Diseño de cerchas de madera 1. Cerchas 1.1- Clasificación de las Cerchas. Las cerchas de madera se pueden clasificar de acuerdo a los siguientes criterios: a)
Según su forma: con cordón superior triangular, rectangular, curvo o combinaciones de ellos.
b)
Según distribución de diagonales: Howe, Pratt, Warren, etc.
c)
Según tipo de madera: aserrada, elaborada o cepillada, laminada encolada o mezclas de estas.
d)
Según tipo de cordones: ya sean de uno, dos o varios elementos. En el caso de cordones superiores e inferiores con dos elementos, las diagonales se ubicarán entre ellos.
La introducción de los conectores metálicos ha hecho posible el aprovechamiento más eficiente de la madera en el diseño de cerchas. Antes eran necesarias grandes secciones transversales a fin de tener uniones seguras y sólo se utilizaba entre el 40 y el 60 % de capacidad de resistencia de la madera. Ahora, al utilizar conectores metálicos, es posible obtener el 80 y hasta el 100 % de la resistencia de los diferentes elementos de madera que conforman una cercha.
1.2-
Selección del Tipo de Cercha.
Se ha demostrado que la cercha del tipo cordón superior curvo es la más económica cuando las cargas solicitantes son uniformemente repartidas, ya que en ella estas cargas inducen esfuerzos pequeños en las diferentes barras, sean estas internas o externas. Esto es particularmente importante, debido a que resultan elementos de unión simples y compactos. La cercha del tipo triangular se recomienda cuando las cargas se transmiten a la cercha en puntos específicos
(cargas
concentradas
y/o
puntuales).
Para
las
barras
traccionadas
es
aconsejable utilizar tensores de acero. En cuanto a cerchas de madera laminada encolada, éstas son recomendables para salvar grandes luces y además permiten obtener mayores tensiones de diseño, pueden curvarse con facilidad y variar su sección transversal a lo largo de su longitud. Las cerchas fabricadas con elementos constituidos por una pieza soportaran cargas a lo menos iguales que aquellas fabricadas con elementos conformados por dos o más piezas que proporcionen igual sección transversal, pero estarán propensas a pandearse con mayor facilidad.
1.3-
Geometría de la Cercha.
Como ya se mencionó, las cerchas, según la forma de su cordón superior, se clasifican en triangulares, rectangulares y curvas. Para las triangulares se recomienda una pendiente 1:3 como mínimo; en las rectangulares, alturas comprendidas entre 1/8 y 1/10 de la luz de la cercha y en las de cordón superior curvo, radios de curvatura de magnitud igual a la luz de la cercha y altura total igual al 0,134 de la luz; sin embargo, en este último caso, si las cerchas deben tener una altura menor a 0,134 de la luz se pueden tomar radios de curvatura mayores y viceversa. La distancia entre nudos estará determinada por la ubicación deseada de las costaneras, por las
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cargas concentradas o por el arriostramiento entre cerchas. Para cerchas de cordón superior curvo, sometidas a cargas uniformemente distribuidas, conviene elegir una distancia entre nudos comprendida entre 2,4 y 3,6 m, dependiendo de la luz de la cercha. La distancia entre cerchas estará controlada por la disposición más economica que sea capaz de soportar las cargas que actúan sobre la techumbre. Para costaneras de madera aserrada, la distancia más económica y práctica es 4,8 m. Cuando es utilicen costaneras de madera laminada, esta distancia sólo será limitada por aspectos económicos, pues dichos elementos laminados se pueden fabricar de cualquier longitud, considerándose económicas distancias de 9 m.
1.4-
Reglas Generales para el Diseño de Cerchas.
El procedimiento a seguir en el diseño de cerchas es el siguiente: a) Determinación de las cargas solicitantes, con las prescripciones de las normas para el diseño. b) Calculo de las solicitaciones en los diferentes elementos de la cercha. c) Selección de la especie y grado de calidad a usar. En la selección de la especie dependerá del sitio en donde se ubicara la estructura y de las maderas más comunes de la zona. El grado de calidad debe seleccionarse en función de la resistencia que de la madera se desea; sin embrago, algunos grados son más fáciles de obtener y, por lo tanto, se usan con mayor frecuencia. Como regla general, deben preferirse los grados con las tensiones más bajas, porque proveen prove en el diseño más eficiente y económico. d) Determinación de las escuadrías requeridas en los distintos elementos de la cercha. e) Diseño de las las uniones, considerando primero aquellas que soportan las solicitaciones mayores. Se debe establecer el espaciamiento entre elemetos de unión y la distancia de ellos al borde y a los extremos de la pieza que se une. Además, se debe tomar en cuenta que en las uniones se debe evitar la distribución excéntrica de los elementos de unión. Si ello ocurre, se debe considerar el efecto de los momentos que esto induce.
2. Diseño 2.1-
Factores de Modificación.
Estos son los factores de modificación que se utilizarán en las distintas etapas del calculo estructural, por esta razón es muy importante tener claro, cual es su utilización.
2.1.1- Factor de Modificación Modificación por Contenido de Humedad ( K H ). La asignación de las tensiones admisibles y del módulo elástico a piezas de madera aserrada
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K H =
factor de modificación por humedad, aplicable a las tensiones admisibles y módulo elástico, definidos para una humedad de 12 %.
DH =
diferencia entre el valor de contenido de humedad de servicio (HS) y 12 %.
DR =
variación de la resistencia por cada 1 % de variación de contenido de humedad.
2.1.2- Factor de Modificación Modificación por Duración de la Carga ( K D ). Según sea la duración de la carga que afecta la estructura, se aplicará el factor de modificación siguiente: K D
=
1,747 t0,0464
+
0,295
En que: t=
duración de la carga, en segundos.
El factor de modificación por duración de carga no afecta al módulo de elasticidad en flexión ni a la tensión admisible de compresión normal a la fibra.
2.1.3- Factor de Modificación por Trabajo Conjunto ( K C ). Las tensiones admisibles para elementos estructurales que conforman un sistema que comparte la carga, consistente en tres o más elementos paralelos distanciados en no más de 610 mm y dispuestos de tal forma que en conjunto pueden soportar la carga
aplicada, deben ser
multiplicadas por el factor de modificación por trabajo en conjunto.
2.1.4- Factor de Modificación por Temperatura. Cuando por razones excepcionales las condiciones de servicio de una estructura de madera determinen temperaturas ambientales marcadamente superiores a las normales, se deberá modificar el valor de las propiedades mecánicas admisibles, pudiendo adoptarse para estos efectos, los factores de corrección establecidos en la Tabla N° 1
Tabla N° 1 Incremento o decremento de los Valores de Resistencia por cada 1°C de Incremento o Decremento de temperatura.
Contenido de Propiedad
Humedad %
Incremento por enfriamiento
Decremento por calentamiento
Bajo 20° C (no inferior
sobre 20° C (no superior
a -180° C)
a 67° C)
Ct
Ct
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2.1.5- Factor de Modificación por Tratamiento Químico. Cuando las condiciones ambientales son favorables para el desarrollo de pudrición u otro tipo de deterioro en estructuras permanentes, la madera de tales estructuras debe ser sometida, antes de ser construida a un proceso de preservación con método y tipos de preservantes especificados en normas. Todo tipo de perforación, rebaje o corte debe ejecutarse en lo posible antes del proceso de preservación. En caso contrario se efectuarán después de éste, sometiendo los cortes a un nuevo proceso de preservación. La madera no preservada de estructuras permanentes no debe estar en contacto directo con hormigón, albañilería o suelo si estos materiales pueden transferir humedad a la madera. Se considera como una protección adecuada cualquier método que logre eliminar tal transferencia de humedad. Cuando la madera debe ser sometida a procesos de ignifugación que incrementen su higroscopicidad, debiliten su integridad física o alteren sus propiedades mecánicas, se deberá modificar el valor de las tensiones admisibles, pudiendo adoptarse para estos efectos, los valores de corrección establecidos por normas.
2.1.6- Factor de Modificación por Esbeltez ( K l ). El factor de modificación por esbeltez se evalúa con la expresión:
K l = A - Ö ( A² - B) Con:
A
B * c * ( 1 + l/200) + 1
=
2*c B
=
4 * E dis c * l ² * F cp, dis
En que: c=
coeficiente coeficiente de proporcional proporcionalidad idad (obtenid (obt enidoo en tablas) tabla s)
Edis =
módulo elástico de diseño.
F cp, dis =
tensión de diseño en compresión paralela (excluyendo K C).
2.1.7- Factor por Concentración de Tensiones ( K ctct ). El factor de modificación que considera el efecto de las concentraciones de tensiones en regiones traccionadas de la madera con perforaciones, vaciados, entalladuras, etc, se puede
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1/9 K hf hf = (50/h)
En que: K hf hf
=
factor de modificación por altura.
h
=
ancho de la pieza traccionada o altura de la viga.
Para piezas de Pino radiata de altura superior a 90 mm, la expresión que se debe considerar es: 1/5 K hf < 1 hf = (90/h)
3. Uniones en la madera estructural 3.1-
Elementos Mecánicos de Unión.
Son aquellos que, al quedar solicitados por fuerza de cizalle, admiten corrimientos relativos entre las piezas conectadas, los que se originan como consecuencia de las deformaciones por aplastamiento de la madera en la zona de contacto entre ella y elemento de unión, y adicionalmente, en el caso de medios de unión de forma cilíndrica, por las deformaciones de flexión que ellos experimentan. Dependiendo de su disposición en la unión pueden, también, quedar solicitados según su dirección axial.
3.2-
Uniones Clavadas.
Las presentes especificaciones para uniones clavadas en construcciones de madera rigen para empleo de los tipos de clavos fabricados según norma.
3.2.1- Solicitaciones de Extracción Lateral. En general se exige la presencia de al menos cuatro clavos en cada uno de los planos de cizalle que presenten en una unión clavada de dos o más piezas de madera. La exigencia anterior no rige para la fijación de revestimientos, entablados y contraventaciones. En todo caso, para elementos constituyentes de uniones un iones estructurales, se deben usar us ar espesores mayores o iguales que 18 mm, en uniones de clavado directo y 16 mm en uniones con perforación guía.
3.2.4- Hileras de Clavos en Elementos Elementos Traccionados. Traccionados. Si en un empalme o unión de elementos traccionados se disponen hileras de más de 10 clavos, en cada hilera se debe reducir en 1/3 las capacidades de carga de los clavos adicionales. Para efectos de cálculo se puede considerar un máximo de 30 clavos por hilera.
3.2.5- Perforaciones Guías.
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Para espesores de madera, e, menores de 6 * D, las capacidades admisibles de cargadeben ser afectadas por el factor de modificación, K cpg cpg, siguiente:
K cpg cpg
=
E 6*D
3.2.6- Espaciamientos. La distribución del clavado debe definirse respetando los espaciamientos mínimos especificados en tablas, tomando en consideración el diámetro del clavo, D, y el ángulo, que forma la fibra con la dirección de la fuerza. En general los clavos se deben alternar, desplazándolos en un diámetro de clavo con respecto al gramil de clavado.
Espaciamientos Mínimos de Clavos de Diámetro, D, en mm.
Clavado con
Clavado sin perforación guía Separación mínima
Entre clavos Desde el borde cargado Desde el borde descargado
0° < a < 30°
perforación guía
30° < a < 90°
Para cualquier a
D < 4,2
D > 4,2
D < 4,2
D > 4,2
// a fibra (s p)
10 D
12 D
10 D
12 D
5D
a fibra (sn)
5D
5D
5D
5D
5D
// a fibra (s bcp)
15 D
15 D
15 D
15 D
10 D
a fibra (s bcn)
5D
7D
7D
10 D
5D
// a fibra (s bdp)
7D
10 D
7D
10 D
5D
a fibra (s bdn)
5D
5D
5D
5D
3D
Para cualquier D
Cuando en una unión de tres maderos, los clavos hincados desde lados opuestos, se traslapan en el madero central de una unión, se deben respetar las siguientes disposiciones: a)
Si la punta del clavo dista al menos 8 * D de la superficie de cizalle de los clavos hincados en el lado opuesto se puede repetir el mismo esquema de clavado desde ambos lados.
b)
Si la penetración del clavo, p, excede el espesor del madero central, ec, rigen los espaciamientos mínimos señalados en la Tabla N° 8.
c)
En situaciones intermedias, esto es si: p < ec < p + 8 * D. Se debe respetar espaciamientos iguales al 50 % de los señalados para, s , en la Tabla N° 8.
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3.3-
Uniones Apernadas.
Las siguientes disposiciones se aplicarán sólo a uniones con pernos corrientes que cumplan con las especificaciones de las normas. Las cargas admisibles que se establecen se aplicarán para aquellos casos en los cuales la dirección de la solicitación es perpendicular al eje del perno. Las cargas admisibles establecidas se aplicarán cualquiera sea el grado de calidad de la madera usada, pues se ha demostrado que los defectos de la madera no inciden significativamente en la uniones con pernos. Las cargas admisibles que se establecen se aplicarán a madera acondicionada a un contenido de humedad aproximadamente igual al que tendrá la unión durante se vida en servicio. Para uniones con madera en estado verde y cuyo contenido de humedad se reducirá durante el servicio a valores menores que 25%, las cargas admisibles serán iguales a un 40%. Si la unión va a estar a la intemperie, se deberá tomar un 75% de las cargas admisibles prescritas y un 67% de dichas cargas si la unión va a permanecer siempre húmeda. Cuando la unión se diseñe con una cubre junta metálica, las cargas admisibles para solicitaciones paralelas a las fibras podrán incrementarse en un 25% (Factor de Modificación = 1,25). Este incremento no será aplicable para cargas normales a la dirección de las fibras de la madera (Factor de Modificación = 1,00).
3.3.1- Uniones de Cizalle Cizalle Doble. Las cargas admisibles para uniones de tres elementos solicitaciones a cizalle doble con carga paralela y normal a las fibras serán, para los diferentes grupos de especies y para los distintos estados de preparación de la madera. Capacidades de Carga en Uniones Apernadas a Cizalle Doble.
Espesor Elemento Central tc
Diámetro del Perno d
Maderas Grupo A // a fibras (Pp) Ase.
Cep.
^
Maderas Grupo B
a fibras (Pn)
Ase.
Cep.
// a fibras (Pp) Ase.
Cep.
^
a fibras (Pn)
Ase.
Cep.
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1 25,40
2
920
880
690
640
1750
1680
910
830
1 1/8
28,58
1080
1020
760
700
2020
1940
1010
930
1 1/4
31,75
1200
1160
830
760
2300
2210
1110
1020
3/8
9,52
300
300
360
340
570
560
450
420
1/2 12,70
430
410
450
430
810
790
580
550
5/8 15,89
560
540
550
520
1060
1040
710
670
50,8*
3/4 19,05
700
680
630
600
1330
1300
830
790
45**
7/8 22,22
830
810
720
680
1600
1560
940
900
1 25,40
930
960
800
760
1890
1840
1080
1020
1 1/8
28,58
1130
1100
880
840
2180
2120
1200
1130
1 1/4
31,75
1280
1250
960
910
2480
2410
1320
1240
* Aserrada
** Cepillada
Las cargas tabuladas se deben aplicar cuando los espesores de los elementos laterales (t1, t2) son, cada uno de ellos, mayores o iguales a la mitad del espesor del elemento central (tc).
(t1, t2) > ( tc/2 , tc/2 ) Si el espesor (t1) de un elemento lateral es menor que la mitad del correspondiente a la pieza central (tc), la carga admisible de la unión será igual a la que soportaría una unión con un perno de diámetro (d) y un elemento central de espesor ficticio (t´) igual a 2 t1.
t1 < t2 ; t1 < tc/2 ; t´ < 2 t1 El esfuerzo admisible para pernos en uniones de cizalle doble solicitadas por una carga cuya dirección forma un ángulo dado con la dirección de las fibras, debe determinarse mediante la fórmula de HANKINSON:
Pq, adm
=
Pp * Pn Pp * sen²q + Pn * cos²q
En que: P , adm =
carga admisible por perno, para solicitaciones cuya dirección forma un ángulo con la dirección de las fibras (Kg).
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admisible que le correspondería a una unión de cizalle doble (con tres elementos), con un perno del mismo diámetro (d) y un espesor (t´) del elemento central igual al doble del espesor menor (t1) de la unión de cizalle simple.
3.3.3- Uniones de Cizalle Cizalle Múltiple. La carga admisible de una unión de cizalle múltiple será igual a la suma resultante de considerar cada plano de cizalle como una unión de cizalle simple.
3.3.4- Espaciamientos. Los espaciamientos mínimos en uniones con carga paralela o normal a las fibras serán los indicados Espaciamientos Mínimos de Pernos a los Bordes.
Dirección de la fuerza con respecto a la fibra. Paralela Normal
Tipo de borde Cargado
7D
4D
Descargado
4D
1,5 D
Espaciamientos Mínimos entre Pernos.
Dirección
Designación
Paralela a la dirección de la fibra
4D
Normal a la dirección de la fibra
2D
Cuando la dirección de la carga que se aplica forma un ángulo dado con las fibras de la madera, es prácticamente imposible presentar reglas generales para los diferentes espaciamientos. Sin embargo, se obtienen esfuerzos uniformes en el elemento central centr al (cizalle doble) y una adecuada distribución de la carga en todos los pernos al agruparlos de modo que el centro de gravedad de ellos quede sobre el eje longitudinal de las piezas que se unen.
3.5-
Uniones Adheridas.
Las uniones adheridas o pegadas, no son muy comunes y es difícil su utilización por si solas
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3.5.3- Clasificación de los Adhesivos. La clasificación de los diferentes tipos de adhesivos podría llevarse a cabo de acuerdo a un gran número de parámetros como ser: composición química de los constituyentes principales, durabilidad, resistencia, uso, características técnicas y otros. Sin embargo, se hace difícil el ordenarlos ya que la mayoría de estos conceptos están a su vez influenciados por otro tipo de factores tales como humedad de la madera, temperatura, formulaciones del adhesivo y otros.
3.5.3.1-
Clasificación según Composición Química.
De todos los tipos de clasificaciones que pretenden ordenar los diferentes adhesivos adh esivos existentes, la más aceptada es aquella que hace discriminación en base a la composición química de sus ingredientes principales. De acuerdo a esto se pueden clasificar en adhesivos a base de materiales naturales y de resinas sintéticas. Adhesivos a base de materiales naturales. a) Resinas vegetales, dextrinas y almidones. b) Proteínas vegetales a base de harina de soya, maní y otros. c) Colas derivadas de proteínas animales. d) Lacas. e) Gomas. f)
Asfalto.
g) Silicatos de sodio, oxicloruro de magnesio y otros minerales.
3.5.3.2-
Clasificación según Durabilidad.
De acuerdo a las normas British Standard Specifications los adhesivos se pueden clasificar según su durabilidad. Esta resistencia se puede determinar luego de exposiciones naturales durante algunos años, o bien mediante ensayos de probetas estandarizadas, con inmersiones en agua fría, caliente, hirviendo o en vapor, ordenándolas de acuerdo a su mayor o menor resistencia a estas condiciones. Se han determinado cuatro clases las cuales se describen a continuación:
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ureaformaldehido cuando tiene más de un 25% de carga, albumina de sangre caseína, acetato de polivinilo, adhesivos de contacto.
3.5.4- Tensiones Admisibles. Las cargas admisibles se establecen dependiendo del tipo de adhesivo, es decir, dependiendo de sus características, este se aplicara en la zona donde se quiere unir, en la área de contacto las piezas, sometido a esfuerzo de cizalle simple, cualquiera sea la unión.
3.5.5- Tensión de Diseño. La carga de diseño para el área de aplicación de un adhesivo se determinará por la aplicación sucesivamente a la carga admisible los factores de modificación por duración de carga (K D) y modificación por contenido de humedad ( K H ).
T dis = Tadm * K H * K D
En que: T dis
=
tensión de diseño (resistencia al cizalle) ( Kg/cm²).
Tadm
=
tensión admisible (resistencia al cizalle) ( Kg/cm²).
K H
=
factor de modificación por contenido de humedad.
K D
=
factor de modificación por duración de la carga.
3.5.6- Área de Contacto (Ac). El área de contacto, es el área necesaria de extensión del adhesivo para cubrir la necesidades de carga axial aplicada en la unión:
Ac En que:
=
N T dis
Tdis = tensión de diseño (resistencia al cizalle).( Kg/cm²).
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4. Memoria Memoria de calculo 4.2-
Calculo de Cercha.
4.2.1- Obtención de Cargas. Antes de realizar cualquier cálculo, se debe tener en cuenta lo siguientes datos: Separación entre cerchas (S)
=
2,0 mts
Separación entre costaneras (Sc)
=
0,5 mts
Largo aproximado madera cercha (La)
=
25 mts.
Luz cercha (L)
=
6,0 mts.
Altura cercha (H)
=
1,2 mts.
Angulo (q)
=
21,8°
Se debe calcular el Peso Propio de los elementos de la estructura de techumbre, descritos en la Figura, los cuales son los siguientes:
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Entramado
=
40 Kg/m²
Fieltro
=
5 Kg/m²
Aislante
=
15 Kg/m²
Dos volcanitas de 10 mm
=
30 Kg/m²
Peso Propio Cielo
=
90 Kg/m²
Se calcularan las Sobre Cargas, las cuales son las siguientes:
Sobre carga de Uso
=
60 Kg/m²
4.2.2- Geometría. La geometría de la cercha es muy importante, ya que sin esto no se puede tener una clara relación, con los cálculos obtenidos y a realizar, por esta razón se muestra su geometría en forma
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6000 mm 1000 mm
1000 mm
1000 mm
1000 mm
1000 mm
1000 mm
482 Kg
482 Kg 8 4
482 Kg
N10
VIGA 10
482 Kg
N11
VIGA 11
241 Kg
VIGA 20
VIGA 19
VIGA 16
N12
VIGA 21
VIGA 18 VIGA 13
N1
VIGA 1
N2
216 Kg
VIGA 2
N3
216 Kg
VIGA 3
1200 mm
VIGA 8 VIGA 15
VIGA 14
N8
VIGA 12
VIGA 9
N9
N4
216 Kg
VIGA 4
N5
216 Kg
Dimensiones y Cargas en Cordon Superior e Inferior
VIGA 5
VIGA 17
N6
216 Kg
241 Kg VIGA 7 VIGA 6
N7
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4.2.3- Diseño. Para el diseño de nuestra cercha se simula el uso Pino Insigne, del cual se obtendrán las siguientes propiedades:
4.2.3.1-
Propiedades Geométricas.
Se utilizará una escuadría de 2 x 5”, la cual cuando es cepillada toma las dimensiones de 45 x 120 mm (Figura). Y
X
h
=
120 mm
b
=
45 mm
A
=
54 cm²
h
Ixx = r
=
b
. Escuadría
4.2.3.2-
Propiedades Mecánicas.
Grado Estructural
=
2,
RR
Grupo Estructural
=
E6 – ES5 ES5
Clase Estructural
=
F7 – F14 F14
=
0,60
b * h³
= 648 (cm4
12 (
Ixx A
) = 3,46 (cm)
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=
lp rx
=
156,2 3,46
=
45,145
<
170
OK
Por lo tanto cumple con la condición de esbeltez. La longitud efectiva de pandeo del elemento a diseñar (Viga 7 y 12), con lp = 107,7 cm, con lo cual tendremos que analizar la esbeltez del elemento: =
lp rx
=
107,7 3,46
=
31,127
<
170
OK
Por lo tanto cumple con la condición de esbeltez. La tensión de trabajo de una columna simple sometida a compresió n paralela a su fibra se calcula de acuerdo a la siguiente expresión, teniendo en cuenta que la mayor Compresión Paralela (Viga 7 y 12) es 3640,96 Kg.
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f cp
=
N
=
A
3640,96
=
54
67,43 (Kg/cm²)
Ahora, se debe obtener o btener si existe o no inestabilidad lateral, con lo cual:
=
lp rx
=
107,7 3,46
=
31,127
>
5
Por lo tanto si existe inestabilidad lateral y se tendrá que utilizar el siguiente expresión para obtener la tensión de diseño. Fcp, donde :
, dis
= Fcp, dis * K
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K D
=
0,653
K D
=
0,948
K D
=
0,95 aprox.
+
0,295
. c) Factor de Modificación por Trabajo Conjunto ( K C ), se encuentra definido en el punto 4.1.3. Tabla N° 17, con lo cual K C = 1,10. d) Factor de Modificación por Esbeltez ( K ), se encuentra definido en el punto 4.1.6. Donde: Grado Estructural N° 2, entones c = 0,85 (Tabla N° 19). Compresión Paralela Admisible = F cp = 90,28 Kg/cm².(Tabla N° 38)
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A
=
B * c * ( 1 + /200) + 1 2*c
4,681 * 0,85 * ( 1 + (31,127/200)) + 1
=
2 * 0,85
Entones: Fcp,
, dis
=
Fcp, dis * K
(Kg/cm²)
Fcp,
, dis
=
84,90 * 0,80
(Kg/cm²)
Fcp,
, dis
=
68,0
(Kg/cm²)
Por lo tanto:
f cp
<
Fcp, l, dis
OK
=
3,30
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e) Factor por Concentración de Tensiones ( K ct ), se encuentra definido en el punto 2.1.7. Tabla N° 5. Los datos de K ctct que se encuentran en esta tabla se utilizaran en su totalidad, ya que se analizara cada una de estos tipos de debilitamiento en madera aserrada. f) Factor de Modificación Modificación por Altura ( K hf ), se encuentra definido en el punto 2.1.8. Se debe decir que la altura (h) de la escuadría es mayor que 50 mm y la especie a utilizar no es pino radiata, entonces se debe utilizar la expresión:
1/9 K hf = (50/120)1/9 = 0,91 hf = (50/h)
Entonces se tendrá lo siguiente :
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4.3-
Calculo de Uniones. En este punto se obtendrán los diseños y cálculos, definitivos de las distintas uniones
4.3.1- Unión Clavada. Primeramente, debemos obtener la Tensión de Trabajo, teniendo en cuenta que nuestra unión es simétrica, entonces se utilizara por razones de comodidad en el calculo solo un costado de esta muestra, por esta razón se dividirá la compresión paralela máxima, obtenida anteriormente en las piezas de la cercha en dos, que en este caso será:
N
=
Compresión Paralela Maxima 2
=
3640,96 2
=
1820
(Kg)
Luego, se debe tener en cuenta las dimensiones de la escuadría, para poder escoger las
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Donde el diámetro del clavo a utilizar (D) es de 4,3 mm y la densidad anhidra para el pino insigne es de 370 (Kg/m³). Entonces: P cl,ad
=
3,5 * D1,5
P cl,ad
=
3,5 * (4,3)1,5 * 370
(N)
P cl,ad
=
11547
(N)
P cl,ad
=
118
(Kg)
(
o,k )
0,5
(N)
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Entonces la cantidad de clavos por cada lado de la unión es de 16 y se deduce de la siguiente relación: N
<
118 * 16 (Kg)
1820 (Kg)
<
1880 (Kg)
OK
Ahora, se debe obtener los espaciamientos de los clavos, en la unión correspondientes y
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UNION CLAVADA ESC : 1:5
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4.3.2- Unión Apernada. Primeramente, debemos obtener la Tensión de Trabajo, teniendo en cuenta que nuestra unión es simétrica, entonces se utilizara por razones de comodidad en el calculo solo un costado de esta muestra, por esta razón se dividirá la compresión paralela máxima, obtenida anteriormente en las piezas de la cercha en dos, que en este caso será:
N
=
Compresión Paralela Maxima 2
=
3640,96 2
=
1820
(Kg)
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P , adm
P
, adm
=
=
P p * Pn P p * sen² + Pn * cos² 540 * 520 540 * sen²0° + 520 * cos²0° 540 * 520
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Tabla N° 27
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UNION APERNADA ESC : 1:5
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4.3.3- Uniones con Conectores. Primeramente, debemos obtener la Tensión de Trabajo, teniendo en cuenta que nuestra unión es simétrica, entonces se utilizara por razones de comodidad en el cálculo solo un costado
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Entonces .
Pp = 895 (Kg) P = 370 (Kg)
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Tendremos:
P
=
P
* K * K * K
(Kg)
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