ejercicios resueltos de mecanica de materiales I del tema relacionado a presión en recipientes de pared delgada, tambien...
UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
“Año del Diálogo y la Reconciliación Nacional”
UNIVERSIDAD SAN IGNACIO DE LOYOLA
“RECIPIENTES A PRESION”
Curso: MECANICA DE MATERIALES
Profesor: QUIROZ TORREZ, LUIS
Estudiantes: ✓
CAMPOS RODRIGUEZ, Sergio
1421294
✓
SAENZ PAULINO , Isaac
1521662
✓
REYES SOLIS , Frank
1521662
✓
FORES HUAMANI , Luis
1520936
✓
RODRÍGUEZ CCOLQQUE , Orlando
1321120
✓
MAMANI SALCEDO, Sarely Leonor
1521276
Lima – Perú Perú 2018 – 00 00
1
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
Contenido RECIPIENTES A PRESION .................................................................................................................................. 3 Introduccion .................................................................................................................................................... 3 Objetivos ......................................................................................................................................................... 3 Marco teórico .................................................................................................................................................. 4 Manual de uso del programa ......................................................... .............................................................. .... 5 Resolución de problemas ................................................................................................................................ 7 Conclusiones ................................................................................................................................................. 23 Referencias bibliográficas ............................................................................................................................. 23 Anexo ............................................................................................................................................................ 23 Videos: .......................................................................................................................................................... 23 ✓ Link 1, (manual) https://www.youtube.com/watch?v=L7fuiWhDhaI&feature=youtu.be ................... 23 Link 2,(Mdsolid) https://www.youtube.com/watch?v=Cyug7EgJu2c................................................. 23 ✓
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
RECIPIENTES A RECIPIENTES A PRESION Campos Rodríguez Sergio, Sáenz Paulino Isaac, Re yes Solís Frank, Flores Huamani Luis, Rodríguez Colque Orlando y Mamani Salcedo Sarely Universidad San Ignacio de Loyola, Perú.
[email protected]
Introduccion El presente documento está escrito en el formato correspondiente a Reportes de trabajo y el mismo ha sido concebido usando un conjunto de estilos especialmente diseñado de modo tal que los autores puedan crear sus propios únicamente a partir de esta plantilla. Los reportes deberán escribirse en español empleando preferentemente el procesador de textos MS Word ®, recomendándose la utilización del Sistema Internacional (S.I.) de unidades. unidades. Los recipientes a Presión son definidos actualmente como contenedores con una presión interna que normalmente es más alta que la externa. Estos son ampliamente usados en las industrias, ya sea de: gas, químicos, petroleras, petroquímica, hasta nuclear. También se pueden utilizar para el transporte, producción, manipulación, almacenamiento de líquidos o gases. Su uso se ha expandido alrededor del mundo por ser muy eficiente. En este presente trabajo se ha realizado una serie de problemas respecto a Recipientes (cilíndrica o esférica) sometidos a Presión, con el fin de poder demostrar los conocimientos adquiridos en las clases. Y así poder mostrar adecuadamente la resolución de dichos problemas, ya sea de manera manual o a través del programa MDSolids software. Este programa ayuda a estudiantes de la carrera de ingeniería a resolver problemas basados en el curso de mecánica de materiales, ya que este posee doce módulos referentes a una amplia gama de problemas comunes donde los conceptos básicos, son: son: Torsión, Flexión, Flexión, análisis general, recipientes recipientes a presión, presión, transformaciones transformaciones del círculo círculo de Mohr, Mohr, estructuras estructuras axialmente indeterminadas, etc. Por aquella razón A través de este programa MDSolids Software se ha podido resolver diferentes tipos de ejercicios ya se dificultoso o simple obteniendo resultados satisfactorios y así poder emplearlo más adelante en diferentes tipos de trabajos de estructuras: estructuras: Solicitaciones internas, Centros de áreas, vigas, perfiles, presiones, reticulados, marcos y máquinas, columnas, etc. Además, se pudo realizar un breve concepto sobre recipientes a presión y un manual de como poder manejar el programa MDSolids adecuadamente para resolver ejercicios de recipientes a presión, ya que nos enfocaremos en ese tema en específico. Por último, confiando en el software se pudo comparar nuestros resultados obtenidos manualmente y usando el software, en lo cual los dos resultados eran lo mismo. Comprobando tal hecho podemos decir que MDSolids es un software muy útil para los estudiantes de la carrera de ingeniería.
Objetivos
Objetivos g enerales: enerales: ✓ ✓
Aprender a usar el programa MDsolids. Demostrar lo aprendido en clases acerca de recipientes a presión de pared delgada.
Objetivos específicos: ✓ ✓
Comparar los ejercicios resueltos manualmente y resueltos con el programa MDsolids. Definir si existe un margen de error entre nuestros resultados y el del programa MDsolids.
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
Marco teórico Envolventes de pequeño espesor-recipientes de paredes delgadas Una envolvente es como aquel solido elástico en el que una de sus dimensiones es mucha mejor que las otras, en el caso de paredes delgadas delgadas cumplen cumplen con las siguientes siguientes premisas: premisas: ✓ ✓ ✓
La relación entre su radio de curvatura y su espesor es mayor a 10. Son superficies de revolución (esfera, cono, cilindro, etc.). Se encuentran cargadas simétricamente respecto a un eje.
Los recipientes de pared delgada constituyen una aplicación importante del análisis de esfuerzo plano. Con sus paredes oponen poca resistencia a la flexión. Por eso, puede suponerse que las fuerzas internas ejercidas sobre una parte de la pared son tangentes a la superficie del recipiente.
Esfuerzos en recipientes de pared delgada Siempre que la pared sea “delgada”, la distribución de esfuerzos en todo su grosor no variará significativamente, por lo que se supone que es uniforme. En los casos de esfuerzos a presión cilíndrico y esférico, la presión en el recipiente se entiende como la presión atmosférica, ya que se supone que la presión atmosférica existe tanto dentro como fuera de la pared del recipiente antes de presurizarlo. presurizarlo.
Cilindros y esferas de pared delgada: delgada: Una esfera es la geometría óptima para un recipiente a presión cerrado, ya que es la forma geométrica estructuralmente más eficiente. En cambio, un recipiente cilíndrico es menos eficiente por dos razones: 1. 2.
Los esfuerzos de pared cambian con la dirección. El hecho de cerrarlo con tapas puede alterar significativamente el estado ideal de membrana, requiriendo refuerzos locales adicionales.
Usando la ecuación de Laplace-Young se estima la tensión circunferencial creada por una presión interna en un recipiente a presión cilíndrico cilíndrico de la pared pared delgada: delgada:
Donde:
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
Manual de uso del progr ama
Figura 1.- Modulos de MDsolid
Figura 1.- Modulos de MDsolid Figura 2.- Manual de uso de MDsolid
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
Figura 3.- Resultados MDsolid
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
Resolución de problemas
1. Un Un tanque esférico g rande (consulte la fig ura) conti ene gas a una presión de 450 450 psi. El tanque tiene un diámetro de 42 ft y está const ruido de acero de alta resistencia resistencia co n un esfuerzo de fluencia en tensió n de 80 ksi. Determine el espesor requerido (hasta el 1/4 in más cercano) de la pared del tanque si se requiere un factor de seguridad d e 3.5 3.5 con respecto a la fluencia. (Gere (Gere 8.2.1).
Datos: d= 42 in P= 450 psi F.S =3.5
Pide: t (espesor)
Solución:
En (1)
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
Resoluc Resoluc ión con el pro grama MDSolids MDSolids
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
2.Se 2.Se está está diseñando un tanqu e de buceo (consu lte la fig ura) para una presión interna de 1600 1600 psi con un factor de seguridad de 2.0 2.0 con respecto a la fluencia. El El esfuerzo d e fluenc ia del acero es 35,000 35,000 psi en tens ión y 16,000 16,000 psi en cortante. Si el diámetro d el tanque es 7.0 in, ¿cuál es el espesor d e pared mínimo requerido? (Gere. 8.3.1).
Nos piden pared pared mínima mínima requerido
Datos: d=7 in P= 1600 psi F.S =2
Solución:
Para Para el esfuerzo de fluencia en tensión:
En (1)
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
En (2)
De la intersección.
Resoluc Resoluc ión co n el progr ama MDS MDSolids olids .
1. ingresamos al programa MDSolids y seleccionamos la ventana de
pressure vessels.
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
2. seleccionamos el tipo de recipiente e ingresamos lo datos y seleccionamos las unidades correspondientes.
3. al calcular el resultado nos muestra lo siguiente.
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
3.El 3.El tanque de compresor de aire está está sometido a una presión in terna de 90 90 psi. Si el el diámetro int erior del tanque es de 22 pulgadas y el gro sor d e su pared es 0.25 pulgadas. Determine: (a) las componentes del esfuerzo que actuan en el pun to A. (b) Esfuerzo cortante máximo al girarlo 45 grados. (c) Reprensentar Reprensentar los esfuerzos en elementos elementos de volum en proyectados en u n plano d e la parte (a) (a).. (Todos los esfuezos sobre La parte exterior exterior del cilindro). Datos:
Piden: (a) (b) (c) Diagramas.
Solucion: Parte (a) VERIFICANDO SI ES EL CASO DE UNA PARED DELGADA. ...OK ESFUERZO TANGENCIAL O CIRCUNFERENCIAL CIRCUNFERENCIAL
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
Resoluc Resoluc ión con el pro grama MDSolids MDSolids
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
4.El tanque cilíndrico de 3m de longitud, tiene un espesor de 8mm, y una soldadura en un plano transversal de α=20 o La presión interna del tanque es 600 KPa, a) Determinar los esfuerzos normales y cortante a la sold adura. b) Determinar Determinar el grosor mínimo requerido del cilindro, si este tiene un esfuerzo permisib le de 70 MPa. MPa.
Nos piden: • • • •
Datos: • • • • • •
Resolución: Para Para la parte a), Se conoce las sig uientes for mulas:
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
Hallamos los esfuerzos inclinados:
Elemento Elemento de volum en:
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
Método de resolución a través de MDSolids MDSolids Una vez instalado el programa MDSolids seguir los siguientes pasos: 1.
Una vez abierto la ventana del software, ingresar a los módulos del MDSolids y elegir el módulo de “Pressure Vessels”.
2.
Se abrira una ventana donde nos pedira seleccionar que tipo de recipiente utilizaremos, para este ejercicio eligiremos eligiremos el recipiente cilindrico:
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
3.
Ingresamos los datos para la resolución del problema del ítem a) con sus respectivas unidades y dar click en “compute” para hallar los esfuerzos principales:
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
5.
Después de ingresar el grado de inclinación, damos click en “Details”.
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
5.El tanque 5.El tanqu e esférico esférico para gas se fabrica empernándolos empernándolo s corazas semiesféricas delgadas con groso g rosorr de 30 mm. Si el gas contenido contenid o en el depósito está est á bajo una presión manométrica manom étrica de 2 MPa, MPa, determine el esfuerzo normal norm al desarrollado desarroll ado en la pared del tanqu tanque e y en en cada uno de los pernos. p ernos. El tanque tiene un diámetro interio i nteriorr de 8 m y está sellado con 900 pernos de 25 mm de d e diámetro cada uno. Datos:
→ Me piden: A) B)
= ??? = ???
Solución: Ya que la relación entre el radio y el espesor esférico. A)
el análisis de pared delgada es válido para la pared del tanque
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
Método de resolución a través de MDSolids MDSolids
Para el esfuerzo normal desarrollado en la pared el tanque, se coloca el tipo de recipiente a presión y los datos requeridos
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
6.El 6.El tanque para almacenamiento almacenamiento d e gas se fabrica empernando dos corazas semicilíndricas de pared delgada y dos cor azas azas hemisféricas com o se muestra en la figu ra. Si Si el tanque está diseñado para soportar un a presión de 3Mpa. 3Mpa. Determine Determine el grosor mínim o requerido d e las corazas corazas semicilíndr icas y hemisféricas, y el número mínim o requerido de pernos para cada tapa semiesférica. semiesférica. El tanque y los p ernos de 25mm de diámetro están hechos de un material que tiene un esfuerzo norm al permisib le de 150 y 250MPa 250MPa.respectivame .respectivamente. nte. el tanque tiene un diámetr o in terio r d e 4m. (RUSS (RUSSELL ELL C. HIBBELER 8.9) 8.9)
Me piden: a) b) Numero mínimo mínimo de pernos pernos para cada cada tapa semiesférica semiesférica
Solución: Esfuerzo normal: para la porción cilíndrica del tanque, la tensión circunferencial es dos veces más grande que la tensión longitudinal.
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
Método de resolución a través de MDSolids MDSolids Para el cálculo del grosor mínimo requerido de la coraza semicilíndrica, se coloca los datos necesarios al programa:
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UNIVERSIDAD SAN IGNACIO DE LOYOLA FACULTAD DE INGENIERIA CARRERA DE INGENIERIA CIVIL MECANICA DE MATERIALES I
Conclusiones
✓
Los valores obtenidos por el software MDSolids y resueltos manualmente son numéricamente iguales.
✓
además, MDSolids nos proporcionas varias opciones como el círculo de Mohr para visualizar los esfuerzos normales, principales, cortantes tambien nos proporciona para ingresar un ángulo con lo cual vemos como varia los esfuerzos; todo ello conlleva a disminuir el tiempo y el error cometido ya sea en el desarrollo del problema manualmente.
✓
MDsolid es importante para el desarrollo estudiantil ya que muestra resultados exactos y confiables.
