Método del Área de Momento para Deflexiones en Vigas

¿Qué es el Método del Área de Momento?
El método Área-Momento es una forma de determinar la pendiente y deflexión en las vigas. [url=http://ingcivil-2008.blogspot.com/2008/05/mtodo-de-area-de-momentos.html]http://ingcivil-2008.blogspot.com/2008/05/mtodo-de-area-de-momentos.html[/url]. Se basa en el comportamiento geométrico de los diagramas de momento y el cálculo diferencial.[br][br]ACTIVIDAD 1.[br][br]a. Para entender este método, lo primero que harás es dibujar una curva en un pedazo de papel y marcar dos puntos, A y B, preferiblemente utiliza 2 colores distintos. Luego haz dos líneas "tangentes" de los puntos y la curva.[br][br]b. Haz una línea horizontal que atraviese la curva y señala:[br][list][*]Los ángulos entre las dos líneas tangentes.[/*][*]Dibuja unas línea perpendicular entre el punto A y la horizontal.[/*][*]Realiza el paso anterior con el punto B.[/*][/list]
El resultado debe ser similar al que se presenta a continuación. Juega con los deslizadores A y B, observa lo que sucede y responde las siguientes preguntas.
PREGUNTA 01
¿Cómo se calcula la recta tangente a una curva?
De la curva de una función a la curva elástica
Juega un poco más con la aplicación de GeoGebra. [br][br]ACTIVIDAD 2.[br][br]a. Coloca el deslizador B en un valor igual a 1.4. y dibuja una paralela al eje horizontal en este punto.[br]b. Encuentra los extremos visibles de la función.[br]c. Lleva el deslizador A hacia el extremo de la función y contesta las siguientes preguntas.[br]
PREGUNTA 02
¿Cómo es la línea tangente del deslizador A?
PREGUNTA 03
Si imaginamos que la línea paralela determinada por el deslizador B delimita una viga, y la función dibujada es realmente el comportamiento de la curva elástica. ¿Qué son los segmentos C[sub]A[/sub]D y D[sub]B[/sub]E?
TEOREMA II (ver la Sección 6-3 del libro Resistencia de Materiales de Pytel y Singer (4a. Ed., 1994)
La distancia desde el punto B de la elástica, medida perpendicularmente a la posición inicial de la viga, hasta la tangente trazada a la curva por otro punto cualquiera A, es la suma de [i]dt[/i] interceptados por las tangentes sucesivas trazadas a la elástica en puntos sucesivos. Cada uno de estos segmentos [i]dt[/i] puede considerarse como un arco de radio x y ángulo [i]d[/i][math]\theta[/math][code][/code], [math]dt=xd\theta[/math], de donde [math]t_{\frac{B}{A}}=\int dt=\int xd\theta=\frac{1}{EI}\int^{x_B}_{_{x_A}}x\left(Mdx\right)[/math].[br][br][color=#0000ff][b]La desviación tangencial de un punto B con respecto a la tangente trazada a la elástica en otro punto cualquiera A, en dirección perpendicular a la inicial de la viga, es igual al producto de 1/EI por el momento con respecto a B del Área de la porción del diagrama de momentos entre los puntos A y B.[/b][/color][br][br][i]EI = rigidez a la flexión[/i][br]
PREGUNTA 04
¿Cómo se puede aprovechar el Teorema II para la lectura de deflexiones de vigas?
ENCONTRANDO LA DEFLEXIÓN MÁXIMA DE UN VOLADIZO APLICANDO EL MÉTODO DEL ÁREA DE MOMENTOS
Se tomará como base el problema 637 del libro de texto (Singer, 1994). 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[/img][br][br]ACTIVIDAD 3.[br][br]a. Resuelve el problema por el método de doble integración. Apunta las ecuaciones de momento, pendiente y curva elástica.[br][br]b. Dibuja la curva elástica ayudándote con GeoGebra.
Curva elástica del voladizo. Con las casillas de verificación muestra la función f(x), h, i, A. Encuentra la deflexión máxima del voladizo.
PREGUNTA 05
¿Cuál es el valor de la deflexión máxima?
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Information: Método del Área de Momento para Deflexiones en Vigas