ESTRUCTURAS DE MADERA
CAPÍTULO VI
CAPITULO 6
ARMADURAS DE MADERA 6.1 GENERALIDADES.Las armaduras de madera tienen una gran diversidad de usos, entre los que destacan la construcción de techos para diversos tipos de edificaciones, la construcción de puentes, etc. Las armaduras de madera presentan grandes ventajas para la construcción de techos de casas, estas son: su reducido peso propio (lo que facilita su montaje), su capacidad de cubrir grandes luces, y se ajustan a muchas formas de perfiles para techos. Una armadura es una estructura reticulada, con un sistema de miembros ordenados y asegurados entre sí, de modo que los esfuerzos transmitidos de un miembro a otro son de compresión o de tensión axial. Básicamente una armadura esta compuesta por una serie de triángulos, porque el triángulo es el único polígono cuya forma no puede cambiarse sin modificar la longitud de uno o más de sus lados. Con respecto a los techos soportados por armaduras: 1. Una crujía es una parte de la estructura del techo limitada por dos armaduras adyacentes; la separación entre centros de las armaduras es el ancho de la crujía. 2. Una correa es una viga que va de armadura a armadura, y que les transmite las cargas debidas a nieve, viento y el peso de la construcción del techo. 3. La parte parte de una armadur armaduraa que se presenta presenta entre entre dos nudos nudos adyacent adyacentes es de la cuerda superior se llama celosía. 4. La carga carga llevad llevadaa al nudo nudo de una una cuerda cuerda super superior ior opunto o punto de celosía es, por lo tanto, la carga de diseño del techo en kilogramos por metro cuadrado, multiplicada por la longitud de la celosía y por el ancho de la crujía; a esto se le llama una carga de celosía. celosía. Cuerda Superior
Figura 6.1 PARTES DE UNA ARMADURA DE TECHO Carga de Celosía Carga de Celosía
a í a o s l o e C
e t l a r e P
Cuerda Inferior Reacción Claro Ref.: Fig. 12.1 Pág.: 184 “ Diseño Simplificado de Estructuras de Madera” Parker-Ambrose Pendiente
UNIVERSIDAD MAYOR MAYOR DE SAN SIMON
132
FACULT FACULTAD DE CIENCIAS Y TECNOLOGIA
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
6.2 TIPOS DE ARMADURAS.En la siguiente figura se ilustran algunas de las armaduras para techo más comunes. Figura 6.2 FORMAS DE ARMADURAS DE TECHO TECHO MAS COMUNES
a) Fink o W
b) En Abanico
c) Fink combada
d) Howe
e) De pendolón
f) Pratt
g) Warren Plana
h) Pratt plana
i) De arco y cuerda
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
En el“Manual de Diseño para Madera del Grupo Andino” se muestran también similares formas de armaduras, con sus luces recomendadas (Pág. 11-3). La altura o peralte de una armadura dividida entre el claro se llama relación peralte a claro; claro; el peralte dividido entre la mitad del claro es la pendiente. pendiente. A continuación se presenta la Tabla 6.1 en la cual se muestran la relación peralte a claro y sus respectivas pendientes para los techos más comunes. Tabla 6.1 RELACIÓN RELACIÓ N PERALTE PERALTE A CLARO Y PENDIENTES PENDIENT ES DE TECHOS Relacion peralte a claro
1/8
1/6
1/5
1/4
1/3.46
1/3
1/2
-----------------------------------------------------------------------------------------------------------------------------------------------------------
Grados
14º3'
18º26'
21º48'
26º34'
30º0'
33º0'
45º0'
-----------------------------------------------------------------------------------------------------------------------------------------------------------
Pendiente
1/4
1/3
1/2.5
1/2
1/1.73
2/3
1
Ref.: Tabla Tabla 12.1 Pág.:185 “ Diseño Simplificado de Estructuras de Madera ” Parker-Ambrose
Para armaduras de techo, para evitar e vitar en lo posible esfuerzos de flexión de la cuerda superior es conveniente la ubicación de los nudos directamente debajo de las correas. También se debe procurar que la pendiente no sea excesivamente plana, debido a que es antieconómica, así así como como poco poco pera peralt lte. e. En zonas zonas de vient vientos os fuer fuerte tess es conve conveni nien ente te usar usar pendi pendient entes es pequeñas, implicando esto mayores cargas horizontales, como nieve (si la hay), u otras sobrecargas. Espaciamiento de las armaduras.El espaciamiento más económico depende del costo relativo de las armaduras, las correas y la cobertura. El tamaño de las correas ésta determinado por el momento flector que soportan y limitación de sus deformaciones; su costo por lo tanto varía con el cubo o cuadrado de la luz (que viene a ser el espaciamiento). También debe considerarse c onsiderarse lo siguiente:
El costo de los materiales y de la mano de obra de las armaduras por m 2 de techo, es normalmente varias veces el de las correas.
El costo de la cobertura varía con su naturaleza misma, pero probablemente no
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
Por lo tanto debe usarse por lo general aquel espaciamiento igual a la máxima luz que cubran cubran las correas correas más económi económicas cas;; conside considerand randoo que ellas ellas trabaj trabajan an como como vigas continuas ya que cubren cuando menos dos tramos. Configuración interna.La configuración de elementos internos de las armaduras debe procurar paños tales que reduzcan
el número de nudos, debido al alto costo involucrado en su fabricación total.
También debe considerarse:
Que la esbeltez de los elementos a compresión no debe ser excesiva, ya que la capacidad de carga disminuye rápidamente con el incremento de la esbeltez (ver Capítulo 4).
Que la flexión en las cuerdas superiores, debido a cargas en el tramo, no debe ser excesiva ya que el efecto magnificador de la presencia simultanea de la carga axial la hace más mucho más desfavorable.
Que el ángulo interno entre las cuerdas y entre éstas y las diagonales no sea muy pequeño, porque esto resulta en fuerzas muy grandes en las respectivas barras y requiere uniones excesivamente reforzadas.
6.3 MIEMBROS Y NUDOS DE ARMADURAS.-
En armadu armadura rass de made madera ra se usa usa por lo gener general al eleme element ntos os simp simple less y mú múlt ltip iple les. s. La combinación más apropiada de elementos depende de la magnitud de las cargas, de las luces por cubrir y de las conexiones adoptadas. Las tres formas más comunes de configuración de armadura son las que se muestran a continuación en la figura 6.3.
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
a) Armadura ligera de madera de un solo elemento, con placas de conexión clavadas.
b) Miembros de madera pesada con placas de conexión de acero y nudos atornillados.
c) Miembros con varios elementos con nudos empalma almaddos con cubrejuntas de madera y empernados.
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
El tipo de miembro individual, con todos los miembros en un solo plano, el cual se muestra en a), es la que se usa con mayor frecuencia para producir la armadura simple Fink o W, W, con miembros cuyo espesor es por lo general de 2 pulgadas. En armaduras más grandes se puede usar la forma que se muestra en c), con miembros que constan de varios elementos de madera. Si el elemento trabaja a compresión, se diseñará, por lo general, como una columna formada por varios miembros (ver capitulo 4).Para claros pequeños, los miembros son por lo general, de dos elementos con espesor de 2 pulgadas; sin embargo para claros grandes o cargas pesadas, los elementos individuales sobrepasan las 2 pulgadas de espesor. espesor. En la denominada denominada armadura pesada, los miembros individuales son elementos grandes de madera, que por lo general presentan un solo plano, como lo muestra la figura c). Un tipo común de nudo para este caso, es en el que se usa placas de acero unidas con tornillos tirafondo o pernos que la atraviesan. Un tipo de unión muy común para un miembro miembro diagonal a compresión compresión que será conectado con la cuerda inferior es el embarbillado (ver capítulo 5), pero este tipo de unión requiere trabajo de carpintería para su ejecución, a continuación se muestra un esquema de este:
C
α
T
Aunque los miembros de madera tienen una resistencia considerable a la tracción, no es sencillo construir uniones que resistan a tensión, en especial si las armaduras son de madera pesada. pesada. Así como una solución a esto en la actualidad se acostumbra a que los miembros de la armadura sujetos a tensión sean de acero (con excepción a las cuerdas); como así también es muy común que se construyan armaduras en que solo las cuerdas son
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
6.4 REQUISITOS DE RESISTENCIA Y RIGIDEZ.Cargas.Las armaduras se deben diseñar para resistir las cargas aplicadas (el ingeniero deberá identificar identificarlas las y determinar determinar la magnitud magnitud de las mismas). mismas). También se debe tomar en cuenta cargas de montaje o construcción, y algunas otras cargas especiales. En el caso de que una cuerda inferior soporte un cielo raso, se debe considerar una carga mínima de 30 kg/m2 . Deflexiones.Para el cálculo de las deflexiones el “Manual de Diseño para Madera del Grupo Andino” acepta los métodos de cálculo habituales en la práctica de la ingeniería, como ser las deflexiones elásticas por métodos de trabajos virtuales que suponen las articulaciones como perfectas e indeformables. Cabe señalar que con el desarrollo de la tecnología, los programas computacionales realizan el cálculo de las deflexiones mediante el método matricial (método más exacto); por lo tanto ya no será necesario realizar los cálculos de manera manual, por lo que en este capítulo en la parte de tutoriales de programas, se realizará el procedimiento para encontrar éstas deflexiones por medio de los programas comput computaci aciona onale less (ya sea sea en “SAP2000”, SAP2000”, “Robot Millenium Millenium”” , o “Cercha “Cercha para para la calcul calculador adoraa HP”). HP”). Sie Siendo ndo ya calcul calculadas adas las deflex deflexion iones es “elást “elástica icas” s” lo que la norma norma recomienda es: “Si la armadura ligera es tipo Fink o abanico, abanico, y cuyas uniones son clavadas, clavadas, y son fabricadas con cartelas de tableros contrachapados se debe utilizar la fórmula siguiente para hallar la deflexión máxima en e n una barra de la cuerda inferior:
w L4 10 4
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
acabados), las deflexiones se deben limitar a las deflexiones máximas admisibles dadas en el capítulo antes mencionado. En el caso de que el espaciamiento de las armaduras sea menor o igual que 60 cm, cm, se recomienda utilizar el módulo de elasticidad promedio: “E promedio”, y en caso contrario, se debe considerar el modulo de elasticidad mínimo: “E0.05”. En armaduras ligeras por lo general no se considera la contraflecha, pero si por una razón especifica es necesaria, se recomienda que sea del orden de 1300 de la luz de la armadura. 6.5 CRITER CRITERIOS IOS DE DISE DISEÑO. ÑO.-A continuación se dan una serie de recomendaciones, que deben ser tomadas a la hora de realizar el diseño:
Es recomendable el uso de maderas del Grupo C, debido a su baja densidad son más livianas para su montaje, y son fáciles de clavar. Para el uso de Maderas de los los demá demáss grup grupos os debe debe usar usarse se pref prefer eren ente teme ment ntee unio unione ness empe empern rnad adas as o atornilladas.
Las secciones de los elementos no deben ser menores de 6.5 cm de peralte y 4 cm de ancho. A menos que se utilicen cuerdas de elementos múltiples.
Las uniones deben cumplir los requisitos expuestos en el capítulo 5.
En el caso de usar cartelas de madera contrachapada, se recomienda un espesor no menor de 10 mm.
Las Las car cargas gas admi admisi sibl bles es de los los elem elemen ento toss indi indivi vidu dual ales es se dete determ rmin inar aran an
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
Para armaduras de techos: Las cargas de la cobertura se transmiten a través de las correas; estas a su vez pueden descansar directamente en los nudos o en los tramos entre nudos
de la cuerda superior originando momentos flectores en
estos elementos.
Las fuerzas internas axiales en las barras de las armaduras pueden calcularse suponiendo que las cargas externas actúan en los nudos. Cuando este no sea el caso, se podrá reemplazar la acción de las cargas repartidas por su efecto equivalente en cada nudo.
Los efectos de flexión debidos a las cargas del tramo se superpondrán a las fuer fuerzas zas inte intern rnas as axia axiale les, s, para para dise diseña ñarr los los elem elemen ento toss como como viga viga-c -col olum umna na sometida a flexocompresión.
Esbeltez.El valor máximo de la relación de esbeltez para el diseño será:
λ = Lef d
≤ 50
Para elementos sometidos a cargas axiale axialess de com com resión resión
≤ 80
Para elementos sometidos a cargas axiales de tracción.
En el caso de cuerdas sometidas a compresión, habrá dos relaciones de esbeltez, una en el plano de la armadura y otra fuera del mismo. En el plano de la armadura, la dimensión de la sección sección transversal transversal que es resistente resistente al pandeo será el alto o peralte de la cuerda: h. Fuera del plano de la armadura, la dimensión resistente resistente será la base: b si se trata de una sección
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
Figura 6.4 LONGITUDES PARA CALCULO DE Lef (para Tabla Tabla 6.2)
L 3 L 2
L c L c
L 1
L d
CL
Ref.: Figura 11.5 Pág.:11-13 “ Manual de Diseño para Maderas del Grupo Andino”
Tabla 6.2 LONGITUD EFECTIVA EFECTIVA Elemento
d
Lef
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
Cuerdas con Carga en el Tramo.Este tipo de elementos deben diseñarse a flexo-compresión; donde las cargas axiales son obtenidas mediante una primer análisis de la armadura con cargas concentradas en los nudos nudos,, y los los mo mome ment ntos os flect flector ores es son son dete determ rmin inad ados os supo suponi nien endo do que que las las cuer cuerdas das se comportan como vigas continuas apoyadas apo yadas en los extremos de las diagonales y montantes. Para los casos descritos en la Tabla Tabla 6.3 pueden usarse las formulas de momento dadas allí. Tabla 6.3 MOMENTOS DE FLEXIÓN DE DISEÑO
w Cuerdas Superiores:
L
w ⋅ L2 M= 9
L1
L2
w ⋅ L2 M= 10
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
La luz que entra en las anteriores formulas de momentos se determina como lo muestra la figura 6.5: Figura 6.5 Luces para el cálculo de L (para Tabla Tabla 6.2)
L1
L2
L3
L = mayor promedio de los tramos consecutivos
L=
L4
L1 + L2 2
ó L=
L2 + L3
L5
Ref.: Figura 11.2 Pág.:11-6 “ Manual de Diseño para Maderas del Grupo Andino”
Si la longitud de uno de los tramos es menor que 0.80 de la luz mayor, se tomará el mayor
2
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
Ref.: Figura 12.7 Pág.: 195 “ Diseño Simplificado de Estructuras de Madera ” Parker-Ambrose Es un sistema estructural, donde la cuerda superior de la armadura está arriostrada en
cada nudo de éstas por las correas. Si además la cubierta de la techumbre es un elemento suficientemente rígido, esto constituye un arriostramiento muy adecuado de la cuerda a compresión (que es el principal problema de la armadura). Pero también es necesario reforzar la armadura contra movimientos fuera de su plano en toda su altura;
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
proporciona un arriostramiento continuo, de modo que la longitud de apoyo de la cuerda es cero en realidad. El arriostramiento adicional se limita a una serie de varillas o angulares individuales pequeños, que se unen con la cuerda inferior, de manera alternada entre los puntos de celosía.
Tercera alternativa: Figura 6.8 Arriostramiento de armaduras. 3º Alternativa
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ESTRUCTURAS DE MADERA
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
Procedimiento Paso 1.- Establecer la geometría a)
Haga doble click en el icono de SAP2000, situado en la barra de escritorio para comenzar SAP2000 Nonlinear v.8.08.
b)
Seleccione File/New Model… del menú desplegable, se mostrará una ventana en la cual figuran: Las unidades con las cuales se trabajará y además además figura figurass geométr geométrica icass que pueden pueden cambiar cambiarse se para adaptars adaptarsee a nuestra geometría. Cambiar las unidades a Kgf, m, C.
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
estructura podrá hacerse más rápidamente de esta manera). Para nuestro caso, en esta ventana pulse el botón Vertical ertica l Truss d)
Se habilita una ventana en la cual se debe poner los valores particulares de la cercha:
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
d) Con el anterior paso ya se estará tomando en cuenta el peso propio del material en los nudos, sin embargo es necesario asignar a las barras las propiedades del
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
f) Sele Selecci ccion onar ar toda todass las las barr barras as y asig asignar nar las las dife difere rent ntes es secc seccio iones nes segú segúnn les les corresponda: Assign / Frame/Cable / Sections y posteriormente elegir la opción anteriormente definida:
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
Paso 4.- Liberación de nudos Como dijimos anteriormente, las armaduras se ven afectadas principalmente por esfuerzos de tracción y compresión. Es por este motivo que se procede a la liberación de nudos. a) Seleccionar todas las barras a las que se desea liberar los momentos. b) De la barra de menú seleccionar la opción Assign / Frame/Cable una vez seleccionada la opción se desplega un ventana de la cual se debe escoger: Releases / Partial Fixity. Se procede a las liberación de los nudos tal como se muestra en la figura:
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
opción Edit/Auto Relabel / All in the list. list. Es posible observar como cambiaron los nombres en la lista inferior de la ventana, una vez hecho todo esto pulsar OK.
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
Paso 7.- Análisis de datos a) Una vez hecho todo esto se procede a ejecutar el programa, para se puede ir a la barra de menú y seleccionar Analyze seleccionar Analyze / Run Analysis, Analysis, o caso contrario buscar el
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
Paso 8.- Salida de datos a) De la barra de herramientas seleccionar el icono de Show Forces/Stresses, a continuación se desplegará opciones en la que podrás elegir los elementos de los
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
se desea y se habilitará una ventana en la que se detallará las características de la barra.
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
Database Table Format. En esta ventana también se podrá escoger los valo alores en un rango de dat datos que nos interese por por ejempl emploo. (Operador/Between). Una Una vez vez esta establ bleci ecido do todos todos los los form format atos os de
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
Luego Presionar ENTER:
Para las fuerzas internas de las barras teclear “1”, entonces: entonce s:
Luego Presionar ENTER, entonces aparecen las fuerzas internas en las barras; pero cabe aclararla convención del programa para interpretar los resultados:
En primer lugar el sentido positivo se toma de acuerdo del nudo final al nudo inicial (esto define el eje local longitudinal positivo), por ejemplo la barra 1 va desde el nudo 1 al nudo 2, entonces:
+
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
La convención para definir la tracción y la compresión es la siguiente:
COMPRESIÓN
o
TRACCIÓN
Por ejemplo para la barra 2 se tiene:
+ 3
2
b2
Y de los resultados se tiene que el nudo 2 tiene un F=-1.65 ton y el nudo 3 tiene un F=1.65 ton , lo que equivaldría a:
1.65 t 2
2
o
TRACCIÓN 1.65 t b2
b2
3
3
Como otro ejemplo para la barra 8 se tiene:
8 b8 1
+
Y de los resultados se tiene que el nudo 8 tiene un F=2.4 ton y el nudo 1 tiene un F=-2.4 ton , lo que equivaldría a:
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
8 b8 2.4 t
1 2.4 t
COMPRESIÓN
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ESTRUCTURAS DE MADERA
Al concluir de ver las fuerzas internas Presionar ENTER:
CAPÍTULO VI
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ESTRUCTURAS DE MADERA
CAPÍTULO VI
Para guardar los resultados presionar la tecla “ F ” :
Para salir del programa: presione la tecla “
“:
Los datos, y los resultados se encuentran grabados en la carpeta SUB, SUB, allí se puede volver a entrar (sin necesidad de correr el programa otra vez), y ver los valores que nos interesen (sobre todo los resultados):
El prog progra rama ma se pued puedee desc descar arga garr desd desdee Inte Intern rnet et de mane manera ra grat gratui uita ta de la pági página na http://www.geocities.com/hp48_civil/
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