúa. Responder a las preguntas abiertas que hace el profesor en las clases, realizar preguntas, sugerencias y comentarios en forma continua y adecuada se considera con un puntaje de 10% sobre la calificación final del curso. After a exhaustive literature review of the most important vibration-based damage detection methods, it was determined that the most promising techniques are: Methods based on Wavelet Analysis: we can mention in this category the Continuous Wavelet Transform (CWT), the Discrete Wavelet Analysis (DWA), the Wavelet Packet Signature (WPS) and the combined method (CWT-DI) method; Furthermore, It was considered methods based on curvatures of the mode shapes, it means, its second derivative. In this category fails the curvature and the well-known Damage Index (DI) method. It was also considered methods based on changes in the stiffness matrix of the structure: the stiffness and flexibility change matrix methods are included in this category; All the before mentioned methods can detect and locate the position of the damage in the structure. (methods of level II). Into the category of those methods able to detect damage are included the change of frequency method and the Modal Assurance Criterion method and its derivatives as the Normalized Modal Difference (NMD) method.
15 Aclaraciones de los criterios de evaluaciónTodos tienen derecho a presentar los exámenes sin importar el número de asistencias. Los exámenes sólo se aplicarán, sin excepción, en las fechas indicadas. En caso de tener una razón justificada, presentar los documentos que así lo comprueben. Cualquier intento de copiar durante las evaluaciones se sancionará con la anulación del examen. Se podrá exentar de Examen Ordinario si se obtiene una calificación promedio mayor a 8.5/10 en los exámenes parciales. Si se presenta al examen y desiste sin contestar nada tendrá una calificación de UNO. Para aprobar el curso deberá cumplirse con los criterios mínimos de evaluación. After a exhaustive literature review of the most important vibration-based damage detection methods, it was determined that the most promising techniques are: Methods based on Wavelet Analysis: we can mention in this category the Continuous Wavelet Transform (CWT), the Discrete Wavelet Analysis (DWA), the Wavelet Packet Signature (WPS) and the combined method (CWT-DI) method; Furthermore, It was considered methods based on curvatures of the mode shapes, it means, its second derivative. In this category fails the curvature and the well-known Damage Index (DI) method. It was also considered methods based on changes in the stiffness matrix of the structure: the stiffness and flexibility change matrix methods are included in this category; All the before mentioned methods can detect and locate the position of the damage in the structure. (methods of level II). Into the category of those methods able to detect damage are included the change of frequency method and the Modal Assurance Criterion method and its derivatives as the Normalized Modal Difference (NMD) method.
16 Aclaraciones de los criterios de evaluaciónEn las evaluaciones de los exámenes, el llegar a la respuesta cierta no se considera suficiente sino se presenta el desarrollo lógico y adecuado del problema. Cualquier resultado numérico de un problema no tiene validez si no se expresa en las unidades correctas. El problema se considera resuelto satisfactoriamente cuando: Se llega al resulta correcto, Se presenta el adecuado desarrollo del problema Se presentan los comentarios y conclusiones pertinentes. After a exhaustive literature review of the most important vibration-based damage detection methods, it was determined that the most promising techniques are: Methods based on Wavelet Analysis: we can mention in this category the Continuous Wavelet Transform (CWT), the Discrete Wavelet Analysis (DWA), the Wavelet Packet Signature (WPS) and the combined method (CWT-DI) method; Furthermore, It was considered methods based on curvatures of the mode shapes, it means, its second derivative. In this category fails the curvature and the well-known Damage Index (DI) method. It was also considered methods based on changes in the stiffness matrix of the structure: the stiffness and flexibility change matrix methods are included in this category; All the before mentioned methods can detect and locate the position of the damage in the structure. (methods of level II). Into the category of those methods able to detect damage are included the change of frequency method and the Modal Assurance Criterion method and its derivatives as the Normalized Modal Difference (NMD) method.
17 Aclaraciones de los criterios de evaluación Sugerencias para aprobar el curso Un error numérico en la solución de un problema reduce la calificación final del examen en un 5%. Más de 3 errores numéricos en un problema lo anulan completamente. Un error en el planteamiento para la solución del problema, se considera una falta grave resultando en la anulación del problema. Estudie continuamente, realice ejercicios y pregunte al profesor aunque la respuesta sea obvia. NO SE CONFÍE. Si estudia hasta las fechas indicadas para las evaluaciones no tendrá tiempo para estudiar todas sus EEs. After a exhaustive literature review of the most important vibration-based damage detection methods, it was determined that the most promising techniques are: Methods based on Wavelet Analysis: we can mention in this category the Continuous Wavelet Transform (CWT), the Discrete Wavelet Analysis (DWA), the Wavelet Packet Signature (WPS) and the combined method (CWT-DI) method; Furthermore, It was considered methods based on curvatures of the mode shapes, it means, its second derivative. In this category fails the curvature and the well-known Damage Index (DI) method. It was also considered methods based on changes in the stiffness matrix of the structure: the stiffness and flexibility change matrix methods are included in this category; All the before mentioned methods can detect and locate the position of the damage in the structure. (methods of level II). Into the category of those methods able to detect damage are included the change of frequency method and the Modal Assurance Criterion method and its derivatives as the Normalized Modal Difference (NMD) method.
18 Trabajos Tareas Proyecto final
19 Trabajos y tareas AclaracionesDescripción de los trabajos Se encargarán 3 trabajos durante el curso: Trabajo 1: agosto-septiembre Trabajo 2: septiembre-octubre Trabajo 3: octubre-noviembre Trabajo 1 Esfuerzos y deformaciones Trabajo 2 Modelos reológicos y elasticidad aplicada. Trabajo 3 Dinámica estructural y mecánica de la fractura Aclaraciones Se reciben trabajos hasta 3 días después de la fecha estipulada. No obstante, su calificación tendrá 2 puntos menos por cada día de retraso. Después de 3 días no se reciben trabajos y su calificación se considera nula. After a exhaustive literature review of the most important vibration-based damage detection methods, it was determined that the most promising techniques are: Methods based on Wavelet Analysis: we can mention in this category the Continuous Wavelet Transform (CWT), the Discrete Wavelet Analysis (DWA), the Wavelet Packet Signature (WPS) and the combined method (CWT-DI) method; Furthermore, It was considered methods based on curvatures of the mode shapes, it means, its second derivative. In this category fails the curvature and the well-known Damage Index (DI) method. It was also considered methods based on changes in the stiffness matrix of the structure: the stiffness and flexibility change matrix methods are included in this category; All the before mentioned methods can detect and locate the position of the damage in the structure. (methods of level II). Into the category of those methods able to detect damage are included the change of frequency method and the Modal Assurance Criterion method and its derivatives as the Normalized Modal Difference (NMD) method.
20 Descripción de los trabajosProyecto Final Descripción de los trabajos Consistirá en la solución de un problema de la mecánica estructural 1ª etapa: Establecimiento del problema: 28/sep/2012 3ª etapa: Revisión a la solución de los problemas: 15/nov/2012 4ª etapa: Entrega de resultados en un reporte: día del examen ordinario. 2ª etapa: Aplicación de las teorías y soluciones propuestas. Revisión: 15/nov/2012 After a exhaustive literature review of the most important vibration-based damage detection methods, it was determined that the most promising techniques are: Methods based on Wavelet Analysis: we can mention in this category the Continuous Wavelet Transform (CWT), the Discrete Wavelet Analysis (DWA), the Wavelet Packet Signature (WPS) and the combined method (CWT-DI) method; Furthermore, It was considered methods based on curvatures of the mode shapes, it means, its second derivative. In this category fails the curvature and the well-known Damage Index (DI) method. It was also considered methods based on changes in the stiffness matrix of the structure: the stiffness and flexibility change matrix methods are included in this category; All the before mentioned methods can detect and locate the position of the damage in the structure. (methods of level II). Into the category of those methods able to detect damage are included the change of frequency method and the Modal Assurance Criterion method and its derivatives as the Normalized Modal Difference (NMD) method.
21 Básica ComplementariaBibliografía Básica Complementaria
22 Bibliografía Básica ComplementariaEngineering Mechanics of Solids, Popov, E., Edit. Prentice Hall, 1990. Complementaria Elementos de Mecánica del Medio Continuo, E. Levi, Editorial Limusa, 12ª reimpresión, 1996, Introduction to the Mechanics of Continuous Médium, L. Malvern, Editorial Prentice-Hall, 1969, (referencia) Introduction to Continuum Mechanics, Lai, M., Rubin, D. & Krempl E., Edit. Prentice Hall, 1992 Dynamics of Structures, Chopra, A. K., Editorial Prentice Hall, 1996. Roark’s formulas for strain and stress, Young, W & Budynas R., Editorial McGraw Hill, 2002. Theory of Elasticity, S.P. Timoshenko, J.N. Goodier, Editorial McGraw-Hill, 1970. After a exhaustive literature review of the most important vibration-based damage detection methods, it was determined that the most promising techniques are: Methods based on Wavelet Analysis: we can mention in this category the Continuous Wavelet Transform (CWT), the Discrete Wavelet Analysis (DWA), the Wavelet Packet Signature (WPS) and the combined method (CWT-DI) method; Furthermore, It was considered methods based on curvatures of the mode shapes, it means, its second derivative. In this category fails the curvature and the well-known Damage Index (DI) method. It was also considered methods based on changes in the stiffness matrix of the structure: the stiffness and flexibility change matrix methods are included in this category; All the before mentioned methods can detect and locate the position of the damage in the structure. (methods of level II). Into the category of those methods able to detect damage are included the change of frequency method and the Modal Assurance Criterion method and its derivatives as the Normalized Modal Difference (NMD) method.
23 Artículos de investigación, de divulgación científica y técnicaBibliografía Bibliografía… Complementaria Finite Element Procedures, K.J. Bathe, Editorial Pretice Hall, 1996. Introducción Mecánica de Fractura, Martínez, E., apuntes, 2012. Biblioteca virtual, Universidad Veracruzana An introduction to the Finite Element Method, J. N. Reddy, Segunda Edición, Edit. McGraw Hill, 2005. Artículos de investigación, de divulgación científica y técnica Base de datos de la Biblioteca virtual de la Universidad Veracruzana,
24 No dudes en comunicar al Profesor cualquier duda y/o comentario en: skype y hotmail: odnalor73 Thank you
25 Mecánica Estructural Clase 1Profesor Rolando Salgado Estrada Profesor de Tiempo Completo Dr. Ingeniería (Estructuras) Correo-e: Celular: Thank you People of the Jury and all the audience for being here to attend my defences named Damage detection methods in bridges through vibration monitoring: Evaluation and Application. This thesis was under the supervision of Professor Paulo Cruz at the University of Minho in Guimarães, Portugal and Professor Gustavo Ayala from the National Autonomous University of México. Boca del Río, Veracruz, 7 de agosto 2012
26 Mecánica Estructural:Disciplina que estudia las fuerzas que se ejercen sobre los cuerpos materiales y los efectos que éstas producen, generando modelos matemáticos que intentan simular y predecir el comportamiento real de dichas fuerzas y cuerpos.
27 Ingeniería EstructuralMecánica Estructural Mecánica del Medio Continuo Dinámica Estructural Mecánica de la Fractura
28 Esfuerzos cortante Alumno Fatiga y fractura Esfuerzos grietasModelos reológicos Concreto y acero Elasticidad Viga de Bernoulli Plasticidad viga Alumno Columnas Pandeo lateral Torsión Secciones rectangulares Dinámica Parámetros modales