INGENIERÍA SISMORRESISTENTE PERÚ
CURSO DE ESPECIALIZACIÓN ONLINE “
ANÁLISIS Y DISEÑO SISMORRESISTENTE DE UN COLEGIO CON COBERTURA A DOS AGUAS
”
SESIÓN N° 01 Y 02 “
ANÁLISIS ANÁLISIS SÍSMICO Y DISEÑO DE LOSAS
Ing. ERLY MARVIN ENRIQUEZ QUISPE
[email protected] CIP. 165680
17 de Enero del 2019 Lima – Perú
”
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ÍNDICE CAPÍTULO I GENERALIDADES 1.1
OBJETIVOS
01
1.2
DESCRIPCIÓN DESCRIPCIÓ N GENERAL DEL PROYECTO
01
1.3
CARACTERÍSTICAS CARACTERÍSTICAS DE LOS MATERIALES
03
1.4
CARGAS UNITARIAS
03
1.5
REGLAMENTOS REGLAMENTO S Y NORMAS
03
CAPÍTULO II ESTRUCTURACIÓN 2.1
LOSAS
04
2.2
VIGAS
04
2.3
COLUMNAS
04
2.4
PLACAS
04
2.5
ESCALERA
04
CAPÍTULO III PREDIMENSIONAMIENTO 3.1
LOSAS
05
3.2
VIGAS
05
3.3
COLUMNAS
06
3.4
PLACAS
06
3.5
ESCALERA
07
CAPÍTULO IV METRADO DE CARGAS 4.1
LOSAS
08
4.2
ESCALERA
08
CAPÍTULO V
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CAPÍTULO VIII CONCLUSIONES, RECOMENDACIONES Y BIBLIOGRAFÍA 8.1
CONCLUSIONES CONCLUSIONE S
61
8.2
RECOMENDACIONES RECOMENDACIO NES
61
8.3
BIBLIOGRAFÍA
61
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ANÁLISIS Y DISEÑO SISMORRESISTENTE DE UN COLEGIO A DOS AGUAS
CAPÍTULO I INTRODUCCIÓN El análisis Sismorresistente de una estructura es de gran importancia tanto para garantizar un apropiado comportamiento frente a un evento sísmico, así como, para entender y predecir la respuesta estructural. Entender el comportamiento estructural es fundamental para poder caracterizar de manera más adecuada el nivel de daño que pueda presentar una estructura debido a un evento sísmico. La filosofía del Diseño Sismorresistente según la Norma E.030 consiste en: a. Evitar pérdida de vidas humanas. b. Asegurar la continuidad de los servicios básicos. c.
Minimizar los daños a la propiedad. propiedad. Se reconoce que dar protección completa frente a todos los sismos no es técnica ni
económicamente factible para la mayoría de las estructuras. En concordancia con tal filosofía se establecen en la presente Norma los siguientes principios: a. La estructura no debería colapsar ni causar daños graves a las personas, aunque podría presentar daños importantes, debido a movimientos sísmicos calificados como severos para el lugar del proyecto. b.
La estructura estructur a debería soportar movimientos movimiento s del suelo calificados como moderados para el lugar del proyecto, pudiendo experimentar daños reparables dentro de límites aceptables.
c.
Para las edificaciones edificacio nes esenciales, esenciales, definidas en la Tabla Nº 5 (Norma E.030), se tendrán consideraciones especiales orientadas a lograr que permanezcan en condiciones operativas luego de un sismo severo. Sin embargo el estado del arte actual no puede garantizar el punto exacto de
comportamiento de los edificios (punto de desempeño), en otras palabras no está lo suficientemente suficientemente desarrollado como para explicar la capacidad real de las estructuras.
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ANÁLISIS Y DISEÑO SISMORRESISTENTE DE UN COLEGIO A DOS AGUAS
1.1
PROCEDIMIENTOS PROCEDIMIENTOS DE ANÁLISIS SÍSMICO Existen varios procedimientos de análisis sísmico de edificios, estos procedimientos procedimientos pueden ser lineales o no lineales, y estos a la vez pueden ser estáticos o dinámicos. Según el ASCE/SEI 41-13, el análisis sísmico de las estructuras se llevará a cabo mediante los procedimientos lineales (análisis estático lineal (AEL) y análisis dinámico lineal (ADL)) y procedimientos no lineales (análisis estático no lineal (AENL) y análisis dinámico no lineal (ADNL)).
Figura 1.1. Procedimientos de Análisis Sísmico según el ASCE/SEI 41-13
1.1.1 PROCEDIMIENTO PROCEDIMIENTO DE ANÁLISIS LINEAL En el procedimiento de análisis lineal se calcula la demanda sísmica y se compara con la capacidad estructural mediante la realización de un análisis lineal elástico.
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ANÁLISIS Y DISEÑO SISMORRESISTENTE DE UN COLEGIO A DOS AGUAS
La mayoría de normas de diseño sismorresistente están basados en procedimientos de análisis lineales elásticos debido a su fácil aplicación. Estos procedimientos de análisis lineales son: el análisis estático lineal y análisis dinámico lineal. Los procedimientos de análisis lineales pueden predecir la capacidad elástica de la estructura e indicar donde ocurrirá primero la fluencia, sin embargo, estos procedimientos no predicen los mecanismos de falla y no toman en consideración la redistribución de fuerzas que se producirá cuando la fluencia avanza en la estructura. Para tener en cuenta la incursión de la estructura en el rango no lineal, las normas de diseño sismorresistente incluyen un factor de reducción “R” para reducir la fuerza
sísmica el cual depende del tipo de sistema estructural.
Figura 1.3. Factor de reducción de fuerza sísmica En un análisis lineal las propiedades estructurales, tales como la rigidez y el amortiguamiento son constantes, no varían con el tiempo. Los desplazamientos, esfuerzos, reacciones, son directamente proporcionales a la magnitud de las fuerzas aplicadas.
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ANÁLISIS Y DISEÑO SISMORRESISTENTE DE UN COLEGIO A DOS AGUAS
1.1.1.1 ANÁLISIS ESTÁTICO O DE FUERZAS EQUIVALENTES Este método representa las solicitaciones sísmicas mediante un conjunto de fuerzas actuando en el centro de masas de cada nivel de la edificación para obtener los desplazamientos y las fuerzas de diseño.
Figura 1.4. Análisis estático o de fuerzas equivalentes Dentro del mismo se asumen dos hipótesis importantes; la primera es que el método implica que las acciones equivalentes de diseño son capaces de representar la acción símica, lógicamente esto es una simplificación que debe cumplir con los requerimientos para algunas edificaciones. Por ejemplo según la Norma E.030 podrán analizarse mediante este procedimiento todas las estructuras regulares o irregulares
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ANÁLISIS Y DISEÑO SISMORRESISTENTE DE UN COLEGIO A DOS AGUAS
1.1.1.2 ANÁLISIS DINÁMICO MODAL ESPECTRAL Y TIEMPO - HISTORIA La estructura es modelada como un sistema de uno o varios grados de libertad, con una matriz de rigidez elástica lineal y una matriz de amortiguamiento viscoso equivalente. Para saber la demanda a la cual someteremos la estructura en este método, se puede usar el espectro de diseño sísmico que imponga la norma para el caso del método de análisis modal espectral o varios registros en el caso del método de tiempo-historia.
Figura 1.5. Análisis modal espectral y tiempo-historia El análisis por combinación modal espectral supone que la respuesta dinámica de un edificio puede ser estimada a partir de la respuesta independiente de cada modo natural de vibración usando el espectro de respuesta elástico lineal. Solamente se consideran los modos que contribuyen de forma significativa a la respuesta de la estructura. La Norma E.030 indica que se considere aquellos modos de vibración cuya suma de masas efectivas sea por lo menos el 90% de la masa total de la estructura.
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ANÁLISIS Y DISEÑO SISMORRESISTENTE DE UN COLEGIO A DOS AGUAS
Las incertidumbres involucradas en la determinación exacta de las propiedades del material, capacidad de los elementos y de la estructura, la limitada predicción de los movimientos del terreno que la estructura va experimentar y las limitaciones en el modelado preciso del comportamiento estructural hacen que la evaluación de desempeño sísmico de las estructuras sea un proceso complejo y difícil. Los procedimientos de análisis no lineales proporcionan un enfoque más racional a estas cuestiones en comparaciones a los procedimientos lineales por considerar deformaciones inelásticas inelásticas en lugar de fuerzas elásticas. Los procedimientos de análisis no lineales tienen por objetivo, predecir la respuesta global de la estructura, más allá de la capacidad elástica-lineal, con la finalidad de identificar la evolución de la degradación de los elementos de la estructura hasta alcanzar los mecanismos de colapso. El proceso genérico del análisis no lineal es similar a los procedimientos lineales convencionales donde el ingeniero estructural desarrolla un modelo del edifico, para después someter a una representación del movimiento sísmico del suelo. Los resultados del análisis son la predicción de la demanda dentro del modelo estructural que se utilizan posteriormente para determinar el desempeño basado en criterios de aceptación. Los parámetros de la demanda comprenden normalmente desplazamientos globales (ejemplo, desplazamiento del nodo de control), drifts de los pisos, las fuerzas en la base, distorsiones y fuerzas en los elementos de la estructura (FEMA 440, 2005).
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ANÁLISIS Y DISEÑO SISMORRESISTENTE DE UN COLEGIO A DOS AGUAS
1.1.2.1 ANÁLISIS ESTÁTICO NO LINEAL O PUSHOVER El procedimiento de análisis estático no lineal conocido como “Pushover” es el método más usado para la evaluación del desempeño sísmico de las estructuras debido a su simplicidad, menor esfuerzo computacional y precisión. El análisis Pushover en su modelo matemático incorpora las características no lineales del material a partir de cierto nivel de fuerzas. El procedimiento de análisis estático no lineal consiste en aplicar fuerzas laterales a la estructura que van incrementándose gradualmente, el análisis se lleva hasta el colapso de la estructura, por lo tanto, permite la determinación de la carga de colapso y la capacidad de ductilidad de la estructura. Las fuerzas laterales se aplican de acuerdo a un patrón de carga predefinido y son aplicadas en forma monotónica en una sola dirección, la magnitud de la fuerza lateral se incrementa, pero el patrón de fuerza lateral sigue siendo igual hasta el final del proceso.
Figura 1.7. Esquema del procedimiento de análisis estático no lineal Como resultado del análisis Pushover se obtiene la curva capacidad (curva
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ANÁLISIS Y DISEÑO SISMORRESISTENTE DE UN COLEGIO A DOS AGUAS
1.1.2.2 ANÁLISIS DINÁMICO NO LINEAL El procedimiento de análisis dinámico no lineal es el procedimiento de análisis sísmico más preciso para estimar las demandas sísmicas. Sin embargo, el uso de análisis dinámico no lineal es limitado debido a que la respuesta dinámica es muy sensible a las características del modelado y de los terremotos. Se requiere el modelado adecuado de las características de deformación de cargas cíclicas teniendo en cuenta las propiedades de deterioro de los elementos importantes de la estructura. Además, se requiere la disponibilidad disponibilidad de un conjunto de registros representativos representativos del movimiento de la tierra que represente las incertidumbres y diferencias en severidad, frecuencias y características de duración. Por otra parte, el tiempo de cálculo, el tiempo requerido para la elaboración de datos de entrada e interpretar los datos de salida hace que el uso del análisis dinámico no lineal sea poco práctico. El procedimiento de análisis dinámico no lineal nos permite conocer la variación de la respuesta la estructura en el tiempo como los desplazamientos del edificio, derivas, fuerzas en los elementos de la estructura, etc.
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ANÁLISIS Y DISEÑO SISMORRESISTENTE DE UN COLEGIO A DOS AGUAS 1.92
1.92
3.50
3.50
3.50
3.50
3.50
3.50
ELEVACIÓN Y CORTE
2.3
CARACTERÍSTICAS CARACTERÍSTI CAS DE LOS MATERIALES Albañilería -
Resistencia a la compresión (f’ m)
:
65 Kg/cm2
-
Resistencia al corte puro (v’ m)
:
8.1 Kg/cm2
-
Módulo de elasticidad (E m=500 f’m)
:
32500 Kg/cm2
Módulo de corte (G =E /2(µ +1))
13000 Kg/cm2
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ANÁLISIS Y DISEÑO SISMORRESISTENTE DE UN COLEGIO A DOS AGUAS
2.4
CARGAS UNITARIAS UNITARI AS Pesos Volumétricos -
Peso volumétrico del concreto armado :
2400 Kg/m 3
-
Peso volumétrico de la albañilería
:
1800 Kg/m 3
-
Peso volumétrico del tarrajeo
:
2000 Kg/m 3
Techos -
Sobrecarga Sobrecarga en piso típico
:
250 Kg/m2
-
Sobrecarga en azotea
:
30 Kg/m 2
-
Acabados
:
120 Kg/m2
Muros -
Peso volumétrico de muros de cabeza de albañilería con 1 cm de tarrajeo: (1800 x 0.23 + 2000 x 0.02)/0.23 = 1974 Kg/m 3
2.5
REGLAMENTOS Y NORMAS -
Norma E.020 “Cargas”
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CAPÍTULO III ESTRUCTURACIÓN 3.1
LOSAS Se utilizó losas aligeradas armadas en una sola dirección paralela a la menor dimensión del paño, procurando que sean continuas.
3.2
VIGAS La ubicación de las vigas peraltadas fue conforme a la arquitectura, se buscó vigas con peraltes uniformes y de sección variable en volados con ancho igual al de las columnas que las reciben. Tenemos así definidas las vigas peraltadas para ambas direcciones. En la dirección Y (Vigas Portantes), contamos con las siguientes vigas: Ejes 2, 4, 6 y en los volados desde el eje 1 al eje 7. En la dirección X (Vigas Sísmicas), contamos con las siguientes vigas: Ejes A y C.
3.3
COLUMNAS
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CAPÍTULO IV PREDIMENSIONAMIENTO 4.1
LOSAS Para los aligerados armados en una dirección y con sobrecargas de hasta 350 kg existe una regla práctica que se utiliza con buenos resultados para determinar su espesor. Esta regla consiste en dividir la longitud de luz libre (Ln) del paño entre 25. Este espesor de la losa incluye tanto al espesor del ladrillo como a los 5 cm de losa superior. Siguiendo este criterio, y debido a que la luz libre del paño es de 3.975 m, el peralte resultaría ser de 16 cm, pero se utilizará un peralte de 20 cm.
5cm h
h ladrillo
10cm
4.2
VIGAS
30cm
10cm
30cm
10cm
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4.3
COLUMNAS El peralte de las columnas depende de la longitud de desarrollo del acero en las vigas.
4.4
PLACAS Se consideró 6 placas de 1.45 m de longitud y 25 cm de espesor en el eje X.
4.5
MUROS Para las zonas sísmicas 3 y 4, el espesor efectivo mínimo, descontando tarrajeos es t = h/20 = 290/20 = 0.145 m, donde “h” es la altura libre de la albañilería. Con lo cual,
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ANÁLISIS Y DISEÑO SISMORRESISTENTE DE UN COLEGIO A DOS AGUAS
CAPÍTULO V ANÁLISIS SÍSMICO CON ETABS 5.1 1)
MODELAMIENTO Abrir el programa ETABS
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3)
Completar la información informació n de los ejes y número de pisos
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5)
Ir a Custom Story Data/ Edit Story Data/ Display Grid Data as Spacing/ Completar la información de los espacios espacios de los pisos/ OK/ OK.
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8)
Ir a File/ Save As/ Seleccionar la ubicación y guardar.
9)
Ir a Define/ Material Properties/ Properties / Seleccionar Selecciona r 4000Psi y hacer clic en Modify-Show Modify-S how Material/ Completar las propiedades del material.
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ANÁLISIS Y DISEÑO SISMORRESISTENTE DE UN COLEGIO A DOS AGUAS
11)
Seleccionar A615Gr60 y hacer clic en Modify-Show Material/ Completar las las propiedades del material.
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13)
Hacer clic en Add New Material/ Seleccionar el material/ OK.
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15)
Ir a Define/ Section Properties/ Properties / Reinforcing Bar Sizes/ Hacer clic Clear All Bars y hacer clic en Add Common Bar Set/ U.S. Customary/ OK.
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16)
Ir a Define/ Section Properties/ Frame Sections/ Hacer clic en Delete Multiple Properties/ Seleccionar todas las secciones y hacer clic en Delete Selected Frame Sections/ Nuevamente seleccionar todas las secciones excepto una/ Delete Selected Frame Sections/ OK.
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17)
Hacer clic en Add New Property/ Propert y/ Seleccionar Rectangular Section/ Completar las propiedades de la sección/ Hacer clic en Modify – Show Rebar/ Completar la información/ OK/ OK.
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