Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
VIVIENDA DE ACERO DE DOS PISOS
Figura 1.- Esquema del edificio en planta.
Figura 2.- Esquema del edificio en elevación y espacial.
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Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
ESTIMACIÓN DE CARGAS CARGA MUERTA: La carga muerta se la va a analizar de tal manera que nos sirva para poder predimensionar los elementos de soporte, estos son: viguetas, vigas, losas colaborantes (deck) y columnas. Para adoptar el espesor de la placa colaborante, se ha impuesto una separación entre viguetas de apoyo de 1.17m de distancia. No se incluye el peso propio de la estructura en éste análisis debido a que el programa estructural ETABS lo hace de forma automática. p.p. placa colaborante: p.p. hormigón sobre placa colaborante(deck) e=5cm 0.075m3/m2*2400kg/m3 p.p. masillado/acabados: masillado/acabados: 0.04m*1m*1m*2200kg/m 0.04m*1m*1m*2200kg/m3 p.p. cielo falso: p.p. paredes: (edificios) Carga muerta (CM):
6.48 kg/m2 180.00 88.00 20.00 150.00 444.48
kg/m2 kg/m2 kg/m2 kg/m2 kg/m2
CARGA VIVA: Según en código Ecuatoriano de la construcción, para edificaciones de vivienda se debe utilizar la carga viva de 200 kg/m2. Carga viva (CV):
200.00 kg/m2
PRE-DIMENSIONAMIENTO DE ELEMENTOS ESTRUCTURALES PREDIMENSIONAMIENTO DE LOSA COOPERANTE Como se menciona en los párrafos anteriores, la separación entre viguetas de apoyo de la losa colaborante se la va a asumir de 1.17m, razón por la que los manuales de los fabricantes de deck recomiendan que se adopte de acuerdo a la carga sobreimpuesta, es decir la carga muerta mas la carga viva, pero descontando el peso propio del hormigón que está sobre la placa colaborante. Para este caso: CM: 444.48 kg/m2 (-) p.p placa colaborante 6.48 kg/m2 (-) p.p hormigón 180.00 kg/m2 CM1= 258.00 kg/m2
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Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
Para ésta magnitud de carga, los catálogos de los fabricantes nos recomienda un espesor de 5cm de hormigón sobre el cumbrero del deck, así como un deck de espesor no menor a 0.65mm. Hay que tener muy en cuenta que la máxima luz sin apuntalar que nos da el catálogo del fabricante es de 1.63m, es decir que a partir de ésta dimensión en el momento de la fundición hará falta apuntalar la placa colaborante, para evitar pandeos de la misma. METALDECK
VIGA SOPORTE
VIGA SOPORTE
APUNTALAMIENTO TEMPORAL
GATOS METALICOS
APOYO INTERMEDIO PARA EVITAR DEFLEXIONES EN EL METALDECK AL MOMENTO DE HACER EL VACIADO DEL CONCRETO. ES UTILIZADO PARA GRANDES LUCES.
Figura 3.- Apuntalamiento intermedio en caso de que la luz supere a la máxima que emiten los catálogos del fabricante.
Para evitar lo mostrado en la figura anterior, se asume una separación entre viguetas de apoyo de 1.17m la misma que es menor a la máxima luz sin apuntalar que nos recomienda las catálogos del fabricante, quedando la repartición tal como se muestra a continuación.
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Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
PRE-DIMENSIONADO DE ELEMENTOS PRE-DIMENSIONAMIENTO DE VIGUETAS DE SOPORTE DE DECK. Area cooperante para la vigueta a diseñar.
Vigueta para diseño
Figura 5.- Determinación del ancho colaborante de la placa deck.
Para el prediseño de las viguetas se ha considerado la más crítica, con el área cooperante mas grande, debido a que esta es la más esforzada. Longitud libre Llibre=3.00 m Ancho cooperante ac = ac =
L1 + L2
2 1.17 + 1.17
2 ac = 1.17 m
Cargas para prediseño
[m]
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Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
en el alma de las vigas principales cargadoras y por ende no representa una fijación total de empotramiento perfecto. D = 444.48 L = 200.00
Kg m2
Kg
W D + L = 644.48
m2 Kg m2
Calculo de las carga Uniformes q = (W D + L )× ac q = (644.48) × 1.17 m q = 754.04
Kg m
Kg m
Calculo del momento último M u = M u =
q×l2
8 754.04 × 3.00 2
8 M u = 848.30.00 [Kg.m]
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Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
Esfuerzo Admisible (F b ) (se asume que la sección es no compacta) F b = 0.6 × Fy F b = 0.6 × 2531 F b = 1518.6
Kg cm 2
Kg cm 2
Módulo resistente (W ) F b = W =
M .c
con
I M
W =
I c
F b
848.30 Kg .m × W =
1518.6
100cm 1m
Kg cm 2
W = 55.86 cm 3
Se ha basado en los catálogos de perfilaría China importada por DIPAC. DIPAC. Se tiene algunas vigas que cumplen con el módulo resistente necesario, pero también se va a analizar los pesos por cada metro lineal de elemento, tal como se tiene a continuación: Designación HEB 100x100 IPE 150x75
Wxx [cm3] 76.50 90.60
Peso [kg/m] 17.20 14.30 O.K.
Si se analiza las condiciones presentadas se puede ver que el módulo
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Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
150x75 es mas liviana, razón por la que se escogería la segunda opción, ya que a menor peso se tiene menor costo. IPE 150X75 A= 18.16 cm2 d= 150 puld Peso/m= 14.3 kg/m Ixx= 679 cm4 Wxx= 90.60 cm3 rxx= 6.12 cm PRE-DIMENSIONAMIENTO DE VIGAS PRINCIPALES VIGAS CENTRALES EN SENTIDO X-X Area cooperante para la viga a diseñar.
Viga para diseño
Figura 6.- Determinación del ancho colaborante de la placa deck para la viga principal central.
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Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
Calculo de las carga Uniformes q = (W D + L )× Ltransv × 2lados q = (644.48) × 1.50 m × 2lados q = 1933.44.40
Kg m
Kg m
Pasando de carga trapezoidal a carga uniforme distribuida, se tiene como se muestra a continuación:
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Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
Calculo del momento último (−) u
M
(−) u
M
= =
q×l
2
(+) u
M
12 2071.54 × 3.50 2
(+) u
M
12
M u( − ) = 2114.70 [Kg.m]
= =
q×l
2
24 2071.54 × 3.50 2 24
M u( + ) = 1057.35 [Kg.m]
Esfuerzo Admisible (F b ) (se asume que la sección es no compacta) F b = 0.6 × Fy F b = 0.6 × 2531 F b = 1518.6
Módulo resistente (W )
Kg cm 2
Kg cm 2
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Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
La sección que cumple de la manera más opcionada, es decir por que tiene un módulo resistente mayor y también por que muestra el menor peso por unidad 200X100, la misma que presenta las siguientes de longitud, es la IPE 200X100, propiedades de la sección: IPE200X100 A= 27.57 cm2 d= 200 mm Peso/m= 21.7 kg/m Ixx= 1880 cm4 Wxx= 188 cm3 rxx= 8.25 cm Para las vigas perimetrales, como se tiene el área cooperante de la mitad de la viga central, se toma el módulo resistente también de la mitad, de tal manera que: Módulo resistente (W )
F b = W =
M .c
con
I M
W =
I c
F b
1057.35 Kg.m × W =
1518.6
100cm 1m
Kg cm 2
W = 62.63 cm 3
La sección que cumple de la manera más opcionada y que tiene un módulo 150X75, la misma que presenta las siguientes resistente mayor es la IPE 150X75,
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Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
VIGAS CENTRALES EN SENTIDO Y-Y Area cooperante para la viga a diseñar. Viga para diseño
Figura 6.- Determinación del ancho colaborante de la placa deck para la viga principal central sentido y-y.
De manera análoga a la de las vigas del sentido x-x, se ha predimensionado éstas, quedando una sección necesaria de IPE 150X75, 150X75, cuyos datos característicos de la sección son los siguientes: IPE 150X75 A= 18.16 cm2 d= 150 puld Peso/m= 14.3 kg/m Ixx= 679 cm4 Wxx= 90.60 cm3 rxx= 6.12 cm
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Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
Área cooperante crítica: 3m x 3.50m = 10.50m2 # de pisos que cooperan: 2 pisos Cargas muertas actuantes: 1º piso: 444.48 kg/m2 2º piso: 294.48 kg/m2 Cargas vivas actuantes: 1º piso 200 kg/m2 2º piso 100 kg/m2 Pu = 10.5m 2 × (444.48 + 200)kg / m 2 + (294.48 + 100 )kg / m 2 Pu = 10909.08kg A = A = A =
Pu + 20% Fa 10909.08kg + 20%
15% * Fy 13090.90kg 379.65kg / cm 2
A = 34.48cm 2
∴ Se recomienda usar una sección que por lo menos tenga la sección anteriormente indicada
Esbeltez máxima: λ=k*L/rmin
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Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
DISEÑO DE ELEMENTOS La estructura se la ingresó en el programa ETABS v9.0, el mismo que es un programa diseñado solo para el cálculo de edificios, prestando mayores facilidades que SAP2000 en lo que respecta a edificios de acero. DETERMINACIÓN DEL CORTANTE BASAL Basándose en el código Ecuatoriano de la Construcción del año 2000, se puede estimar la carga sísmica estática tal como se detalla a continuación: • Zona sísmica: Z4=0.4g • Importancia de la estruc.: I=1.00 • Determinación de coeficiente C Tipo de suelo: S3 S=1.5 Cm=2.8 • Período de la estructura: o
T = 0.09 * (hn )
3
4
T = 0.09 * (5.20) T = 0.31s
3
4
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Vivienda de Acero laminado en caliente
DISEÑO DE VIGAS A FLEXIÓN VIGA EJE “2”- (IPE200X100) IPE200X100 A= 27.57 cm2 d= 200 mm Peso/m= 21.7 kg/m Ixx= 1880 cm4 Wxx= 188 cm3 rxx= 8.25 cm Mmax(-)=2.19 t-m Mmax(+)=1.29 t-m L=3.50m (longitud total de la viga principal) L’=1.17m (longitud de separación de apoyos laterales) Lc=1.27 m (Longitud máxima para perfil compacto) Lu=2.19 m (longitud máxima para perfil semi compacto) L' = 1.17m ≤ Lc = 1.127 m ≤ Lu = 2.19
Por lo tanto:
F b = 0.66 * F y F b = 0.66 * 2531kg / cm 2
Ing. Xavier Vallejo R.
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Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
DISEÑO DE COLUMNAS A FLEXO-COMPRESIÓN Pu=26.20 Kip Mxx=49.54 Kip-in Myy=46.72 Kip-in Según Bresler. B, en el libro de “Diseño de Estructuras de Acero”, se tiene una ecuación que para los perfiles W sirve como un diseño rápido, la misma que se muestra a continuación: P EQ = Pu + 0.2 M xx + 0.6M yy
Reemplazando se tiene: P EQ = 26.20 + 0.2(49.57 ) + 0.6(46.72) P EQ = 64.14kip = 29157 kg
De acuerdo a los datos obtenidos en el predimensionamiento de columnas, se tiene: A=48.06 cm2 Ixx=1858.20 cm4 rxx=6.22 cm G = 1 00
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Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
K=1.38
Fa =
⎡ 2 1 ⎛ λ ⎞ 2 ⎤ ⎢ − ⎜ ⎟ ⎥ * Fy ⎣⎢ 3 2 ⎝ Cc ⎠ ⎦⎥ 1 ⎛ λ ⎞ + * − *⎜ ⎟ 3 8 Cc 8 ⎝ Cc ⎠ 5
K * L
3
λ
3
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Vivienda de Acero laminado en caliente
Ing. Xavier Vallejo R.
VIVIENDA DE HORMIGÓN ARMADO
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Vivienda de Acero laminado en caliente
C = C =
1.25 * S
Ing. Xavier Vallejo R.
S
T
1.25 *1.51.5
0.27 s C = 7.41 > Cm = 2.80
∴ C Adop = 2.80 • •
Factores de modificación en planta: no se presenta ninguna variación debido a que todo es regular. Factores de modificación en elevación: no se presenta ninguna variación ya que el edificio es bien estructurado en elevación.
V basal =
Z * I * C
φ * φ * R
* W estructura