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CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
CAPITULO III
MARCO METODOLOGICO
3.1 Tipo de Investigación
Con el desarrollo de esta investigación se busca determinar la influencia del Factor de
Reducción de Respuesta en el daño estructural de pórticos de concreto armado, de manera de
emitir juicio objetivo del factor utilizado por la Norma COVENIN. Esta investigación se
considera, según Gordon Dankhe (1986) de tipo exploratoria ya que su objetivo “... es investigar
un tema o problema poco estudiado o que no ha sido abordado antes” (Hernández y otros, 1998,
p.58) (22).
Luego de revisar la literatura no se consiguió trabajo previo donde se diseñaran pórticos para
diferentes Factores de Reducción de Respuesta y que luego fuesen analizados para determinar la
influencia del daño para cada caso, con los resultados que proporcione este estudio se podrá tener
información que permita evaluar si el factor dado por la Norma COVENIN, es adecuado para
garantizar daños reparables ante un sismo de diseño.
3.2 Diseño de la Investigación.
El diseño de la investigación se refiere a la “estrategia que adopta el investigador para
responder al problema planteado” (Arias, 1999, p.47) (24).
El diseño de esta investigación es experimental del tipo cuasiexperimental de acuerdo con las
categorías de Campbell y Stanley (1966), citado por Hernández y otros (1998).
Es experimental, cuando “... se manipulan una o mas variables independientes (supuestas
causas) para analizar las consecuencias que la manipulación tiene sobre una o más variables
dependientes (supuestos efectos), dentro de una situación de control para el investigador”.
(Hernández y otros, 1998, p.107) (22).
En este sentido, en la presente investigación se utilizarán pórticos diseñados variando el Factor
de Reducción de Respuesta, para someterlos a la acción de excitaciones sísmicas empleando un
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
80
análisis dinámico espacial y determinar así el nivel de daño estructural que sufren cada uno de
sus elementos portantes, para finalmente definir la influencia de esta variable en el daño
estructural de pórticos sismorresistentes de concreto armado. Se cumplen entonces, los tres
requisitos citados por Hernández y otros (1998) “manipulación intencional de una o más
variables independientes” (variación del Factor de Reducción de Respuesta), “medición del
efecto que la variable independiente tiene sobre la variable dependiente” (cuantificación del daño
estructural), y “control de la situación experimental” (los pórticos serán sometidos a
solicitaciones sísmicas, apegados a la normativa sismorresistente).
Es cuasiexperimental, cuando “... los sujetos no son asignados al azar a los grupos ni
emparejados; sino que dichos grupos ya estaban formados antes del experimento, son grupos
intactos”. (Hernández y otros, 1998, p.169) (22). En esta investigación, los modelos no son
teóricos, ni seleccionados al azar; son producto de un diseño previo al experimento.
3.3 Población y Muestra de Estudio
En general, las estructuras pueden ser agrupadas en tres grandes categorías; medios continuos
sólidos, cáscaras y sistemas reticulares. Las estructuras reticulares pueden a su vez dividirse en
seis subcategorías: vigas, armaduras planas, armaduras espaciales, pórticos planos, parrillas y
pórticos espaciales.
El número de aplicaciones prácticas que utilizan estructuras tipo pórticos es muy superior al
que usa otro tipo de estructuras, Siendo esta la razón del interés en estudiar su comportamiento.
Los pórticos planos son estructuras formadas por miembros cuya longitud es muy grande en
comparación con las dimensiones de su sección transversal, los mismos están contenidos en un
solo plano y tienen su eje de simetría en dicho plano. Los nodos son puntos de intersección de sus
miembros y representan conexiones rígidas entre ellos. Las fuerzas aplicadas y los
desplazamientos están en el mismo plano de la estructura. Todos los momentos por flexión tienen
sus vectores normales al plano. Las fuerzas generalizadas en extremo de miembro consisten en
general, de un momento de flexión, una fuerza de corte y una axial.
Este estudio ha sido delimitado a pórticos planos de concreto armado que cumplen la
condición de haber sido diseñados con estricto apego a las prescripciones de la norma
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
81
COVENIN. Esta muestra, representa un amplio rango de edificaciones con posibilidades de
conformar futuros proyectos a ser construidos.
3.3.1 Características de los Pórticos Estudiados
Para el estudio se seleccionó una muestra de pórticos que cumplen con la condición de estar
diseñados según COVENIN, limitándose a las zonas sísmicas Z3 y Z7, suelo S2 y S4, con
porcentaje de acero en columnas de entre el 2% y 3% y un factor de resistencia en nodos
superior a 1.2 tal como especifica la Norma. Según el uso: edificios de oficina de baja ocupación
la edificación pertenece al grupo B2 dentro de las normas sismorresistentes COVENIN-2001 art.
6.1.1 (I3). A continuación se describen las características de los pórticos utilizados:
3.3.1.1 Características Geométricas
El pórtico muestra o de estudio, es el señalado en el eje “B” de un edificio cuya planta se
indica en la Figura 3.1. El estudio comprende el análisis de pórticos representativos de 4, 8 y 12
niveles. Los pórticos tienen tres tramos, dos exteriores de 7.00 metros y uno interior de 9.00
metros. El piso inferior es de 4.75 metros de altura y el resto de los pisos tienen 3.60 metros.
B
D
41
A
C
2 3
6.00
6.00
6.00
9.00 7.007.00
Fig. 3.1 Planta del Edificio considerado.
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
82
3.3.1.2 Características Dinámicas
Las características dinámicas para el modo fundamental de los pórticos estudiados se muestran
en la Tabla 3.2. En la Tabla 3.1 se muestra la nomenclatura utilizada para diferenciar los
pórticos.
Tabla 3.1. Nomenclatura de los Pórticos.
A B C
A = 4P; 4 PISOS B = Z3; ZONA Z3 C = S2, SUELO S2A = 8P; 8 PISOS B = Z7; ZONA Z7 C = S4, SUELO S4
A = 12P; 12 PISOS
NOMENGLATURA
4P-Z3S24P-Z3S44P-Z7S24P-Z7S4
8P-Z3S28P-Z3S48P-Z7S28P-Z7S4
12P-Z3S212P-Z3S412P-Z7S212P-Z7S4
NUMERO DE PISOS
A-BC
Portico 12 niveles, zona 3, suelo S4, R = 3.32; 4.50 o 6.00Portico 12 niveles, zona 7, suelo S2, R = 3.32; 4.50 o 6.00Portico 12 niveles, zona 7, suelo S4, R = 3.32; 4.50 o 6.00
Portico 8 niveles, zona 3, suelo S4, R = 3.32; 4.50 o 6.00Portico 8 niveles, zona 7, suelo S2, R = 3.32; 4.50 o 6.00Portico 8 niveles, zona 7, suelo S4, R = 3.32; 4.50 o 6.00
Portico 12 niveles, zona 3, suelo S2, R = 3.32; 4.50 o 6.00
Portico 4 niveles, zona 3, suelo S4, R = 3.32; 4.50 o 6.00Portico 4 niveles, zona 7, suelo S2, R = 3.32; 4.50 o 6.00Portico 4 niveles, zona 7, suelo S4, R = 3.32; 4.50 o 6.00
Portico 8 niveles, zona 3, suelo S2, R = 3.32; 4.50 o 6.00
DESCRIPCION
Portico 4 niveles, zona 3, suelo S2, R = 3.32; 4.50 o 6.00
NOTACION GENERAL PARA LA CARACTERIZACION DE LOS PORTICOS
ZONA SISMICA TIPO DE SUELO
FACTOR DE REDUCCION 3.32; 4.50 O 6.00
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
83
Tabla 3.2. Características Dinámicas de los Pórticos.
PERIODO
PORTICO " T " en seg " f " en cps " w " en rad/seg
4P-Z3S2 0.800 1.250 7.8504P-Z3S4 0.680 1.471 9.2354P-Z7S2 0.560 1.786 11.2144P-Z7S4 0.480 2.083 13.083
4P-Z3S2 0.850 1.176 7.3884P-Z3S4 0.790 1.266 7.9494P-Z7S2 0.670 1.493 9.3734P-Z7S4 0.550 1.818 11.418
4P-Z3S2 0.880 1.136 7.1364P-Z3S4 0.810 1.235 7.7534P-Z7S2 0.760 1.316 8.2634P-Z7S4 0.620 1.613 10.129
8P-Z3S2 1.490 0.671 4.2158P-Z3S4 1.130 0.885 5.5588P-Z7S2 0.980 1.020 6.4088P-Z7S4 0.750 1.333 8.373
8P-Z3S2 1.520 0.658 4.1328P-Z3S4 1.260 0.794 4.9848P-Z7S2 1.310 0.763 4.7948P-Z7S4 0.820 1.220 7.659
8P-Z3S2 1.570 0.637 4.0008P-Z3S4 1.830 0.546 3.4328P-Z7S2 1.360 0.735 4.6188P-Z7S4 0.820 1.220 7.659
12P-Z3S2 1.850 0.541 3.39512P-Z3S4 1.590 0.629 3.95012P-Z7S2 1.110 0.901 5.65812P-Z7S4 0.920 1.087 6.826
12P-Z3S2 1.980 0.505 3.17212P-Z3S4 1.720 0.581 3.65112P-Z7S2 1.280 0.781 4.90612P-Z7S4 1.050 0.952 5.981
12P-Z3S2 1.990 0.503 3.15612P-Z3S4 1.950 0.513 3.22112P-Z7S2 1.580 0.633 3.975
FACTOR DE REDUCCION 6.00
FACTOR DE REDUCCION 3.32
PORTICOS DE 8 PISOS
PORTICOS DE 12 PISOS
FACTOR DE REDUCCION 3.32
FACTOR DE REDUCCION 4.50
FACTOR DE REDUCCION 6.00
FRECUENCIA
PORTICOS DE 4 PISOS
FACTOR DE REDUCCION 4.50
FACTOR DE REDUCCION 6.00
FACTOR DE REDUCCION 3.32
FACTOR DE REDUCCION 4.50
12P-Z7S4 1.050 0.952 5.981
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
84
3.3.1.3 Cargas Consideradas
A continuación se presentan las cargas por metro cuadrado que actúan en la edificación. Para
el diseño del pórtico deberán calcularse las reacciones que producen estas cargas sobre el pórtico
en estudio (pórtico eje B).
- Cargas Permanentes:*
. Peso propio de la losa: 314 Kg/m2 (314 Kg/m2 ).
. Peso por acabados: 100 Kg/m2 (120 Kg/m2 ). (25)
. Peso por cielo raso y ductos: 50 Kg/m2 (50 Kg/m2 ).
. Peso por tabiquería: 150 Kg/m2 (0 Kg/m2 ). (25)
. Peso propio de los elementos estructurales (vigas y columnas):**
- Cargas Accidentales:
. Carga viva: 300 Kg/m2.
. Cargas sísmicas: ***
* El valor entre paréntesis corresponde a la carga actuante en el techo de la edificación.
** Este valor es calculado internamente por el programa de análisis.
*** Determinada según lo especifica la norma COVENIN 1756-2001. Según el art. 7.1 (13),
se tomará como masa sísmica efectiva el 50% de la carga variable de servicio en entrepiso y el
0% en el techo. (Edificaciones con una concentración de público de más de 200 personas).
Cargas de Servicio Techo Entrepiso
Carga Muerta (Kg/m) 3197 4055
Carga Viva (Kg/m) 720 2160
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
85
Espectro de Respuesta elásticos y de diseño:
Para obtener las fuerzas horizontales, todos los pórticos se sometieron a un análisis espacial
dinámico espectral, calculando los efectos por el método de superposición modal considerando
seis grados de libertad por nodo1. El espectro utilizado es obtenido a partir de las fórmulas 7.1,
7.2 y 7.3 de la Norma COVENIN (13), para lo cual se utilizaron los parámetros que se muestran a
continuación, correspondientes a las zona Z3 y Z7, suelo S2 y S4. Para forma de los espectros
elásticos (base para los de diseño) ver Figura. 3.2.
Información Básica Zona sísmica 3 3 7 7
Forma espectral S2 S4 S2 S4
0.80 0.75 0.90 0.80 Grupo B2 B2 B2 B2 Tipo Sist. Est. I I I I Irregularidad N N N N Tipo Est. Concreto Concreto Concreto Concreto
Parámetros para definir el Espectro de Diseño Nivel de Diseño ND3 ND3 ND3 ND3 Ao = 0.20 0.20 0.40 0.40 = 1.00 1.00 1.00 1.00 T* = 0.70 1.30 0.70 1.30 2.60 3.00 2.60 3.00 p = 1.00 0.80 1.00 0.80 To = 0.18 0.33 0.18 0.33 T+ = 0.00 0.00 0.00 0.00 c = 1.23 1.19 1.23 1.19
1 Aún cuando la norma COVENIN no obliga este nivel de análisis para estructuras regulares, el programa utilizado “STAAD PRO” así lo considera.
ESPECTRO DE ACELERACION ELASTICOZ3S2GB2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 0.5 1 1.5 2 2.5 3 3.5
PERIODO (seg)
A/g
ESPECTRO(NORMA)
ESPECTRO(SIMULADO)
ESPECTRO DE ACELERACION ELASTICOZ3S4GB2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 0.5 1 1.5 2 2.5 3 3.5
PERIODO (seg)
A/g
ESPECTRO(NORMA)
ESPECTRO(SIMULADO
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
86
Fig. 3.2a Espectro Elástico Z3, S2. Fig. 3.2b Espectro Elástico Z3, S4.
ESPECTRO DE ACELERACION ELASTICOZ7S2GB2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 0.5 1 1.5 2 2.5 3 3.5
PERIODO (seg)
A/g
ESPECTRO(NORMA)
ESPECTRO(SIMULADO)
ESPECTRO DE ACELERACION ELASTICOZ7S4GB2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 0.5 1 1.5 2 2.5 3 3.5
PERIODO (seg)
A/g
ESPECTRO(NORMA)
ESPECTRO(SIMULADO)
Fig. 3.2c Espectro Elástico Z7, S2. Fig. 3.2d Espectro Elástico Z7, S4.
En la Figura.3.3, se presentan los cuatro espectros elásticos utilizados en el análisis de los
pórticos.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 0.5 1 1.5 2 2.5 3 3.5
T (seg)
A/g
Zona 3,Suelo 2,Grupo B2 Zona 3,Suelo 4,Grupo B2
Zona 7,Suelo 2,Grupo B2 Zona 7,Suelo 4,Grupo B2
Fig. 3.3 Comparación de Espectros Elásticos.
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
87
A continuación se muestran (Figuras 3.4, 3.5, 3.6 y 3.7) 4 gráficos comparativos de los
espectros de diseño, para los diferentes Factores de Reducción de Respuesta utilizados en este
trabajo.
COMPARACION DE ESPECTROS DE DISEÑO PARA ZONA Z3, SUELO S2
0.0000
0.0200
0.0400
0.0600
0.0800
0.1000
0.1200
0.1400
0.1600
0.1800
0.000 0.500 1.000 1.500 2.000 2.500
PERIODO (T)
AD
ESPECTRO DE DISEÑO PARA R = 3,32 ESPECTRO DE DISEÑO R =4,50
ESPECTRO DE DISEÑO PARA R = 6,00
Fig. 3.4 Comparación de Espectros de diseño, Z3S2.
COMPARACION DE ESPECTROS DE DISEÑO PARA ZONA Z3, SUELO S4
0.0000
0.0500
0.1000
0.1500
0.2000
0.000 0.500 1.000 1.500 2.000 2.500
PERIODO (T)
Ad
ESPECTRO DE DISEÑO PARA -R=3,32 ESPECTRO DE DISEÑO PARA R=4,50
ESPECTRO DE DISEÑO PARA R=6,00
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
88
Fig. 3.5 Comparación de Espectros de diseño, Z3S4.
COMPARACION DE ESPECTROS DE DISEÑO PARA ZONA Z7, SUELO S2
0.0000
0.0500
0.1000
0.1500
0.2000
0.2500
0.3000
0.3500
0.4000
0.000 0.500 1.000 1.500 2.000 2.500
PERIODO (T)
Ad
ESPECTRO DE DISEÑO PARA R= 3,32 ESPECTRO DE DISEÑO PARA R = 4,50
ESPECTRO DE DISEÑO PARA R = 6,00
Fig. 3.6 Comparación de Espectros de diseño, Z7S2.
COMPARACION DE ESPECTROS DE DISEÑO PARA ZONA Z7, SUELO S4
0.0000
0.0500
0.1000
0.1500
0.2000
0.2500
0.3000
0.3500
0.000 0.500 1.000 1.500 2.000 2.500
PERIODO (T)
Ad
ESPECTRO DE DISEÑO PARA R = 3,32 ESPECTRO DE DISEÑO PARA R = 4,50
ESPECTRO DE DISEÑO PARA R = 6,00
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
89
Fig. 3.7 Comparación de Espectros de diseño, Z7S4.
3.3.1.4 Combinaciones de cargas:
El diseño de la edificación se realizará para soportar las solicitaciones mayoradas más
exigentes producto las combinaciones sugeridas en la propuesta de Norma Fonacit-Socvis2, en el
art. 9.3 (14):
Cargas Primarias:
CM: Carga muerta.
CV: Carga viva en entrepiso.
CVt: Carga viva en techo.
Sx,z: Sismo en las direcciones X y Z respectivamente.
Combinaciones Últimas:
Q1: 1.4 CM
Q2: 1.2 CM + 1.6 CV + 0.5 CVt
Q3: 1.2 CM + 1.6 CVt + CV
Q4: 1.2 CM + CV ± SX ± 0.3 Sz
Q5: 0.9 CM ± Sx ± 0.3 Sz
Q6: 1.2 CM + CV ± Sz ± 0.3 Sx
Q7: 0.9 CM ± Sz ± 0.3 Sx
3.4 Procedimiento de análisis y diseño
El procedimiento para el análisis y diseño de la estructura se explica como sigue: - Utilizando las cargas descritas en el punto 3.3.1.3, se realizo la corrida de la losa nervada tipo,
para obtener las reacciones sobre las vigas, este análisis se hizo utilizando el programa “Análisis
2 Propuesta basada en el ACI 318-2002 para modificar la Norma COVENIN 1753-1987.
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
90
y diseño de losas”, realizado por el profesor Otto Rojas de la facultad de ingeniería civil de La
Universidad del Zulia.
- Para el diseño de los pórticos se creo un modelo tridimensional del edificio siguiendo la
distribución geométrica descrita en el aparte 3.3.1.1.
El programa utilizado para este análisis y el diseño de vigas y columnas fue el programa
comercial STAAD PRO versión 2003, el cual realiza un análisis dinámico espacial considerando
tres grado de libertad por nivel.
Finalmente para el cumplimiento del nivel de diseño ND3, se utilizaron hojas de cálculo, que
realizan las verificaciones del capitulo 18 de la propuesta de Norma Fonacit-Socvis, COVENIN
1753, comentadas mas adelante.
3.4.1 Consideraciones en el Diseño:
De la Norma COVENIN 1756-2001 (13), se tiene:
- Las edificaciones se analizarán bajo la acción de dos componentes sísmicas horizontales
actuando simultáneamente según dos direcciones ortogonales.
- Las masas efectivas por nivel se considerarán ubicadas en los correspondientes centros de
masa.
- Se deberá considerar en el análisis un número de modos de vibración que garantice que la
sumatoria de las masas participativas exceda el 90% de la masa total del edificio, para cada una
de las direcciones de análisis.
- Para el análisis inelástico posterior al diseño, la excitación sísmica será inducida con sismos
simulados, según el punto 3.4.4 de esta obra.
3.4.2 Criterios para el Diseño de las Secciones:
Luego de determinar las cargas y efectuar las combinaciones especificadas por COVENIN, se
diseñaron las vigas con secciones tipo rectangular y las columnas con secciones cuadradas. Una
vez dispuesto el acero de vigas, se verificó el criterio de capacidad en nodos, para confirmar que
la suma de resistencia de las columnas fuesen mayor de 1.20 veces la suma de resistencia de las
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
91
vigas en dicho nodo. En caso contrario se incrementó la resistencia de las columnas, aumentando
sus dimensiones y volviendo a realizar el análisis para ajustar las cantidades de acero tanto en
vigas y columnas.
La distribución de acero teórico en las columnas se plantea simétrica en las cuatro caras, de
modo que la columna tiene la misma capacidad resistente en sus dos planos de flexión principal.
Se siguió el siguiente criterio para determinar el número de capas de acero en las secciones:
0 cm2 < As < 20 cm2 2 capas
20 cm2 < As < 40 cm2 3 capas
40 cm2 < As < 60 cm2 4 capas
60 cm2 < As < 80 cm2 5 capas
80 cm2 < As < 100 cm2 6 capas
100 cm2 < As 7 capas
3.4.3 Verificación de Desplazamientos y Derivas:
La Norma COVENIN en su Capítulo 10 (13) obliga el control de los desplazamientos
laterales. La verificación consiste en el cumplimiento de un valor límite de deriva “diferencia de
los desplazamientos laterales totales entre dos niveles consecutivos”. Este valor límite debe
satisfacerse en cada línea resistente de la edificación, así como en los puntos más alejados del
centro de rigidez. En tal sentido se tiene:
eii R 80.0 (3.1)
Donde:
R : factor de ductilidad o de reducción de respuesta.
ei : desplazamiento lateral del nivel i calculado para la fuerza de diseño, suponiendo que la
estructura se comporta elásticamente, incluyendo efectos traslacionales, de torsión en planta y
efecto P.
i = i – i-1 (3.2)
Donde:
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
i : deriva lateral.
Se tiene que para estructuras susceptibles a sufrir daños por deformaciones de la estructura y
pertenecen al grupo B2, el límite que establece la norma viene dado por la siguiente expresión:
018.01
ii
i
hh
(3.3)
Donde:
hi - hi-1: altura del entrepiso analizado.
La verificación de las derivas laterales en los pórticos analizados comprende dos
verificaciones:
- Comparación de las derivas inelásticas esperadas obtenidas según el procedimiento de la
Norma, con las derivas obtenidas del análisis inelástico (según procedimiento descrito en el punto
3.5.2 - procedimiento 2).
- Comparación de las derivas obtenidas con el límite señalado por la Norma.
3.4.4 Características de los Sismos Utilizados
Se utilizaron cuatro acelerogramas (ver Figura 3.8) generados artificialmente Z3S2GB2,
Z3S4GB2, Z7S2GB2, Z7S4GB2 obtenidos con el programa SIMQKE (Vanmarcke 1976), para lo
cual, se tomó como espectro de referencia el espectro elástico base para el diseño de los pórticos.
En general, los espectros elásticos (Figura 3.2) correspondientes a un amortiguamiento de 5%
para los cuatro acelerogramas, se aproximan conservadoramente al espectro de referencia. La
duración del movimiento se fijó en 30.0 seg., la amplitud máxima especificada es de 0.20g para
los espectros correspondientes a la zona 3 y 0.40g para los correspondientes a la zona 7 tal y
como lo indica la Norma Sismorresistente, el intervalo entre puntos generados es de 0.01 seg., las
amplitudes máximas se ajustaron entre las duraciones de 2 seg. y 15 seg.
92
ACELEROGRAMAZ3S2GB2
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CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
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Fig. 3.8a Acelerograma Z3, S2. Fig. 3.8b Acelerograma Z3, S4.
ACELEROGRAMAZ7S2GB2
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Fig. 3.8c Acelerograma Z7, S2. Fig. 3.8d Acelerograma Z7, S4.
3.4.5 Propiedades Mecánicas de los Materiales Utilizados
En todos los pórticos estudiados, se utilizarán las siguientes características de los materiales
utilizados:
- Concreto para vigas y columnas Resistencia a la compresión mínima f’c=250
kg/cm2 a los 28 días de vaciado.
Características que definen la curva esfuerzo-
deformación del concreto:
Según Kent – Park modificado:
- Para εc < εcco curva propuesta por Kent –
Park, fc vs εc.
- Para εcco < εc < εccu la relación fc vs εc es
una línea recta que va desde fc = K.f’c hasta
fc = K.f’c(1-Zm(εccu - εcco)).
- Para εc > εccu, una línea recta constante hasta
alcanzar εmáx
Donde :
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
94
εcco: deformación del concreto para el máximo
esfuerzo = 0.002
εccu: deformación última del concreto
confinado = 0.008
εmax: 0.004 + s.fy/3400
εcu: deformación última del concreto no
confinado = 0.004 (según Högnestad, para el
análisis del concreto no confinado
recubrimiento)
E: módulo de elasticidad =238752 Kg/cm2.
- Acero de refuerzo Según ASTM A615 Grado 60 (COVENIN
316).
- Entre 0 < εs < εy fs = Es.εs
- Entre εy < εs < εsm fs = fy
- Entre εsm < εs < εsh el esfuerzo varía
linealmente desde fy hasta 1.5fy
- Para valores εsm > εs fs = 1.5fy
Donde:
εsm: deformación máxima = 0.08
εy: deformación en la fluencia = 0.002
εsh: deformac. al final de la fluencia = 0.01
fsu: esfuerzo último = 6300 Kg/cm2.
fy: esfuerzo de fluencia = 4200 Kg/cm2
3.4.6 Calculo de índices de Confiabilidad
Los índices de confiabilidad para los diferentes pórticos serán calculados con base al estado
límite de daño referencial, los cuales fueron tomados del estudio realizado por Pérez O. (8) como:
d REFERENCIAL VIGA = 0.45
d REFERENCIAL COLUMNA = 0.40
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
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Se determinarán los índices de confiabilidad agrupando los pórticos en función del tipo de
suelo, de la zona sísmica, y Factores de Reducción de Respuesta analizados, con la finalidad de
interpretar la confiabilidad de la norma para diferentes situaciones de análisis.
3.5 Instrumentos para la Obtención de la Información
El instrumento para procesar la información está conformado por un sistema que considera
dos aspectos:
- Hardware
- Software
3.5.1 Hardware Utilizado
Para el análisis de los edificios se utilizaron dos computadores. En una primera etapa la
generación de los archivos .frm, .INP, y la corrida de cada uno de los pórticos se realizaron en el
computador del centro de cálculo electrónico de La Universidad de Los Andes, operado vía
internet. Posteriormente, el procesamiento y análisis de los resultados se efectuó en un
computador personal.
A continuación se describen las características principales de los equipos involucrados:
Computador Central (ULA):
Número de procesadores 4MIPS R10000-175 MHz Memoria por procesador 712 Mbytes de RAM Velocidad pico 260 Mflops Espacio en Discos 17.2 Gbytes Sistema Operativo IRIS 6.4 Dirección IP 150.200.140.3
Terminal cliente (Personal):
Procesadores Pentium IV. Intel Memoria por procesador 512 Mbytes de RAM Espacio en Discos 80 Gbytes Sistema Operativo Windows XP Dirección IP 172.16.28.107
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
96
3.5.2 Software Utilizado
Para el análisis de los pórticos estudiados se utilizo un programa desarrollado por ULA con
apoyo de UCLA y LUZ, llamado “PORTAL DE DAÑOS”, el cual simula la respuesta física de
los pórticos ante cargas externas de manera que, se sometieron los mismos a excitaciones
sísmicas en su base. La dirección para acceder al PORTAL es
http://www.portalofdamage.ula.ve:8080/PDP/.
El procedimiento efectuado se describe a continuación:
- La información requerida para realizar los cálculos es almacenada en archivos electrónicos con
extensión .frm cuyo nombre es colocado por el analista.
La información requerida para generar los archivos .frm se mencionan de manera condensada:
o Geometría del Pórtico:
Número de niveles, número de tramos (internamente el programa calcula las coordenadas
de los nodos y las incidencias de miembros).
Características de las secciones.
Características de cargas actuantes (estáticas para el primer paso y especificación del
archivo que contiene el registro del sismo para el segundo paso).
o Características y disposición de aceros transversales y longitudinales en todas las secciones
(para cada extremo i+, i-, j+ y j-).
o Solicitaciones actuantes (cargas distribuidas sobre las vigas).
o Características de los materiales (concreto y acero).
- Una vez introducida toda la información necesaria se procede a generar los archivos .INP,
pidiendo como paso previo los diagramas de interacción en el agrietamiento, en la fluencia, en
condiciones últimas de carga, curvatura última, para cada elemento del pórtico; para este
procedimiento se considera concreto confinado, internamente el programa calcula los diagramas
de parámetros C vs P, My vs P, Gcr vs P y q vs P, necesarios para el análisis y calculo de daños.
El portal reordena las características de los pórticos, de modo que genera archivos de forma que
pueda ser interpretado por el procesador y sea posible realizar los cálculos.
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
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- Finalmente se procesa cada uno de los pórticos con el programa arrojando los resultados del
análisis en el archivo .fin.
3.5.2.1 Procedimiento de Análisis
A continuación se explica la metodología para implementar el modelo de daños en el
programa utilizado.
La solución numérica de este tipo de análisis, se divide en dos problemas uno global y uno
local.
El problema global se encarga de la solución numérica del sistema de ecuaciones no-lineales
de equilibrio de los nodos, el método utilizado es paso a paso e iterativo, para obtener los
desplazamientos generalizados de la estructura. Esta ecuación es escrita en forma genérica:
{L(X)} = {Qr}b {Qr}b + [m]b { 2q(X)/t2} – {P} = 0 (3.4)
En cada iteración se resuelve el siguiente problema lineal:
{L(X)}s = {L(X)}s-1 + { L/X }s-1 ({X}s - {X}s-1 } = 0 (3.5)
Donde, el jacobiano global es la suma del jacobiano local en coordenadas globales más el
jacobiano inercial, tal como se expone en la siguiente expresión.
{ L/X }s-1 = - {Q/X}s-1 - [m]b {2q/X2}s-1 (3.6)
El vector {X}s-1 son los desplazamientos generalizados de la estructura calculados en la
iteración precedente. El problema local resuelve las fuerzas internas de miembro, el aporte de
cada miembro a la estructura total con el jacobiano local y el jacobiano inercial.
El algoritmo planteado determina las variables de miembro lo cual se describe a continuación:
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
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- Cálculo de las Variables Internas de Miembro
Las deformaciones generalizadas se obtienen a partir de los desplazamientos generalizados,
utilizando las ecuaciones de compatibilidad.
Las constantes del modelo (c, q, My, Gcr) no varían en el intervalo de tiempo de análisis, pero
varían en los diferentes instantes durante el análisis de la estructura. Estas constantes dependen
de las propiedades de la sección como lo son el momento de agrietamiento (Magr), el momento
de fluencia (Mp), el momento último (Mu) y la rotación última ( u), los cuales a su vez
dependen de la carga axial, de las propiedades geométricas y de las características de los
materiales.
La secuencia utilizada para el cálculo de las constantes es la siguiente:
o Se determina el valor de carga axial en cada paso a partir del alargamiento o acortamiento de
la cuerda.
o Se determinan los valores de Magr, Mp, Mu, u para el nivel de carga axial en cada paso, por
interpolación de los diagramas de interacción para acciones positivas y negativas en ambos
extremos de cada miembro.
o Finalmente se calculan las constantes del modelo.
Los esfuerzos generalizados, las deformaciones plásticas y los daños positivos y negativos en
los extremos de miembro, se obtienen a través de la ley de comportamiento y consiste en resolver
un sistema de ecuaciones en las cuales estas son las únicas incógnitas. La ley de comportamiento
formada por la ley de estado y las leyes de evolución, conforman el sistema de ecuaciones
mencionado. Al resolver este sistema de ecuaciones, no se conoce si las rotaciones plásticas o los
daños evolucionan durante el paso en cuestión, por ello, debe aplicarse un algoritmo especial
denominado Predictor-Corrector-Verificador, el cual consiste en efectuar los cálculos requeridos
en tres etapas:
Primera etapa de predicción elástica, en este paso, se supone que no hay evolución de las
rotaciones plásticas ni de los daños, utilizando la ley de estado para calcular los esfuerzos
generalizados. Esta predicción es verificada calculando las funciones de fluencia y de daño, con
lo cual se determina una de dos posibilidades. Si todas las funciones inelásticas son negativas o
nulas, significa que no hay incremento de ningún variable interna durante el paso y los esfuerzos
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
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99
generalizados calculados en la predicción son correctos. Si este fuera el caso terminaría el cálculo
de los esfuerzo el paso en cuestión. La segunda posibilidad se da cuando una o varias funciones
inelásticas son positivas, lo cual significa que la predicción no fue correcta y que en al menos una
de las variables internas durante el paso se requiere pasar a la segunda etapa.
Segunda etapa de corrección inelástica, la cual consiste en recalcular los esfuerzos
generalizados, las rotaciones plásticas y los daños al final de cada paso, sabiendo que existen
incrementos en al menos una variable interna del modelo. Se suponen activas aquellas variables
cuyas funciones de fluencia y/o de daño resultó positiva. Las restantes se supondrán pasivas. Esta
etapa ahora puede ser resuelta por el método de Newton. Luego se debe verificar si las variables
supuestas activas lo son, lo cual es realizado durante la tercera etapa.
Tercer etapa de Verificación, en la cual se verifican las consideraciones referentes a las
variables activas o pasivas durante el paso, esta etapa se efectúa en dos fases; una inicial en la
cual se calculan las funciones inelásticas de las variables internas que fueron supuestas pasivas
durante el segundo paso, si alguna de las variables resulta activa, debe entonces realizarse una
nueva corrección inelástica. El la otra fase, se calculan los términos de disipación de las
desigualdades termodinámicas asociadas a las variables internas que fueron supuestas activas
durante el paso dos, si alguna de las desigualdades en cuestión no es válida, debe realizarse otra
corrección.
En el caso de que todas las desigualdades se cumplan, usando solamente las variables activas
y las funciones de las variables supuestas pasivas son negativas o cero, entonces los valores
obtenidos para los esfuerzos, las rotaciones plásticas y los daños son correctos.
Las fuerzas en extremo de miembro se calculan a partir de los esfuerzos generalizados,
aplicando en forma directa las ecuaciones de equilibrio del miembro.
3.6 Validez y Confiabilidad del Instrumento
La validez de contenido se refiere a que el instrumento mida todos los factores de la variable
que se esta estudiando. Es necesario efectuar una prueba piloto para mejorar la validez del
instrumento.
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
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En tal sentido se presentan a continuación, los resultados de la aplicación del modelo para
reproducir el ensayo ejecutado por Scribner y Wigth (1978) y reportado por Wang y Shah (1987).
Ver Figura 3.9
Fig. 3.9. Características Geométricas y Propiedades del Material del ensayo. Historia de Desplazamiento.
En la Figura 3.9 se muestran los detalles de la sección y la junta viga-columna ensayada, y la
historia de desplazamiento. En la Figura 3.11 se observa la simulación del ensayo usando el
modelo de daño utilizado en este trabajo. En la misma puede notarse la perdida gradual de
resistencia y de rigidez a medida que el daño aumenta, tal como la curva experimental de la
Figura 3.10 lo indica, así como la coincidencia de los valores de carga y desplazamiento, lo cual
representa la validación experimental del modelo y programa utilizado. Se afirma que los
parámetros e hipótesis de simplificación incorporados en el modelo de daño propuesto, han sido
validados para cargas monotónicas de forma exitosa en forma experimental en la Universidad de
los Andes.
cm
kN22
L
EI
Fy+ = 5337kN Fy - = 4438kN
127cm
-6
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0
2
4
6
Tiempo
Des
pla
zam
ien
tos A
A 2#6
25.4cm
4#2
2#5 20cm
CAPITULO III. MARCO METODOLOGICO Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
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-90
-60
-30
0
30
60
90
-63 -42 -21 0 21 42 63
Desplazamiento
Fuerz
a
Fig. 3.10 Curva experimental de Carga Desplazamiento.
Fig. 3.11 Simulaciones Numéricas con el Modelo.
La confiabilidad se refiere a la estabilidad, consistencia y exactitud de los resultados, es decir,
que los resultados obtenidos por el instrumento sean similares si se vuelven a aplicar sobre las
mismas muestras en igualdad de condiciones.
En los resultados obtenidos en esta investigación “los valores de daño” no existe posibilidad de
dispersión entre ellos si se realizan varios análisis, pues el computador es el encargado de realizar
las operaciones matemáticas. La confiabilidad se limita entonces, a la garantía de que el usuario
encargado de suministrar la data al programa lo haga en forma correcta, en todo caso, para un
corrido en particular siempre se obtendrán los mismos resultados.
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
CAPITULO IV
ANALISIS Y DISCUSION DE RESULTADOS
4.1 Análisis de los resultados
Una vez efectuados los cálculos, se ordenaron de acuerdo a las variables a analizar, con el fin
de facilitar su interpretación.
La nomenclatura utilizada es la siguiente:
- Área: área tributaria del pórtico B, por el número de pisos, en m2.
- Altura: altura del pórtico en m, medida desde el nivel de la base.
- 4P-Z3S2: 4 pisos Zona 3, suelo S2.
- 4P-Z3S4: 4 pisos Zona 3, suelo S4.
- 4P-Z7S2: 4 pisos Zona 7, suelo S2.
- 4P-Z7S4: 4 pisos Zona 7, suelo S4.
- 8P-Z3S2: 8 pisos Zona 3, suelo S2.
- 8P-Z3S4: 8 pisos Zona 3, suelo S4.
- 8P-Z7S2: 8 pisos Zona 7, suelo S2.
- 8P-Z7S4: 8 pisos Zona 7, suelo S4.
- 12P-Z3S2: 12 pisos Zona 3, suelo S2.
- 12P-Z3S4: 12 pisos Zona 3, suelo S4.
- 12P-Z7S2: 12 pisos Zona 7, suelo S2.
- 12P-Z7S4: 12 pisos Zona 7, suelo S4
4.1.1 Parámetros del consumo promedio y Costos :
Estos parámetros dan un valor promedio de la cantidad de concreto y acero por m2 de
construcción, la tabla 4.1 muestra las áreas para las diferentes alturas del pórtico.
Es importante mencionar que en los cómputos de los consumos promedio no se considero el
aporte de la infraestructura.
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Las tablas de resultados 4.2, 4.3, 4.4 y 4.5, muestran los parámetros de consumo de concreto
en vigas, columnas y el consumo total para las diferentes alturas así como para los diferentes
Suelos, Zonas Sísmicas y Factores de Reducción de Respuesta estudiados, de igual manera las
tablas 4.6, 4.7, 4.8 y 4.9 muestran los consumos para el acero.
En general para las alturas estudiadas 4, 8 y 12 niveles los pórticos con mayor consumo de
concreto fueron los ubicados en la Zona 7, suelo S4.
En las figuras 4.1, 4.2, 4.3 y 4.4, se observan gráficamente las variaciones en el consumo total
de concreto respecto al valor de R.
En los pórticos ubicados en Z3S2 no hubo una variación significativa en el consumo entre
uno y otro valor de R, sin embargo la tendencia siempre es a aumentar el consumo mientras R es
menor, lógicamente, puesto que se diseñan con fuerzas mayores, lo que da lugar a dimensiones
más grandes en los elementos.
Al igual que para el concreto, los pórticos con mayor consumo de acero fueron los ubicados
en Zona 7, suelo S4.
En las figuras 4.5, 4.6, 4.7 y 4.8, se observan gráficamente las variaciones en el consumo
total de acero respecto al valor de R, las líneas de tendencia indican para todos los casos, que
mientras el valor de R es mayor, disminuye el consumo de acero.
Con el calculo de los consumos promedios de concreto y acero total y la aplicación de precios
unitarios (m3 de concreto igual a 13UT y Kg. de acero igual a 0.08UT), se determinó la
variación en costos tomando como referencia el consumo para R igual a 6.00, que corresponde al
dado por la Norma COVENIN.
Se encontraron valores relativos de costos, para cada altura, Zona, Suelo y Factor de
Reducción de Respuesta estudiado, estos se muestran en la tabla 4.10.
Gráficamente se muestran estos resultados en las figuras 4.9, 4.10, 4.11 y 4.12.
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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Se observa que la tendencia de las graficas para los casos analizados corresponde a una curva
potencial descendiente, los pórticos diseñados con R igual a 3.32 presentan una mayor variación,
así como los pórticos de 8 y 12 niveles con respecto a los de 4 niveles.
El Factor de Reducción de Respuesta no influyo en la variación de costo para los pórticos
ubicados en Z3S2. A medida que la zona y suelo solicita una mayor exigencia la variación en los
costos se hace mayor, esto es para Z7S4.
4.1.2 Desplazamientos y derivas :
En las tablas 4.11 a la 4.21 se muestran los valores de desplazamientos y derivas inelásticos,
según se especifica en la Norma COVENIN, calculados en la etapa de diseño multiplicando los
desplazamientos obtenidos con el programa STAAD PRO por 0.8R, se muestran también los
obtenidos del análisis inelástico con el PORTAL DE DAÑOS, de manera de confrontar dichos
resultados. Los desplazamientos se observan gráficamente el las figuras 4.13 a la 4.23, y las
derivas en las figuras 4.28 a la 4.38.
Al comparar los desplazamientos inelásticos reales con las predicciones inelásticas a partir del
modelo elástico, en los pórticos de cuatro (4) pisos, se tiene:
Pórticos Z3S2: el uso del método elástico en la etapa de diseño arroja valores de
desplazamientos menores, que los reales con el método inelástico tal como se esperaba, excepto
en el último nivel donde para los tres casos de R estudiados es mayor para el método elástico.
Las derivas según las deformaciones reales para los diferentes valores de R, resultaron menores
que el valor permisible dado por la Norma de 0.018.
Pórticos Z3S4: en este caso, el comportamiento es similar a los pórticos ubicados en suelo S2,
pero con mayor diferencia entre los desplazamientos elásticos e inelásticos, en el primer nivel los
desplazamientos doblan el valor dado en la etapa de diseño para R igual a 6.00.
Las derivas para R igual a 4.50 y 6.00 superan el valor permisible, solo para los pórticos
diseñados con R igual a 3.32 las derivas son menores que 0.018.
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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Pórticos Z7S2: los desplazamientos elásticos en estos pórticos, superan los desplazamientos
reales inelásticos, sin embargo se puede decir que para los pórticos diseñados con R igual a 3.32,
ambos son similares, para R igual a 6.00 la deriva permisible es superada.
Pórticos Z7S4: los desplazamientos reales para R igual a 4.50 y 6.00 superan los
desplazamientos elásticos; las derivas resultan mayores que 0.018 alcanzando hasta un valor de
0.036 en el piso 1 del pórtico diseñado con R igual a 6.00, solo para R igual a 3.32 las derivas
son cumplidas.
Para los pórticos de 4 niveles en forma general se cumple que:
- Los pórticos ubicados en Z3S2, cumplen los requisitos de derivas exigidos por la Norma
COVENIN, para los tres factores de Reducción de Respuesta analizados.
- Los desplazamientos inelásticos obtenidos en pórticos ubicados en zona 3, superan los
desplazamientos calculados según el análisis elástico, para pórticos ubicados en zona 7 se da el
caso contrario.
- Para pórticos ubicados en Z3S4, Z7S2 y Z7S4 las derivas reales según el análisis inelásticos
para R igual a 6.00 y 4.50 superan la deriva permisible. Todos los pórticos diseñados con R igual
a 3.32 cumplen con esta exigencia.
Pórticos de ocho (8) pisos,
Pórticos Z3S2: de forma general los desplazamientos para R igual a 3.32 y 4.50 son superiores
según el diseño elástico, para R igual a 6.00 estos se asemejan siendo mayores los
desplazamientos inelásticos, en relación a las derivas para todos los casos los valores son
menores al valor permisible.
Pórticos Z3S4: el comportamiento de estos pórticos fue similar a los ubicados en suelo S2,
mayores para el diseño elástico, sin embargo para R igual a 6.00 la diferencia es notoria,
mayores según análisis inelástico exceptuando los últimos 2 niveles, las derivas solo son
superadas con este factor.
Pórticos Z7S2: los desplazamientos encontrados en la etapa de diseño elástico superan los
inelásticos para todos los Factores de Reducción de Respuesta; las derivas son sobrepasadas para
los pórticos diseñados con R igual a 6.00.
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Pórticos Z7S4: en este caso, los desplazamientos elásticos se asemejan a los inelásticos,
especialmente para los pórticos diseñados con R igual a 4.50, en los diseñados con R igual a
3.32 y 6.00 resultan ligeramente mayores los desplazamientos elásticos en los pisos superiores, y
ligeramente menores en los pisos inferiores, las derivas son sobrepasadas para R igual a 4.50 y
6.00.
De forma general en estos pórticos se cumple que:
- AL igual que para los pórticos de 4 pisos las derivas resultan menores al valor permisible en los
pórticos ubicados en Z3S2, para los diferentes R.
- Todos los pórticos diseñados con R igual a 3.32 cumplen la deriva permisible y los diseñados
con R igual a 6.00 sobrepasan este valor para Z3S4, Z7S2 y Z7S4.
Para los pórticos de pisos (12) pisos,
Pórticos Z3S2: para todos los casos, los desplazamientos elásticos son mayores que los
inelásticos, con valores hasta del doble en los pórticos con R igual a 4.50 y 6.00; lo mismo
ocurre con las derivas.
Pórticos Z3S4: el mismo comportamiento se da en estos pórticos, mayores los
desplazamientos elásticos, para el caso de las derivas hay una proximidad entre ambos análisis,
pero siempre respetando el valor permisible.
Pórticos Z7S2: igual que en los dos casos anteriores, los desplazamientos según análisis
elástico son mayores que en el análisis inelástico, al igual que las derivas.
Pórticos Z7S4: estos pórticos no serán considerados en el análisis de los resultados, pues fue
imposible realizar las corridas completas hasta lograr un 100%, cualquier juicio que se haga con
los análisis obtenidos sin completar la corrida serian errados.
Estos pórticos fueron los que tuvieron un mejor comportamiento, los desplazamientos y
derivas en todos los casos resultaron menores a los especificados según el procedimiento de la
Norma COVENIN, el cambio en el valor de R no tiene relevancia, pues para R igual a 6.00, se
consigue un comportamiento adecuado y valores inferiores a las exigencias de la Norma.
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Las figuras 4.24, 4.25, 4.26 y 4.27 muestran una comparación de los desplazamientos
máximos según análisis inelástico para las diferentes alturas, la tendencia en el comportamiento
es a obtener desplazamientos mayores mientras R es mayor. En las figuras 4.39, 4.40, 4.41 y
4.42 se hace la misma comparación para las derivas, el comportamiento es similar a los
desplazamientos sin embargo la variación para los pórticos Z3S2, no es significativa.
4.1.3 Análisis de daños:
Las figuras 4.43 a la 4.75, muestran a la derecha los mapas numéricos de daños, los mismos
mapas de daño se muestran a la izquierda, con círculos a escala relativa, para lograr mejor
interpretación. A continuación se muestra los valores asignados a la escala mencionada:
Diámetro Daños entre
1 0.10 – 0.20
2 0.21 – 0.30
3 0.31 – 0.40
4 0.41 – 0.50
5 0.51 – 0.60
6 0.61 – 0.70
7 > 0.71
Para una mayor comprensión de los resultados se calculará el porcentaje de rótulas que
alcanzan daños (positivos o negativos) mayores que los valores máximos de daños referenciales,
igual a 0.40 para columnas y 0.45 para las vigas. Luego, se determinará que porcentaje de ellos,
corresponden a daños en rótulas de vigas y cual de columnas. Además, se determinará el
porcentaje de daños en las rótulas de vigas y columnas mayores que los valores máximos de
daños referenciales, con respecto al número total de vigas y columnas respectivamente.
Para esto se seguirán dos procedimientos: primero, se calculará el porcentaje referido
considerando todas las rótulas del pórtico sin importar los niveles de daño presentes; en un
segundo análisis, el cálculo de los porcentajes, sólo incluirá el caso en que los niveles de daño
superaron los valores de los daños máximos de referencia para columnas y vigas por separado.
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A continuación se presentan y analizan los resultados, para cada uno de los pórticos:
Pórticos de 4 pisos:
Los daños máximos obtenidos para cada pórtico se muestran en la tabla 4.22. En la tabla
4.23 se muestran los porcentaje de rotulas que presentan un daño mayor al daño referencial en
base al total de rotulas y en la tabla 4.24 los porcentaje de daños en las rótulas de vigas y
columnas mayores que los valores máximos de daños referenciales, con respecto al número total
de vigas y columnas respectivamente.
Pórticos Z3S2: de forma genérica, los daños máximos se ubican en la base de las columnas de
planta baja, entre el 11.2 y 13.4 % sufren daños superiores a los daños referenciales considerados
(Dref) (8), los cuales se ubican consistentemente en las columnas del primer nivel, si se compara
el % de rotulas dañadas para R igual a 3.32 y 6.00 el porcentaje no aumenta considerablemente,
varia de 11.20 a 13.40, esta variación no se considera significativa.
Pórticos Z3S4: los daños máximos se ubican en la base de las columnas de planta baja, sin
embargo comienzan a aparecer daños en el tope de las columnas del nivel 2, entre el 11.60 y
15.20 % sufren daños superiores al Dref., ahora el % de rotulas dañadas para R igual a 3.32 y
6.00 varia en un 3.60%.
Pórticos Z7S2: el comportamiento es similar a los pórticos anteriores, sin embargo para R
igual a 6.00 hay una mayor distribución de daños todos en las columnas del primer y segundo
piso, alcanzando un 20,50 % del total de rotulas dañadas, para R igual a 3.32, solo el 6.30% de
las rotulas presentan daños superiores a Dref., una variación del 14.20%.
Pórticos Z7S4: estos son los pórticos con mas daños, con porcentajes de entre el 3.57 y 25%
de las rotulas con daños mayores a 0.4 y 0.45 en columnas y vigas respectivamente, la variación
es significativa al comparar R igual a 3.32 con R 6.00. La mayoría de los daños se concentran
en las columnas del primer y segundo nivel y aparecen daños superiores al valor referencial en
las vigas del primer nivel para R igual a 4.50 y 6.00.
El hecho de que la frecuencia del primer modo para estos pórticos de poca altura 4, inclusive
para los de 8 pisos, esté ubicada en el centro de la banda de frecuencias predominantes para los
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casos estudiados, da como resultado un factor de amplificación dinámica mayor que para los
pórticos de 12 pisos como se verá mas adelante.
Cabe destacar, que los pórticos diseñados con R igual a 4.50 y 6.00 arrojan daños máximos al
Dref. tanto en la base como en el tope de las columnas de planta baja, en muchos casos este daño
alcanza el valor de 0.60 el cual según los análisis experimentales realizados en la universidad de
los Andes se consideran como daño no reparable, este efecto, denota un comportamiento
estructural deficiente, puesto que supone fragilidad al ser atacados ambos extremos de todas las
columnas de un mismo nivel con magnitud de daños superior al de las vigas. No se cumple en
estos pórticos, la hipótesis de ocurrencia de daños, predominantemente en las vigas.
Por otro lado, el diseño de las vigas de estos pórticos, está controlado por las cargas
gravitacionales para cuya condición no se requieren columnas más grandes que las vigas. Se
obtiene entonces como resultado, columnas con dimensiones modestas, necesarias solo para
cumplir una relación Mc/Mv igual a 1.20, requerida por el nivel de diseño tres (ND3) de la
Norma. Este último es el criterio que controla el tamaño de las columnas del pórtico.
Pórticos de 8 pisos:
Los daños máximos obtenidos para cada pórtico se muestran en la tabla 4.25. En la tabla 4.26
se muestran los porcentaje de rotulas que presentan un daño mayor al daño referencial en base al
total de rotulas y en la tabla 4.27 los porcentaje de daños en las rótulas de vigas y columnas
mayores que los valores máximos de daños referenciales, con respecto al número total de vigas y
columnas respectivamente.
Pórticos Z3S2: los daños máximos se ubican en la base de las columnas de planta baja, entre
el 2.20 y 6.30 % sufren daños superiores a los daños referenciales considerados, los cuales se
ubican en las columnas del primer nivel, si se compara el % de rotulas dañadas para R igual a
3.32 y 6.00 el porcentaje resulta mayor para 3.32, aparecen daños en las columnas del 5 y 6 piso,
se da una mayor distribución de daños pero con valores de daños menores que para R igual a
6.00.
Pórticos Z3S4: los daños máximos se ubican en la base de las columnas de planta baja para
los pórticos diseñados con R igual a 4.50 y 6.00, para R igual a 3.32 este se ubica en el tope de la
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columna del piso 5, sin embargo comienzan a aparecer daños en las columnas de los niveles 5 y
6 para los tres casos, entre el 10.30 y 11.61 % sufren daños superiores al Dref.
Pórticos Z7S2: estos resultan los pórticos con más daños, entre el 20.54 y 21.43% sufren
daños mayores que el Dref. , la mayoría ubicados entre los pisos 3 y 7, solo para R igual a 6.00
aparecen daños superiores al Dref. en vigas, para R igual a 3.32 y 4.50, todos los daños se ubican
en las columnas.
Pórticos Z7S4: para R igual a 3.32 los daños mayores se concentran en las columnas de los
pisos 4 y 5, para R igual a 4.50 y 6.00 en las columnas del nivel de planta baja, entre el 3.13 y
el 7.59% de las rotulas sufren daños mayor al Dref.
Pórticos de 12 pisos:
Los daños máximos obtenidos para cada pórtico se muestran en la tabla 4.28, los resultados
arrojan valores de daños en todos los casos inferiores a los daños máximos referenciales tanto en
vigas como en columnas. El comportamiento de estos pórticos es excelente, la variación de R no
se ve justificada en estos pórticos.
4.1.4. Comparación entre Costos, Daños e Índices de Confiabilidad.
La tabla 4.30 muestra un resumen comparativo, entre el porcentaje de variación en costos, el
porcentaje de disminución de daño y el índice de confiabilidad obtenidos según los diferentes
valores de R, con la finalidad de evaluar si la variación en el costo tiene un impacto importante en
la disminución de los daños y establecer así las conclusiones y recomendaciones de la
investigación.
Pórticos Z3S2:
- Para los pórticos de 4 pisos la disminución de R no tiene influencia en el daño máximo,
en costos la variación es mínima (2% para R igual a 4.50 y 7% para R igual a 3.32), no se
consigue bajar el daño al disminuir R, el sismo no tiene mucha influencia en estos
pórticos, el diseño lo controla la carga vertical., el índices de confiabilidad aumenta para
R igual a 3.32 pero se mantiene alrededor de 1.5.
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- Para los pórticos de 8 pisos, se consigue bajar el daño para R igual a 3.32 en un 10%, con
un consumo solo del 4% adicional; para R igual a 4.50 con el 3% mas de costos solo se
consigue bajar el daño máximo en un 4%, los índices de confiabilidad se mantienen
alrededor de 2.
- Para 12 pisos se consigue bajar el daño para R igual a 3.32 en un 10% con un costo
adicional de 9%, sin embargo no es necesario puesto que los valores de daños son bajos,
ninguna rotula sobrepase el daño máximo referencial.
Pórticos Z3S4:
- Para los pórticos de 4 pisos la variación de R influye en el daño máximo, para R igual a
4.50 se consigue bajar el daño en un 11.59% con un gasto adicional del 3%, para R igual a
3.32 la influencia es aun mayor de 30.43% con un costo adicional de 16%, el índice de
confiabilidad aumenta significativamente de 1.1 a 1.65 para R igual a 3.32, es
recomendable para estos pórticos utilizar un R menor que 6.00 y menor que 4.50, puesto
que con 4.50 aun el daño es muy grande (0.61).
- Para los pórticos de 8 pisos, se consigue bajar el daño para R igual a 3.32 en un 33.78%,
con un costo adicional del 23%, para R igual a 4.50 con el 10% mas en costos se consigue
bajar el daño máximo en 24.32%, el índice de confiabilidad baja para R igual a 3.32, esto
porque se presenta una mayor distribución de rotulas dañadas pero con valores de daños
mas bajos que con R igual a 6.00.
- Para 12 pisos se consigue con R igual a 3.32 bajar el daño en un 21.95% con un costo
adicional de 18%, sin embargo al igual que en el caso anterior no es necesario puesto que
los valores de daños son bajos.
Pórticos Z7S2:
- Para los pórticos de 4 pisos se consigue bajar el daño en un 25 y 35.29% con un gasto
adicional del 13 y 37%, para R igual a 4.50 y 3.32 respectivamente, vemos que la
influencia de R se hace aun mas importante, el índice de confiabilidad aumenta
significativamente de 0.95 a 1.22 y 1.65.
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- Para los pórticos de 8 pisos, se consigue bajar el daño para R igual a 3.32 y 4.50 en un
10.00%, con un costo adicional del 14 y 36%, respectivamente, el índice de confiabilidad
disminuye poco para R igual a 3.32.
- Para 12 pisos se consigue con R igual a 3.32 bajar el daño en un 26.19% con un costo
adicional de 50%, para R igual a 4.50 el daño baja en 2.38% con un costo adicional
elevado de 19%, para la disminución que se consigue.
Y finalmente para los pórticos Z7S4:
- 4 pisos: el daño disminuye en 21.21 y 28.79% para R igual a 4.50 y 3.32 respectivamente
con consumos mayores de 12 y 34%, igual en los casos anteriores los índices de
confiabilidad aumenta de manera importante de 0.82 a 1.08 y 1.74.
- 8 pisos: en estos pórticos se produce un costo adicional muy elevado para la disminución
de daño alcanzado, para R igual a 4.50 el gasto es mayor en 22% y la disminución de
daño del 6% y para R igual a 3.32 el costo adicional fue de 71% para bajar el daño en
8%, no se amerita la disminución de R en estos porticos.
Los resultados muestran que a medida que la zona y el tipo de suelo se vuelve mas exigente, el
costo aumenta de manera significativa para R igual a 3.32, de la misma manera que disminuye el
porcentaje de daño en el pórtico y aumenta el índice de confiabilidad, , sin embargo es en los
pórticos de 4 pisos donde mejor se observa que este aumento en el costo vale la pena, pues se
obtiene un mejor comportamiento, también en el análisis de derivas se demostró que para los
pórticos de 4 pisos diseñados con R igual a 3.32 se cumplen los requisitos de deriva máxima dado
por la Norma.
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4.2. Presentación de figuras y tablas de resultados
4.2.1 Parámetros de consumo promedio
Tabla. 4.1 Información general del pórtico estudiado
12
AREA (m2)
1104
1656
15.55
29.95
44.35
ALTURA (m)
Nº DE PISOS
4
8
552
Consumo de Concreto:
Tabla. 4.2 Consumo de concreto para pórticos Z3S2
N° DE PISOS m3 m3/m2 % m3 m3/m2 % m3/m2 %
4 24.44 0.0443 58.066 17.65 0.032 41.934 0.0763 1008 46.54 0.0422 57.943 33.78 0.0306 42.06 0.0728 10012 79.40 0.0479 54.117 67.32 0.0407 45.883 0.0886 100
N° DE PISOS m3 m3/m2 % m3 m3/m2 % m3/m2 %
4 22.65 0.041 57.825 16.52 0.0299 42.175 0.071 1008 45.25 0.041 57.629 33.27 0.0301 42.371 0.0711 10012 74.88 0.0452 54.073 63.60 0.0384 45.927 0.0836 100
N° DE PISOS m3 m3/m2 % m3 m3/m2 % m3/m2 %
4 22.06 0.04 57.931 16.02 0.029 42.069 0.069 1008 43.97 0.0398 57.62 32.34 0.0293 42.38 0.0691 10012 70.29 0.0424 53.718 60.56 0.0366 46.282 0.079 100
TOTAL
6.00VIGAS COLUMNAS TOTAL
VIGAS COLUMNAS
VIGAS COLUMNAS TOTAL
Z3S232
.50
3.
4
R =
R =
R =
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Tabla. 4.3 Consumo de concreto para pórticos Z3S4
N° DE PISOS m3 m3/m2 % m3 m3/m2 % m3/m2 %
4 25.54 0.0463 53.814 21.92 0.0397 46.19 0.086 1008 57.84 0.0524 54.908 47.50 0.043 45.09 0.0954 10012 85.74 0.0518 51.173 81.81 0.0494 48.83 0.1012 100
N° DE PISOS m3 m3/m2 % m3 m3/m2 % m3/m2 %
4 23.78 0.0431 56.66 18.19 0.033 43.34 0.076 1008 55.14 0.0499 56.624 42.24 0.0383 43.38 0.0882 10012 83.83 0.0506 53.837 71.88 0.0434 46.163 0.094 100
N° DE PISOS m3 m3/m2 % m3 m3/m2 % m3/m2 %
4 22.52 0.0408 56.314 17.47 0.0316 43.686 0.0724 1008 50.86 0.0461 57.281 37.93 0.034 42.72 0.080 10012 74.75 0.0451 53.123 65.96 0.0398 46.877 0.085 100
Z3S43.32
VIGAS COLUMNAS TOTAL
.50VIGAS COLUMNAS TOTAL
VIGAS COLUMNAS TOTAL
Tabla. 4.4 Consumo de concreto para pórticos Z7S2
4
6.00
R =
R =
R =
N° DE PISOS m3 m3/m2 % m3 m3/m2 % m3/m2 %
4 29.02 0.0526 50.408 28.55 0.0517 49.592 0.1043 1008 63.36 0.0574 53.275 55.57 0.0503 46.72 0.1077 10012 104.80 0.0633 46.20 122.02 0.0737 53.796 0.137 100
N° DE PISOS m3 m3/m2 % m3 m3/m2 % m3/m2 %
4 26.13 0.0473 53.436 22.77 0.0413 46.56 0.0886 1008 57.96 0.0525 57.90 42.15 0.0382 42.10 0.0907 10012 96.26 0.0581 49.979 96.34 0.0582 50.021 0.1163 100
N° DE PISOS m3 m3/m2 % m3 m3/m2 % m3/m2 %
4 25.01 0.0453 56.494 19.26 0.0349 43.506 0.080 1008 53.32 0.0483 58.108 38.44 0.035 41.89 0.0831 10012 82.78 0.050 52.359 75.32 0.045 47.64 0.0955 100
Z7S23.32
VIGAS COLUMNAS TOTAL
.50VIGAS COLUMNAS TOTAL
.00VIGAS COLUMNAS TOTAL
4
6R =
R =
R =
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Tabla. 4.5 Consumo de concreto para pórticos Z7S4
N° DE PISOS m3 m3/m2 % m3 m3/m2 % m3/m2 %
4 28.99 0.0525 45.40 34.87 0.0632 54.604 0.1157 1008 83.46 0.0756 45.829 98.65 0.0894 54.17 0.165 10012 167.60 0.1012 47.453 185.59 0.1121 52.547 0.2133 100
N° DE PISOS m3 m3/m2 % m3 m3/m2 % m3/m2 %
4 27.14 0.0492 48.40 28.94 0.0524 51.605 0.1016 1008 77.54 0.070 52.40 70.44 0.0638 47.60 0.134 10012 113.93 0.0688 48.263 122.13 0.0738 51.737 0.1425 100
N° DE PISOS m3 m3/m2 % m3 m3/m2 % m3/m2 %
4 26.06 0.0472 51.309 24.73 0.0448 48.69 0.092 1008 77.54 0.0702 52.40 70.44 0.0638 47.60 0.134 10012 113.93 0.0688 48.269 122.10 0.0737 51.731 0.1425 100
Z7S43.32
VIGAS COLUMNAS TOTAL
.50VIGAS COLUMNAS TOTAL
.00VIGAS COLUMNAS TOTAL
Consumo de Acero:
Tabla. 4.6 Consumo de acero para pórticos Z3S2
4
6
R =
R =
R =
N° DE PISOS Kg Kg/m2 % Kg Kg/m2 % Kg/m2 %
4 3289 5.9583 27.939 8483 15.368 72.061 21.326 1008 6397 5.7944 26.733 17532 15.88 73.27 21.675 10012 11398 6.8829 27.712 29732 17.954 72.288 24.837 100
N° DE PISOS Kg Kg/m2 % Kg Kg/m2 % Kg/m2 %
4 3092 5.6014 26.913 8397 15.212 73.087 20.813 1008 6152 5.5725 25.738 17750 16.078 74.262 21.65 10012 10602 6.4022 27.943 27340 16.51 72.057 22.912 100
N° DE PISOS Kg Kg/m2 % Kg Kg/m2 % Kg/m2 %
4 3021 5.4728 26.794 8254 14.953 73.206 20.426 1008 5965 5.4031 25.902 17064 15.457 74.098 20.86 10012 10381 6.2687 27.073 27963 16.886 72.927 23.155 100
TOTAL
6.00VIGAS COLUMNAS TOTAL
VIGAS COLUMNAS
VIGAS COLUMNAS TOTAL
Z3S2.32
.50
3
4
R =
R =
R =
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Tabla. 4.7 Consumo de acero para pórticos Z3S4
N° DE PISOS Kg Kg/m2 % Kg Kg/m2 % Kg/m2 %
4 3564 6.4565 26.02 10133 18.357 73.98 24.813 1008 8798 7.9692 28.965 21577 19.544 71.04 27.514 10012 13783 8.3231 28.254 34999 21.135 71.75 29.458 100
N° DE PISOS Kg Kg/m2 % Kg Kg/m2 % Kg/m2 %
4 3299 5.9764 27.092 8878 16.083 72.908 22.06 1008 7701 6.9755 28.94 18909 17.128 71.06 24.10 10012 12600 7.6087 28.283 31950 19.293 71.717 26.90 100
N° DE PISOS Kg Kg/m2 % Kg Kg/m2 % Kg/m2 %
4 3082 5.5833 25.70 8910 16.141 74.30 21.725 1008 7088 6.420 29.323 17084 15.475 70.68 21.89 10012 11547 6.9728 27.962 29749 17.964 72.038 24.937 100
Z3S43.32
VIGAS COLUMNAS TOTAL
.50VIGAS COLUMNAS TOTAL
.00VIGAS COLUMNAS TOTAL
Tabla. 4.8 Consumo de acero para pórticos Z7S2
4
6R =
R =
R =
N° DE PISOS Kg Kg/m2 % Kg Kg/m2 % Kg/m2 %
4 4709 8.5308 26.967 12753 23.10 73.033 31.634 1008 10058 9.1105 28.938 24699 22.372 71.06 31.483 10012 19184 11.585 26.95 52001 31.40 73.051 42.986 100
N° DE PISOS Kg Kg/m2 % Kg Kg/m2 % Kg/m2 %
4 3875 7.0199 27.258 10341 18.734 72.74 25.754 1008 8285 7.5045 28.60 20682 18.734 71.40 26.238 10012 14829 8.9547 27.286 39517 23.863 72.714 32.818 100
N° DE PISOS Kg Kg/m2 % Kg Kg/m2 % Kg/m2 %
4 3480 6.3043 28.055 8924 16.167 71.945 22.471 1008 7196 6.5181 28.911 17694 16.027 71.09 22.545 10012 12846 7.757 27.748 33450 20.199 72.25 27.957 100
Z7S23.32
VIGAS COLUMNAS TOTAL
.50VIGAS COLUMNAS TOTAL
.00VIGAS COLUMNAS TOTAL
4
6R =
R =
R =
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Tabla. 4.9 Consumo de acero para pórticos Z7S4
N° DE PISOS Kg Kg/m2 % Kg Kg/m2 % Kg/m2 %
4 4532 8.2101 22.11 15963 28.918 77.887 37.129 1008 15984 14.478 24.121 50281 45.544 75.88 60.023 10012 31807 19.207 28.35 80388 48.543 71.65 67.751 100
N° DE PISOS Kg Kg/m2 % Kg Kg/m2 % Kg/m2 %
4 4164 7.5435 25.10 12425 22.509 74.899 30.053 1008 12749 11.548 28.73 31628 28.649 71.27 40.197 10012 19773 11.94 27.676 51672 31.20 72.324 43.143 100
N° DE PISOS Kg Kg/m2 % Kg Kg/m2 % Kg/m2 %
4 3768 6.8261 25.50 11008 19.942 74.50 26.768 1008 10254 9.288 32.17 21617 19.581 67.83 28.869 10012 17066 10.306 29.163 41453 25.032 70.837 35.338 100
Z7S43.32
VIGAS COLUMNAS TOTAL
VIGAS COLUMNAS TOTAL
VIGAS COLUMNAS TOTAL
Gráficos comparativos:
Consumo de concreto total:
Fig. 4.1 Consumo de concreto total para pórticos Z3S2
4.50
6.00
R =
R =
R =
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
3.00 4.00 5.00
R
(m3/m
2 )
6.00
`
12 pisos4 pisos
8 pisos
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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118
Fig. 4.2 Consumo de concreto total para pórticos Z3S4
Fig. 4.3 Consumo de concreto total para pórticos Z7S2
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
3.00 4.00 5.00
R
(m3/m
2 )
6.00
`
12 pisos
4 pisos
8 pisos
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
3.00 4.00 5.00
R
(m3/m
2 )
6.00
`
12 pisos
4 pisos
8 pisos
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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119
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
3.00 4.00 5.00
R
(m3 /m
2 )
6.00
`
12 pisos
4 pisos
8 pisos
Fig. 4.4 Consumo de concreto total para pórticos Z7S4
Consumo de acero total:
Fig. 4.5 Consumo de acero total para pórticos Z3S2
20
25
30
35
40
45
50
55
60
65
70
3.00 4.00 5.00
R
Kg
/m2
6.00
`
12 pisos4 pisos
8 pisos
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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120
Fig. 4.6 Consumo de acero total para pórticos Z3S4
Fig. 4.7 Consumo de acero total para pórticos Z7S2
20
25
30
35
40
45
50
55
60
65
70
3.00 4.00 5.00
R
Kg
/m2
6.00
`
12 pisos8 pisos
4 pisos
20
25
30
35
40
45
50
55
60
65
70
3.00 4.00 5.00
R
Kg
/m2
6.00
`12 pisos
8 pisos
4 pisos
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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20
25
30
35
40
45
50
55
60
65
70
3.00 4.00 5.00 6.00
R
Kg
/m2
`
12 pisos
8 pisos
4 pisos
Fig. 4.8 Consumo de acero total para pórticos Z7S4
Tabla. 4.10 Porcentaje de Variación en Costos con respecto a R = 6.00
CONSUMO % CONSUMO % CONSUMO %
CONCRETO ACERO VARIAC. CONCRETO ACERO VARIAC. CONCRETO ACERO VARIAC. (m3/m2) Kg/m2
COSTOS (m3/m2) Kg/m2COSTOS (m3/m2) Kg/m2
COSTOS
4 0.0690 20.4257 1.00 0.0710 20.8134 1.02 0.0763 21.3261 1.07
8 0.0691 20.8596 1.00 0.0711 21.6504 1.03 0.0728 21.6748 1.0412 0.0790 23.1546 1.00 0.0836 22.9118 1.01 0.0886 24.8370 1.09
4 0.0724 21.7246 1.00 0.0760 22.0598 1.03 0.0860 24.8134 1.16
8 0.0804 21.8949 1.00 0.0882 24.1033 1.10 0.0954 27.5136 1.2312 0.0850 24.9372 1.00 0.0940 26.9022 1.09 0.1012 29.4577 1.18
4 0.0802 22.4710 1.00 0.0886 25.7536 1.13 0.1043 31.6341 1.37
8 0.0831 22.5453 1.00 0.0907 26.2382 1.14 0.1077 31.4828 1.3612 0.0955 27.9565 1.00 0.1163 32.8176 1.19 0.1370 42.9861 1.50
4 0.0920 26.7681 1.00 0.1016 30.0525 1.12 0.1157 37.1286 1.34
8 0.1340 28.8687 1.00 0.1340 40.1966 1.22 0.1650 60.0226 1.71
12 0.1425 35.3376 1.00 0.1425 43.1431 1.13 0.2133 67.7506 1.75
m3 CONCRETO 13 UTKg ACERO 0.08 UT
Z3S4
Z7S4
Z7S2
Z3S2
PISOS
" R "
6.00 4.50 3.32
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Fig. 4.9 Porcentaje de Variación en costos para Z3S2
Fig. 4.10 Porcentaje de Variación en costos para Z3S4
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
3.00 4.00 5.00
S
6.00
% V
AR
IAC
ION
EN
CO
ST
O
R
`
12 pisos8 pisos
4 pisos
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
3.00 4.00 5.00
S
6.00
% V
AR
IAC
ION
EN
CO
ST
O
R
`
12 pisos 8 pisos
4 pisos
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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Fig. 4.11 Porcentaje de Variación en costos para Z7S2
Fig. 4.12 Porcentaje de Variación en costos para Z7S4
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
3.00 4.00 5.00
S
6.00
% V
AR
IAC
ION
EN
CO
ST
O
R
`12 pisos
4 pisos
8 pisos
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
3.00 4.00 5.00 6.00
% V
AR
IAC
ION
EN
CO
ST
OS
R
`
12 pisos
8 pisos4 pisos
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4.2.2 Desplazamientos y derivas
Pórticos de 4 pisos:
Tabla. 4.11 Desplazamientos y Derivas 4P-Z3S2.
COVENIN PORTAL COVENIN PORTAL
e(x)*0.8*R i
4 10.49 10.00 0.0040 0.0012 0.0183 9.06 9.58 0.0061 0.0023 0.0182 6.85 8.74 0.0082 0.0050 0.0181 3.90 6.93 0.0082 0.0146 0.018
0.00 0.00 0.0000 0.0000 0.018
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
4 11.124 10.350 0.0041 0.0008 0.0183 9.648 10.060 0.0067 0.0028 0.0182 7.236 9.040 0.0091 0.0054 0.0181 3.960 7.110 0.0083 0.0150 0.018
0.00 0.00 0.0000 0.0000 0.018
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
4 11.568 9.920 0.0040 0.0014 0.0183 10.128 9.410 0.0071 0.0033 0.0182 7.584 8.210 0.0093 0.0063 0.0181 4.224 5.940 0.0089 0.0125 0.018
0.00 0.00 0.0000 0.0000 0.018
PisoDESPLAZAM.
Pisoδx/(hi-h(i-1))
Piso
Desplazamientos y derivas del portico "B" según X para 4P-Z3-S2 R=3.32
Desplazamientos y derivas del portico "B" según X para 4P-Z3-S2 R=4.50
DESPLAZAM. DERIVASDeriva limite
DERIVASDeriva limite
δx/(hi-h(i-1))
4P-Z3-S2R=3.32
R=4.50
R=6.00
DESPLAZAM. DERIVAS
Deriva limite
δx/(hi-h(i-1))
Desplazamientos y derivas del portico "B" según X para 4P-Z3-S2 R=6.00
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125
Tabla. 4.12 Desplazamientos y Derivas 4P-Z3S4.
COVENIN PORTAL COVENIN PORTAL
e(x)*0.8*R i
4 11.90 12.51 0.0051 0.0019 0.0183 10.07 11.81 0.0075 0.0042 0.0182 7.38 10.29 0.0100 0.0129 0.0181 3.77 5.66 0.0079 0.0119 0.018
0.00 0.00 0.0000 0.0000 0.018
COVENIN PORTAL COVENIN PORTAL
e(x)*0.8*R i
4 15.264 16.470 0.0058 0.0018 0.0183 13.176 15.820 0.0087 0.0033 0.0182 10.044 14.620 0.0122 0.0123 0.0181 5.652 10.180 0.0119 0.0214 0.018
0.00 0.00 0.0000 0.0000 0.018
COVENIN PORTAL COVENIN PORTAL
e(x)*0.8*R i
4 15.984 15.110 0.0061 0.0014 0.0183 13.776 14.600 0.0092 0.0021 0.0182 10.464 13.850 0.0125 0.0038 0.0181 5.952 12.500 0.0125 0.0263 0.018
0.00 0.00 0.0000 0.0000 0.018
4P-Z3-S4R=3.32
Desplazamientos y derivas del portico "B" según X para 4P-Z3-S4 R=3.32
R=4.50
Desplazamientos y derivas del portico "B" según X para 4P-Z3-S4 R=4.50
R=6.00
Piso
DESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
Piso
DESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
Piso
DESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
Desplazamientos y derivas del portico "B" según X para 4P-Z3-S4 R=6.00
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126
Tabla. 4.13 Desplazamientos y Derivas 4P-Z7S2.
COVENIN PORTAL COVENIN PORTAL
e(x)*0.8*R i
4 16.73 15.12 0.0080 0.0061 0.0183 13.84 12.91 0.0108 0.0095 0.0182 9.93 9.49 0.0141 0.0131 0.0181 4.86 4.79 0.0102 0.0101 0.018
0.00 0.00 0.0000 0.0000 0.018
COVENIN PORTAL COVENIN PORTAL
e(x)*0.8*R i
4 19.476 13.460 0.0080 0.0019 0.0183 16.596 12.790 0.0119 0.0048 0.0182 12.312 11.060 0.0158 0.0128 0.0181 6.624 6.440 0.0139 0.0136 0.018
0.00 0.00 0.0000 0.0000 0.018
COVENIN PORTAL COVENIN PORTAL
e(x)*0.8*R i
4 22.080 15.860 0.0084 0.0018 0.0183 19.056 15.220 0.0127 0.0038 0.0182 14.496 13.860 0.0172 0.0082 0.0181 8.304 10.920 0.0175 0.0230 0.018
0.00 0.00 0.0000 0.0000 0.018
4P-Z7-S2R=3.32
R=4.50
R=6.00
Desplazamientos y derivas del portico "B" según X para 4P-Z7-S2 R=3.32
Desplazamientos y derivas del portico "B" según X para 4P-Z7-S2 R=4.50
δx/(hi-h(i-1))
Piso
DESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
Piso
DESPLAZAM. DERIVAS
Deriva limite
Piso
DESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
Desplazamientos y derivas del portico "B" según X para 4P-Z7-S2 R=6.00
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Tabla. 4.14 Desplazamientos y Derivas 4P-Z7S4.
COVENIN PORTAL COVENIN PORTAL
e(x)*0.8*R i
4 14.24 11.92 0.0082 0.0031 0.0183 11.29 10.82 0.0105 0.0123 0.0182 7.52 6.40 0.0117 0.0109 0.0181 3.32 2.47 0.0070 0.0052 0.018
0.00 0.00 0.0000 0.0000 0.018
COVENIN PORTAL COVENIN PORTAL
e(x)*0.8*R i
4 18.144 20.230 0.0093 0.0029 0.0183 14.796 19.190 0.0120 0.0100 0.0182 10.476 15.590 0.0156 0.0196 0.0181 4.860 8.530 0.0102 0.0180 0.018
0.00 0.00 0.0000 0.0000 0.018
COVENIN PORTAL COVENIN PORTAL
e(x)*0.8*R i
4 22.080 31.320 0.0101 0.0031 0.0183 18.432 30.190 0.0145 0.0108 0.0182 13.200 26.310 0.0180 0.0255 0.0181 6.720 17.120 0.0141 0.0360 0.018
0.00 0.00 0.0000 0.0000 0.018
4P-Z7-S4R=3.32
Desplazamientos y derivas del portico "B" según X para 4P-Z7-S4 R=3.32
R=4.50
Desplazamientos y derivas del portico "B" según X para 4P-Z7-S4 R=4.50
R=6.00
Piso
DESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
Piso
DESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
Piso
DESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
Desplazamientos y derivas del portico "B" según X para 4P-Z7-S4 R=6.00
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128
Pórticos de 8 pisos:
Tabla. 4.15 Desplazamientos y Derivas 8P-Z3S2
COVENIN PORTAL COVENIN PORTAL
e(x)*0.8*R i
8 16.892 13.730 0.0021 0.0032 0.0187 16.148 12.570 0.0035 0.0068 0.0186 14.874 10.140 0.0051 0.0091 0.0185 13.041 6.860 0.0059 0.0057 0.0184 10.916 4.800 0.0069 0.0045 0.0183 8.420 3.170 0.0073 0.0036 0.0182 5.790 1.890 0.0075 0.0028 0.0181 3.081 0.880 0.0065 0.0019 0.018
0.000 0.000 0.0000 0.0000 0.018
COVENIN PORTAL COVENIN PORTAL
e(x)*0.8*R i
8 16.668 13.010 0.002 0.0012 0.0187 15.948 12.590 0.003 0.0019 0.0186 14.688 11.910 0.005 0.0027 0.0185 12.888 10.950 0.006 0.0035 0.0184 10.728 9.690 0.007 0.0041 0.0183 8.352 8.210 0.007 0.0057 0.0182 5.760 6.150 0.008 0.0076 0.0181 2.988 3.400 0.006 0.0072 0.018
0.000 0.000 0.0000 0.018
COVENIN PORTAL COVENIN PORTAL
e(x)*0.8*R i
8 16.464 16.420 0.002 0.0016 0.0187 15.600 15.830 0.003 0.0021 0.0186 14.352 15.060 0.005 0.0028 0.0185 12.624 14.070 0.006 0.0042 0.0184 10.608 12.550 0.006 0.0057 0.0183 8.352 10.510 0.007 0.0082 0.0182 5.712 7.570 0.008 0.0096 0.0181 2.928 4.120 0.006 0.0087 0.018
0.000 0.000 0.0000 0.018
Desplazamientos y derivas del portico "B" según X para 8P-Z3-S2 R=3.32
Desplazamientos y derivas del portico "B" según X para 8P-Z3-S2 R=4.50
Piso
DESPLAZAM.
DERIVAS
Deriva limiteδx/(hi-h(i-1))
DERIVAS
Deriva limiteδx/(hi-h(i-1))
R=6.00
8P-Z3-S2R=3.32
Piso
DESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
R=4.50
Piso
DESPLAZAM.
Desplazamientos y derivas del portico "B" según X para 8P-Z3-S2 R=6.00
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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129
Tabla. 4.16 Desplazamientos y Derivas 8P-Z3S4.
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
8 29.296 21.650 0.0044 0.0020 0.0187 27.729 20.930 0.0066 0.0038 0.0186 25.338 19.570 0.0094 0.0071 0.0185 21.965 17.030 0.0110 0.0096 0.0184 18.008 13.590 0.0121 0.0108 0.0183 13.652 9.710 0.0131 0.0106 0.0182 8.924 5.900 0.0128 0.0089 0.0181 4.303 2.680 0.0091 0.0056 0.018
0.000 0.000 0.0000 0.0000 0.018
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
8 33.012 21.970 0.005 0.0020 0.0187 31.284 21.260 0.007 0.0031 0.0186 28.656 20.130 0.010 0.0049 0.0185 25.056 18.370 0.012 0.0062 0.0184 20.844 16.130 0.013 0.0078 0.0183 16.056 13.320 0.014 0.0098 0.0182 11.016 9.800 0.015 0.0124 0.0181 5.760 5.340 0.012 0.0112 0.018
0.000 0.000 0.000 0.0000 0.018
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
8 36.288 32.740 0.005 0.0013 0.0187 34.560 32.270 0.008 0.0020 0.0186 31.728 31.540 0.011 0.0024 0.0185 27.840 30.690 0.013 0.0041 0.0184 22.992 29.200 0.014 0.0068 0.0183 17.808 26.740 0.016 0.0137 0.0182 12.048 21.810 0.016 0.0230 0.0181 6.192 13.520 0.013 0.0285 0.018
R=6.00
8P-Z3-S4R=3.32
Desplazamientos y derivas del portico "B" según X para 8P-Z3-S4 R=3.32
Desplazamientos y derivas del portico "B" según X para 8P-Z3-S4 R=4.50
R=4.50
PisoDESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
PisoDESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
PisoDESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
0.000 0.000 0.000 0.0000 0.018
Desplazamientos y derivas del portico "B" según X para 8P-Z3-S4 R=6.00
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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130
Tabla. 4.17 Desplazamientos y Derivas 8P-Z7S2.
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
8 31.686 22.940 0.0055 0.0019 0.0187 29.694 22.260 0.0075 0.0037 0.0186 26.985 20.930 0.0097 0.0079 0.0185 23.479 18.070 0.0122 0.0153 0.0184 19.097 12.550 0.0131 0.0115 0.0183 14.396 8.420 0.0142 0.0089 0.0182 9.269 5.210 0.0136 0.0074 0.0181 4.382 2.550 0.0092 0.0054 0.018
0.000 0.000 0.0000 0.0000 0.018
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
8 36.756 26.340 0.005 0.0013 0.0187 34.812 25.860 0.008 0.0038 0.0186 31.932 24.490 0.011 0.0088 0.0185 28.080 21.320 0.014 0.0151 0.0184 23.148 15.880 0.014 0.0123 0.0183 17.964 11.440 0.016 0.0106 0.0182 12.384 7.620 0.017 0.0100 0.0181 6.444 4.030 0.014 0.0085 0.018
0.000 0.000 0.000 0.0000 0.018
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
8 38.784 27.260 0.005 0.0016 0.0187 36.960 26.700 0.008 0.0023 0.0186 34.128 25.890 0.011 0.0035 0.0185 30.000 24.620 0.014 0.0049 0.0184 24.816 22.850 0.015 0.0080 0.0183 19.296 19.980 0.017 0.0125 0.018
R=6.00
8P-Z7-S2R=3.32
Desplazamientos y derivas del portico "B" según X para 8P-Z7-S2 R=3.32
Desplazamientos y derivas del portico "B" según X para 8P-Z7-S2 R=4.50
R=4.50
PisoDESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
PisoDESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
PisoDESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
2 13.296 15.480 0.017 0.0180 0.0181 7.056 8.990 0.015 0.0189 0.018
0.000 0.000 0.000 0.0000 0.018
Desplazamientos y derivas del portico "B" según X para 8P-Z7-S2 R=6.00
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
131
Tabla. 4.18 Desplazamientos y Derivas 8P-Z7S4.
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS
132
Ing. Ada Moreno LA UNIVERSIDAD DEL ZULIA
Pórticos de 12 pisos:
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
.900 32.150 0.0073 0.0034 0.0187 32.270 30.930 0.0085 0.0050 0.018
0.0180.018
4 19.575 20.700 0.0170 0.0178 0.0183 13.466 14.280 0.0156 0.0154 0.0182 7.862 8.750 0.0130 0.0129 0.0181 3.187 4.120 0.0067 0.0087 0.018
0.000 0.000 0.0000 0.0000 0.018
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R
8 34
6 29.216 29.130 0.0117 0.00915 24.993 25.840 0.0151 0.0143
i8 39.492 39.810 0.007 0.0025 0.0187 36.936 38.910 0.009 0.0042 0.0186 33.840 37.390 0.012 0.0108 0.0185 29.412 33.510 0.015 0.0150 0.0184 23.976 28.110 0.018 0.0199 0.0183 17.676 20.950 0.018 0.0211 0.0182 11.196 13.340 0.018 0.0184 0.0181 4.860 6.710 0.010 0.0141 0.018
0.000 0.000 0.000 0.0000 0.018
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R
i8 39.504 37.140 0.007 0.0012 0.0187 36.912 36.710 0.009 0.0018 0.0186 33.840 36.070 0.012 0.0037 0.0185 29.424 34.750 0.015 0.0114 0.0184 23.952 30.640 0.017 0.0198 0.0183 17.664 23.520 0.018 0.0224 0.0182 11.232 15.470 0.018 0.0206 0.0181 4.848 8.050 0.010 0.0169 0.018
0.000 0.000 0.000 0.0000 0.018
Desplazamientos y derivas del portico "B" según X para 8P-Z7-S4 R=6.00
Desplazamientos y derivas del portico "B" según X para 8P-Z7-S4 R=4.50
R=6.00
PisoDESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
R=4.50
Desplazamientos y derivas del portico "B" según X para 8P-Z7-S4 R=3.32
PisoDESPLAZAM. DERIVAS
Deriva limiteδx/(hi-h(i-1))
R=3.328P-Z7-S4
DERIVAS
δx/(hi-h(i-1))
DESPLAZAM.Deriva limitePiso
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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133
Tabla. 4.19 Desplazamientos y Derivas 12P-Z3S2
Tabla. 4.20 Desplazamientos y Derivas 12P-Z3S4
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
12 30.810 20.000 0.00258 0.00186 0.01811 29.880 19.330 0.00384 0.00225 0.01810 28.499 18.520 0.00561 0.00239 0.0189 26.480 17.660 0.00649 0.00433 0.0188 24.143 16.100 0.00738 0.00525 0.0187 21.487 14.210 0.00834 0.00619 0.0186 18.486 11.980 0.00819 0.00625 0.0185 15.538 9.730 0.00863 0.00594 0.0184 12.430 7.590 0.00885 0.00594 0.0183 9.243 5.450 0.00930 0.00611 0.0182 5.896 3.250 0.00856 0.00508 0.0181 2.815 1.420 0.00593 0.00299 0.018
0.000 0.000 0.00000 0.00000 0.018
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
12 33.480 15.040 0.00270 0.00044 0.01811 32.508 14.880 0.00420 0.00092 0.01810 30.996 14.550 0.00590 0.00175 0.0189 28.872 13.920 0.00680 0.00167 0.0188 26.424 13.320 0.00770 0.00206 0.0187 23.652 12.580 0.00890 0.00414 0.0186 20.448 11.090 0.00910 0.00514 0.0185 17.172 9.240 0.00960 0.00514 0.0184 13.716 7.390 0.00990 0.00519 0.0183 10.152 5.520 0.01010 0.00519 0.0182 6.516 3.650 0.00960 0.00503 0.0181 3.060 1.840 0.00644 0.00387 0.018
0.000 0.000 0.00000 0.00000 0.018
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
12 33.744 17.090 0.00293 0.00208 0.01811 32.688 16.340 0.00387 0.00311 0.01810 31.296 15.220 0.00600 0.00333 0.0189 29.136 14.020 0.00693 0.00322 0.0188 26.640 12.860 0.00800 0.00342 0.0187 23.760 11.630 0.00867 0.00372 0.0186 20.640 10.290 0.00973 0.00483 0.0185 17.136 8.550 0.00960 0.00544 0.0184 13.680 6.590 0.01040 0.00550 0.0183 9.936 4.610 0.01000 0.00467 0.0182 6.336 2.930 0.00947 0.00436 0.0181 2.928 1.360 0.00616 0.00286 0.018
0.000 0.000 0.00000 0.00000 0.018
Desplazamientos y derivas del portico "B" según X para 12P-Z3-S2 R=6.00
Desplazamientos y derivas del portico "B" según X para 12P-Z3-S2 R=4.5
PisoDESPLAZAM. DERIVAS
Deriva limδx/(hi-hi-1)
R=6.00
Desplazamientos y derivas del portico "B" según X para 12P-Z3-S2 R=3.32
PisoDESPLAZAM. DERIVAS
Deriva limδx/(hi-hi-1)
R=4.50
Deriva limδx/(hi-hi-1)
ite
ite
iteDERIVAS
PisoDESPLAZAM.
12P-Z3-S2R=3.32
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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134
DESPLAZAM. DERIVASR=3.32
Tabla. 4.21 Desplazamientos y Derivas 12P-Z7S2 Tabla. 4.21 Desplazamientos y Derivas 12P-Z7S2
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
12 41.195 27.740 0.00362 0.00128 0.01811 39.893 27.280 0.00539 0.00236 0.01810 37.954 26.430 0.00716 0.00294 0.0189 35.378 25.370 0.00893 0.00367 0.0188 32.164 24.050 0.00944 0.00361 0.0187 28.764 22.750 0.01085 0.00486 0.0186 24.860 21.000 0.01203 0.00781 0.0185 20.531 18.190 0.01247 0.01125 0.0184 16.042 14.140 0.01254 0.01269 0.0183 11.527 9.570 0.01180 0.01150 0.0182 7.277 5.430 0.01121 0.00906 0.0181 3.240 2.170 0.00682 0.00457 0.018
0.000 0.000 0.00000 0.00000 0.018
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
12 49.716 37.360 0.00430 0.00117 0.01811 48.168 36.940 0.00650 0.00161 0.01810 45.828 36.360 0.00810 0.00256 0.0189 42.912 35.440 0.01030 0.00447 0.0188 39.204 33.830 0.01170 0.00594 0.0187 34.992 31.690 0.01260 0.00786 0.0186 30.456 28.860 0.01390 0.01164 0.0185 25.452 24.670 0.01400 0.01400 0.0184 20.412 19.630 0.01480 0.01569 0.0183 15.084 13.980 0.01490 0.01517 0.0182 9.720 8.520 0.01420 0.01308 0.0181 4.608 3.810 0.00970 0.00802 0.018
0.000 0.000 0.00000 0.00000 0.018
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
12 58.368 48.830 0.00440 0.00194 0.01811 56.784 48.130 0.00720 0.00219 0.01810 54.192 47.340 0.01000 0.00619 0.0189 50.592 45.110 0.01213 0.00903 0.0188 46.224 41.860 0.01360 0.01325 0.0187 41.328 37.090 0.01547 0.01661 0.0186 35.760 31.110 0.01640 0.01700 0.0185 29.856 24.990 0.01760 0.01767 0.0184 23.520 18.630 0.01787 0.01642 0.0183 17.088 12.720 0.01720 0.01383 0.0182 10.896 7.740 0.01640 0.01175 0.0181 4.992 3.510 0.01051 0.00739 0.018
0.000 0.000 0.00000 0.00000 0.018
Desplazamientos y derivas del portico "B" según X para 12P-Z3-S4 R=3.32
Desplazamientos y derivas del portico "B" según X para 12P-Z3-S4 R=4.50
R=4.50
PisoDESPLAZAM. DERIVAS
Deriva limiteδx/(hi-hi-1)
R=6.00
Desplazamientos y derivas del portico "B" según X para 12P-Z3-S4 R=6.00
PisoDESPLAZAM. DERIVAS
Deriva limiteδx/(hi-hi-1)
Piso Deriva limiteδx/(hi-hi-1)
12P-Z3-S4
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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135
12P-Z7-S2
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R i
12 38.326 28.430 0.00376 0.00119 0.01811 36.972 28.000 0.00487 0.00233 0.01810 35.219 27.160 0.00694 0.00678 0.0189 32.722 24.720 0.00812 0.00939 0.0188 29.800 21.340 0.00959 0.01144 0.0187 26.348 17.220 0.00996 0.01072 0.0186 22.762 135 18.778 9.
4.2.2.1 Graficas comparativas de desplazamientos y derivas según diseño y análisis
inelástico.
.360 0.01107 0.00972 0.018860 0.01114 0.00778 0.018
4 14.767 7.060 0.01136 0.00672 0.01810.677 4.640 0.01107 0.00553 0.0186.693 2.650 0.01033 0.00431 0.018
1 2.975 1.100 0.00626 0.00232 0.0180.000 0.000 0.00000 0.00000 0.018
COVENIN PORTAL COVENIN PORTALe(x)*0.8*R
32
i12 45.360 29.250 0.00430 0.00142 0.01811 43.812 28.740 0.00620 0.00367 0.01810 41.580 27.420 0.00860 0.00975 0.0189 38.484 23.910 0.00960 0.00928 0.0188 35.028 20.570 0.01090 0.00808 0.0187 31.104 17.660 0.01200 0.00669 0.0186 26.784 15.250 0.01270 0.00667 0.0185 22.212 12.850 0.01290 0.00728 0.0184 17.568 10.230 0.01310 0.00797 0.0183 12.852 7.360 0.01300 0.00797 0.0182 8.172 4.490 0.01220 0.00692 0.0181 3.780 2.000 0.00796 0.00421 0.018
0.000 0.000 0.00000 0.00000 0.018
e(x)*0.8*RCOVENIN PORTAL COVENIN PORTAL
i12 57.552 35.160 0.00533 0.00214 0.01811 55.632 34.390 0.00733 0.00439 0.01810 52.992 32.810 0.00987 0.00603 0.0189 49.440 30.640 0.01147 0.00503 0.0188 45.312 28.830 0.01293 0.00525 0.0187 40.656 26.940 0.01467 0.00622 0.0186 35.376 24.700 0.01573 0.00847 0.0185 29.712 21.650 0.01640 0.01117 0.0184 23.808 17.630 0.01773 0.01331 0.0183 17.424 12.840 0.01733 0.01322 0.0182 11.184 8.080 0.01693 0.01217 0.0181 5.088 3.700 0.01071 0.00779 0.018
0.000 0.000 0.00000 0.00000 0.018
DESPLAZAM. DERIVASR=3.32
Desplazamientos y derivas del portico "B" según X para 12P-Z7-S2 R=4.50
Deriva limiteδx/(hi-hi-1)
R=6.00
esplazamientos y derivas del portico "B" según X para 12P-Z7-S2 R=3.32
PisoDESPLAZAM. DERIVAS
Deriva limiteδx/(hi-hi-1)
R=4.50
Desplazamientos y derivas del portico "B" según X para 12P-Z7-S2 R=6.00
Deriva limiteδx/(hi-hi-1)
Piso
PisoDESPLAZAM. DERIVAS
D
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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136
En las siguientes figuras se presenta una comparación de los desplazamientos y derivas
alculados en la etapa de diseño según especifica la Norma COVENIN 1756-2001, y los
obtenidos en el análisis inelástico con el programa PORTAL DE DAÑOS. Es importante
encionar que en la etapa de diseño se respeto para todos los pórticos los requerimientos de
eriva máxima permisible de 0.018.
Pórticos de 4 pisos:
c
m
d
Desplazamientos
Fig. 4.13 Desplazamientos 4P-Z3S2
Fig. 4.14 Desplazamientos 4P-Z3S4
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(4P-Z3-S2) EN LA DIRECCIÓN X
0
2
4
6
8
10
12
14
16
18
0.00 3.00 6.00 9.00 12.00 15.00 18.00 21.00 24.00 27.00 30.00
DESPLAZAMIENTOS EN X. PORTAL DE DAÑOS (cms)
H (
m)
R=3.32 R=4.50 R=6.00
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(4P-Z3-S2) EN LA DIRECCIÓN X
0
2
4
6
8
10
12
18
0.00 3.00 6.00 9.00 12.00 15.00 18.00 21.00 24.00 27.00 30.00
DESPLAZAMIENTOS EN X. COVENIN . (cms)
H (
m)
14
16
R=3.32 R=4.50 R=6.00
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(4P-Z3-S4) EN LA DIRECCIÓN X
0
2
4
6
8
10
12
14
16
18
0.00 3.00 6.00 9.00 12.00 15.00 18.00 21.00 24.00 27.00 30.00
DESPLAZAMIENTOS EN X. PORTAL DE DAÑOS. (cms)
H (
m)
R=3.32 R=4.50 R=6.00
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(4P-Z3-S4) EN LA DIRECCIÓN X
4
6
8
10
12
14
16
18
0. 3.00 6.00 9.00 12.00 15.00 18.00 21.00 24.00 27.00 30.00
DESPLAZAMIENTOS EN X. COVENIN (cms)
H (
m)
0
2
00
R=3.32 R=4.50 R=6.00
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COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(4P-Z7-S2) EN LA DIRECCIÓN X
0
2
4
6
8
10
12
14
16
18
0.00 3.00 6.00 9.00 12.00 15.00 18.00 21.00 24.00 27.00 30.00
DESPLAZAMIENTOS EN X. PORTAL DE DAÑOS (cms)
H (
m)
R=3.32 R=4.50 R=6.00
Fig. 4.15 Desplazamientos 4P-Z7S2
Fig. 4.16 Desplazamientos 4P-Z7S4
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(4P-Z7-S2) EN LA DIRECCIÓN X
0
2
4
6
8
10
12
14
16
18
0.00 3.00 6.00 9.00 12.00 15.00 18.00 21.00 24.00 27.00 30.00
DESPLAZAMIENTOS EN X. COVENIN (cms)
H (
m)
R=3.32 R=4.50 R=6.00
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(4P-Z7-S4) EN LA DIRECCIÓN X
0
2
4
6
8
10
12
14
16
18
0.00 3.00 6.00 9.00 12.00 15.00 18.00 21.00 24.00 27.00 30.00
DESPLAZAMIENTOS EN X. PORTAL DE DAÑOS (cms)
H (
m)
R=3.32 R=4.50 R=6.00
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(4P-Z7-S4) EN LA DIRECCIÓN X
3.00 6.00 9.00 12.00 15.00 18.00 21.00 24.00 27.00 30.00
DESPLAZAMIENTOS EN X. COVENIN (cms)
0
2
4
6
8
10
12
14
16
18
0.00
H (
m)
R=3.32 R=4.50 R=6.00
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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Pórticos de 8 pisos:
17 Desplazamientos 8P-Z3S2
Fig. 4.18 Desplazamientos 8P-Z3S4
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(8P-Z3-S2) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00
DESPLAZAMIENTOS EN X. PORTAL DE DAÑOS (cms)
H (
m)
R=3.32 R=4.50 R=6.00
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(8P-Z3-S2) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00
DESPLAZAMIENTOS EN X. COVENIN (cms)
H (
Fig. 4.
m)
R=3.32 R=4.50 R=6.00
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(8P-Z3-S4) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00
DESPLAZAMIENTOS EN X. PORTAL DE DAÑOS (cms)
H (
m)
R=3.32 R=4.50 R=6.00
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(8P-Z3-S4) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00
DESPLAZAMIENTOS EN X. COVENIN (cms)
H (
m)
R=3.32 R=4.50 R=6.00
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(8P-Z7-S2) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00
DESPLAZAMIENTOS EN X. PORTAL DE DAÑOS (cms)
H (
m)
R=3.32 R=4.50 R=6.00
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(8P-Z7-S2) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00
DESPLAZAMIENTOS EN X. COVENIN (cms)
H (
m)
Fig. 4.19 Desplazamientos 8P-Z7S2
Fig. 4.20 Desplazamientos 8P-Z7S4
R=3.32 R=4.50 R=6.00
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(8P-Z7-S4) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00
DESPLAZAMIENTOS EN X. PORTAL DE DAÑOS (cms)
H (
m)
R=3.32 R=4.50 R=6.00
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(8P-Z7-S4) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00
DESPLAZAMIENTOS EN X. COVENIN (cms)
H (
m)
R=3.32 R=4.50 R=6.00
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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Pórticos de 12 pisos:
Fig. 4.21 Desplazamientos 12P-Z3S2
Fig. 4.22 Desplazamientos 12P-Z3S4
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(12P-Z3-S2) EN LA DIRECCIÓN X
0369
121518212427303336394245
0.00 6.00 12.00 18.00 24.00 30.00 36.00 42.00 48.00 54.00 60.00
DESPLAZAMIENTOS EN X. PORTAL DE DAÑOS (cms)
H (
m)
R=3.32 R=4.50 R=6.00
`
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(12P-Z3-S2) EN LA DIRECCIÓN X
0369
121518212427303336394245
0.00 6.00 12.00 18.00 24.00 30.00 36.00 42.00 48.00 54.00 60.00
DESPLAZAMIENTOS EN X. COVENIN (cms)
H (
m)
R=3.32 R=4.50 R=6.00
`
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(12P-Z3-S4) EN LA DIRECCIÓN X
0369
121518212427303336394245
0.00 6.00 12.00 18.00 24.00 30.00 36.00 42.00 48.00 54.00 60.00
DESPLAZAMIENTOS EN X. PORTAL DE DAÑOS (cms)
H (
m)
R=3.32 R=4.50 R=6.00
`̀
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(12P-Z3-S4) EN LA DIRECCIÓN X
0369
121518212427303336394245
0.00 6.00 12.00 18.00 24.00 30.00 36.00 42.00 48.00 54.00 60.00
DESPLAZAMIENTOS EN X. COVENIN (cms)
H (
m)
R=3.32 R=4.50 R=6.00
`̀
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
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COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(12P-Z7-S2) EN LA DIRECCIÓN X
0369
121518212427303336394245
0.00 6.00 12.00 18.00 24.00 30.00 36.00 42.00 48.00 54.00 60.00
DESPLAZAMIENTOS EN X. PORTAL DE DAÑOS ( cms)
H (
m)
R=3.32 R=4.50 R=6.00
`̀
COMPARACIÓN DE DESPLAZAMIENTOS DELPORTICO "B"(12P-Z7-S2) EN LA DIRECCIÓN X
0369
121518212427303336394245
0.00 6.00 12.00 18.00 24.00 30.00 36.00 42.00 48.00 54.00 60.00
DESPLAZAMIENTOS EN X. COVENIN ( cms)
H (
m)
R=3.32 R=4.50 R=6.00
`̀
ig. 4.24 Comparación de desplazamientos máximos para las diferentes alturas, en pórticos Z3S2 gún análisis inelástico.
Fig. 4.23 Desplazamientos 12P-Z7S2
8
9
10
11
12
13
14
15
16
17
18
19
20
21
3.00 4.00 5.00 6.00
R
cms
`
12 pisos
8 pisos
4 pisos
Fse
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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142
8
13
18
23
28
33
38
43
48
3.00 4.00 5.00 6.00
R
cms
`
12 pisos
8 pisos
4 pisos
Fig. 4.25 Comparación de desplazamientos máximos para las diferentes alturas, en pórticos Z3S4 según análisis inelástico.
8
13
18
23
28
33
38
43
48
3.00 4.00 5.00 6.00
R
cms
`
12 pisos
8 pisos
4 pisos
Fig. 4.26 Comparación de desplazamientos máximos para las diferentes alturas, en pórticos Z7S2 gún análisis inelástico. se
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
143
8
13
18
23
28
33
38
43
48
3.00 4.00 5.00 6.00
R
cms
`
8 pisos
4 pisos
Fse
ig. 4.27 Comparación de desplazamientos máximos para las diferentes alturas, en pórticos Z7S4 gún análisis inelástico.
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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144
Derivas:
órticos de 4 pisos:
P
Fig. 4.28 Derivas 4P-Z3S2
COMPARACIÓN DE DERIVAS DELPORTICO "B"(4P-Z3-S2) EN LA DIRECCIÓN X
0
2
4
6
8
10
12
14
16
18
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS . PORTAL DE DAÑOS.
H (
m)
R=3.32 R=4.50 R=6.00 DERIVA MAX. PERMISIBLE
COMPARACIÓN DE DERIVAS DELPORTICO "B"(4P-Z3-S2) EN LA DIRECCIÓN X
000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS COVENIN
0
2
4
6
8
10
12
14
16
18
0.
H (
m)
R=3.32 R=4.50 R=6.00 DERIVA MAX. PERMISIBLE
COMPARACIÓN DE DERIVAS DELPORTICO "B"(4P-Z3-S4) EN LA DIRECCIÓN X
0
2
4
6
8
10
12
14
16
18
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS PORTAL DE DAÑOS.
H (
m)
R=3.32 R=4.50 R=6.00 DERIVA MAX. PERMISIBLE
COMPARACIÓN DE DERIVAS DELPORTICO "B"(4P-Z3-S4) EN LA DIRECCIÓN X
0
2
4
6
8
10
12
14
16
18
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS COVENIN
H (
m)
R=3.32 R=4.50 R=6.00 DERIVA MAX. PERMISIBLE
Fig. 4.29 Derivas 4P-Z3S4
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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145
COMPARACIÓN DE DERIVAS DELPORTICO "B"(4P-Z7-S2) EN LA DIRECCIÓN X
0
2
4
6
8
10
12
14
16
18
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS PORTAL DE DAÑOS
H (
m)
R=3.32 R=4.50 R=6.00 DERIVA MAX. PERMISIBLE
COMPARACIÓN DE DERIVAS DELPORTICO "B"(4P-Z7-S2) EN LA DIRECCIÓN X
0
2
4
6
8
10
12
14
16
18
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS COVENIN
H (
m)
R=3.32 R=4.50 R=6.00 DERIVA MAX. PERMISIBLE
Fig. 4.30 Derivas 4P-Z7S2
COMPARACIÓN DE DERIVAS DELPORTICO "B"(4P-Z7-S4) EN LA DIRECCIÓN X
0
2
4
6
8
10
12
14
16
18
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS. PORTAL DE DAÑOS.
H (
m)
R=3.32 R=4.50 R=6.00 DERIVA MAXIMA
COMPARACIÓN DE DERIVAS DELPORTICO "B"(4P-Z7-S2) EN LA DIRECCIÓN X
0
2
4
6
8
10
12
14
16
18
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS COVENIN
H (
m)
R=3.32 R=4.50 R=6.00 DERIVA MAX. PERMISIBLE
Fig. 4.31 Derivas 4P-Z7S4
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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146
Porticos de 8 pisos:
Fig. 4.32 Derivas 8P-Z3S2
Fig. 4.33 Derivas 8P-Z3S4
COMPARACIÓN DE DERIVAS DELPORTICO "B"(8P-Z3-S2) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.000 0.005 0.010 0.015 0.020
DERIVAS. PORTAL DE DAÑOS.
H (
m)
R=3.32 R=4.50 R=6.00 "DERIVA MAX. PERMISIBLE"
COMPARACIÓN DE DERIVAS DELPORTICO "B"(8P-Z3-S2) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS. COVENIN
H (
m)
R=3.32 R=4.50 R=6.00 "DERIVA MAX. PERMISIBLE"
COMPARACIÓN DE DERIVAS DELPORTICO "B"(8P-Z3-S4) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS. PORTAL DE DAÑOS.
H (
m)
R=3.32 R=4.50 R=6.00 "DERIVA MAX. PERMISIBLE"
COMPARACIÓN DE DERIVAS DELPORTICO "B"(8P-Z3-S4) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS. COVENIN
H (
m)
R=3.32 R=4.50 R=6.00 "DERIVA MAX. PERMISIBLE"
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
147
COMPARACIÓN DE DERIVAS DELPORTICO "B"(8P-Z7-S2) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS. PORTAL DE DAÑOS.
H (
m)
R=3.32 R=4.50 R=6.00 "DERIVA MAX. PERMISIBLE"
COMPARACIÓN DE DERIVAS DELPORTICO "B"(8P-Z7-S2) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS. COVENIN
H (
m)
R=3.32 R=4.50 R=6.00 "DERIVA MAX. PERMISIBLE"
Fig. 4.34 Derivas 8P-Z7S2
COMPARACIÓN DE DERIVAS DELPORTICO "B"(8P-Z7-S4) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS. PORTAL DE DAÑOS.
H (
m)
R=3.32 R=4.50 R=6.00 "DERIVA MAX. PERMISIBLE"
COMPARACIÓN DE DERIVAS DELPORTICO "B"(8P-Z7-S4) EN LA DIRECCIÓN X
0
3
6
9
12
15
18
21
24
27
30
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS. COVENIN
H (
m)
R=3.32 R=4.50 R=6.00 "DERIVA MAX. PERMISIBLE"
Fig. 4.35 Derivas 8P-Z7S4
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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148
Porticos de 12 pisos:
Fig. 4.36 Derivas 12P-Z3S2
Fig. 4.37 Derivas 12P-Z3S4
COMPARACIÓN DE DERIVAS DELPORTICO "B"(12P-Z3-S2) EN LA DIRECCIÓN X
0369
121518212427303336394245
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS. PORTAL DE DAÑOS
H (
m)
R=3.32 R=4.50 R=6.00 DERIVA MAXIMA
COMPARACIÓN DE DERIVAS DELPORTICO "B"(12P-Z3-S2) EN LA DIRECCIÓN X
369
121518212427303336394245
DERIVAS. COVENIN
)
`̀
0
0.000 0.005 0.010 0.015 0.020
H (
m
R=3.32 R=4.50 R=6.00 DERIVA MAXIMA
`̀
COMPARACIÓN DE DERIVAS DELPORTICO "B"(12P-Z3-S4) EN LA DIRECCIÓN X
0369
121518212427303336394245
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS. PORTAL DE DAÑOS
H (
m)
R=3.32 R=4.50 R=6.00 DERIVA MAXIMA
COMPARACIÓN DE DERIVAS DELPORTICO "B"(12P-Z3-S4) EN LA DIRECCIÓN X
0369
121518212427303336394245
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
H (
m)
`̀
DERIVAS. COVENIN
R=3.32 R=4.50 R=6.00 DERIVA MAXIMA
`̀
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
149
COMPARACIÓN DE DERIVAS DELPORTICO "B"(12P-Z7-S2) EN LA DIRECCIÓN X
0369
121518212427303336394245
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS. PORTAL DE DAÑOS.H
(m
)
R=3.32 R=4.50 R=6.00 DERIVA MAXIMA
`̀
COMPARACIÓN DE DERIVAS DELPORTICO "B"(12P-Z7-S2) EN LA DIRECCIÓN X
0369
121518212427303336394245
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
DERIVAS. COVENIN
H (
m)
R=3.32 R=4.50 R=6.00 DERIVA MAXIMA
`̀
Fig. 4.38 Derivas 12P-Z7S2
ig. 4.39 Comparación de derivas máximas para las diferentes alturas, en pórticos Z3S2 según nálisis inelástico.
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
3.00 4.00 5.00
R
der
iva
max
ima
6.00
`
12 pisos
8 pisos
4 pisos
Fa
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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150
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
3.00 4.00 5.00 6.00
R
der
iva
max
ima
`
12 pisos
8 pisos
4 pisos
Fig. 4.40 Comparación de derivas máximas para las diferentes alturas, en pórticos Z3S4 según
ig. 4.41 Comparación de derivas máximas para las diferentes alturas, en pórticos Z7S2 según nálisis inelástico.
análisis inelástico.
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
3.00 4.00 5.00 6.00
R
der
iva
max
ima
`
12 pisos
8 pisos
4 pisos
Fa
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
151
0.04
Fa
ig. 4.42 Comparación de derivas máximas para las diferentes alturas, en pórticos Z7S4 según nálisis inelástico.
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0
3.00 4.00 5.00 6.00
R
der
iva
max
ima
`
4 pisos
8 pisos
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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152
4.2.3 Daños en extremos de miembros.
órticos de 4 pisos: P
Daños 4P-Z3S2. R = 4.50
0.04 0.02 0.02 0.03 0.01 0.040.03 0.05 0.07 0.05 0.06 0.01
0.1
1
0.1
3
0.0
6
0.0
8
0.0
6
0.0
9
0.1
1
0.1
3
0.1
2
0.1
0
0.0
7
0.0
7
0.0
8
0.0
6
0.1
1
0.1
0
0.08 0.06 0.05 0.07 0.04 0.120.13 0.11 0.16 0.12 0.15 0.08
0.1
9
0.2
0
0.1
6
0.2
1
0.1
5
0.2
1
0.1
6
0.2
3
0.1
3
0.2
4
0.1
4
0.1
5
0.1
4
0.1
5
0.2
3
0.1
2
0.19 0.11 0.11 0.11 0.12 0.190.17 0.17 0.17 0.17 0.17 0.16
0.35
0.15
0.32
0.28
0.33
0.27
0.17
0.33
0.14
0.27
0.21
0.19
0.19
0.22
0.32
0.09
0.23 0.28 0.26 0.27 0.27 0.240.20 0.17 0.18 0.18 0.18 0.19
0.42
0.37
0.45
0.51
0.45
0.50
0.33
0.46
0.4
5
0.4
6
0.5
6
0.5
1
0.5
5
0.5
1
0.5
0
0.3
9
0.56Max:
Fig. 4.43 Daños 4P-Z3S2. R = 3.32
0.04 0.01 0.02 0.01 0.01 0.020.01 0.03 0.03 0.04 0.03 0.02
0.1
0
0.0
9
0.0
5
0.0
4
0.0
5
0.0
5
0.1
2
0.0
9
0.0
9
0.0
9
0.0
4
0.0
5
0.0
4
0.0
5
0.0
8
0.1
0
0.08 0.03 0.04 0.04 0.04 0.070.07 0.09 0.09 0.10 0.09 0.08
0.2
4
0.2
2
0.1
9
0.2
2
0.1
9
0.2
2
0.2
1
0.2
4
0.1
3
0.2
9
0.1
2
0.1
2
0.1
2
0.1
2
0.2
5
0.1
3
0.18 0.13 0.10 0.12 0.11 0.180.16 0.17 0.17 0.17 0.17 0.17
0.37
0.20
0.26
0.35
0.26
0.34
0.21
0.36
0.14
0.34
0.19
0.19
0.18
0.20
0.28
0.24
0.21 0.30 0.26 0.29 0.26 0.220.20 0.18 0.18 0.18 0.18 0.19
0.37
0.42
0.43
0.51
0.43
0.51
0.28
0.49
0.4
7
0.4
8
0.5
8
0.5
2
0.5
8
0.5
2
0.5
3
0.4
0
0.58Max:
Fig. 4.44
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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153
0.04 0.02 0.03 0.02 0.02 0.060.04 0.05 0.06 0.06 0.04 0.02
0.1
6
0.1
5
0.0
7
0.0
8
0.0
7
0.0
8
0.1
6
0.1
5
0.1
5
0.1
5
0.0
5
0.0
5
0.0
5
0.0
6
0.1
4
0.1
5
0.09 0.05 0.05 0.06 0.04 0.100.11 0.09 0.14 0.10 0.12 0.09
0.2
3
0.2
6
0.1
7
0.2
2
0.1
7
0.2
3
0.2
0
0.2
8
0.1
5
0.2
9
0.1
5
0.1
4
0.1
6
0.1
4
0.3
1
0.1
5
0.18 0.12 0.12 0.12 0.12 0.180.17 0.16 0.17 0.17 0.17 0.17
0.41
0.25
0.30
0.28
0.31
0.29
0.25
0.41
0.23
0.29
0.19
0.14
0.18
0.15
0.33
0.19
0.22 0.28 0.29 0.28 0.30 0.220.19 0.18 0.18 0.18 0.18 0.19
0.45
0.30
0.47
0.44
0.47
0.43
0.35
0.39
0.4
1
0.4
9
0.5
2
0.5
8
0.5
2
0.5
8
0.4
8
0.4
3
0.58Max:
Fig. 4.45 Daños 4P-Z3S2. R = 6.00
0.13 0.03 0.02 0.03 0.02 0.140.16 0.08 0.06 0.05 0.10 0.16
0.1
0
0.0
6
0.1
0
0.1
0
0.0
9
0.1
0
0.0
6
0.1
1
0.0
4
0.1
2
0.0
8
0.0
8
0.0
8
0.0
8
0.1
0
0.0
6
0.21 0.12 0.07 0.11 0.10 0.200.17 0.17 0.17 0.16 0.17 0.18
0.2
5
0.1
4
0.2
1
0.3
3
0.2
2
0.3
2
0.1
2
0.2
6
0.0
7
0.2
5
0.1
9
0.1
6
0.1
7
0.1
8
0.2
8
0.0
5
0.26 0.27 0.23 0.24 0.26 0.270.20 0.17 0.18 0.17 0.18 0.20
0.42
0.32
0.45
0.48
0.46
0.48
0.31
0.44
0.13
0.21
0.33
0.26
0.34
0.26
0.27
0.09
0.34 0.39 0.33 0.37 0.35 0.380.24 0.21 0.22 0.20 0.22 0.22
0.15
0.07
0.18
0.20
0.18
0.21
0.06
0.18
0.3
8
0.4
2
0.4
7
0.4
3
0.4
7
0.4
3
0.4
4
0.3
4
0.48Max:
Fig. 4.46 Daños 4P-Z3S4. R = 3.32
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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154
0.05 0.02 0.03 0.03 0.02 0.040.05 0.06 0.06 0.07 0.05 0.02
0.1
0
0.0
8
0.0
6
0.0
6
0.0
6
0.0
7
0.0
9
0.0
9
0.0
7
0.0
8
0.0
6
0.0
7
0.0
6
0.0
6
0.0
7
0.0
8
0.10 0.06 0.06 0.06 0.05 0.110.14 0.13 0.14 0.14 0.14 0.11
0.2
1
0.1
6
0.1
9
0.2
5
0.2
0
0.2
5
0.1
4
0.2
3
0.0
9
0.3
4
0.1
7
0.1
1
0.1
4
0.1
4
0.3
2
0.0
6
0.22 0.17 0.14 0.16 0.17 0.230.19 0.17 0.18 0.17 0.17 0.19
0.43
0.34
0.47
0.51
0.47
0.50
0.34
0.46
0.09
0.37
0.33
0.29
0.34
0.28
0.41
0.13
0.34 0.38 0.35 0.36 0.37 0.350.24 0.20 0.21 0.20 0.21 0.23
0.44
0.33
0.50
0.50
0.50
0.50
0.32
0.47
0.5
3
0.5
2
0.6
1
0.5
5
0.6
1
0.5
5
0.5
7
0.4
8
0.61Max:
Fig. 4.47 Daños 4P-Z3S4. R = 4.50
0.03 0.01 0.02 0.02 0.01 0.030.01 0.03 0.05 0.04 0.04 0.03
0.1
0
0.1
0
0.0
6
0.0
6
0.0
5
0.0
7
0.1
1
0.1
0
0.0
9
0.0
9
0.0
5
0.0
4
0.0
6
0.0
4
0.0
9
0.0
90.12 0.05 0.06 0.05 0.06 0.100.10 0.14 0.12 0.15 0.12 0.13
0.2
4
0.1
7
0.2
5
0.1
9
0.2
5
0.1
8
0.2
1
0.2
0
0.1
2
0.2
1
0.1
2
0.1
3
0.1
2
0.1
3
0.2
6
0.1
1
0.20 0.16 0.19 0.14 0.20 0.200.17 0.17 0.17 0.18 0.17 0.18
0.38
0.21
0.41
0.40
0.42
0.39
0.22
0.37
0.23
0.39
0.21
0.25
0.20
0.24
0.37
0.23
0.26 0.32 0.32 0.31 0.32 0.260.20 0.19 0.19 0.19 0.19 0.21
0.46
0.51
0.52
0.65
0.51
0.64
0.38
0.59
0.5
8
0.5
1
0.6
9
0.5
6
0.6
9
0.5
7
0.6
2
0.4
5
0.69Max:
Fig. 4.48 Daños 4P-Z3S4. R = 6.00
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
155
0.30 0.13 0.10 0.09 0.13 0.290.21 0.20 0.15 0.19 0.18 0.24
0.1
7
0.0
8
0.2
8
0.2
4
0.2
9
0.2
5
0.0
8
0.1
7
0.0
8
0.2
6
0.2
6
0.3
0
0.2
4
0.3
2
0.2
7
0.1
3
0.30 0.26 0.26 0.22 0.27 0.250.19 0.18 0.17 0.18 0.17 0.22
0.3
5
0.2
5
0.3
6
0.3
0
0.3
8
0.2
8
0.2
4
0.3
6
0.0
6
0.3
1
0.1
6
0.2
0
0.1
8
0.1
8
0.3
0
0.0
7
0.37 0.32 0.33 0.31 0.35 0.330.22 0.23 0.20 0.21 0.21 0.24
0.41
0.30
0.41
0.38
0.41
0.38
0.29
0.44
0.17
0.31
0.29
0.32
0.31
0.32
0.29
0.22
0.40 0.38 0.37 0.35 0.40 0.380.24 0.24 0.21 0.22 0.24 0.25
0.10
0.04
0.13
0.12
0.13
0.12
0.04
0.09
0.3
1
0.3
9
0.4
0
0.4
1
0.3
9
0.4
2
0.3
8
0.3
3
0.44Max:
Fig. 4.49 Daños 4P-Z7S2. R = 3.32
0.20 0.06 0.07 0.07 0.06 0.200.18 0.16 0.15 0.15 0.16 0.18
0.1
4
0.0
8
0.1
2
0.1
2
0.1
1
0.1
5
0.1
0
0.1
6
0.0
8
0.2
1
0.1
6
0.1
5
0.1
6
0.1
4
0.2
1
0.0
80.23 0.17 0.14 0.14 0.15 0.230.19 0.17 0.17 0.17 0.18 0.19
0.3
5
0.2
7
0.3
8
0.4
3
0.3
9
0.4
1
0.2
4
0.3
5
0.1
2
0.3
4
0.3
7
0.3
1
0.3
8
0.3
1
0.3
8
0.1
1
0.31 0.30 0.29 0.27 0.30 0.310.24 0.20 0.18 0.19 0.19 0.24
0.42
0.32
0.48
0.51
0.48
0.51
0.28
0.43
0.15
0.30
0.42
0.35
0.41
0.34
0.36
0.15
0.38 0.40 0.35 0.37 0.38 0.400.26 0.22 0.22 0.21 0.24 0.25
0.26
0.15
0.27
0.29
0.27
0.29
0.12
0.29
0.4
0
0.4
4
0.5
0
0.4
7
0.4
9
0.4
7
0.4
6
0.3
8
0.51Max:
Fig. 4.50 Daños 4P-Z7S2. R = 4.50
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
156
0.07 0.04 0.03 0.04 0.02 0.100.10 0.07 0.10 0.08 0.09 0.08
0.1
1
0.1
1
0.0
8
0.0
8
0.0
7
0.1
0
0.1
0
0.1
2
0.1
1
0.1
1
0.1
1
0.0
7
0.1
3
0.0
6
0.1
3
0.0
6
0.17 0.08 0.07 0.08 0.08 0.170.16 0.16 0.16 0.16 0.17 0.16
0.3
3
0.1
9
0.2
8
0.2
9
0.2
8
0.2
9
0.2
2
0.3
1
0.1
4
0.3
5
0.2
6
0.1
7
0.2
2
0.2
2
0.3
1
0.1
5
0.23 0.23 0.18 0.20 0.20 0.240.19 0.17 0.18 0.18 0.18 0.20
0.40
0.23
0.43
0.47
0.44
0.47
0.24
0.40
0.18
0.43
0.26
0.31
0.31
0.29
0.39
0.16
0.32 0.34 0.32 0.33 0.33 0.330.23 0.20 0.20 0.20 0.20 0.22
0.50
0.45
0.54
0.63
0.54
0.63
0.40
0.57
0.6
1
0.5
5
0.6
8
0.5
8
0.6
8
0.5
9
0.6
4
0.5
2
0.68Max:
Fig. 4.51 Daños 4P-Z7S2. R = 6.00
0.15 0.02 0.04 0.02 0.04 0.160.13 0.14 0.08 0.12 0.10 0.15
0.16
0.06
0.28
0.20
0.28
0.21
0.06
0.15
0.04
0.18
0.17
0.18
0.14
0.20
0.21
0.02
0.28 0.23 0.20 0.19 0.23 0.270.19 0.18 0.17 0.17 0.17 0.18
0.44
0.29
0.45
0.42
0.47
0.41
0.33
0.38
0.08
0.30
0.31
0.34
0.28
0.37
0.18
0.19
0.36 0.35 0.34 0.32 0.37 0.360.21 0.21 0.20 0.22 0.21 0.23
0.24
0.14
0.33
0.25
0.30
0.28
0.15
0.25
0.12
0.35
0.23
0.32
0.22
0.34
0.23
0.23
0.34 0.35 0.33 0.34 0.35 0.350.22 0.21 0.21 0.21 0.21 0.21
0.03
0.03
0.03
0.04
0.04
0.05
0.02
0.04
0.24
0.31
0.33
0.31
0.32
0.32
0.32
0.23
0.47Max:
Fig. 4.52 Daños 4P-Z7S4. R = 3.32
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
157
0.24 0.07 0.08 0.07 0.08 0.240.21 0.18 0.14 0.17 0.17 0.21
0.1
2
0.0
6
0.1
5
0.1
3
0.1
4
0.1
3
0.0
5
0.1
2
0.0
7
0.2
3
0.1
6
0.1
7
0.1
5
0.1
7
0.2
1
0.0
5
0.28 0.21 0.20 0.20 0.24 0.280.22 0.19 0.18 0.18 0.17 0.22
0.4
2
0.3
3
0.4
6
0.4
5
0.4
7
0.4
4
0.3
4
0.4
1
0.0
8
0.2
0
0.2
8
0.3
6
0.3
0
0.3
4
0.2
1
0.0
7
0.43 0.38 0.35 0.36 0.38 0.400.24 0.24 0.22 0.21 0.23 0.25
0.45
0.37
0.47
0.49
0.48
0.50
0.32
0.50
26 45 39 44 38 45 36 33
0.10
0.04
0.08
0.08
0.07
0.08
0.04
0.08
0.4
5
0.4
2
0.5
2
0.4
3
0.5
2
0.4
3
0.5
0
0.3
5
0.52Max:
Fig. 4.53 Daños 4P-Z7S4. R = 4.50
Fig. 4.54 Daños 4P-Z7S4. R = 6.00
0. 0. 0. 0. 0. 0. 0. 0.
0.40 0.50 0.39 0.45 0.42 0.480.28 0.23 0.26 0.23 0.27 0.25
0.18 0.06 0.04 0.06 0.03 0.190.18 0.10 0.14 0.09 0.15 0.17
0.1
0
0.0
7
0.1
0
0.1
3
0.0
9
0.1
4
0.0
5
0.0
9
0.0
3
0.1
9
0.1
1
0.1
2
0.1
0
0.1
1
0.1
8
0.0
70.24 0.15 0.13 0.13 0.15 0.240.20 0.18 0.18 0.16 0.18 0.20
0.3
4
0.2
8
0.4
0
0.4
5
0.4
1
0.4
4
0.2
4
0.3
7
0.51
0.51
0.56
0.65
0.56
0.65
0.41
0.59
0.27
0.34
0.45
0.43
0.45
0.43
0.40
0.21
0.46 0.59 0.42 0.53 0.46 0.590.35 0.24 0.30 0.24 0.32 0.27
0.16
0.06
0.15
0.18
0.14
0.17
0.07
0.15
0.5
8
0.4
8
0.6
6
0.5
0
0.6
6
0.5
0
0.6
2
0.4
0
0.66Max:
0.0
6
0.3
0
0.2
8
0.3
5
0.3
0
0.2
9
0.2
6
0.0
9
0.34 0.35 0.30 0.33 0.31 0.380.24 0.20 0.21 0.19 0.23 0.21
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
158
Tabla. 4.22 Daños máximos en pórticos de 4 pisos.
abla. 4.23 Porcentaje de rotulas mayor que el daño referencial en pórticos de 4 pisos en base al tal de rotulas.
abla. 4.24 Porcentaje de daños en las rótulas de vigas y columnas mayores que los valores áximos de daños referenciales, con respecto al número total de vigas y columnas
ente, en pórticos de 4 pisos.
FACTOR DE REDUCCION " R"
3.32 4.50 6.00
4P-Z3S2 0.56 0.58 0.584P-Z3S4 0.48 0.61 0.694P-Z7S2 0.44 0.51 0.684P-Z7S4 0.47 0.52 0.66
PORTICO
4 PISOS
DAÑO MAXIMO
Tto
% VIGA 0.00 % VIGA 0.00 % VIGA 0.00% COL 100.00 % COL 100.00 % COL 100.00% VIGA 0.00 % VIGA 0.00 % VIGA 0.00% COL 100.00 % COL 100.00 % COL 100.00% VIGA 0.00 % VIGA 0.00 % VIGA 0.00% COL 100.00 % COL 100.00 % COL 100.00% VIGA 0.00 % VIGA 12.00 % VIGA 17.86% COL 100.00 % COL 88.00 % COL 82.14
o referencial en vigas = 0.45
Daño referencial en columnas = 0.40 Ref. (8)
FACTOR DE REDUCCION "R"
3.32
13.39
15.20
20.50
25.00
11.60
18.80
15.20
22.30
4P-Z7S2
4P-Z7S4
11.60
6.30
3.57
11.204P-Z3S2
4P-Z3S4
PORTICO
4.50 6.00
PORTICOS DE 4 PISOS
DE ROTULAS CON DAÑO MAYOR DE DAÑO REFERENCIAL
Dañ
Tmrespectivam
VIGA COL. VIGA COL. VIGA
4P-Z3S2 0.00 20.30 0.00 20.30 0.00
4P-Z7S4 0.00 6.25 6.30 34.40 10.40
Daño referencial en vigas = 0.45
Daño referencial en columnas = 0.40 Ref. (8)
PORTICOS DE 4 PISOS
3.32 4.50
DE ROTULAS CON DAÑO > DE Dref.
RPORTICO
COL.
23.4426.6035.90
35.90
6.00
4P-Z3S4 0.00 18.80 0.00 32.80 0.004P-Z7S2 0.00 10.90 0.00 26.60 0.00
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
159
Porticos de 8 pisos:
0.08 0.04 0.04 0.06 0.02 0.070.03 0.07 0.14 0.10 0.10 0.03
0.20
0.26
0.11
0.13
0.11
0.15
0.20
0.26
0.25
0.18
0.13
0.13
0.15
0.09
0.23
0.20
0.13 0.11 0.14 0.14 0.09 0.130.08 0.16 0.16 0.16 0.16 0.09
0.38
0.33
0.36
0.30
0.35
0.32
0.36
0.37
0.35
0.36
0.27
0.22
0.27
0.21
0.34
0.38
0.17 0.25 0.27 0.26 0.25 0.160.14 0.17 0.17 0.18 0.16 0.14
0.43
0.39
0.39
0.34
0.38
0.35
0.42
0.41
0.34
0.45
0.34
0.41
0.35
0.41
0.43
0.37
0.17 0.24 0.24 0.26 0.23 0.180.16 0.18 0.18 0.18 0.17 0.17
0.41
0.29
0.26
0.25
0.27
0.26
0.28
0.41
0.20
0.42
0.24
0.29
0.23
0.29
0.34
0.29
0.20 0.19 0.22 0.21 0.22 0.190.17 0.17 0.17 0.17 0.17 0.17
0.28
0.12
0.20
0.15
0.21
0.16
0.15
0.25
0.19
0.26
0.22
0.16
0.22
0.17
0.32
0.10
0.21 0.20 0.19 0.19 0.18 0.210.17 0.17 0.17 0.17 0.17 0.17
0.27
0.09
0.19
0.14
0.19
0.13
0.12
0.24
0.09
0.23
0.16
0.12
0.16
0.12
0.25
0.07
0.23 0.24 0.21 0.23 0.22 0.220.17 0.17 0.17 0.17 0.16 0.18
0.23
0.09
0.18
0.22
0.19
0.20
0.09
0.24
0.04
0.19
0.12
0.12
0.12
0.13
0.18
0.06
0.24 0.30 0.29 0.30 0.30 0.230.19 0.18 0.18 0.19 0.17 0.20
0.21
0.13
0.22
0.23
0.22
0.22
0.13
0.22
0.28
0.35
0.42
0.43
0.41
0.43
0.31
0.32
Max: 0.45
Fig. 4.55 Daños 8P-Z3S2. R = 3.32
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
160
0.04 0.03 0.05 0.05 0.02 0.100.03 0.07 0.10 0.11 0.08 0.03
0.20
0.19
0.10
0.11
0.09
0.12
0.20
0.19
0.19
0.17
0.11
0.08
0.14
0.07
0.17
0.19
0.13 0.06 0.10 0.11 0.08 0.130.09 0.16 0.17 0.16 0.11 0.09
0.34
0.31
0.34
0.24
0.32
0.28
0.32
0.33
0.32
0.30
0.24
0.19
0.25
0.17
0.28
0.33
0.16 0.19 0.21 0.24 0.21 0.160.15 0.17 0.17 0.18 0.16 0.15
0.31
0.33
0.28
0.23
0.26
0.23
0.35
0.28
0.24
0.36
0.23
0.35
0.23
0.34
0.29
0.31
0.18 0.14 0.20 0.18 0.20 0.170.16 0.18 0.17 0.18 0.16 0.17
0.33
0.26
0.19
0.21
0.19
0.21
0.22
0.35
0.23
0.33
0.18
0.24
0.18
0.24
0.32
0.24
0.19 0.16 0.19 0.17 0.17 0.190.18 0.17 0.17 0.17 0.16 0.18
0.27
0.12
0.14
0.09
0.14
0.10
0.15
0.24
0.15
0.26
0.14
0.07
0.14
0.08
0.28
0.12
0.19 0.22 0.20 0.22 0.18 0.190.17 0.17 0.17 0.17 0.17 0.18
0.30
0.10
0.22
0.14
0.22
0.14
0.16
0.24
0.09
0.24
0.15
0.11
0.16
0.12
0.23
0.09
0.24 0.29 0.29 0.28 0.29 0.230.18 0.19 0.18 0.19 0.17 0.19
0.27
0.10
0.25
0.24
0.26
0.24
0.10
0.26
0.06
0.18
0.14
0.16
0.13
0.17
0.17
0.08
0.25 0.32 0.32 0.31 0.33 0.240.19 0.19 0.19 0.20 0.18 0.21
0.21
0.12
0.22
0.21
0.22
0.21
0.14
0.20
0.32
0.42
0.42
0.47
0.42
0.48
0.34
0.42
Max: 0.48
Fig. 4.56 Daños 8P-Z3S2. R = 4.50
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
161
0.01 0.03 0.04 0.06 0.02 0.050.02 0.05 0.12 0.09 0.08 0.01
0.19
0.24
0.08
0.14
0.09
0.13
0.18
0.24
0.23
0.16
0.09
0.10
0.09
0.08
0.22
0.18
0.12 0.07 0.08 0.10 0.06 0.140.11 0.12 0.17 0.16 0.16 0.08
0.29
0.33
0.22
0.26
0.21
0.25
0.31
0.34
0.33
0.27
0.18
0.18
0.19
0.17
0.28
0.32
0.16 0.14 0.13 0.17 0.10 0.160.16 0.17 0.18 0.17 0.17 0.15
0.30
0.35
0.21
0.29
0.19
0.31
0.33
0.33
0.29
0.33
0.28
0.20
0.29
0.18
0.41
0.28
0.17 0.17 0.16 0.21 0.14 0.160.16 0.17 0.18 0.18 0.18 0.16
0.33
0.31
0.21
0.24
0.20
0.25
0.31
0.39
0.25
0.30
0.20
0.19
0.20
0.19
0.28
0.26
0.18 0.24 0.24 0.24 0.20 0.180.18 0.17 0.18 0.18 0.17 0.18
0.30
0.20
0.17
0.19
0.17
0.19
0.22
0.26
0.16
0.31
0.18
0.15
0.18
0.16
0.28
0.17
0.20 0.30 0.28 0.29 0.26 0.210.18 0.18 0.19 0.19 0.18 0.19
0.38
0.21
0.31
0.28
0.32
0.28
0.25
0.37
0.16
0.27
0.17
0.17
0.17
0.16
0.28
0.13
0.23 0.34 0.31 0.33 0.33 0.240.20 0.19 0.20 0.20 0.19 0.21
0.24
0.12
0.21
0.26
0.22
0.26
0.12
0.27
0.12
0.20
0.17
0.19
0.16
0.19
0.19
0.09
0.23 0.34 0.33 0.33 0.34 0.230.21 0.20 0.20 0.20 0.19 0.21
0.17
0.11
0.20
0.18
0.21
0.18
0.13
0.16
0.33
0.35
0.48
0.50
0.48
0.50
0.33
0.34
Max: 0.50
Fig. 4.57 Daños 8P-Z3S2. R = 6.00
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
162
0.16 0.02 0.04 0.03 0.03 0.150.15 0.09 0.08 0.10 0.09 0.15
0.13
0.13
0.11
0.08
0.09
0.09
0.11
0.12
0.16
0.10
0.10
0.11
0.12
0.08
0.12
0.13
0.15 0.08 0.13 0.10 0.09 0.140.13 0.16 0.15 0.17 0.13 0.14
0.24
0.18
0.30
0.17
0.28
0.21
0.25
0.18
0.17
0.22
0.16
0.24
0.18
0.21
0.27
0.13
0.19 0.16 0.22 0.21 0.20 0.180.17 0.17 0.16 0.17 0.16 0.18
0.43
0.18
0.46
0.39
0.46
0.39
0.34
0.29
0.14
0.40
0.26
0.42
0.26
0.41
0.29
0.20
0.29 0.26 0.30 0.26 0.31 0.260.18 0.20 0.17 0.20 0.17 0.21
0.34
0.22
0.47
0.49
0.47
0.49
0.14
0.41
0.14
0.34
0.35
0.44
0.35
0.44
0.28
0.17
0.31 0.32 0.32 0.31 0.32 0.310.20 0.20 0.19 0.20 0.19 0.21
0.30
0.17
0.37
0.43
0.37
0.44
0.13
0.40
0.10
0.31
0.25
0.33
0.25
0.33
0.28
0.12
0.32 0.36 0.32 0.35 0.33 0.340.22 0.20 0.20 0.20 0.20 0.21
0.31
0.23
0.36
0.43
0.35
0.43
0.13
0.40
0.14
0.30
0.27
0.29
0.28
0.29
0.31
0.14
0.33 0.38 0.33 0.37 0.34 0.370.22 0.20 0.21 0.20 0.21 0.21
0.31
0.11
0.35
0.31
0.35
0.31
0.13
0.28
0.13
0.24
0.30
0.25
0.29
0.26
0.28
0.11
0.31 0.38 0.33 0.36 0.35 0.340.22 0.19 0.21 0.20 0.20 0.22
0.16
0.07
0.09
0.09
0.10
0.08
0.08
0.13
0.30
0.34
0.48
0.43
0.47
0.43
0.38
0.29
Max: 0.49
Fig. 4.58 Daños 8P-Z3S4. R = 3.32
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
163
0.10 0.02 0.05 0.04 0.02 0.080.03 0.08 0.10 0.11 0.08 0.08
0.18
0.15
0.09
0.06
0.08
0.08
0.16
0.17
0.21
0.16
0.11
0.08
0.14
0.06
0.15
0.18
0.13 0.07 0.13 0.13 0.10 0.090.07 0.16 0.16 0.16 0.11 0.10
0.29
0.19
0.35
0.21
0.35
0.22
0.30
0.17
0.21
0.23
0.20
0.25
0.22
0.24
0.25
0.18
0.19 0.17 0.24 0.22 0.24 0.170.16 0.18 0.16 0.18 0.16 0.17
0.40
0.24
0.43
0.35
0.42
0.33
0.32
0.33
0.15
0.39
0.30
0.42
0.30
0.41
0.28
0.24
0.24 0.25 0.27 0.26 0.28 0.230.18 0.19 0.17 0.19 0.17 0.20
0.33
0.16
0.34
0.38
0.35
0.37
0.14
0.36
0.11
0.33
0.23
0.35
0.23
0.35
0.28
0.14
0.27 0.29 0.28 0.29 0.29 0.270.19 0.19 0.18 0.19 0.18 0.20
0.30
0.19
0.28
0.41
0.29
0.40
0.13
0.38
0.12
0.36
0.19
0.34
0.19
0.34
0.29
0.16
0.29 0.33 0.31 0.32 0.32 0.310.21 0.20 0.20 0.20 0.20 0.21
0.35
0.17
0.35
0.38
0.35
0.37
0.17
0.38
0.09
0.25
0.21
0.23
0.22
0.23
0.26
0.08
0.34 0.37 0.34 0.36 0.35 0.350.21 0.21 0.21 0.21 0.21 0.21
0.35
0.16
0.41
0.37
0.43
0.37
0.17
0.36
0.13
0.22
0.31
0.20
0.30
0.22
0.28
0.07
0.37 0.39 0.37 0.37 0.39 0.370.23 0.22 0.21 0.22 0.21 0.23
0.15
0.07
0.13
0.13
0.14
0.13
0.06
0.16
0.36
0.48
0.53
0.56
0.53
0.56
0.45
0.43
Max: 0.56
Fig. 4.59 Daños 8P-Z3S4. R = 4.50
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
164
0.08 0.03 0.05 0.05 0.02 0.120.06 0.08 0.11 0.11 0.10 0.04
0.20
0.19
0.12
0.12
0.09
0.14
0.17
0.22
0.20
0.18
0.11
0.14
0.13
0.10
0.20
0.19
0.14 0.09 0.13 0.12 0.09 0.150.11 0.15 0.17 0.17 0.17 0.09
0.34
0.31
0.29
0.31
0.27
0.33
0.30
0.35
0.24
0.34
0.25
0.24
0.27
0.22
0.32
0.28
0.17 0.20 0.18 0.23 0.14 0.170.16 0.17 0.18 0.17 0.17 0.16
0.34
0.24
0.28
0.30
0.25
0.31
0.26
0.33
0.19
0.34
0.31
0.23
0.32
0.21
0.36
0.18
0.20 0.23 0.19 0.24 0.16 0.210.18 0.17 0.18 0.18 0.17 0.18
0.41
0.20
0.33
0.30
0.33
0.31
0.24
0.39
0.18
0.35
0.26
0.27
0.26
0.29
0.35
0.18
0.25 0.30 0.27 0.29 0.28 0.260.19 0.19 0.18 0.19 0.18 0.20
0.32
0.15
0.21
0.33
0.22
0.32
0.13
0.39
0.10
0.35
0.15
0.22
0.14
0.23
0.33
0.10
0.29 0.33 0.31 0.33 0.32 0.300.21 0.20 0.20 0.20 0.19 0.21
0.40
0.30
0.39
0.52
0.39
0.52
0.20
0.46
0.14
0.37
0.28
0.19
0.26
0.18
0.38
0.10
0.35 0.41 0.35 0.40 0.37 0.400.25 0.22 0.23 0.22 0.23 0.23
0.44
0.36
0.46
0.54
0.47
0.53
0.21
0.51
0.08
0.18
0.22
0.16
0.21
0.17
0.19
0.04
0.42 0.49 0.41 0.47 0.43 0.480.29 0.24 0.26 0.24 0.26 0.25
0.43
0.28
0.49
0.48
0.48
0.48
0.32
0.42
0.59
0.63
0.74
0.68
0.74
0.69
0.69
0.54
Max: 0.74
Fig. 4.60 Daños 8P-Z3S4. R = 6.00
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
165
0.22 0.14 0.21 0.15 0.19 0.220.20 0.18 0.19 0.19 0.18 0.22
0.2
7
0.1
9
0.2
3
0.1
9
0.2
6
0.2
1
0.1
6
0.2
4
0.3
0
0.2
6
0.3
1
0.2
9
0.3
1
0.3
1
0.2
7
0.2
8
0.19 0.23 0.25 0.24 0.25 0.170.17 0.17 0.17 0.18 0.15 0.18
0.3
3
0.3
0
0.4
1
0.4
1
0.4
1
0.4
1
0.3
5
0.3
2
0.2
6
0.3
8
0.3
7
0.4
1
0.3
8
0.4
1
0.3
7
0.2
6
0.25 0.27 0.27 0.27 0.28 0.230.19 0.19 0.19 0.18 0.19 0.20
0.4
3
0.2
2
0.4
7
0.4
4
0.4
7
0.4
4
0.2
6
0.4
0
0.1
8
0.4
2
0.4
4
0.4
4
0.4
4
0.4
3
0.4
4
0.1
4
0.31 0.28 0.28 0.29 0.30 0.290.20 0.19 0.19 0.19 0.19 0.21
0.5
1
0.2
7
0.5
4
0.4
5
0.5
3
0.4
5
0.3
6
0.4
5
0.2
7
0.4
6
0.4
8
0.4
9
0.4
8
0.4
9
0.4
3
0.3
1
0.34 0.31 0.33 0.29 0.36 0.290.20 0.20 0.18 0.21 0.18 0.23
0.4
0
0.2
1
0.4
6
0.4
4
0.4
6
0.4
3
0.1
7
0.4
2
0.1
8
0.3
8
0.3
7
0.4
6
0.4
1
0.4
2
0.3
2
0.2
4
0.34 0.31 0.33 0.30 0.35 0.300.19 0.21 0.19 0.21 0.19 0.22
0.40
0.31
0.45
0.48
0.46
0.47
0.23
0.49
0.1
8
0.3
1
0.2
7
0.3
5
0.3
1
0.3
2
0.2
6
0.2
30.34 0.35 0.34 0.32 0.36 0.320.20 0.21 0.19 0.20 0.19 0.21
0.36
0.18
0.43
0.35
0.45
0.34
0.23
0.32
0.2
2
0.2
6
0.3
4
0.2
8
0.3
5
0.2
7
0.3
0
0.2
0
0.32 0.35 0.34 0.32 0.37 0.290.21 0.20 0.19 0.20 0.19 0.23
0.09
0.08
0.08
0.09
0.08
0.09
0.07
0.12
0.1
8
0.3
8
0.3
1
0.4
4
0.2
8
0.4
5
0.3
0
0.2
8
Max: 0.54
Fig. 4.61 Daños 8P-Z7S2. R = 3.32
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
166
0.18 0.10 0.15 0.14 0.11 0.170.17 0.18 0.18 0.19 0.17 0.19
0.2
6
0.2
2
0.2
3
0.1
9
0.1
9
0.2
1
0.2
4
0.2
5
0.3
5
0.2
1
0.3
0
0.2
8
0.2
8
0.2
6
0.1
8
0.3
3
0.17 0.22 0.27 0.25 0.26 0.150.15 0.17 0.17 0.18 0.16 0.17
0.3
8
0.3
3
0.4
5
0.3
8
0.4
5
0.3
8
0.4
2
0.3
3
0.2
8
0.4
0
0.3
4
0.4
0
0.3
5
0.3
9
0.3
6
0.2
7
0.24 0.26 0.31 0.26 0.32 0.200.18 0.21 0.18 0.21 0.18 0.22
0.4
8
0.2
5
0.4
8
0.4
0
0.4
8
0.4
1
0.3
2
0.3
8
0.2
3
0.4
6
0.4
0
0.4
5
0.4
1
0.4
5
0.4
2
0.1
9
0.30 0.26 0.33 0.26 0.34 0.240.19 0.20 0.18 0.20 0.17 0.23
0.5
1
0.2
9
0.5
1
0.4
8
0.5
2
0.4
8
0.3
7
0.4
2
0.3
0
0.5
3
0.4
5
0.5
3
0.4
4
0.5
3
0.4
5
0.3
7
0.33 0.30 0.33 0.30 0.34 0.290.20 0.21 0.19 0.21 0.19 0.23
0.3
5
0.1
4
0.3
3
0.3
7
0.3
4
0.3
6
0.1
2
0.4
0
0.1
6
0.3
7
0.2
2
0.3
6
0.2
2
0.3
7
0.3
3
0.1
4
0.32 0.32 0.32 0.31 0.33 0.300.19 0.20 0.19 0.20 0.18 0.21
0.40
0.32
0.41
0.48
0.41
0.48
0.25
0.47
0.1
1
0.3
2
0.2
5
0.1
9
0.2
5
0.1
8
0.3
2
0.1
0
0.34 0.37 0.30 0.35 0.32 0.350.21 0.21 0.20 0.21 0.20 0.21
0.40
0.24
0.46
0.47
0.47
0.47
0.23
0.41
0.1
3
0.2
8
0.2
8
0.2
7
0.2
8
0.2
9
0.2
8
0.1
2
0.38 0.41 0.38 0.39 0.40 0.390.22 0.22 0.21 0.22 0.21 0.24
0.23
0.09
0.17
0.16
0.18
0.15
0.09
0.19
0.3
7
0.4
8
0.5
1
0.5
4
0.5
1
0.5
4
0.4
6
0.4
3
Max: 0.54
Fig. 4.62 Daños 8P-Z7S2. R = 4.50
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
167
0.14 0.07 0.11 0.11 0.09 0.140.09 0.16 0.17 0.17 0.13 0.13
0.3
1
0.3
0
0.2
5
0.2
0
0.2
4
0.2
4
0.3
1
0.3
1
0.3
2
0.2
9
0.2
3
0.2
5
0.2
1
0.2
3
0.2
9
0.3
2
0.16 0.24 0.25 0.25 0.26 0.160.15 0.17 0.17 0.18 0.16 0.16
0.3
8
0.3
8
0.3
9
0.4
2
0.3
9
0.4
2
0.3
7
0.3
8
0.3
0
0.3
8
0.3
7
0.3
9
0.3
7
0.3
9
0.3
7
0.3
2
0.19 0.29 0.27 0.28 0.27 0.200.19 0.18 0.19 0.18 0.18 0.19
0.4
1
0.3
2
0.4
5
0.4
2
0.4
5
0.4
3
0.3
4
0.4
0
0.3
0
0.4
4
0.4
5
0.4
3
0.4
5
0.4
4
0.4
3
0.3
1
0.21 0.27 0.28 0.27 0.28 0.210.20 0.18 0.18 0.19 0.18 0.20
0.4
7
0.3
4
0.4
2
0.4
7
0.4
1
0.4
8
0.3
0
0.4
8
0.2
7
0.4
5
0.3
8
0.4
1
0.3
7
0.4
2
0.4
4
0.3
0
0.25 0.33 0.30 0.32 0.31 0.270.21 0.19 0.20 0.20 0.20 0.21
0.3
8
0.2
1
0.2
8
0.4
2
0.2
8
0.4
0
0.1
7
0.4
6
0.1
7
0.3
8
0.3
6
0.2
5
0.3
5
0.2
5
0.4
1
0.1
4
0.30 0.35 0.32 0.35 0.33 0.330.21 0.20 0.21 0.20 0.21 0.21
0.48
0.23
0.46
0.45
0.46
0.45
0.26
0.47
0.1
5
0.3
5
0.3
2
0.2
8
0.3
1
0.2
9
0.3
9
0.1
50.35 0.41 0.37 0.39 0.38 0.380.24 0.22 0.23 0.22 0.22 0.24
0.43
0.28
0.44
0.50
0.46
0.50
0.19
0.46
0.0
7
0.2
7
0.2
3
0.2
0
0.2
3
0.2
0
0.3
1
0.0
5
0.39 0.46 0.40 0.44 0.43 0.430.26 0.23 0.25 0.24 0.24 0.25
0.31
0.17
0.28
0.28
0.28
0.27
0.17
0.33
0.5
0
0.5
8
0.5
9
0.5
9
0.6
0
0.5
9
0.5
9
0.5
0
Max: 0.60
Fig. 4.63 Daños 8P-Z7S2. R = 6.00
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
168
0.31 0.24 0.20 0.22 0.20 0.320.22 0.20 0.20 0.19 0.20 0.22
0.1
2
0.0
4
0.1
9
0.1
6
0.1
6
0.1
8
0.0
3
0.0
7
0.13
0.15
0.25
0.25
0.25
0.26
0.17
0.12
0.22 0.26 0.25 0.25 0.25 0.220.20 0.18 0.18 0.18 0.17 0.21
0.1
7
0.1
1
0.3
1
0.3
2
0.3
2
0.3
0
0.1
0
0.1
4
0.0
6
0.1
2
0.2
1
0.2
1
0.2
4
0.1
7
0.1
2
0.0
8
0.29 0.29 0.28 0.28 0.29 0.300.21 0.21 0.19 0.20 0.21 0.21
0.30
0.19
0.37
0.40
0.37
0.39
0.22
0.30
0.1
0
0.1
4
0.2
5
0.2
8
0.2
6
0.2
7
0.1
0
0.1
3
0.33 0.33 0.30 0.31 0.32 0.340.23 0.21 0.21 0.21 0.21 0.23
0.3
7
0.2
6
0.4
3
0.4
3
0.4
5
0.4
1
0.2
5
0.3
8
0.1
8
0.2
0
0.3
8
0.4
0
0.3
8
0.3
9
0.1
8
0.1
9
0.40 0.36 0.30 0.33 0.33 0.430.23 0.25 0.24 0.23 0.26 0.23
0.3
9
0.2
6
0.4
5
0.4
2
0.4
6
0.4
2
0.2
2
0.4
4
0.2
3
0.4
5
0.4
1
0.4
2
0.3
8
0.4
4
0.4
5
0.2
9
0.33 0.40 0.30 0.36 0.33 0.410.29 0.23 0.26 0.22 0.27 0.25
0.0
8
0.1
7
0.1
5
0.1
5
0.1
4
0.1
7
0.1
9
0.0
8
0.20
0.24
0.20
0.22
0.20
0.22
0.28
0.20
0.30 0.39 0.29 0.35 0.31 0.390.29 0.21 0.25 0.21 0.26 0.23
0.0
2
0.0
8
0.0
4
0.0
5
0.0
4
0.0
5
0.0
8
0.0
3
0.19
0.11
0.21
0.16
0.23
0.15
0.14
0.17
0.30 0.36 0.27 0.33 0.29 0.370.25 0.23 0.24 0.21 0.27 0.22
0.0
2
0.0
1
0.0
1
0.0
0
0.0
1
0.0
1
0.0
1
0.0
1
0.30
0.27
0.40
0.27
0.37
0.27
0.42
0.20
Max: 0.46
Fig. 4.64 Daños 8P-Z7S4. R = 3.32
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
169
0.20 0.04 0.07 0.05 0.06 0.200.11 0.14 0.09 0.13 0.12 0.13
0.0
9
0.0
2
0.1
3
0.0
9
0.0
8
0.0
9
0.0
3
0.1
1
0.09
0.16
0.15
0.20
0.14
0.20
0.12
0.15
0.12 0.14 0.15 0.15 0.15 0.130.12 0.11 0.11 0.10 0.11 0.12
0.1
2
0.1
7
0.2
4
0.2
6
0.2
3
0.2
5
0.1
1
0.1
9
0.0
9
0.2
0
0.1
1
0.1
8
0.1
3
0.1
4
0.1
9
0.0
9
0.18 0.21 0.20 0.20 0.20 0.190.14 0.13 0.13 0.12 0.14 0.13
0.32
0.22
0.32
0.35
0.32
0.35
0.20
0.33
0.0
9
0.2
2
0.2
2
0.2
5
0.2
4
0.2
3
0.1
7
0.1
5
0.22 0.22 0.18 0.21 0.19 0.260.16 0.15 0.16 0.14 0.17 0.15
0.3
3
0.2
1
0.3
3
0.3
5
0.3
4
0.3
4
0.1
9
0.3
3
0.1
9
0.2
2
0.3
7
0.3
2
0.3
5
0.3
4
0.2
8
0.2
0
0.25 0.29 0.22 0.26 0.24 0.300.19 0.15 0.16 0.15 0.17 0.16
0.3
8
0.2
8
0.3
6
0.3
9
0.3
7
0.3
8
0.2
2
0.4
0
0.2
0
0.2
2
0.3
1
0.2
8
0.3
2
0.2
4
0.2
2
0.1
7
0.31 0.33 0.25 0.30 0.26 0.380.20 0.17 0.19 0.15 0.20 0.16
0.4
1
0.2
1
0.3
9
0.3
9
0.4
1
0.3
7
0.2
1
0.3
9
0.20
0.30
0.35
0.26
0.34
0.26
0.33
0.17
0.29 0.36 0.27 0.33 0.29 0.360.24 0.16 0.20 0.16 0.21 0.18
0.1
2
0.1
6
0.2
2
0.2
2
0.2
1
0.2
2
0.1
7
0.1
3
0.19
0.19
0.28
0.20
0.29
0.19
0.21
0.16
0.27 0.35 0.26 0.32 0.28 0.340.22 0.17 0.19 0.16 0.21 0.18
0.0
4
0.0
6
0.0
5
0.0
4
0.0
5
0.0
4
0.0
4
0.0
5
0.37
0.41
0.45
0.35
0.43
0.37
0.47
0.24
Max: 0.47
Fig. 4.65 Daños 8P-Z7S4. R = 4.50
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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170
0.13 0.01 0.03 0.02 0.02 0.130.10 0.09 0.04 0.07 0.08 0.10
0.0
5
0.0
2
0.0
6
0.0
3
0.0
4
0.0
5
0.0
2
0.0
6
0.08
0.11
0.08
0.12
0.11
0.09
0.09
0.09
0.10 0.02 0.06 0.06 0.03 0.090.07 0.09 0.10 0.10 0.08 0.09
0.1
0
0.0
9
0.1
6
0.1
1
0.1
4
0.1
3
0.1
0
0.0
8
0.0
9
0.0
8
0.0
8
0.1
1
0.0
9
0.1
0
0.1
3
0.0
7
0.13 0.13 0.16 0.15 0.16 0.130.11 0.11 0.10 0.11 0.10 0.12
0.26
0.14
0.30
0.28
0.30
0.27
0.19
0.19
0.1
1
0.2
1
0.1
9
0.2
0
0.1
8
0.1
8
0.2
0
0.1
1
0.20 0.19 0.20 0.19 0.20 0.190.13 0.14 0.12 0.13 0.13 0.14
0.3
6
0.2
2
0.3
8
0.3
9
0.3
8
0.3
8
0.2
2
0.3
7
0.1
1
0.1
9
0.2
4
0.2
7
0.2
6
0.2
5
0.2
0
0.0
8
0.27 0.27 0.24 0.26 0.25 0.280.15 0.15 0.15 0.14 0.15 0.15
0.4
2
0.2
6
0.4
3
0.4
5
0.4
3
0.4
5
0.2
7
0.4
3
0.1
7
0.2
3
0.2
5
0.3
1
0.2
5
0.2
6
0.2
4
0.1
7
0.34 0.38 0.30 0.35 0.34 0.380.19 0.18 0.18 0.17 0.18 0.18
0.3
7
0.2
3
0.3
5
0.4
1
0.3
6
0.4
0
0.1
9
0.4
0
0.17
0.25
0.23
0.24
0.24
0.24
0.27
0.18
0.32 0.42 0.32 0.38 0.35 0.400.21 0.17 0.18 0.17 0.20 0.19
0.30 0.38 0.30 0.36 0.32 0.360.18 0.17 0.17 0.16 0.18 0.16
0.0
4
0.0
4
0.0
4
0.0
4
0.0
4
0.0
4
0.0
4
0.0
4
0.36
0.46
0.47
0.41
0.46
0.43
0.50
0.28
Max: 0.50
0.2
2
0.1
5
0.2
2
0.1
9
0.2
1
0.1
9
0.1
7
0.2
3
0.16
0.23
0.24
0.24
0.24
0.23
0.29
0.15
Fig. 4.66 Daños 8P-Z7S4. R = 6.00
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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171
Tabla. 4.25 Daños máximos en pórticos de 8 pisos.
abla. 4.26 Porcentaje de rotulas mayor que el daño referencial en pórticos de 8 pisos en base al tal de rotulas.
abla. 4.27 Porcentaje de daños en las rótulas de vigas y columnas mayores que los valores áximos de daños referenciales, con respecto al número total de vigas y columnas spectivamente, en pórticos de 8 pisos.
FACTOR DE REDUCCION " R"
3.32 4.50 6.00
8P-Z3S2 0.45 0.48 0.508P-Z3S4 0.49 0.56 0.748P-Z7S2 0.54 0.54 0.608P-Z7S4 0.46 0.47 0.50
8 PISOS
DAÑO MAXIMO
PORTICO
Tto
% VIGA 0.00 % VIGA 0.00 % VIGA 0.00% COL 100.00 % COL 100.00 % COL 100.00% VIGA 0.00 % VIGA 0.00 % VIGA 11.54% COL 100.00 % COL 100.00 % COL 88.46% VIGA 0.00 % VIGA 0.00 % VIGA 2.08% COL 100.00 % COL 100.00 % COL 97.92% VIGA 0.00 % VIGA 0.00 % VIGA 0.00% COL 100.00 % COL 100.00 % COL 100.00
Daño referencial en vigas = 0.45
Daño referencial en columnas = 0.40 Ref. (8)
PORTICOS DE 8 PISOS
PORTICO DE ROTULAS CON DAÑO MAYOR DE DAÑO REFERENCIAL
FACTOR DE REDUCCION "R"
3.32 4.50 6.00
8P-Z3S2 6.30 2.70 2.20
8P-Z3S4 10.30 6.30 11.61
8P-Z7S2 20.54 20.98 21.43
8P-Z7S4 7.59 3.13 6.30
Tmre
VIGA COL. VIGA COL. VIGA
8P-Z3S2 0.00 10.90 0.00 4.70 0.008P-Z3S4 0.00 18.00 0.00 10.90 3.108P-Z7S2 0.00 35.94 0.00 36.72 1.04
8P-Z7S4 0.00 13.30 0.00 5.47 0.00
Daño referencial en vigas = 0.45
PORTICOS DE 8 PISOS
PORTICO
DE ROTULAS CON DAÑO > DE Dref.
R
3.32 4.50
COL.
3.9018.0036.72
10.90
6.00
Daño referencial en columnas = 0.40 Ref. (8)
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Porticos de 12 pisos:
Fig. 4.67 Daños 12P-Z3S2. R = 3.32
0.05 0.01 0.03 0.02 0.01 0.040.04 0.05 0.05 0.06 0.03 0.04
0.1
2
0.0
9
0.0
5
0.0
5
0.0
6
0.0
5
0.1
1
0.0
8
0.0
8
0.1
3
0.0
5
0.0
6
0.0
5
0.0
6
0.0
8
0.1
0
0.08 0.03 0.04 0.04 0.03 0.080.09 0.07 0.10 0.09 0.08 0.07
0.1
5
0.1
6
0.1
2
0.2
0
0.1
1
0.2
2
0.1
3
0.2
0
0.1
1
0.2
4
0.1
0
0.1
1
0.1
0
0.1
0
0.1
6
0.1
7
0.09 0.14 0.09 0.14 0.06 0.120.13 0.12 0.13 0.12 0.12 0.10
0.1
8
0.2
0
0.1
4
0.2
4
0.1
3
0.2
6
0.1
3
0.2
7
0.0
9
0.2
1
0.1
8
0.1
5
0.2
0
0.1
4
0.1
6
0.1
2
0.13 0.17 0.08 0.14 0.12 0.110.13 0.13 0.13 0.11 0.11 0.11
0.1
9
0.1
7
0.1
8
0.2
0
0.1
5
0.2
3
0.1
3
0.2
5
0.1
3
0.1
7
0.1
7
0.1
5
0.1
8
0.1
4
0.2
1
0.1
0
0.18 0.17 0.14 0.15 0.14 0.140.13 0.13 0.12 0.11 0.12 0.12
0.1
3
0.1
6
0.0
8
0.1
7
0.0
7
0.1
9
0.0
6
0.2
5
0.0
6
0.1
6
0.0
8
0.1
3
0.0
8
0.1
2
0.1
3
0.0
9
0.20 0.20 0.17 0.15 0.14 0.130.14 0.12 0.13 0.11 0.12 0.12
0.1
7
0.1
1
0.1
0
0.1
4
0.1
1
0.1
4
0.1
1
0.1
9
0.1
2
0.1
1
0.1
7
0.0
8
0.1
8
0.0
8
0.1
9
0.0
7
0.20 0.22 0.15 0.14 0.13 0.200.14 0.12 0.13 0.12 0.13 0.09
0.1
4
0.1
1
0.1
3
0.1
7
0.1
4
0.1
7
0.1
0
0.1
6
0.0
7
0.1
2
0.1
1
0.0
8
0.1
0
0.1
0
0.1
3
0.0
7
0.14 0.23 0.20 0.15 0.13 0.200.14 0.13 0.13 0.12 0.13 0.12
0.1
0
0.0
7
0.0
8
0.1
0
0.0
8
0.1
0
0.0
5
0.1
1
0.0
7
0.0
9
0.1
2
0.0
8
0.1
2
0.0
9
0.1
4
0.0
3
0.15 0.24 0.21 0.23 0.21 0.170.14 0.13 0.14 0.13 0.13 0.13
0.0
9
0.0
4
0.0
5
0.0
3
0.0
6
0.0
3
0.0
6
0.0
9
0.0
4
0.0
8
0.0
9
0.0
6
0.0
8
0.0
6
0.1
1
0.0
2
0.16 0.24 0.21 0.23 0.22 0.170.14 0.13 0.14 0.13 0.13 0.13
0.0
7
0.0
3
0.0
3
0.0
3
0.0
4
0.0
3
0.0
4
0.0
7
0.0
2
0.0
7
0.0
4
0.0
4
0.0
4
0.0
4
0.0
8
0.0
1
0.18 0.23 0.21 0.22 0.21 0.180.13 0.13 0.14 0.13 0.13 0.13
0.0
5
0.0
1
0.0
0
0.0
1
0.0
1
0.0
0
0.0
1
0.0
5
0.0
0
0.0
5
0.0
2
0.0
1
0.0
2
0.0
1
0.0
5
0.0
0
0.17 0.21 0.18 0.19 0.18 0.180.13 0.12 0.13 0.12 0.12 0.13
0.0
1
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
0.0
1
0.0
9
0.1
1
0.1
5
0.1
5
0.1
5
0.1
5
0.1
1
0.0
9
0.27Max:
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
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173
0.05 0.01 0.03 0.03 0.02 0.040.03 0.07 0.07 0.08 0.05 0.05
0.1
5
0.0
6
0.0
8
0.0
6
0.0
7
0.0
7
0.1
2
0.1
0
0.0
8
0.1
4
0.0
7
0.0
8
0.0
9
0.0
8
0.1
1
0.1
2
0 .09 0.05 0.07 0.08 0.05 0.090.08 0.11 0.11 0.11 0.10 0.09
0.1
9
0.1
4
0.2
1
0.1
4
0.2
0
0.1
8
0.1
8
0.1
5
0.1
3
0.1
9
0.1
2
0.1
9
0.1
4
0.1
7
0.1
6
0.1
8
0 .11 0.12 0.11 0.12 0.08 0.110.12 0.12 0.12 0.12 0.11 0.10
0.1
9
0.1
6
0.2
0
0.2
2
0.1
7
0.2
5
0.1
4
0.2
1
0.1
1
0.1
9
0.1
8
0.1
8
0.2
0
0.1
4
0.2
0
0.1
0
0 .17 0.20 0.15 0.16 0.11 0.070.12 0.12 0.12 0.11 0.10 0.12
0.2
9
0.1
0
0.2
7
0.1
6
0.2
6
0.1
7
0.1
6
0.2
3
0.0
9
0.2
2
0.1
9
0.2
2
0.1
8
0.2
2
0.2
0
0.1
0
0 .19 0.20 0.20 0.18 0.16 0.170.12 0.13 0.11 0.13 0.11 0.12
0.1
8
0.0
9
0.1
5
0.1
7
0.1
4
0.1
6
0.0
6
0.1
9
0.0
5
0.1
8
0.1
0
0.1
5
0.1
0
0.1
5
0.1
5
0.0
8
0 .16 0.19 0.15 0.18 0.18 0.180.13 0.12 0.12 0.12 0.12 0.12
0.1
9
0.1
1
0.1
5
0.1
6
0.1
5
0.1
6
0.1
0
0.2
1
0.1
0
0.1
8
0.1
8
0.1
3
0.1
9
0.1
3
0.2
1
0.0
6
0 .13 0.15 0.12 0.20 0.17 0.180.13 0.13 0.13 0.12 0.12 0.12
0.1
5
0.0
4
0.1
0
0.1
1
0.1
0
0.1
1
0.0
5
0.1
4
0.0
4
0.1
4
0.1
0
0.0
9
0.1
0
0.0
9
0.1
4
0.0
4
0 .19 0.18 0.15 0.20 0.19 0.150.13 0.12 0.12 0.13 0.12 0.13
0.1
3
0.0
5
0.1
0
0.1
3
0.1
1
0.1
2
0.0
4
0.1
5
0.0
4
0.1
2
0.0
6
0.0
6
0.0
5
0.0
6
0.1
3
0.0
30 .20 0.24 0.20 0.23 0.20 0.210.13 0.13 0.13 0.13 0.13 0.13
0.1
1
0.0
3
0.0
7
0.0
9
0.0
8
0.0
9
0.0
2
0.1
2
0.0
2
0.1
0
0.0
6
0.0
6
0.0
6
0.0
6
0.1
0
0.0
2
0 .21 0.24 0.22 0.23 0.23 0.220.14 0.13 0.14 0.14 0.14 0.13
0.1
1
0.0
3
0.0
4
0.0
6
0.0
5
0.0
6
0.0
2
0.1
3
0.0
2
0.1
1
0.0
5
0.0
5
0.0
5
0.0
6
0.1
1
0.0
2
0 .21 0.24 0.22 0.23 0.23 0.220.14 0.13 0.14 0.13 0.13 0.14
0.0
6
0.0
1
0.0
3
0.0
3
0.0
3
0.0
2
0.0
1
0.0
7
0.0
1
0.0
7
0.0
5
0.0
2
0.0
5
0.0
3
0.0
9
0.0
0
0 .20 0.24 0.22 0.23 0.24 0.200.13 0.13 0.13 0.13 0.13 0.13
0.0
4
0.0
0
0.0
2
0.0
1
0.0
2
0.0
1
0.0
0
0.0
3
0.1
1
0.1
4
0.1
9
0.2
0
0.1
9
0.2
1
0.1
5
0.1
2
0.29Max:
Fig. 4.68 Daños 12P-Z3S2. R = 4.50
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
174
0.03 0.01 0.02 0.02 0.00 0.020.01 0.03 0.05 0.04 0.03 0.01
0.0
8
0.0
8
0.0
4
0.0
4
0.0
4
0.0
5
0.0
6
0.1
0
0.0
8
0.0
8
0.0
4
0.0
4
0.0
5
0.0
3
0.1
0
0.0
6
0 .08 0.02 0.05 0.04 0.02 0.080.05 0.07 0.10 0.11 0.07 0.07
0.1
9
0.1
5
0.1
8
0.1
8
0.1
6
0.1
9
0.1
8
0.1
7
0.1
5
0.2
5
0.1
1
0.1
1
0.1
3
0.0
9
0.1
6
0.1
9
0 .12 0.16 0.12 0.16 0.09 0.110.13 0.12 0.13 0.12 0.12 0.11
0.2
3
0.2
5
0.1
9
0.2
8
0.1
7
0.3
0
0.1
9
0.2
7
0.1
3
0.2
6
0.2
2
0.1
8
0.2
3
0.1
6
0.2
3
0.1
7
0 .14 0.21 0.12 0.15 0.11 0.130.13 0.13 0.13 0.11 0.11 0.12
0.2
4
0.1
5
0.1
4
0.1
4
0.1
2
0.1
6
0.1
4
0.2
6
0.1
0
0.2
2
0.1
7
0.1
5
0.1
8
0.1
4
0.2
1
0.1
3
0 .16 0.17 0.13 0.16 0.14 0.180.13 0.13 0.12 0.12 0.12 0.12
0.1
7
0.1
7
0.0
8
0.2
5
0.0
7
0.2
6
0.0
7
0.2
8
0.0
7
0.1
8
0.1
3
0.1
4
0.1
4
0.1
3
0.1
9
0.0
7
0 .19 0.19 0.16 0.19 0.15 0.140.13 0.13 0.13 0.12 0.13 0.12
0.1
9
0.0
7
0.1
3
0.1
4
0.1
3
0.1
3
0.0
6
0.2
1
0.0
6
0.1
5
0.1
5
0.0
8
0.1
5
0.0
8
0.1
9
0.0
4
0 .18 0.20 0.16 0.21 0.18 0.170.13 0.12 0.13 0.12 0.13 0.12
0.2
0
0.0
9
0.1
5
0.1
7
0.1
4
0.1
7
0.0
8
0.2
0
0.0
7
0.1
7
0.1
3
0.1
2
0.1
3
0.1
3
0.2
0
0.0
6
0 .19 0.23 0.20 0.21 0.19 0.190.14 0.13 0.13 0.13 0.13 0.12
0.1
3
0.0
4
0.0
7
0.1
0
0.0
7
0.0
8
0.0
2
0.1
4
0.0
5
0.1
2
0.0
8
0.0
4
0.0
8
0.0
6
0.1
6
0.0
2
0 .20 0.24 0.20 0.24 0.20 0.210.14 0.13 0.14 0.13 0.13 0.13
0.1
2
0.0
3
0.0
5
0.0
5
0.0
5
0.0
4
0.0
4
0.1
3
0.0
3
0.1
2
0.1
1
0.0
6
0.1
1
0.0
6
0.1
4
0.0
2
0 .20 0.21 0.15 0.20 0.16 0.210.14 0.13 0.13 0.13 0.13 0.13
0.0
9
0.0
2
0.0
2
0.0
2
0.0
2
0.0
2
0.0
3
0.0
9
0.0
1
0.0
8
0.0
3
0.0
2
0.0
2
0.0
2
0.0
8
0.0
0
0 .21 0.20 0.16 0.18 0.17 0.220.14 0.13 0.13 0.13 0.13 0.14
0.0
6
0.0
1
0.0
2
0.0
3
0.0
3
0.0
3
0.0
1
0.0
7
0.0
1
0.0
6
0.0
3
0.0
1
0.0
2
0.0
2
0.0
7
0.0
0
0 .19 0.22 0.18 0.20 0.18 0.200.14 0.12 0.13 0.13 0.13 0.13
0.0
2
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
0.0
3
0.0
8
0.1
1
0.1
7
0.1
6
0.1
7
0.1
6
0.1
1
0.0
8
0.30Max:
Fig. 4.69 Daños 12P-Z3S2. R = 6.00
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
175
0.08 0.00 0.03 0.01 0.00 0.070.01 0.06 0.03 0.06 0.05 0.04
0.0
6
0.0
1
0.0
7
0.0
3
0.0
4
0.0
5
0.0
2
0.0
5
0.0
4
0.0
6
0.0
3
0.0
6
0.0
8
0.0
2
0.0
7
0.0
2
0 .11 0.03 0.08 0.09 0.05 0.110.09 0.11 0.10 0.11 0.10 0.10
0.2
4
0.1
2
0.2
8
0.1
8
0.2
7
0.1
9
0.2
1
0.1
6
0.1
0
0.1
6
0.1
7
0.2
0
0.1
7
0.1
8
0.1
6
0.1
0
0 .20 0.18 0.20 0.18 0.19 0.150.12 0.13 0.12 0.13 0.11 0.13
0.2
0
0.0
7
0.2
9
0.2
3
0.2
8
0.2
3
0.0
9
0.1
6
0.0
4
0.1
7
0.2
0
0.2
4
0.1
9
0.2
4
0.1
5
0.0
6
0 .21 0.19 0.20 0.18 0.17 0.170.12 0.13 0.12 0.13 0.12 0.12
0.1
7
0.0
8
0.2
3
0.2
2
0.2
3
0.2
3
0.0
6
0.1
9
0.0
7
0.2
4
0.1
8
0.3
2
0.1
9
0.3
1
0.1
7
0.1
2
0 .20 0.19 0.19 0.20 0.20 0.180.12 0.13 0.12 0.13 0.11 0.13
0.1
7
0.0
4
0.1
8
0.1
4
0.1
8
0.1
6
0.0
6
0.1
5
0.0
5
0.1
5
0.1
5
0.1
4
0.1
5
0.1
4
0.1
3
0.0
5
0 .21 0.21 0.21 0.21 0.21 0.170.13 0.13 0.13 0.13 0.13 0.13
0.1
9
0.0
7
0.2
2
0.1
8
0.2
2
0.1
8
0.0
9
0.1
7
0.0
6
0.1
4
0.1
6
0.1
3
0.1
6
0.1
4
0.1
6
0.0
7
0 .24 0.23 0.24 0.24 0.21 0.210.13 0.14 0.13 0.14 0.13 0.13
0.2
4
0.1
0
0.2
7
0.2
3
0.2
7
0.2
2
0.1
2
0.2
2
0.0
9
0.1
7
0.1
9
0.1
3
0.1
8
0.1
3
0.1
9
0.0
6
0 .26 0.26 0.27 0.25 0.24 0.240.15 0.15 0.13 0.16 0.13 0.14
0.2
3
0.0
5
0.2
8
0.1
9
0.2
9
0.1
8
0.1
2
0.1
7
0.0
5
0.1
3
0.1
4
0.1
3
0.1
5
0.1
2
0.1
3
0.0
5
0 .30 0.28 0.27 0.28 0.29 0.300.14 0.17 0.15 0.16 0.16 0.16
0.1
8
0.0
6
0.2
1
0.1
7
0.2
1
0.1
7
0.0
8
0.1
6
0.0
4
0.1
2
0.1
2
0.1
4
0.1
1
0.1
5
0.1
1
0.0
6
0 .30 0.30 0.28 0.28 0.30 0.300.16 0.15 0.15 0.16 0.14 0.17
0.0
7
0.0
5
0.0
9
0.1
3
0.1
0
0.1
2
0.0
3
0.1
0
0.0
5
0.1
6
0.1
1
0.1
5
0.1
1
0.1
5
0.1
2
0.0
8
0 .28 0.29 0.27 0.28 0.29 0.290.15 0.16 0.15 0.15 0.15 0.16
0.0
8
0.0
6
0.0
7
0.1
0
0.0
7
0.0
9
0.0
4
0.1
1
0.0
9
0.2
0
0.1
4
0.2
0
0.1
4
0.2
1
0.1
5
0.1
4
0 .25 0.26 0.25 0.25 0.26 0.260.15 0.14 0.14 0.15 0.14 0.15
0.0
2
0.0
1
0.0
0
0.0
1
0.0
0
0.0
1
0.0
0
0.0
2
0.1
7
0.2
0
0.2
0
0.2
3
0.2
0
0.2
3
0.1
8
0.2
0
0.32Max:
Fig. 4.70 Daños 12P-Z3S4. R = 3.32
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
176
0.03 0.00 0.01 0.02 0.00 0.030.00 0.04 0.04 0.04 0.03 0.01
0.0
6
0.0
1
0.0
5
0.0
3
0.0
2
0.0
5
0.0
1
0.0
5
0.0
1
0.0
6
0.0
2
0.0
6
0.0
7
0.0
2
0.0
6
0.0
2
0 .08 0.01 0.07 0.08 0.02 0.070.02 0.09 0.10 0.10 0.08 0.03
0.1
5
0.0
9
0.1
7
0.1
3
0.1
1
0.1
9
0.1
1
0.1
4
0.0
7
0.1
6
0.0
9
0.1
6
0.1
5
0.1
0
0.1
1
0.1
2
0 .12 0.16 0.12 0.16 0.06 0.110.11 0.11 0.11 0.11 0.11 0.10
0.1
8
0.1
2
0.1
9
0.1
8
0.1
5
0.2
2
0.1
3
0.1
7
0.0
6
0.1
7
0.1
1
0.1
1
0.1
1
0.0
9
0.1
2
0.1
1
0 .19 0.20 0.14 0.15 0.11 0.100.12 0.12 0.12 0.12 0.10 0.11
0.2
3
0.1
2
0.2
5
0.2
5
0.2
4
0.2
5
0.1
3
0.2
3
0.0
6
0.2
1
0.2
1
0.2
0
0.2
1
0.1
9
0.2
0
0.0
8
0 .21 0.23 0.21 0.21 0.14 0.190.13 0.13 0.13 0.12 0.11 0.12
0.1
8
0.0
9
0.1
8
0.2
5
0.1
7
0.2
5
0.0
5
0.2
4
0.0
6
0.1
8
0.1
8
0.1
8
0.1
6
0.1
9
0.1
8
0.0
8
0 .22 0.24 0.22 0.23 0.19 0.220.14 0.13 0.14 0.12 0.12 0.13
0.1
5
0.0
6
0.1
6
0.2
0
0.1
6
0.1
9
0.0
4
0.1
9
0.0
7
0.1
5
0.1
6
0.1
1
0.1
6
0.1
1
0.2
0
0.0
5
0 .22 0.26 0.22 0.23 0.20 0.250.15 0.13 0.14 0.12 0.14 0.12
0.2
0
0.1
1
0.2
2
0.2
9
0.2
2
0.2
9
0.0
8
0.2
6
0.0
8
0.1
5
0.1
8
0.1
3
0.1
8
0.1
3
0.1
9
0.0
6
0 .22 0.29 0.24 0.27 0.19 0.260.16 0.14 0.16 0.14 0.14 0.13
0.1
9
0.1
1
0.1
8
0.2
2
0.1
8
0.2
1
0.0
7
0.2
4
0.0
8
0.1
1
0.1
3
0.0
7
0.1
3
0.0
8
0.1
7
0.0
3
0 .24 0.33 0.26 0.32 0.27 0.300.17 0.15 0.17 0.14 0.16 0.15
0.2
1
0.1
0
0.1
9
0.1
9
0.2
0
0.1
8
0.1
0
0.2
2
0.1
2
0.1
5
0.1
6
0.1
1
0.1
6
0.1
1
0.2
2
0.0
6
0 .26 0.34 0.28 0.33 0.29 0.310.18 0.15 0.17 0.15 0.17 0.16
0.1
3
0.0
5
0.1
1
0.1
1
0.1
2
0.1
1
0.0
5
0.1
4
0.0
9
0.1
5
0.1
7
0.1
2
0.1
7
0.1
2
0.2
0
0.0
5
0 .26 0.33 0.28 0.32 0.29 0.300.16 0.16 0.16 0.15 0.17 0.15
0.1
2
0.0
6
0.0
7
0.0
9
0.0
7
0.0
9
0.0
4
0.1
3
0.1
4
0.1
8
0.1
9
0.1
4
0.1
8
0.1
5
0.2
3
0.1
0
0 .23 0.32 0.27 0.30 0.28 0.270.17 0.14 0.15 0.15 0.15 0.15
0.0
8
0.0
3
0.0
4
0.0
3
0.0
4
0.0
3
0.0
4
0.0
5
0.2
5
0.2
6
0.3
5
0.2
3
0.3
5
0.2
3
0.3
2
0.2
1
0.35Max:
Fig. 4.71 Daños 12P-Z3S4. R = 4.50
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
177
0.05 0.00 0.02 0.02 0.00 0.050.01 0.04 0.05 0.05 0.05 0.02
0.0
7
0.0
5
0.0
6
0.0
4
0.0
3
0.0
6
0.0
3
0.0
8
0.0
5
0.0
6
0.0
5
0.0
4
0.0
8
0.0
2
0.0
7
0.0
3
0 .10 0.03 0.06 0.06 0.03 0.090.07 0.11 0.11 0.11 0.09 0.09
0.1
7
0.0
9
0.2
0
0.1
7
0.1
6
0.2
0
0.1
3
0.1
3
0.0
9
0.2
0
0.1
2
0.1
2
0.1
4
0.0
9
0.1
5
0.1
2
0 .14 0.18 0.14 0.18 0.10 0.140.12 0.12 0.12 0.12 0.12 0.12
0.2
5
0.2
0
0.3
2
0.3
4
0.3
1
0.3
5
0.1
7
0.2
9
0.1
3
0.2
3
0.2
1
0.2
5
0.2
1
0.2
5
0.2
3
0.1
3
0 .22 0.23 0.21 0.20 0.13 0.140.14 0.14 0.13 0.13 0.11 0.12
0.1
6
0.1
0
0.1
4
0.2
5
0.1
4
0.2
5
0.0
4
0.2
5
0.0
4
0.2
0
0.1
3
0.1
9
0.1
3
0.1
9
0.1
7
0.0
7
0 .22 0.25 0.22 0.24 0.18 0.230.15 0.13 0.14 0.12 0.14 0.13
0.1
8
0.1
5
0.1
6
0.3
2
0.1
5
0.3
2
0.0
5
0.3
2
0.0
5
0.2
3
0.1
5
0.2
0
0.1
5
0.1
9
0.1
8
0.0
8
0 .23 0.29 0.23 0.28 0.20 0.260.17 0.13 0.16 0.12 0.14 0.13
0.1
8
0.1
1
0.1
9
0.3
1
0.1
9
0.3
1
0.0
5
0.2
9
0.0
9
0.2
2
0.2
3
0.2
3
0.2
3
0.2
2
0.2
4
0.0
9
0 .24 0.31 0.25 0.31 0.21 0.300.18 0.14 0.18 0.14 0.17 0.12
0.1
8
0.0
8
0.1
8
0.2
2
0.1
8
0.2
2
0.0
5
0.2
2
0.0
4
0.1
4
0.1
5
0.1
1
0.1
5
0.1
2
0.1
9
0.0
5
0 .25 0.33 0.26 0.32 0.23 0.320.18 0.14 0.18 0.14 0.19 0.13
0.1
9
0.1
3
0.2
0
0.2
9
0.2
1
0.2
9
0.0
7
0.2
8
0.0
8
0.1
5
0.2
0
0.1
4
0.2
0
0.1
4
0.2
3
0.0
4
0 .26 0.35 0.26 0.34 0.27 0.330.19 0.14 0.19 0.15 0.18 0.15
0.1
7
0.0
5
0.1
6
0.1
2
0.1
6
0.1
2
0.0
6
0.1
8
0.1
1
0.1
8
0.2
1
0.1
5
0.2
1
0.1
5
0.2
4
0.0
7
0 .26 0.34 0.27 0.32 0.28 0.320.19 0.14 0.18 0.15 0.17 0.15
0.1
1
0.0
4
0.0
7
0.0
7
0.0
7
0.0
7
0.0
3
0.1
1
0.0
8
0.1
2
0.1
4
0.0
8
0.1
4
0.0
9
0.1
9
0.0
3
0 .26 0.32 0.27 0.31 0.28 0.310.17 0.15 0.17 0.15 0.17 0.15
0.1
0
0.0
3
0.0
8
0.0
8
0.0
9
0.0
7
0.0
3
0.1
1
0.0
7
0.1
2
0.1
6
0.0
8
0.1
5
0.0
9
0.1
7
0.0
4
0 .25 0.31 0.27 0.30 0.28 0.280.17 0.14 0.16 0.14 0.16 0.15
0.0
6
0.0
1
0.0
5
0.0
3
0.0
5
0.0
2
0.0
2
0.0
5
0.2
7
0.2
5
0.4
1
0.3
3
0.4
1
0.3
4
0.3
1
0.2
1
0.41Max:
Fig. 4.72 Daños 12P-Z3S4. R = 6.00
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
178
0.14 0.05 0.09 0.08 0.06 0.150.11 0.11 0.12 0.11 0.13 0.10
0.0
9
0.0
3
0.0
4
0.0
2
0.0
3
0.0
3
0.0
4
0.0
8
0.1
1
0.0
5
0.0
6
0.0
8
0.0
6
0.0
7
0.1
0
0.0
7
0.12 0.15 0.15 0.15 0.15 0.110.12 0.10 0.11 0.11 0.10 0.12
0.1
7
0.1
9
0.2
4
0.2
2
0.2
4
0.2
3
0.1
9
0.1
5
0.1
7
0.1
3
0.1
5
0.1
6
0.1
5
0.1
4
0.1
4
0.1
3
0.20 0.20 0.20 0.20 0.20 0.140.12 0.12 0.12 0.12 0.12 0.13
0.3
0
0.1
9
0.3
1
0.2
8
0.3
1
0.2
7
0.2
1
0.2
3
0.1
3
0.2
1
0.2
2
0.2
0
0.2
2
0.1
9
0.2
0
0.1
3
0.25 0.23 0.25 0.20 0.16 0.200.14 0.14 0.14 0.15 0.13 0.13
0.2
4
0.1
1
0.2
7
0.1
9
0.2
7
0.1
9
0.1
5
0.1
9
0.1
6
0.1
7
0.2
4
0.1
6
0.2
4
0.1
6
0.2
2
0.1
3
0.27 0.24 0.28 0.20 0.22 0.230.14 0.15 0.14 0.15 0.13 0.14
0.2
7
0.1
2
0.3
0
0.1
9
0.2
9
0.1
8
0.1
8
0.2
3
0.1
8
0.2
5
0.3
0
0.2
1
0.3
0
0.2
0
0.2
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0.1
3
0.26 0.22 0.27 0.20 0.24 0.240.13 0.15 0.14 0.15 0.14 0.15
0.1
4
0.0
8
0.1
8
0.1
1
0.1
8
0.1
3
0.1
3
0.1
1
0.0
9
0.1
5
0.1
6
0.1
9
0.1
7
0.1
9
0.1
2
0.1
2
0.24 0.20 0.25 0.20 0.25 0.220.13 0.14 0.14 0.15 0.14 0.15
0.1
5
0.1
4
0.1
8
0.1
9
0.1
7
0.1
8
0.1
4
0.1
6
0.1
4
0.1
7
0.1
9
0.2
0
0.2
0
0.2
0
0.1
6
0.1
6
0.22 0.19 0.24 0.18 0.24 0.210.14 0.15 0.13 0.15 0.14 0.15
0.1
2
0.1
3
0.1
1
0.1
3
0.1
1
0.1
2
0.1
4
0.1
2
0.0
9
0.1
2
0.0
8
0.1
1
0.0
9
0.1
1
0.0
8
0.1
4
0.22 0.19 0.22 0.19 0.22 0.200.13 0.15 0.13 0.14 0.14 0.15
0.1
2
0.1
2
0.1
2
0.1
3
0.1
1
0.1
4
0.1
4
0.1
4
0.1
1
0.1
0
0.0
7
0.0
9
0.0
7
0.0
8
0.0
7
0.1
3
0.21 0.21 0.22 0.20 0.23 0.190.14 0.14 0.13 0.14 0.13 0.16
0.1
0
0.1
1
0.0
9
0.0
6
0.0
9
0.0
5
0.1
4
0.0
8
0.0
8
0.0
9
0.0
4
0.0
7
0.0
5
0.0
6
0.0
8
0.1
1
0.23 0.21 0.22 0.20 0.23 0.200.13 0.16 0.13 0.14 0.14 0.15
0.0
7
0.0
8
0.0
4
0.0
5
0.0
4
0.0
5
0.1
0
0.0
8
0.1
2
0.1
0
0.0
7
0.0
8
0.0
7
0.0
7
0.0
9
0.1
4
0.20 0.23 0.22 0.21 0.25 0.180.15 0.14 0.13 0.14 0.13 0.16
0.0
1
0.0
3
0.0
0
0.0
1
0.0
0
0.0
1
0.0
3
0.0
2
0.1
3
0.1
8
0.1
2
0.2
3
0.1
2
0.2
3
0.1
4
0.1
6
0.31Max:
Fig. 4.73 Daños 12P-Z7S2. R = 3.32
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
179
0.13 0.08 0.06 0.10 0.04 0.130.11 0.12 0.13 0.12 0.12 0.11
0.1
3
0.1
1
0.1
0
0.1
0
0.0
7
0.1
0
0.0
9
0.1
5
0.2
2
0.0
7
0.1
9
0.1
4
0.2
1
0.1
2
0.0
8
0.2
0
0.10 0.15 0.16 0.16 0.15 0.100.11 0.10 0.11 0.11 0.10 0.12
0.3
1
0.2
1
0.3
7
0.2
9
0.3
8
0.2
9
0.3
1
0.2
0
0.2
4
0.2
0
0.2
7
0.2
9
0.2
7
0.3
0
0.2
3
0.2
0
0.23 0.19 0.23 0.19 0.24 0.140.12 0.14 0.12 0.14 0.12 0.16
0.3
4
0.1
9
0.4
1
0.3
4
0.4
1
0.3
5
0.2
6
0.2
6
0.2
0
0.3
4
0.3
2
0.3
8
0.3
0
0.3
7
0.2
6
0.2
6
0.27 0.20 0.29 0.14 0.18 0.170.12 0.15 0.12 0.18 0.12 0.14
0.1
9
0.1
3
0.2
7
0.1
9
0.2
7
0.1
8
0.1
7
0.1
4
0.1
3
0.2
7
0.2
3
0.2
8
0.2
4
0.2
7
0.2
2
0.1
4
0.26 0.20 0.27 0.17 0.21 0.200.13 0.15 0.13 0.15 0.13 0.15
0.2
8
0.1
4
0.2
5
0.1
7
0.2
4
0.1
7
0.1
4
0.2
2
0.1
2
0.2
8
0.1
7
0.2
7
0.1
7
0.2
7
0.1
9
0.1
8
0.25 0.20 0.26 0.16 0.23 0.190.12 0.14 0.12 0.15 0.11 0.16
0.1
6
0.1
3
0.1
2
0.1
3
0.1
2
0.1
3
0.1
0
0.1
7
0.0
8
0.2
4
0.1
0
0.2
0
0.1
0
0.2
0
0.1
3
0.1
4
0.24 0.20 0.24 0.18 0.22 0.200.12 0.14 0.13 0.14 0.13 0.14
0.1
5
0.1
4
0.1
1
0.1
7
0.1
2
0.1
7
0.1
0
0.2
2
0.1
2
0.1
7
0.1
2
0.1
4
0.1
2
0.1
3
0.1
3
0.1
4
0.20 0.22 0.24 0.18 0.22 0.200.14 0.14 0.12 0.15 0.12 0.15
0.1
4
0.1
7
0.0
9
0.1
4
0.0
9
0.1
3
0.1
1
0.1
8
0.0
8
0.1
3
0.0
7
0.0
6
0.0
7
0.0
6
0.1
1
0.0
9
0.22 0.24 0.23 0.24 0.24 0.210.14 0.15 0.14 0.14 0.14 0.14
0.2
0
0.1
1
0.1
0
0.1
1
0.1
0
0.1
1
0.1
3
0.1
7
0.0
8
0.0
9
0.0
6
0.0
5
0.0
5
0.0
5
0.0
9
0.0
8
0.23 0.27 0.24 0.25 0.26 0.220.16 0.14 0.14 0.15 0.14 0.16
0.1
5
0.1
2
0.0
8
0.0
9
0.0
9
0.0
8
0.1
1
0.1
5
0.0
7
0.1
0
0.0
4
0.0
5
0.0
5
0.0
5
0.1
0
0.0
7
0.24 0.26 0.25 0.25 0.26 0.250.14 0.16 0.15 0.15 0.15 0.15
0.1
0
0.1
0
0.0
5
0.0
7
0.0
5
0.0
7
0.0
7
0.1
0
0.1
0
0.1
4
0.0
8
0.1
0
0.0
8
0.1
1
0.1
0
0.1
4
0.22 0.28 0.25 0.25 0.28 0.220.15 0.15 0.15 0.15 0.14 0.16
0.0
5
0.0
5
0.0
3
0.0
3
0.0
3
0.0
3
0.0
4
0.0
6
0.1
7
0.2
6
0.2
4
0.3
3
0.2
4
0.3
2
0.2
9
0.2
4
0.41Max:
Fig. 4.74 Daños 12P-Z7S2. R = 4.50
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
180
0.14 0.04 0.04 0.06 0.03 0.140.12 0.11 0.12 0.08 0.12 0.11
0.1
4
0.0
7
0.0
5
0.0
7
0.0
4
0.1
0
0.0
7
0.1
3
0.1
1
0.1
4
0.1
0
0.0
9
0.1
3
0.0
6
0.1
0
0.1
4
0 .11 0.13 0.17 0.18 0.13 0.110.11 0.11 0.12 0.11 0.11 0.11
0.2
1
0.2
2
0.2
7
0.2
9
0.2
8
0.2
9
0.2
2
0.2
1
0.1
6
0.2
0
0.2
3
0.2
3
0.2
3
0.2
1
0.2
3
0.1
3
0 .20 0.21 0.20 0.21 0.20 0.150.13 0.13 0.13 0.13 0.13 0.12
0.3
0
0.1
9
0.3
1
0.3
2
0.3
1
0.3
2
0.1
9
0.2
9
0.2
2
0.3
1
0.3
3
0.3
3
0.3
3
0.3
2
0.3
2
0.2
2
0 .22 0.23 0.23 0.18 0.15 0.200.14 0.14 0.13 0.14 0.13 0.13
0.3
0
0.1
7
0.3
2
0.2
5
0.3
0
0.2
5
0.1
9
0.2
9
0.1
5
0.2
5
0.2
5
0.2
3
0.2
6
0.2
1
0.2
8
0.1
1
0 .25 0.25 0.25 0.23 0.17 0.240.15 0.14 0.15 0.13 0.14 0.13
0.3
1
0.1
2
0.3
1
0.2
4
0.3
0
0.2
3
0.1
4
0.2
7
0.1
3
0.2
1
0.2
0
0.1
7
0.1
9
0.1
7
0.2
3
0.0
9
0 .27 0.26 0.27 0.24 0.22 0.250.15 0.15 0.14 0.15 0.14 0.15
0.2
3
0.1
0
0.2
2
0.2
3
0.2
2
0.2
4
0.0
9
0.2
5
0.1
1
0.2
2
0.2
2
0.2
2
0.2
3
0.2
2
0.2
4
0.1
1
0 .26 0.26 0.26 0.26 0.24 0.270.15 0.15 0.15 0.14 0.14 0.15
0.2
0
0.1
2
0.2
5
0.2
8
0.2
5
0.2
8
0.1
1
0.2
5
0.1
1
0.2
2
0.2
0
0.2
5
0.2
0
0.2
7
0.1
8
0.1
3
0 .24 0.28 0.26 0.27 0.25 0.270.16 0.14 0.15 0.15 0.15 0.15
0.2
0
0.1
4
0.2
2
0.2
4
0.2
3
0.2
4
0.1
1
0.2
4
0.0
9
0.1
7
0.1
7
0.1
4
0.1
7
0.1
4
0.1
9
0.0
7
0 .23 0.31 0.26 0.30 0.27 0.280.17 0.14 0.16 0.15 0.16 0.15
0.2
5
0.1
2
0.2
9
0.2
1
0.2
8
0.2
2
0.1
5
0.2
4
0.1
3
0.1
4
0.1
9
0.1
3
0.1
8
0.1
3
0.2
0
0.0
8
0 .26 0.33 0.28 0.31 0.29 0.300.17 0.15 0.16 0.15 0.17 0.16
0.1
1
0.1
2
0.1
7
0.1
0
0.1
7
0.1
0
0.1
9
0.0
5
0 .26 0.33 0.28 0.31 0.30 0.290.17 0.15 0.16 0.15 0.16 0.16
0.1
1
0.0
8
0.1
0
0.1
2
0.1
1
0.1
2
0.0
6
0.1
4
0.1
3
0.2
0
0.1
8
0.1
8
0.1
7
0.1
9
0.2
0
0.1
1
0 .24 0.31 0.27 0.29 0.29 0.260.17 0.15 0.15 0.15 0.15 0.16
0.0
9
0.0
4
0.0
4
0.0
4
0.0
4
0.0
4
0.0
5
0.0
7
0.2
5
0.2
7
0.4
2
0.3
3
0.4
1
0.3
3
0.3
1
0.2
3
0.42Max:
0.1
5
0.0
6
0.1
3
0.1
2
0.1
3
0.1
1
0.0
6
0.1
3
Fig. 4.75 Daños 12P-Z7S2. R = 6.00
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
181
Tabla. 4.28 Daños máximos en pórticos de 12 pisos.
ig. 4.76 Comparación de daños máximos para las diferentes alturas, en pórticos Z3S2 según nálisis inelástico.
FACTOR DE REDUCCION " R"
3.32 4.50 6.00
12P-Z3S2 0.27 0.29 0.3012P-Z3S4 0.32 0.35 0.4112P-Z7S2 0.31 0.41 0.4212P-Z7S4 ----- ----- -----
PORTICO
12 PISOS
DAÑO MAXIMO
0.0
0.2
0.3
0.5
0.6
0.8
0.9
3.00 4.00 5.00 6.00
R
Dañ
o
`
12 pisos
8 pisos
4 pisos
Fa
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
182
ig. 4.77 Compara
0.0
0.2
0.3
0.5
0.6
0.8
0.9
3.00 4.00 5.00 6.00
Fa
ción de daños máximos para las diferentes alturas, en pórticos Z3S4 según nálisis inelástico.
Fig. 4.78 Comparación de daños máximos para las diferentes alturas, en pórticos Z7S2 según análisis inelástico.
R
Dañ
o
`
12 pisos
8 pisos
4 pisos
0.0
0.2
0.3
0.5
0.6
0.8
0.9
3.00 4.00 5.00 6.00
R
Dañ
o
`
12 pisos
8 pisos
4 pisos
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
183
inelástico.
.2.4 Índices de confiabilidad
Tabla. 4.29 Índices de confiabilidad
3.32 4.50 6.00
4P-Z3S2 1.54 1.46 1.474P-Z3S4 1.65 1.11 1.104P-Z7S2 1.63 1.22 0.954P-Z7S4 1.74 1.04 0.82
8P-Z3S2 2.15 2.32 1.938P-Z3S4 1.09 1.55 1.548P-Z7S2 0.91 1.02 1.108P-Z7S4 1.85 1.97 1.72
12P-Z3S2 4.59 4.93 5.2312P-Z3S4 3.00 3.54 3.7012P-Z7S2 2.93 3.26 4.3412P-Z7S4 -------- -------- -------
PORTICOS DE 8 PISOS
PORTICOS DE 12 PISOS
PORTICOS DE 4 PISOS
0.0
0.2
0.3
0.5
0.6
0.8
0.9
3.00 4.00 5.00 6.00
R
Dañ
o
`8 pisos
4 pisos
Fig. 4.79 Comparación de daños máximos para las diferentes alturas, en pórticos Z7S4 según análisis
4
FACTOR DE REDUCCION "R"PORTICO
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
184
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
3.00 4.00 5.00 6.00
R
Ind
ice
de
con
fiab
ilid
ad
`
12 pisos
8 pisos
4 pisos
Fig. 4.80 Comparación de Índices de confiabilidad (), para las diferentes alturas en pórticos
Z3S2.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
3.00 4.00 5.00 6.00
R
Ind
ice
de
con
fiab
ilid
ad
`
12 pisos
8 pisos
4 pisos
Fig. 4.81 Comparación de Índices de confiabilidad (), para las diferentes alturas en pórticos
Z3S4.
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
185
Fig. 4.82 Comparación de Índices de confiabilidad (), para las diferentes alturas en pórticos
Z7S2.
Fig. 4.83 Comparación de Índices de confiabilidad (), para las diferentes alturas en pórticos
Z7S4.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
3.00 4.00 5.00 6.00
R
Ind
ices
de
con
fiab
ilid
ad
`12 pisos
8 pisos
4 pisos
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
3.00 4.00 5.00 6.00
R
Ind
ices
de
con
fiab
ilid
ad
`
8 pisos
4 pisos
CAPITULO IV. ANALISIS Y DISCUSION DE LOS RESULTDOS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
186
%%
%%
%%
VA
RIA
C.
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EV
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41.0
00.5
80.0
00.0
01.4
71.0
20.5
80.0
00.0
01.4
61.0
70.5
60.0
23.4
51.5
48
1.0
00.5
00.0
00.0
01.9
31.0
30.4
80.0
24.0
02.3
21.0
40.4
50.0
510.0
02.1
512
1.0
00.3
00.0
00.0
05.2
31.0
10.2
90.0
13.3
34.9
31.0
90.2
70.0
310.0
04.5
9
41.0
00.6
90.0
00.0
01.1
01.0
30.6
10.0
811.5
91.1
11.1
60.4
80.2
130.4
31.6
58
1.0
00.7
40.0
00.0
01.5
41.1
00.5
60.1
824.3
21.5
51.2
30.4
90.2
533.7
81.0
912
1.0
00.4
10.0
00.0
03.7
01.0
90.3
50.0
614.6
33.5
41.1
80.3
20.0
921.9
53.0
0
41.0
00.6
80.0
00.0
00.9
51.1
30.5
10.1
725.0
01.2
21.3
70.4
40.2
435.2
91.6
38
1.0
00.6
00.0
00.0
01.1
01.1
40.5
40.0
610.0
01.0
21.3
60.5
40.0
610.0
00.9
112
1.0
00.4
20.0
00.0
04.3
41.1
90.4
10.0
12.3
83.2
61.5
00.3
10.1
126.1
92.9
3
41.0
00.6
60.0
00.0
00.8
21.1
20.5
20.1
421.2
11.0
41.3
40.4
70.1
928.7
91.7
48
1.0
00.5
00.0
00.0
01.7
21.2
20.4
70.0
36.0
01.9
71.7
10.4
60.0
48.0
01.8
512
1.0
0--
---
----
---
---
----
-1.1
3--
---
----
---
---
----
--1.7
5--
----
----
----
----
----
--
m3 C
ON
CRETO
13 U
T
Kg
ACERO
0.0
8 U
TAlto C
ost
o V
s B
ajo
Ben
efic
io
Bajo
Cost
o V
s Alto B
enef
icio
Baj
o C
ost
o V
s Baj
o B
enef
icio
PIS
OS
Z3
S4
Z3
S2
Z7
S2
Z7
S4
6.0
04
.50
" R
"
3.3
2
conclusiones Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
CONCLUSIONES
En base a los resultados obtenidos se establecen las siguientes conclusiones:
1. En los pórticos de 4 pisos analizados, el uso de un factor de R igual a 6.00 y 4.50,
resulto en comportamientos deficientes con daños superiores a los valores
considerados como aceptables y derivas superiores a los valores limites, mientras que
el uso del valor de 3.32 resulto en una mejora significativa del comportamiento con
reducciones de daños y derivas a valores aceptables, con incrementos de costos
razonables al beneficio obtenido.
2. Los pórticos de 8 pisos estudiados, mostraron un comportamiento ambiguo, en zonas
de mayor sismicidad se comportaron parecidos a los de 12 pisos y en zonas de baja
sismicidad a los de 4 pisos.
3. En todos los pórticos de 12 pisos estudiados el uso de un valor de R = 6.00 tal como lo
especifica la norma resulto en comportamientos adecuados. Valores de R de 4.50 y
3.32 en estos pórticos resultaron en ligeras mejoras en el comportamiento no
justificadas con los valores de incrementos en costos obtenidos.
4. Tomando en consideración que la teoría indica que para valores bajos de periodos el
valor de R debe ser menor que μ, el comportamiento de los pórticos estudiados
muestra esta tendencia.
5. La Norma actual asigna un valor de R igual para todas las estructuras de un mismo
piso, los resultados indican que esto puede resultar en diseños inadecuados para
estructuras de bajo periodo y diseños conservadores para estructuras de periodos altos.
186
RECOMENDACIONES Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
RECOMENDACIONES
Como resultado de la investigación realizada, los valores obtenidos y las conclusiones antes
planteadas, es posible hacer las siguientes recomendaciones:
1. En edificios de 4 pisos se recomienda usar el criterio de igualdad de energía, utilizando un
Factor de Reducción de Respuesta igual a 3.32.
2. Realizar mayor número de análisis en pórticos con un rango de periodos suficientes para
determinar por debajo de cual valor de periodo el Factor de Reducción de Respuesta (R) debe
ser disminuido por debajo de μ.
3. Realizar investigaciones para determinar metodologías de cálculo del valor de R en función
de las características específicas de cada estructura, tales como: periodo y grado de sismicidad
para ser incluidas en versiones futuras de la Norma.
4. Debe hacerse presión sobre la comisión de la Normas para que establezcan posición sobre
los diferentes valores de R en función de las características específicas de cada estructura.
187
Referencias bibliograficas Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
REFERENCIAS BIBLIOGRÁFICAS
1 Ramírez, A. (1995) Análisis Dinámico con Modelos Histeréticos de Daños.
Trabajo de Grado. División de Postgrado. Facultad de Ingeniería. Universidad de los Andes. Mérida, Venezuela.
2 Cipollina, A., López, A., and Flórez, J. (1995) A Simplified Damage Mechanics Approach to Nonlinear Analysis of Frames. Computers & Structures. Vol. 54, Nº 6 1113-26.
3 Perdomo, M. (1997) Modelo Histerético de Daño para Pórticos de Concreto
Armado con Fuerza Axial Variable. Trabajo de Grado. División de Postgrado. Facultad de Ingeniería. Universidad de los Andes. Mérida, Venezuela.
4 Picón, R. (1999) Evolución de la Degradación de Rigidez en Pórticos de Concreto
Armado. Tesis de Grado. División de Postgrado. Facultad de Ingeniería. Universidad de los Andes. Mérida, Venezuela.
5 Delgado S. (2002) Cuantificación del Daño Estructural en Pórticos Planos de
Concreto Armado diseñados según la Norma COVENIN 1756-98 sometidos a Excitaciones Sísmicas. Trabajo de Grado. División de Postgrado. Facultad de Ingeniería. Universidad de Zulia. Maracaibo, Venezuela.
6 Avon, D. (2002) Un Algoritmo para Mejorar la Convergencia de Problemas No
Lineales en Mecánica de Sólidos. Tesis de Grado. División de Postgrado. Facultad de Ingeniería. Universidad de los Andes. Mérida, Venezuela.
7 Jaramillo, N. (2004) Portal de Pórticos: un Programa de Elementos Finitos basada
en la web. Trabajo de Grado. División de Postgrado. Facultad de Ingeniería. Universidad de los Andes. Mérida, Venezuela.
8 Perez, O. (2005). Índices de Confiabilidad estructural en Pórticos
Sismorresistentes de Concreto Armado. Trabajo de Grado. División de Postgrado. Facultad de Ingeniería. Universidad de Zulia. Maracaibo, Venezuela.
9 Vezga, C. (2002). Elementos de Ingeniería Sismorresistente. Servicios de
Imprenta Maracaibo. Venezuela. 10 Graces, J. (1987). Concreto Armado en Zonas Sísmicas. Editorial SIVENSA
Primera Edifición. 11 Flórez, J. (1998) Simplified Model of Unilateral Damage For Rc Frames. Journal
of Structural Engineering. American Society of Civil Engineers. Vol. 121, Nº 12 1765- 1771.
188
Referencias bibliograficas Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
12 Flórez, J. (1998) Frame Analysis and Continuum Damage Mechanics. European Journal of Mechanics A/ Solids. Vol. 17, Nº 2,269-283.
13 COVENIN 1756-2001 Edificaciones Sismorresistentes. Venezuela.
14 ANTEPROYECTO DE NORMA VENEZOLANA - FONACIT-SOCVIS
(2001) Concreto Estructural, Proyecto y Construcción. Venezuela. 15 Krawinkler, H. y Nassar A. (1992) Seismic Design base don ductility and
cumulative damage demands and capacities. Elsevier Applied Science, New York. 16 Miranda, E. y Bertero, V. (1994) Evaluation of Strength Reduction Factors for
Earthquake Spectra, 10(2), 357-380
17 Moses, F. (1974) Reliability of Structural Systems. Journal of the Structural Division, ASCE, 100 (ST9)
18 Newmark, N.M. y Hall W.J. (1982) Earthquake Spectra and Design. EERI
Monograph Series, EERI, Oakland, California. 19 Osteraas A. y Krawinkler H. (1990). Strength and Ductility Considerations in
Seismic Design. John A. Blume Earthquake Engineering Center, Report 90, Standford University, California.
20 Uang C.M y Maarouf (1993) Safety and economic considerations of UBC
seismic force reduction factors. Proceedings of the National Earthquake Conference, Memphis, Tennesse.
21 Florez López, J. Facultad de Ingeniería, Universidad de los Andes, Mérida,
Venezuela, ”Modelo de daño Concentrado para la Simulación Numérica del Colapso de Pórticos Planos” .Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería. (1993) Vol. 9 Nº2.123-139.
22 Hernández, R (1998) Metodología de la Investigación. Editorial Mc Graw-Hill.
México.
23 Chávez, N. (2001) Introducción a la Investigación Educativa. Tercera Edición. Editorial La Columna. Maracaibo-Venezuela.
24 Arias, F. (1999) El Proyecto de Investigación. Tercera Edición. Editorial
Episteme. Caracas-Venezuela.
25 COVENIN-MINDUR 2002 Acciones Mínimas para el Proyecto de Edificaciones. Venezuela.
189
Referencias bibliograficas Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
190
26 ACI 318-2002. American Concrete Institute. Building Code Requirements for Reiforced Concrete. Estados Unidos.
27 Méndez, C. (2001) Metodología Diseño y Desarrollo del Proceso de
Investigación. Editorial Mc Graw-Hill. Colombia. 28 COVENIN-MINDUR 1618-98 Estructuras de Acero para Edificaciones. Venezuela.
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
LUZ =>
As NEGATIVO (cm2) 6.12 6.27
As POSITIVO (cm2) 6.27 7.96
As - 2.39 4.0
As + 2.39 4.5
2R3/8" 2R3/
35 17,5 30.0
1.20 4.15
As NEGATIVO (cm2) 10.68 9.5
As POSITIVO (cm2) 9.50 12.3
As - 2.43 4.0
As + 2.43 4.2
2R3/8" 2R3/
40 17,5 30.0
1.55 3.41
As NEGATIVO (cm2) 15.01 9.5
As POSITIVO (cm2) 9.50 14.8
As - 2.45 4.0
As + 2.45 4.2
2R3/8" 2R3/
40 17,5 30.0
1.55 3.40
As NEGATIVO (cm2) 15.87 9.5
As POSITIVO (cm2) 9.50 17.0
As - 2.45 3.9
As + 2.45 4.1
2R3/8" 2R3/
40 17,5 30.0
1.55 3.39
60
60
PORTIC
55
PIS
O 4
ESTRIBOS
SEPARACIÓN (cm)
Arm
adur
a T
rans
vers
al
LONG, (m)
60
Long
, (m
)Ace
ro
Long
itudi
nal
60
PIS
O 3
Ace
ro
Long
itudi
nal
ESTRIBOS
SEPARACIÓN (cm)
LONG, (m)
77.
5
Long
, (m
)
Arm
adur
a T
rans
vers
al
PIS
O 2
Ace
ro
Long
itudi
nal
SEPARACIÓN (cm)
LONG, (m)
77.5
Long
, (m
)
Arm
adur
a T
rans
vers
al ESTRIBOS
PIS
O 1
Ace
ro
Long
itudi
nal
SEPARACIÓN (cm)
LONG, (m)
77.5
Long
, (m
)
Arm
adur
a T
rans
vers
al ESTRIBOS
6.27 6.27 6.12
10.44 7.96 6.27
3 4.98 4.03 2.39
9 7.80 4.59 2.39
8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
0 17,5 17,5 30.00 17,5 17,5 30 17,5
1.20 1.20 6.05 1.2 1.2 4.15 1.2
0 9.50 9.50 10.68
5 15.97 12.35 9.50
1 4.96 4.01 2.43
1 7.07 4.21 2.43
8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
0 15,0 12,5 30.00 12,5 15,0 30.00 17,5
1.55 1.55 5.33 1.55 1.55 3.41 1.55
0 9.50 9.50 15.01
5 18.13 14.85 9.504
0 4.96 4.00 2.45
0 7.07 4.20 2.45
8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
0 15,0 17,5 30.00 17,5 15,0 30.00 17,5
1.55 1.55 5.33 1.55 1.55 3.40 1.55
0 9.50 9.50 15.87
3 20.70 17.03 9.504
9 4.95 3.99 2.44688
9 7.05 4.19 2.44688
8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
0 15,0 10,0 30.00 10,0 15,0 30.00 17,5
1.55 1.55 5.30 1.55 1.55 3.39 1.55
O Z3S2.
7 9 7
21.32 21.32
10.66 10.66
4.30 4.30
2.70 2.70
27.15 27.15
13.58 13.58
4.31 4.31
3.43 3.43
29.72 29.72
14.86 14.86
4.31 4.31
3.43 3.43
32.35 32.35
16.18 16.18
4.32 4.32
3.45 3.45
LUZ =>
As NEGATIVO (cm2) 9.82 6.27
As POSITIVO (cm2) 6.27 8.45
As - 2.48 4.00
As + 2.48 4.55
2R3/8" 2R3/
35 17,5 30.0
1.20 4.10
As NEGATIVO (cm2) 15.35 10.1
As POSITIVO (cm2) 10.17 13.8
As - 2.49 3.98
As + 2.49 4.07
2R3/8" 2R3/
40 17,5 30.0
1.65 3.16
As NEGATIVO (cm2) 19.47 10.9
As POSITIVO (cm2) 10.17 17.8
As - 2.49 3.98
As + 2.49 4.07
2R3/8" 2R3/
40 17,5 30.0
1.65 3.16
As NEGATIVO (cm2) 22.02 13.6
As POSITIVO (cm2) 11.01 20.7
As - 2.55 3.94
As + 2.55 4.02
2R3/8" 2R3/
40 15,0 30.0
1.65 3.09
82.5
Lon
g,
(m)
Arm
adu
ra
Tra
nsve
rsal ESTRIBOSP
ISO
1
Ace
ro
Lon
gitu
din
al
SEPARACIÓN (cm)
LONG, (m)
82.5
Long
, (m
)
Arm
adur
a
Tra
nsv
ersa
l ESTRIBOSPIS
O 2
Ace
ro
Lon
gitu
dina
l
SEPARACIÓN (cm)
LONG, (m)
82.
5
Lon
g,
(m)
Arm
adu
ra
Tr a
nsve
rsal
60
PIS
O 3
Ace
ro
Long
itud
inal
ESTRIBOS
SEPARACIÓN (cm)
LONG, (m)
60
Lon
g,
(m)A
cero
Lo
ngi
tudi
nal
ESTRIBOS
SEPARACIÓN (cm)
Arm
adur
a T
rans
vers
al
LONG, (m)
60
60
PORTIC
55
PIS
O 4
6.27 6.27 9.82
11.10 8.45 6.27
4.98 4.00 2.48
7.80 4.55 2.48
8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
0 17,5 17,5 30.00 17,5 17,5 30 17,5
1.20 1.20 6.05 1.2 1.2 4.1 1.2
7 10.17 10.17 15.35
6 16.80 13.86 10.17
4.95 3.98 2.49
6.85 4.07 2.49
8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
0 17,5 12,5 30.00 12,5 17,5 30.00 17,5
1.65 1.65 5.10 1.65 1.65 3.16 1.65
1 10.17 10.91 19.47
8 20.36 17.88 10.1707
4.95 3.98 2.49063
6.85 4.07 2.49063
8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
0 15,0 17,5 30.00 17,5 15,0 30.00 17,5
1.65 1.65 5.10 1.65 1.65 3.16 1.65
0 11.44 13.60 22.02
9 22.46 20.79 11.01
4.91 3.94 2.54688
6.77 4.02 2.54688
8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
0 15,0 17,5 30.00 17,5 15,0 30.00 15,0
1.65 1.65 5.03 1.65 1.65 3.09 1.65
16.70 16.70
4.35 4.35
3.73 3.73
33.40 33.40
15.55 15.55
4.32 4.32
3.65 3.65
31.09 31.09
27.19
13.60 13.60
4.32 4.32
3.65 3.65
27.19
21.19
10.60 10.60
4.29 4.29
2.70 2.70
21.19
O Z3S4.
7 9 7
PORTICOS DE 4 PISOS R = 3.32
191
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
LUZ =>
As NEGATIVO (cm2) 15.35 6.84 6.84 6.84 15.35
As POSITIVO (cm2) 7.68 11.69 13.95 11.69 7.68
As - 2.56 3.96 4.95 3.96 2.56
As + 2.56 4.54 7.85 4.54 2.56
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17,5 30.00 17,5 17,5 30.00 17,5 17,5 30 17,5
1.15 4.13 1.15 1.15 6.10 1.15 1.15 4.125 1.15
As NEGATIVO (cm2) 23.24 14.02 11.87 14.02 23.24
As POSITIVO (cm2) 11.87 20.26 21.50 20.26 11.87
As - 2.55 3.95 4.93 3.95 2.55
As + 2.55 3.87 6.50 3.87 2.55
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
42.5 17,5 30.00 15,0 12,5 30.00 12,5 15,0 30.00 17,5
1.80 2.80 1.80 1.80 4.75 1.8 1.8 2.80 1.8
As NEGATIVO (cm2) 31.10 21.39 16.98 21.39 31.1
As POSITIVO (cm2) 16.23 27.73 27.14 27.73 16.23
As - 2.57 3.94 4.93 3.94 2.57188
As + 2.57 3.87 6.50 3.87 2.57188
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
42.5 12,5 30.00 12,5 17,5 30.00 17,5 12,5 30.00 12,5
1.80 2.79 1.80 1.80 4.75 1.8 1.8 2.79 1.8
As NEGATIVO (cm2) 35.91 25.65 19.45 25.65 35.91
As POSITIVO (cm2) 20.47 32.03 29.81 32.03 20.47
As - 2.65 3.89 4.88 3.89 2.64688
As + 2.65 3.79 6.40 3.79 2.64688
2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8"
42.5 12,5 30.00 17,5 10,0 30.00 10,0 17,5 30.00 12,5
1.80 2.69 1.80 1.80 4.65 1.8 1.8 2.69 1.8
90
20.15 20.15
Lon
g,
(m) 4.38 4.38
4.10 4.10
Arm
adu
ra
Tra
nsve
rsal ESTRIBOSP
ISO
1
Ace
ro
Long
itud
inal
40.29 40.29
SEPARACIÓN (cm)
LONG, (m)
90
18.73 18.73
Lon
g,
(m) 4.33 4.33
4.00 4.00
Arm
adur
a T
rans
vers
al ESTRIBOSPIS
O 2
Ace
ro
Lon
gitu
din
al
37.46 37.46
SEPARACIÓN (cm)
LONG, (m)
32.21
90
16.11 16.11
Lon
g,
(m) 4.34 4.34
4.00 4.00
Arm
adur
a
Tra
nsv
ersa
l
62.5
PIS
O 3
Ace
ro
Lon
gitu
din
al
32.21
ESTRIBOS
SEPARACIÓN (cm)
LONG, (m)
23.37
57.5
11.69 11.69
Long
, (m
) 4.31 4.31
2.65 2.65A
cero
L
ongi
tudi
nal
23.37
ESTRIBOS
SEPARACIÓN (cm)
Arm
adur
a
Tra
nsv
ersa
l
LONG, (m)
62.5
62.5
PORTICO Z7S2.
7 9 7
60
PIS
O 4
LUZ =>
As NEGATIVO (cm2) 14.47 6.53 6.53 6.53 14.47
As POSITIVO (cm2) 7.24 11.50 13.45 11.50 7.24
As - 2.56 3.96 4.95 3.96 2.56
As + 2.56 4.45 7.66 4.45 2.56
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30 17.5
1.25 3.93 1.25 1.25 5.90 1.25 1.25 3.925 1.25
As NEGATIVO (cm2) 23.77 15.00 12.13 15.00 23.77
As POSITIVO (cm2) 12.13 20.81 20.89 20.81 12.13
As - 2.59 3.94 4.93 3.94 2.59
As + 2.59 3.71 6.21 3.71 2.59
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 17.5 15 30.00 15 17.5 30.00 17.5
1.95 2.48 1.95 1.95 4.45 1.95 1.95 2.48 1.95
As NEGATIVO (cm2) 32.37 22.24 16.36 22.24 32.37
As POSITIVO (cm2) 17.66 27.91 25.76 27.91 17.66
As - 2.65 3.91 4.90 3.91 2.65313
As + 2.65 3.66 6.16 3.66 2.65313
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30.00 15
1.95 2.41 1.95 1.95 4.40 1.95 1.95 2.41 1.95
As NEGATIVO (cm2) 33.26 23.08 17.38 23.08 33.26
As POSITIVO (cm2) 18.04 28.71 26.67 28.71 18.04
As - 2.74 3.83 4.80 3.83 2.7375
As + 2.74 3.54 5.96 3.54 2.7375
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 12.5 30.00 12.5 12.5 30.00 12.5
1.95 2.25 1.95 1.95 4.20 1.95 1.95 2.25 1.95
60
60
PORTICO Z7S4.
7 9 7
55
PIS
O 4
21.81
ESTRIBOS
SEPARACIÓN (cm)
Arm
adur
a
Tra
nsv
ersa
l
LONG, (m)
21.81
62.5
10.91 10.91
Long
, (m
) 4.31 4.31
2.84 2.84
Ace
ro
Lon
gitu
din
al
60
PIS
O 3
Ace
ro
Lon
gitu
din
al
29.43
ESTRIBOS
SEPARACIÓN (cm)
LONG, (m)
29.43
97.5
14.72 14.72
Lon
g,
(m) 4.33 4.33
4.29 4.29
Arm
adur
a
Tra
nsv
ersa
l
PIS
O 2
Ace
ro
Lon
gitu
din
al
34.87 34.87
SEPARACIÓN (cm)
LONG, (m)
97.5
17.44 17.44
Lon
g,
(m) 4.35 4.35
4.34 4.34
Arm
adur
a T
rans
vers
al ESTRIBOS
PIS
O 1
Ace
ro
Long
itud
inal
36.17 36.17
SEPARACIÓN (cm)
LONG, (m)
97.5
18.09 18.09
Lon
g,
(m) 4.46 4.46
4.54 4.54
Arm
adu
ra
Tra
nsve
rsal ESTRIBOS
192
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 4 PISOS R = 4.50
LUZ =>
As NEGATIVO (cm2) 5.75 6.27 6.27 6.27 5.75
As POSITIVO (cm2) 6.27 7.76 10.44 7.76 6.27
As - 2.39 4.03 4.98 4.03 2.39
As + 2.39 4.59 7.80 4.59 2.39
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.50 30.00 17.50 17.50 30.00 17.5 17.5 30 17.5
1.20 4.15 1.20 1.20 6.05 1.2 1.2 4.15 1.2
As NEGATIVO (cm2) 9.59 8.60 8.60 8.60 9.59
As POSITIVO (cm2) 8.60 11.24 14.70 11.24 8.60
As - 2.41 4.02 4.98 4.02 2.41
As + 2.41 4.28 7.20 4.28 2.41
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
37.5 17.50 30.00 15.00 12.50 30.00 12.5 15 30.00 17.5
1.50 3.54 1.50 1.50 5.45 1.5 1.5 3.54 1.5
As NEGATIVO (cm2) 12.68 8.60 8.60 8.60 12.68
As POSITIVO (cm2) 8.60 13.11 16.53 13.11 8.5975
As - 2.43 4.01 4.98 4.01 2.43125
As + 2.43 4.27 7.20 4.27 2.43125
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
37.5 17.50 30.00 15.00 17.50 30.00 17.5 15 30.00 17.5
1.50 3.53 1.50 1.50 5.45 1.5 1.5 3.53 1.5
As NEGATIVO (cm2) 12.81 8.60 8.60 8.60 12.81
As POSITIVO (cm2) 8.60 14.59 18.25 14.59 8.5975
As - 2.43 4.00 4.95 4.00 2.425
As + 2.43 4.25 7.15 4.25 2.425
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
37.5 17.50 30.00 15.00 10.00 30.00 10 15 30.00 17.5
1.50 3.50 1.50 1.50 5.40 1.5 1.5 3.50 1.5
P
75
15.19 15.19
Lon
g,
(m) 4.33 4.33
3.35 3.35
Arm
adu
ra
Tra
nsve
rsa
l ESTRIBOSPIS
O 1
Ace
ro
Lon
gitu
din
al 30.37 30.37
SEPARACIÓN (cm)
LONG, (m)
75
14.22 14.22
Lon
g,
(m) 4.29 4.29
3.30 3.30
Arm
adu
ra
Tra
nsve
rsa
l ESTRIBOSPIS
O 2
Ace
ro
Lon
gitu
dina
l 28.44 28.44
SEPARACIÓN (cm)
LONG, (m)
26.62
75
13.31 13.31
Lon
g,
(m) 4.30 4.30
3.30 3.30
Arm
adu
ra
Tra
nsv
ers
al
57.5
PIS
O 3
Ace
ro
Lon
gitu
dina
l 26.62
ESTRIBOS
SEPARACIÓN (cm)
LONG, (m)
21.33
60
10.67 10.67
Long
, (m
) 4.30 4.30
2.70 2.70
Ace
ro
Lon
gitu
dina
l
ESTRIBOS
SEPARACIÓN (cm)
Arm
adu
ra
Tra
nsv
ersa
l
LONG, (m)
57.5
57.5
7 9 7
55
PIS
O 4
21.33
ORTICO Z3S2
LUZ =>
As NEGATIVO (cm2) 6.18 6.24 6.24 6.24 6.18
As POSITIVO (cm2) 6.24 8.20 10.73 8.20 6.24
As - 2.38 4.02 4.96 4.02 2.38
As + 2.38 4.58 7.79 4.58 2.38
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30 17.5
1.20 4.14 1.20 1.20 6.03 1.2 1.2 4.1375 1.2
As NEGATIVO (cm2) 12.20 9.19 9.19 9.19 12.20
As POSITIVO (cm2) 9.19 12.43 15.58 12.43 9.19
As - 2.45 4.00 4.96 4.00 2.45
As + 2.45 4.16 6.99 4.16 2.45
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
37.5 17.5 30.00 15 12.5 30.00 12.5 15 30.00 17.5
1.60 3.30 1.60 1.60 5.23 1.6 1.6 3.30 1.6
As NEGATIVO (cm2) 17.40 9.19 9.19 9.19 17.4
As POSITIVO (cm2) 9.19 15.22 18.00 15.22 9.1875
As - 2.45 4.00 4.96 4.00 2.45
As + 2.45 4.16 6.99 4.16 2.45
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
37.5 17.5 30.00 15 17.5 30.00 17.5 15 30.00 17.5
1.60 3.30 1.60 1.60 5.23 1.6 1.6 3.30 1.6
As NEGATIVO (cm2) 18.61 10.44 9.19 10.44 18.61
As POSITIVO (cm2) 9.31 17.83 20.31 17.83 9.305
As - 2.47 3.99 4.95 3.99 2.46875
As + 2.47 4.14 6.96 4.14 2.46875
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
37.5 15 30.00 15 17.5 30.00 17.5 15 30.00 15
1.60 3.28 1.60 1.60 5.20 1.6 1.6 3.28 1.6
80
15.77 15.77
Lon
g,
(m) 4.32 4.32
3.54 3.54
Arm
adu
ra
Tra
nsve
rsal ESTRIBOSP
ISO
1
Ace
ro
Long
itud
inal
31.53 31.53
SEPARACIÓN (cm)
LONG, (m)
80
14.55 14.55
Lon
g,
(m) 4.31 4.31
3.52 3.52
Arm
adur
a T
rans
vers
al ESTRIBOSPIS
O 2
Ace
ro
Lon
gitu
din
al
29.09 29.09
SEPARACIÓN (cm)
LONG, (m)
26.45
80
13.23 13.23
Lon
g,
(m) 4.31 4.31
3.52 3.52
Arm
adur
a
Tra
nsv
ersa
l
57.5
PIS
O 3
Ace
ro
Lon
gitu
din
al
26.45
ESTRIBOS
SEPARACIÓN (cm)
LONG, (m)
21.38
60
10.69 10.69
Long
, (m
) 4.32 4.32
2.72 2.72
Ace
ro
Lon
gitu
din
al
21.38
ESTRIBOS
SEPARACIÓN (cm)
Arm
adur
a
Tra
nsv
ersa
l
LONG, (m)
57.5
57.5
PORTICO Z3S4.
7 9 7
55
PIS
O 4
PORTICO Z3S2
193
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
LUZ =>
As NEGATIVO (cm2) 8.85 6.24 6.24 6.
As POSITIVO (cm2) 6.24 9.28 12.06 9.2
As - 2.47 3.99 4.95 3.9
As + 2.47 4.54 7.76 4.5
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R
35 17.5 30.00 17.5 17.5 30.00 17.5 17.5 3
1.20 4.08 1.20 1.20 6.00 1.2 1.2 4.07
As NEGATIVO (cm2) 16.39 10.47 10.47 1
As POSITIVO (cm2) 10.47 15.43 18.00 1
As - 2.51 3.98 4.95 3.9
As + 2.51 4.02 6.76 4.0
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R
40 17.5 30.00 17.5 12.5 30.00 12.5 17.5 3
1.70 3.05 1.70 1.70 5.00 1.7 1.7 3.
As NEGATIVO (cm2) 22.79 13.68 11.49 1
As POSITIVO (cm2) 11.40 20.54 22.17 2
As - 2.51 3.97 4.94 3.9
As + 2.51 4.01 6.74 4.0
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R
40 15 30.00 15 17.5 30.00 17.5 15 30.
1.70 3.04 1.70 1.70 4.98 1.7 1.7 3.
As NEGATIVO (cm2) 25.41 17.43 14.80 1
As POSITIVO (cm2) 12.71 24.39 25.62 2
As - 2.53 3.95 4.91 3.9
As + 2.53 3.98 6.69 3.9
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R
40 15 30.00 12.5 10 30.00 10 12.5 30.
1.70 3.00 1.70 1.70 4.93 1.7 1.7 3.
85
18.27 18.27
Lon
g,
(m) 4.36 4.36
3.82 3.82
Arm
adu
ra
Tra
nsve
rsal ESTRIBOSP
ISO
1
Ace
ro
Long
itud
inal
36.53 36.53
SEPARACIÓN (cm)
LONG, (m)
85
16.33 16.33
Lon
g,
(m) 4.33 4.33
3.77 3.77
Arm
adur
a T
rans
vers
al ESTRIBOSPIS
O 2
Ace
ro
Lon
gitu
din
al
32.65 32.65
SEPARACIÓN (cm)
LONG, (m)
28.19
85
14.10 14.10
Lon
g,
(m) 4.31 4.31
3.74 3.74
Arm
adur
a
Tra
nsv
ersa
l
60
PIS
O 3
Ace
ro
Lon
gitu
din
al
28.19
ESTRIBOS
SEPARACIÓN (cm)
LONG, (m)
21.37
60
10.69 10.69
Long
, (m
) 4.32 4.32
2.74 2.74
Ace
ro
Lon
gitu
din
al
21.37
ESTRIBOS
SEPARACIÓN (cm)
Arm
adur
a
Tra
nsv
ersa
l
LONG, (m)
60
60
PORTICO Z7S2.
7 9 7
55P
ISO
4
24 8.85
8 6.24
9 2.47
4 2.47
3/8" 2R3/8"
0 17.5
5 1.2
0.47 16.39
5.43 10.47
8 2.51
2 2.51
3/8" 2R3/8"
0.00 17.5
05 1.7
3.68 22.79
0.54 11.395
7 2.50938
1 2.50938
3/8" 2R3/8"
00 15
04 1.7
7.43 25.41
4.39 12.705
5 2.525
8 2.525
3/8" 2R3/8"
00 15
00 1.7
LUZ =>
As NEGATIVO (cm2) 9.54 6.27 6.27 6.
As POSITIVO (cm2) 6.27 10.03 12.99 10.
As - 2.51 3.98 4.95 3.9
As + 2.51 4.51 7.75 4.5
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R
35 17.5 30.00 17.5 17.5 30.00 17.5 17.5 3
1.20 4.05 1.20 1.20 6.00 1.2 1.2 4.
As NEGATIVO (cm2) 17.87 11.17 11.17 1
As POSITIVO (cm2) 11.17 16.94 19.29 1
As - 2.57 3.94 4.93 3.9
As + 2.57 3.87 6.50 3.8
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R
40 17.5 30.00 17.5 15 30.00 15 17.5 3
1.80 2.79 1.80 1.80 4.75 1.8 1.8 2.
As NEGATIVO (cm2) 25.64 16.66 13.70 1
As POSITIVO (cm2) 12.82 23.10 23.85 2
As - 2.57 3.94 4.93 3.9
As + 2.57 3.87 6.50 3.8
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R
40 15 30.00 15 12.5 30.00 12.5 15 30.
1.80 2.79 1.80 1.80 4.75 1.8 1.8 2.
As NEGATIVO (cm2) 30.58 21.95 17.13 2
As POSITIVO (cm2) 17.31 28.53 27.43 2
As - 2.64 3.88 4.85 3.8
As + 2.64 3.77 6.35 3.7
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R
40 12.5 30.00 12.5 17.5 30.00 17.5 12.5 3
1.80 2.66 1.80 1.80 4.60 1.8 1.8 2.
90
18.81 18.81
Lon
g,
(m) 4.42 4.42
4.15 4.15
Arm
adu
ra
Tra
nsve
rsal ESTRIBOSP
ISO
1
Ace
ro
Long
itud
inal
37.62 37.62
SEPARACIÓN (cm)
LONG, (m)
90
16.86 16.86
Lon
g,
(m) 4.33 4.33
4.00 4.00
Arm
adur
a T
rans
vers
al ESTRIBOSPIS
O 2
Ace
ro
Lon
gitu
din
al
33.72 33.72
SEPARACIÓN (cm)
LONG, (m)
28.80
90
14.40 14.40
Lon
g,
(m) 4.33 4.33
4.00 4.00
Arm
adur
a
Tra
nsv
ersa
l
60
PIS
O 3
Ace
ro
Lon
gitu
din
al
28.80
ESTRIBOS
SEPARACIÓN (cm)
LONG, (m)
21.99
60
11.00 11.00
Long
, (m
) 4.31 4.31
2.75 2.75
Ace
ro
Lon
gitu
din
al
21.99
ESTRIBOS
SEPARACIÓN (cm)
Arm
adur
a
Tra
nsv
ersa
l
LONG, (m)
60
60
PORTICO Z7S4.
7 9 7
55
PIS
O 4
27 9.54
03 6.27
8 2.51
1 2.51
3/8" 2R3/8"
0 17.5
05 1.2
1.17 17.87
6.94 11.17
4 2.57
7 2.57
3/8" 2R3/8"
0.00 17.5
79 1.8
6.66 25.64
3.10 12.82
4 2.57188
7 2.57188
3/8" 2R3/8"
00 15
79 1.8
1.95 30.58
8.53 17.31
8 2.64063
7 2.64063
3/8" 2R3/8"
0.00 12.5
66 1.8
194
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 4 PISOS R = 6.00
LUZ =>
As NEGATIVO (cm2) 5.65 6.27 6.27 6.27 5.65
As POSITIVO (cm2) 6.27 7.72 10.44 7.72 6.27
As - 2.39 4.03 4.98 4.03 2.39
As + 2.39 4.59 7.80 4.59 2.39
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.50 30.00 17.50 17.50 30.00 17.5 17.5 30 17.5
1.20 4.15 1.20 1.20 6.05 1.2 1.2 4.15 1.2
As NEGATIVO (cm2) 8.81 8.29 8.29 8.29 8.81
As POSITIVO (cm2) 8.29 10.76 14.30 10.76 8.29
As - 2.39 4.03 4.98 4.03 2.39
As + 2.39 4.34 7.30 4.34 2.39
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
37.5 17.50 30.00 15.00 17.50 30.00 17.5 15 30.00 17.5
1.45 3.65 1.45 1.45 5.55 1.45 1.45 3.65 1.45
As NEGATIVO (cm2) 11.56 8.29 8.29 8.29 11.56
As POSITIVO (cm2) 8.29 11.95 15.55 11.95 8.285
As - 2.43 4.01 4.98 4.01 2.43125
As + 2.43 4.32 7.30 4.32 2.43125
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
37.5 17.50 30.00 15.00 10.00 30.00 10 15 30.00 17.5
1.45 3.63 1.45 1.45 5.55 1.45 1.45 3.63 1.45
As NEGATIVO (cm2) 12.11 8.29 8.29 8.29 12.11
As POSITIVO (cm2) 8.29 13.16 16.76 13.16 8.285
As - 2.43 4.01 4.96 4.01 2.42813
As + 2.43 4.31 7.27 4.31 2.42813
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
37.5 17.50 30.00 15.00 10.00 30.00 10 15 30.00 17.5
1.45 3.61 1.45 1.45 5.53 1.45 1.45 3.61 1.45
PORTICO Z3S2.
57.5
57.5
7 9
55
PIS
O 4
21.32
ESTRIBOS
SEPARACIÓN (cm)
Arm
adu
ra
Tra
nsv
ersa
l
LONG, (m)
21.32
60
10.66 10.66Lo
ng,
(m) 4.30 4.30
2.70 2.70
Ace
ro
Lon
gitu
dina
l
57.5
PIS
O 3
Ace
ro
Lon
gitu
dina
l 27.87
ESTRIBOS
SEPARACIÓN (cm)
LONG, (m)
27.87
72.5
13.94 13.94
Lon
g,
(m) 4.30 4.30
3.20 3.20
Arm
adu
ra
Tra
nsv
ers
al
PIS
O 2
Ace
ro
Lon
gitu
dina
l 28.01 28.01
SEPARACIÓN (cm)
LONG, (m)
72.5
14.01 14.01
Lon
g,
(m) 4.29 4.29
3.20 3.20
Arm
adu
ra
Tra
nsve
rsa
l ESTRIBOS
PIS
O 1
Ace
ro
Lon
gitu
din
al 29.20 29.20
SEPARACIÓN (cm)
LONG, (m)
72.5
14.60 14.60
Lon
g,
(m) 4.31 4.31
3.23 3.23
Arm
adu
ra
Tra
nsve
rsa
l ESTRIBOS
7
LUZ =>
As NEGATIVO (cm2) 5.86 6.27 6.27 6.27 5.86
As POSITIVO (cm2) 6.27 7.79 10.44 7.79 6.27
As - 2.39 4.03 4.98 4.03 2.39
As + 2.39 4.59 7.80 4.59 2.39
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30 17.5
1.20 4.15 1.20 1.20 6.05 1.2 1.2 4.15 1.2
As NEGATIVO (cm2) 9.68 8.61 8.61 8.61 9.68
As POSITIVO (cm2) 8.61 11.11 14.41 11.11 8.61
As - 2.43 4.01 4.96 4.01 2.43
As + 2.43 4.16 6.97 4.16 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 15 12.5 30.00 12.5 15 30.00 17.5
1.60 3.31 1.60 1.60 5.23 1.6 1.6 3.31 1.6
As NEGATIVO (cm2) 13.34 8.61 8.61 8.61 13.34
As POSITIVO (cm2) 8.61 13.14 16.27 13.14 8.60767
As - 2.45 4.00 4.96 4.00 2.45
As + 2.45 4.15 6.97 4.15 2.45
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 15 17.5 30.00 17.5 15 30.00 17.5
1.60 3.30 1.60 1.60 5.23 1.6 1.6 3.30 1.6
As NEGATIVO (cm2) 13.85 8.61 8.61 8.61 13.85
As POSITIVO (cm2) 8.61 14.93 18.16 14.93 8.60767
As - 2.45 3.99 4.95 3.99 2.44688
As + 2.45 4.14 6.95 4.14 2.44688
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 15 17.5 30.00 17.5 15 30.00 17.5
55
55
PORTICO Z3S4.
7 9 7
55
PIS
O 4
21.32
ESTRIBOS
SEPARACIÓN (cm)
Arm
adu
ra
Tra
nsve
rsal
LONG, (m)
21.32
60
10.66 10.66
Long
, (m
) 4.30 4.30
2.70 2.70
Ace
ro
Lon
gitu
din
al
55
PIS
O 3
Ace
ro
Lon
gitu
din
al
25.26
ESTRIBOS
SEPARACIÓN (cm)
LONG, (m)
25.26
80
12.63 12.63
Lon
g,
(m) 4.31 4.31
3.53 3.53
Arm
adur
a T
ran
sve
rsal
PIS
O 2 A
cero
Lo
ngitu
dina
l 27.33 27.33
SEPARACIÓN (cm)
LONG, (m)
80
13.67 13.67
Lon
g,
(m) 4.31 4.31
3.53 3.53
Arm
adur
a
Tra
nsve
rsa
l ESTRIBOS
PIS
O 1
Ace
ro
Lon
gitu
din
al 29.43 29.43
SEPARACIÓN (cm)
80
14.72 14.72
Lon
g,
(m) 4.32 4.32
3.55 3.55
ura
rs
al ESTRIBOS
1.60 3.29 1.60 1.60 5.20 1.6 1.6 3.29 1.6LONG, (m)Arm
ad
Tra
nsve
195
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
196
LUZ =>
As NEGATIVO (cm2) 7.24 6.27 6.27 6.27
As POSITIVO (cm2) 6.27 8.35 10.98 8.35
As - 2.41 4.01 4.96 4.01
As + 2.41 4.57 7.77 4.57
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30
1.20 4.13 1.20 1.20 6.03 1.2 1.2 4.125
As NEGATIVO (cm2) 13.32 9.84 9.84 9.84
As POSITIVO (cm2) 9.84 13.25 16.40 13.25
As - 2.47 3.99 4.96 3.99
As + 2.47 4.14 6.97 4.14
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 15 12.5 30.00 12.5 15 30.00
1.60 3.29 1.60 1.60 5.23 1.6 1.6 3.29
As NEGATIVO (cm2) 17.97 9.84 9.84 9.84
As POSITIVO (cm2) 9.84 16.68 19.58 16.68 9
As - 2.47 3.99 4.95 3.99 2
As + 2.47 4.13 6.95 4.13 2
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 15 17.5 30.00 17.5 15 30.00
1.60 3.28 1.60 1.60 5.20 1.6 1.6 3.28
As NEGATIVO (cm2) 19.76 12.20 10.96 12.20
As POSITIVO (cm2) 9.88 19.99 22.35 19.99
As - 2.49 3.98 4.95 3.98 2
As + 2.49 4.12 6.95 4.12 2
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 10 30.00 10 15 30.00
1.60 3.26 1.60 1.60 5.20 1.6 1.6 3.26
80
16.85 16.85
Lon
g,
(m) 4.32 4.32
3.55 3.55
Arm
adu
ra
Tra
nsve
rsal ESTRIBOSP
ISO
1
Ace
ro
Long
itud
inal
33.70 33.70
SEPARACIÓN (cm)
LONG, (m)
80
15.39 15.39
Lon
g,
(m) 4.32 4.32
3.55 3.55
Arm
adur
a T
rans
vers
al ESTRIBOSPIS
O 2
Ace
ro
Lon
gitu
din
al
30.77 30.77
SEPARACIÓN (cm)
LONG, (m)
27.24
80
13.62 13.62
Lon
g,
(m) 4.30 4.30
3.53 3.53
Arm
adur
a
Tra
nsv
ersa
l
60
PIS
O 3
Ace
ro
Lon
gitu
din
al
27.24
ESTRIBOS
SEPARACIÓN (cm)
LONG, (m)
21.35
60
10.68 10.68
Long
, (m
) 4.31 4.31
2.73 2.73
Ace
ro
Lon
gitu
din
al
21.35
ESTRIBOS
SEPARACIÓN (cm)
Arm
adur
a
Tra
nsv
ersa
l
LONG, (m)
60
60
PORTICO Z7S2.
7 9 7
55P
ISO
4
7.24
6.27
2.41
2.41
2R3/8"
17.5
1.2
13.32
9.84
2.47
2.47
2R3/8"
17.5
1.6
17.97
.83733
.46875
.46875
2R3/8"
17.5
1.6
19.76
9.88
.49063
.49063
2R3/8"
15
1.6
LUZ =>
As NEGATIVO (cm2) 7.82 6.27 6.27 6.27
As POSITIVO (cm2) 6.27 9.27 12.05 9.27
As - 2.47 3.99 4.95 3.99
As + 2.47 4.53 7.75 4.53
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.50 30.00 17.50 17.50 30.00 17.5 17.5 30
1.20 4.08 1.20 1.20 6.00 1.2 1.2 4.075
As NEGATIVO (cm2) 16.08 10.50 10.50 10.50
As POSITIVO (cm2) 10.50 15.11 17.88 15.11
As - 2.53 3.97 4.95 3.97
As + 2.53 4.00 6.75 4.00
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.50 30.00 17.50 12.50 30.00 12.5 17.5 30.00
1.70 3.04 1.70 1.70 5.00 1.7 1.7 3.04
As NEGATIVO (cm2) 22.57 12.93 10.75 12.93
As POSITIVO (cm2) 11.29 19.56 21.33 19.56 1
As - 2.53 3.96 4.94 3.96 2
As + 2.53 3.99 6.72 3.99 2
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.50 30.00 15.00 12.50 30.00 12.5 15 30.00
1.70 3.03 1.70 1.70 4.98 1.7 1.7 3.03
As NEGATIVO (cm2) 24.76 16.17 13.47 16.17
As POSITIVO (cm2) 12.38 23.12 24.08 23.12
As - 2.58 3.92 4.89 3.92 2
As + 2.58 3.93 6.62 3.93 2
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8"
40 15.00 30.00 12.50 17.50 30.00 17.5 12.5 30.00
1.70 2.94 1.70 1.70 4.88 1.7 1.7 2.94
60
60
PORTICO Z7S4.
7 9 7
55
PIS
O 4
21.40
ESTRIBOS
SEPARACIÓN (cm)
Arm
adur
a
Tra
nsv
ersa
l
LONG, (m)
21.40
60
10.70 10.70
Long
, (m
) 4.32 4.32
2.75 2.75
Ace
ro
Lon
gitu
din
al
60
PIS
O 3
Ace
ro
Lon
gitu
din
al
28.17
ESTRIBOS
SEPARACIÓN (cm)
LONG, (m)
28.17
85
14.09 14.09
Lon
g,
(m) 4.31 4.31
3.75 3.75
Arm
adur
a
Tra
nsv
ersa
l
PIS
O 2
Ace
ro
Lon
gitu
din
al
31.85 31.85
SEPARACIÓN (cm)
LONG, (m)
85
15.93 15.93
Lon
g,
(m) 4.33 4.33
3.78 3.78
Arm
adur
a T
rans
vers
al ESTRIBOS
PIS
O 1
Ace
ro
Long
itud
inal
35.00 35.00
SEPARACIÓN (cm)
LONG, (m)
85
17.50 17.50
Lon
g,
(m) 4.38 4.38
3.88 3.88
Arm
adu
ra
Tra
nsve
rsal ESTRIBOS
7.82
6.27
2.47
2.47
2R3/8"
17.5
1.2
16.08
10.50
2.53
2.53
2R3/8"
17.5
1.7
22.57
1.285
.53125
.53125
2R3/8"
17.5
1.7
24.76
12.38
.58438
.58438
2R3/8"
15
1.7
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 8 PISOS R = 3.32
LUZ =>
As NEGATIVO (cm2) 5.06 6.27 6.27 6.27 5.06
As POSITIVO (cm2) 6.27 8.04 10.43 8.04 6.27
As - 2.37 4.03 4.98 4.03 2.37
As + 2.37 4.60 7.80 4.60 2.37
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30 17.5
1.20 4.16 1.20 1.20 6.05 1.2 1.2 4.1625 1.2
As NEGATIVO (cm2) 7.14 8.61 8.61 8.61 7.14
As POSITIVO (cm2) 8.61 9.63 12.94 9.63 8.61
As - 2.39 4.03 4.98 4.03 2.39
As + 2.39 4.19 7.00 4.19 2.39
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 15 30.00 15 12.5 12.5 12.5 15 30 15
1.60 3.35 1.60 1.60 5.25 1.6 1.6 3.35 1.6
55 As NEGATIVO (cm2) 8.50 8.61 8.61 8.61 8.50
As POSITIVO (cm2) 8.61 10.75 14.42 10.75 8.61
As - 2.39 4.03 4.98 4.03 2.39
As + 2.39 4.19 7.00 4.19 2.39
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 15 30.00 15 12.5 30.00 12.5 15 30 15
1.60 3.35 1.60 1.60 5.25 1.6 1.6 3.35 1.6
55 As NEGATIVO (cm2) 10.90 8.61 8.61 8.61 10.9
As POSITIVO (cm2) 8.61 11.87 15.54 11.87 8.61
As - 2.43 4.01 4.96 4.01 2.43
As + 2.43 4.16 6.97 4.16 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 15 30.00 15 12.5 30.00 12.5 15 30 15
1.60 3.31 1.60 1.60 5.23 1.6 1.6 3.3125 1.6
As NEGATIVO (cm2) 12.92 8.61 8.61 8.61 12.92
As POSITIVO (cm2) 8.61 12.88 16.49 12.88 8.61
As - 2.43 4.01 4.96 4.01 2.43
As + 2.43 4.16 6.97 4.16 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 15 30.00 15 12.5 30.00 12.5 15 30 15
1.60 3.31 1.60 1.60 5.23 1.6 1.6 3.3125 1.6
55 As NEGATIVO (cm2) 14.16 8.61 8.61 8.61 14.16
As POSITIVO (cm2) 8.61 13.80 17.27 13.80 8.61
As - 2.45 3.99 4.95 3.99 2.45
As + 2.45 4.14 6.95 4.14 2.45
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 15 12.5 30.00 12.5 15 30 17.5
1.60 3.29 1.60 1.60 5.20 1.6 1.6 3.2875 1.6
55 As NEGATIVO (cm2) 15.36 8.61 8.61 8.61 15.36
As POSITIVO (cm2) 8.61 14.47 17.76 14.47 8.60767
As - 2.44 3.99 4.94 3.99 2.44
As + 2.44 4.13 6.92 4.13 2.44
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 15 12.5 30.00 12.5 15 30 17.5
1.60 3.28 1.60 1.60 5.18 1.6 1.6 3.28 1.6
55 As NEGATIVO (cm2) 14.01 8.61 8.61 8.61 14.01
As POSITIVO (cm2) 8.61 14.86 18.36 14.86 8.61
As - 2.44 3.99 4.94 3.99 2.44
As + 2.44 4.13 6.92 4.13 2.44
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 15 12.5 30.00 12.5 15 30 17.5
1.60 3.28 1.60 1.60 5.18 1.6 1.6 3.275 1.6
80
14.93 14.93
Long
.
(m) 4.34 4.34
3.58 3.58
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
1
Ace
ro
Lon
gitu
dina
l 29.86 29.86
SEPARACIÓN (cm)
LONG. (m)
80
14.62 14.62
Lon
g.
(m) 4.34 4.34
3.58 3.58
Arm
adu
ra
Tra
nsve
rsa
l ESTRIBOSPIS
O 2
Ace
ro
Long
itudi
nal 29.23 29.23
SEPARACIÓN (cm)
LONG. (m)
80
14.28 14.28
Long
.
(m) 4.32 4.32
3.55 3.55
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
3
Ace
ro
Long
itudi
nal 28.56 28.56
SEPARACIÓN (cm)
LONG. (m)
27.61
80
13.81 13.81
Long
.
(m) 4.31 4.31
3.53 3.53
Arm
adur
a
Tra
nsve
rsal
55
PIS
O 4
Ace
ro
Long
itudi
nal 27.61
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
80
13.28 13.28
Lon
g.
(m) 4.31 4.31
3.53 3.53
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
5
Ace
ro
Long
itudi
nal 26.56 26.56
SEPARACIÓN (cm)
LONG. (m)
80
12.62 12.62
Long
.
(m) 4.30 4.30
3.50 3.50
Arm
adu
ra
Tra
nsve
rsal ESTRIBOSP
ISO
6
Ace
ro
Long
itudi
nal 25.23 25.23
SEPARACIÓN (cm)
LONG. (m)
24.54
80
12.27 12.27
Long
.
(m) 4.30 4.30
3.50 3.50
Arm
adur
a
Tra
nsve
rsal
55
PIS
O 7
Ace
ro
Lon
gitu
dina
l 24.54
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
21.34
60
10.67 10.67
Long
.
(m) 4.30 4.30
2.70 2.70
Arm
adur
a
Tra
nsve
rsal
55
PIS
O 8
Ace
ro
Long
itudi
nal 21.34
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z3S2.
7 9
7
197
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
LUZ =>
As NEGATIVO (cm2) 6.54 6.27 6.27 6.27 6.54
As POSITIVO (cm2) 6.27 8.14 11.26 8.14 6.27
As - 2.45 4.00 4.96 4.00 2.45
As + 2.45 4.55 7.77 4.55 2.45
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30 17.5
1.20 4.10 1.20 1.20 6.03 1.2 1.2 4.1 1.2
As NEGATIVO (cm2) 10.18 11.17 11.17 11.17 10.18
As POSITIVO (cm2) 11.17 11.69 16.23 11.69 11.17
As - 2.45 3.99 4.95 3.99 2.45
As + 2.45 3.94 6.55 3.94 2.45
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 15 15 15 30 15
1.80 2.89 1.80 1.80 4.80 1.8 1.8 2.8875 1.8
60 As NEGATIVO (cm2) 15.28 11.17 11.17 11.17 15.28
As POSITIVO (cm2) 11.17 15.23 19.50 15.23 11.17
As - 2.47 3.99 4.95 3.99 2.47
As + 2.47 3.93 6.55 3.93 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30 15
1.80 2.88 1.80 1.80 4.80 1.8 1.8 2.875 1.8
60 As NEGATIVO (cm2) 20.64 12.51 12.33 12.51 20.64
As POSITIVO (cm2) 11.17 19.17 22.51 19.17 11.17
As - 2.51 3.97 4.94 3.97 2.51
As + 2.51 3.90 6.52 3.90 2.51
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.80 2.84 1.80 1.80 4.78 1.8 1.8 2.8375 1.8
As NEGATIVO (cm2) 25.41 16.11 14.63 16.11 25.41
As POSITIVO (cm2) 12.71 22.70 24.97 22.70 12.71
As - 2.53 3.96 4.93 3.96 2.53
As + 2.53 3.88 6.50 3.88 2.53
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.80 2.81 1.80 1.80 4.75 1.8 1.8 2.8125 1.8
60 As NEGATIVO (cm2) 28.03 18.82 16.92 18.82 28.03
As POSITIVO (cm2) 14.02 25.41 27.12 25.41 14.02
As - 2.53 3.95 4.91 3.95 2.53
As + 2.53 3.87 6.47 3.87 2.53
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30 15
1.80 2.80 1.80 1.80 4.73 1.8 1.8 2.8 1.8
60 As NEGATIVO (cm2) 30.34 20.97 18.38 20.97 30.34
As POSITIVO (cm2) 15.19 27.49 28.56 27.49 15.19
As - 2.54 3.94 4.90 3.94 2.54
As + 2.54 3.86 6.45 3.86 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 12.5 30.00 12.5 12.5 30 12.5
1.80 2.78 1.80 1.80 4.70 1.8 1.8 2.78 1.8
60 As NEGATIVO (cm2) 30.24 22.06 19.15 22.06 30.24
As POSITIVO (cm2) 16.62 28.68 29.38 28.68 16.62
As - 2.53 3.91 4.85 3.91 2.53
As + 2.53 3.82 6.35 3.82 2.53
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 17.5 30.00 17.5 12.5 30 12.5
1.80 2.73 1.80 1.80 4.60 1.8 1.8 2.725 1.8
7 9
PORTICO Z3S4.
55P
ISO
8
Ace
ro
Lon
gitu
dina
l 21.34
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
21.34
60
10.67 10.67
Long
.
(m) 4.31 4.31
2.73 2.73
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 25.38
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
25.38
90
12.69 12.69
Long
.
(m) 4.32 4.32
3.95 3.95
Arm
adur
a
Tra
nsve
rsal
PIS
O 6
Ace
ro
Long
itudi
nal 28.85 28.85
SEPARACIÓN (cm)
LONG. (m)
90
14.43 14.43
Long
.
(m) 4.32 4.32
3.95 3.95
Arm
adu
ra
Tra
nsve
rsal ESTRIBOS
PIS
O 5
Ace
ro
Long
itudi
nal
32.07 32.07
SEPARACIÓN (cm)
LONG. (m)
90
16.04 16.04
Long
.
(m) 4.33 4.33
3.98 3.98
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
60
PIS
O 4
Ace
ro
Long
itudi
nal 34.76
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
34.76
90
17.38 17.38
Long
.
(m) 4.34 4.34
4.00 4.00
Arm
adur
a
Tra
nsve
rsal
PIS
O 3
Ace
ro
Long
itudi
nal 37.49 37.49
SEPARACIÓN (cm)
LONG. (m)
90
18.75 18.75
Long
.
(m) 4.36 4.36
4.03 4.03
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 2
Ace
ro
Long
itudi
nal
39.24 39.24
SEPARACIÓN (cm)
LONG. (m)
90
19.62 19.62
Long
.
(m) 4.37 4.37
4.05 4.05
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 1
Ace
ro
Long
itudi
nal 40.09 40.09
SEPARACIÓN (cm)
LONG. (m)
90
20.05 20.05
Long
.
(m) 4.43 4.43
4.15 4.15
Arm
adur
a
Tra
nsv
ersa
l ESTRIBOS
7
198
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
LUZ =>
As NEGATIVO (cm2) 8.79 6.27 6.27 6.27 8.79
As POSITIVO (cm2) 6.27 8.54 11.96 8.54 6.27
As - 2.47 3.99 4.95 3.99 2.47
As + 2.47 4.53 7.75 4.53 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30 17.5
1.20 4.08 1.20 1.20 6.00 1.2 1.2 4.075 1.2
As NEGATIVO (cm2) 11.36 12.50 12.50 12.50 11.36
As POSITIVO (cm2) 12.50 12.39 17.48 12.39 12.50
As - 2.47 3.98 4.94 3.98 2.47
As + 2.47 3.72 6.12 3.72 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 15 15 15 30 15
2.00 2.46 2.00 2.00 4.38 2 2 2.4625 2
60 As NEGATIVO (cm2) 18.42 12.50 12.50 12.50 18.42
As POSITIVO (cm2) 12.50 17.31 21.47 17.31 12.50
As - 2.53 3.96 4.93 3.96 2.53
As + 2.53 3.68 6.10 3.68 2.53
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30 15
2.00 2.41 2.00 2.00 4.35 2 2 2.4125 2
60 As NEGATIVO (cm2) 25.46 16.60 15.55 16.60 25.46
As POSITIVO (cm2) 12.73 22.56 24.96 22.56 12.73
As - 2.55 3.95 4.93 3.95 2.55
As + 2.55 3.67 6.10 3.67 2.55
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30 15
2.00 2.40 2.00 2.00 4.35 2 2 2.4 2
As NEGATIVO (cm2) 30.39 21.21 19.17 21.21 30.39
As POSITIVO (cm2) 16.06 27.10 28.44 27.10 16.06
As - 2.57 3.93 4.90 3.93 2.57
As + 2.57 3.65 6.05 3.65 2.57
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30 15
2.00 2.36 2.00 2.00 4.30 2 2 2.3625 2
60 As NEGATIVO (cm2) 34.71 25.08 21.64 25.08 34.71
As POSITIVO (cm2) 19.74 30.85 30.89 30.85 19.74
As - 2.59 3.93 4.90 3.93 2.59
As + 2.59 3.64 6.05 3.64 2.59
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 12.5 30.00 12.5 12.5 30 12.5
2.00 2.35 2.00 2.00 4.30 2 2 2.35 2
60 As NEGATIVO (cm2) 37.98 28.07 23.35 28.07 37.98
As POSITIVO (cm2) 22.60 33.86 32.71 33.86 22.6
As - 2.60 3.91 4.88 3.91 2.60
As + 2.60 3.61 6.00 3.61 2.60
2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 17.5 12.5 30.00 12.5 17.5 30 12.5
2.00 2.31 2.00 2.00 4.25 2 2 2.31 2
60 As NEGATIVO (cm2) 37.96 29.41 24.31 29.41 37.96
As POSITIVO (cm2) 24.11 35.29 33.68 35.29 24.11
As - 2.59 3.88 4.83 3.88 2.59
As + 2.59 3.57 5.90 3.57 2.59
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 10 12.5 30.00 12.5 10 30 12.5
2.00 2.26 2.00 2.00 4.15 2 2 2.2625 2
PORTICO Z7S2.
7 9
55
PIS
O 8
Ace
ro
Lon
gitu
dina
l 21.32
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
21.32
60
10.66 10.66
Long
.
(m) 4.32 4.32
2.75 2.75A
rmad
ura
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 25.47
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
25.47
100
12.74 12.74
Long
.
(m) 4.33 4.33
4.38 4.38
Arm
adur
a
Tra
nsve
rsal
PIS
O 6
Ace
ro
Long
itudi
nal 29.61 29.61
SEPARACIÓN (cm)
LONG. (m)
100
14.81 14.81
Long
.
(m) 4.34 4.34
4.40 4.40
Arm
adu
ra
Tra
nsve
rsal ESTRIBOS
PIS
O 5
Ace
ro
Long
itudi
nal
33.25 33.25
SEPARACIÓN (cm)
LONG. (m)
100
16.63 16.63
Long
.
(m) 4.34 4.34
4.40 4.40
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
60
PIS
O 4
Ace
ro
Long
itudi
nal 37.39
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
37.39
100
18.70 18.70
Long
.
(m) 4.37 4.37
4.45 4.45
Arm
adur
a
Tra
nsve
rsal
PIS
O 3
Ace
ro
Long
itudi
nal 40.24 40.24
SEPARACIÓN (cm)
LONG. (m)
100
20.12 20.12
Long
.
(m) 4.36 4.36
4.45 4.45
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 2
Ace
ro
Long
itudi
nal
42.23 42.23
SEPARACIÓN (cm)
LONG. (m)
100
21.12 21.12
Long
.
(m) 4.39 4.39
4.50 4.50
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 1
Ace
ro
Long
itudi
nal 43.31 43.31
SEPARACIÓN (cm)
LONG. (m)
100
21.66 21.66
Long
.
(m) 4.45 4.45
4.60 4.60
Arm
adur
a
Tra
nsv
ersa
l ESTRIBOS
7
199
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
LUZ =>
As NEGATIVO (cm2) 15.62 6.84 6.84 6.84 15.62
As POSITIVO (cm2) 7.81 11.03 14.36 11.03 7.81
As - 2.60 3.94 4.94 3.94 2.60
As + 2.60 4.52 7.82 4.52 2.60
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30 17.5
1.15 4.09 1.15 1.15 6.08 1.15 1.15 4.0875 1.15
As NEGATIVO (cm2) 23.84 17.19 17.19 17.19 23.84
As POSITIVO (cm2) 17.19 20.48 24.54 20.48 17.19
As - 2.60 3.90 4.86 3.90 2.60
As + 2.60 3.60 5.97 3.60 2.60
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
55 15 30.00 15 15 15 15 15 30 15
2.00 2.30 2.00 2.00 4.23 2 2 2.3 2
75 As NEGATIVO (cm2) 34.31 23.95 22.41 23.95 34.31
As POSITIVO (cm2) 24.06 30.13 32.13 30.13 24.06
As - 2.64 3.89 4.86 3.89 2.64
As + 2.64 3.58 5.97 3.58 2.64
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
55 15 30.00 12.5 15 30.00 15 12.5 30 15
2.00 2.28 2.00 2.00 4.23 2 2 2.275 2
75 As NEGATIVO (cm2) 45.45 34.36 29.88 34.36 45.45
As POSITIVO (cm2) 34.28 40.45 39.75 40.45 34.28
As - 2.64 3.89 4.86 3.89 2.64
As + 2.64 3.58 5.97 3.58 2.64
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
55 10 30.00 10 17.5 30.00 17.5 10 30 10
2.00 2.28 2.00 2.00 4.23 2 2 2.275 2
As NEGATIVO (cm2) 56.01 44.01 35.61 44.01 56.01
As POSITIVO (cm2) 38.20 50.19 45.52 50.19 38.20
As - 2.69 3.88 4.86 3.88 2.69
As + 2.69 3.56 5.97 3.56 2.69
2R1/2" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 2R1/2"
55 15 30.00 15 17.5 30.00 17.5 15 30 15
2.00 2.25 2.00 2.00 4.23 2 2 2.25 2
75 As NEGATIVO (cm2) 63.33 50.20 38.93 50.20 63.33
As POSITIVO (cm2) 50.48 55.79 49.00 55.79 50.48
As - 2.78 3.81 4.80 3.81 2.78
As + 2.78 3.47 5.85 3.47 2.78
2R1/2" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 2R1/2"
55 12.5 30.00 12.5 15 30.00 15 12.5 30 12.5
2.00 2.13 2.00 2.00 4.10 2 2 2.125 2
75 As NEGATIVO (cm2) 60.57 48.58 38.82 48.58 60.57
As POSITIVO (cm2) 48.10 54.23 48.71 54.23 48.1
As - 2.76 3.76 4.70 3.76 2.76
As + 2.76 3.39 5.65 3.39 2.76
2R1/2" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 2R1/2"
55 12.5 30.00 12.5 15 30.00 15 12.5 30 12.5
2.00 2.03 2.00 2.00 3.90 2 2 2.03 2
75 As NEGATIVO (cm2) 47.52 36.81 30.14 36.81 47.52
As POSITIVO (cm2) 36.46 42.66 39.68 42.66 36.46
As - 2.87 3.69 4.63 3.69 2.87
As + 2.87 3.28 5.50 3.28 2.87
2R1/2" 2R3/8" 2R1/2" 2R3/8" 2R3/8" 2R3/8" 2R1/2" 2R3/8" 2R1/2"
55 15 30.00 15 10 30.00 10 15 30 15
2.00 1.88 2.00 2.00 3.75 2 2 1.875 2
100
37.18 37.18
Long
.
(m) 4.66 4.66
5.00 5.00
Arm
adur
a
Tra
nsv
ersa
l ESTRIBOSPIS
O 1
Ace
ro
Long
itudi
nal 49.92 49.92
SEPARACIÓN (cm)
LONG. (m)
100
47.08 47.08
Long
.
(m) 4.58 4.58
4.85 4.85
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
2
Ace
ro
Long
itudi
nal
61.85 61.85
SEPARACIÓN (cm)
LONG. (m)
100
48.45 48.45
Long
.
(m) 4.46 4.46
4.65 4.65
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
3
Ace
ro
Long
itudi
nal 62.61 62.61
SEPARACIÓN (cm)
LONG. (m)
56.33
100
42.93 42.93
Long
.
(m) 4.39 4.39
4.53 4.53
Arm
adur
a
Tra
nsve
rsal
75
PIS
O 4
Ace
ro
Long
itudi
nal 56.33
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
100
33.94 33.94
Long
.
(m) 4.40 4.40
4.53 4.53
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
5
Ace
ro
Long
itudi
nal
49.19 49.19
SEPARACIÓN (cm)
LONG. (m)
100
24.00 24.00
Long
.
(m) 4.40 4.40
4.53 4.53
Arm
adu
ra
Tra
nsve
rsal ESTRIBOSP
ISO
6
Ace
ro
Long
itudi
nal 41.00 41.00
SEPARACIÓN (cm)
LONG. (m)
33.00
100
17.19 17.19
Long
.
(m) 4.41 4.41
4.53 4.53
Arm
adur
a
Tra
nsve
rsal
75
PIS
O 7
Ace
ro
Long
itudi
nal 33.00
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
23.69
57.5
11.85 11.85
Long
.
(m) 4.32 4.32
2.68 2.68A
rmad
ura
Tra
nsve
rsal
60P
ISO
8
Ace
ro
Lon
gitu
dina
l 23.69
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z7S4.
7 9
7
200
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 8 PISOS R = 4.50
LUZ =>
As NEGATIVO (cm2) 5.06 6.27 6.27 6.27 5.06
As POSITIVO (cm2) 6.27 8.03 10.43 8.03 6.27
As - 2.37 4.03 4.98 4.03 2.37
As + 2.37 4.60 7.80 4.60 2.37
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30 17.5
1.20 4.16 1.20 1.20 6.05 1.2 1.2 4.1625 1.2
As NEGATIVO (cm2) 7.01 8.32 8.32 8.32 7.01
As POSITIVO (cm2) 8.32 9.56 12.63 9.56 8.32
As - 2.39 4.03 4.98 4.03 2.39
As + 2.39 4.24 7.10 4.24 2.39
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 15 30.00 15 12.5 12.5 12.5 15 30 15
1.55 3.45 1.55 1.55 5.35 1.55 1.55 3.45 1.55
55 As NEGATIVO (cm2) 8.09 8.32 8.32 8.32 8.09
As POSITIVO (cm2) 8.32 10.20 13.71 10.20 8.32
As - 2.39 4.03 4.98 4.03 2.39
As + 2.39 4.24 7.10 4.24 2.39
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 15 30.00 15 12.5 30.00 12.5 15 30 15
1.55 3.45 1.55 1.55 5.35 1.55 1.55 3.45 1.55
55 As NEGATIVO (cm2) 10.18 8.32 8.32 8.32 10.18
As POSITIVO (cm2) 8.32 10.94 14.55 10.94 8.32
As - 2.43 4.01 4.98 4.01 2.43
As + 2.43 4.22 7.10 4.22 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 15 30.00 15 12.5 30.00 12.5 15 30 15
1.55 3.43 1.55 1.55 5.35 1.55 1.55 3.425 1.55
As NEGATIVO (cm2) 11.88 8.32 8.32 8.32 11.88
As POSITIVO (cm2) 8.32 11.57 15.19 11.57 8.32
As - 2.43 4.00 4.95 4.00 2.43
As + 2.43 4.20 7.05 4.20 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 15 30.00 15 12.5 30.00 12.5 15 30 15
1.55 3.40 1.55 1.55 5.30 1.55 1.55 3.4 1.55
55 As NEGATIVO (cm2) 12.16 8.32 8.32 8.32 12.16
As POSITIVO (cm2) 8.32 12.22 15.98 12.22 8.32
As - 2.43 4.00 4.95 4.00 2.43
As + 2.43 4.20 7.05 4.20 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 15 12.5 30.00 12.5 15 30 17.5
1.55 3.40 1.55 1.55 5.30 1.55 1.55 3.4 1.55
55 As NEGATIVO (cm2) 13.37 8.32 8.32 8.32 13.37
As POSITIVO (cm2) 8.32 12.72 16.21 12.72 8.316
As - 2.45 3.99 4.95 3.99 2.45
As + 2.45 4.19 7.05 4.19 2.45
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 15 12.5 30.00 12.5 15 30 17.5
1.55 3.39 1.55 1.55 5.30 1.55 1.55 3.39 1.55
55 As NEGATIVO (cm2) 12.55 8.32 8.32 8.32 12.55
As POSITIVO (cm2) 8.32 13.11 16.52 13.11 8.32
As - 2.44 3.99 4.94 3.99 2.44
As + 2.44 4.18 7.02 4.18 2.44
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 15 12.5 30.00 12.5 15 30 17.5
1.55 3.38 1.55 1.55 5.28 1.55 1.55 3.375 1.55
77.5
14.08 14.08
Long
.
(m) 4.34 4.34
3.48 3.48
Arm
adur
a
Tra
nsv
ersa
l ESTRIBOSPIS
O 1
Ace
ro
Long
itudi
nal 28.15 28.15
SEPARACIÓN (cm)
LONG. (m)
77.5
13.94 13.94
Long
.
(m) 4.32 4.32
3.45 3.45
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
2
Ace
ro
Long
itudi
nal
27.87 27.87
SEPARACIÓN (cm)
LONG. (m)
77.5
13.79 13.79
Long
.
(m) 4.33 4.33
3.45 3.45
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
3
Ace
ro
Long
itudi
nal 27.57 27.57
SEPARACIÓN (cm)
LONG. (m)
26.66
77.5
13.33 13.33
Long
.
(m) 4.33 4.33
3.45 3.45
Arm
adur
a
Tra
nsve
rsal
55
PIS
O 4
Ace
ro
Long
itudi
nal 26.66
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
77.5
12.87 12.87
Long
.
(m) 4.29 4.29
3.40 3.40
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
5
Ace
ro
Long
itudi
nal
25.74 25.74
SEPARACIÓN (cm)
LONG. (m)
77.5
12.78 12.78
Long
.
(m) 4.30 4.30
3.40 3.40
Arm
adu
ra
Tra
nsve
rsal ESTRIBOSP
ISO
6
Ace
ro
Long
itudi
nal 25.55 25.55
SEPARACIÓN (cm)
LONG. (m)
25.55
77.5
12.78 12.78
Long
.
(m) 4.30 4.30
3.40 3.40
Arm
adur
a
Tra
nsve
rsal
55
PIS
O 7
Ace
ro
Long
itudi
nal 25.55
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
21.34
60
10.67 10.67
Long
.
(m) 4.30 4.30
2.70 2.70
Arm
adur
a
Tra
nsve
rsal
55
PIS
O 8
Ace
ro
Lon
gitu
dina
l 21.34
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z3S2.
7 9
7
201
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
LUZ =>
As NEGATIVO (cm2) 6.24 6.27 6.27 6.27 6.24
As POSITIVO (cm2) 6.27 7.79 10.44 7.79 6.27
As - 2.41 4.01 4.96 4.01 2.41
As + 2.41 4.57 7.77 4.57 2.41
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30 17.5
1.20 4.13 1.20 1.20 6.03 1.2 1.2 4.125 1.2
As NEGATIVO (cm2) 8.52 10.50 10.50 10.50 8.52
As POSITIVO (cm2) 10.50 10.86 14.98 10.86 10.50
As - 2.41 4.01 4.96 4.01 2.41
As + 2.41 4.07 6.77 4.07 2.41
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 15 15 15 30 15
1.70 3.13 1.70 1.70 5.03 1.7 1.7 3.125 1.7
60 As NEGATIVO (cm2) 12.40 10.50 10.50 10.50 12.40
As POSITIVO (cm2) 10.50 13.25 17.41 13.25 10.50
As - 2.45 4.00 4.96 4.00 2.45
As + 2.45 4.05 6.77 4.05 2.45
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30 15
1.70 3.10 1.70 1.70 5.03 1.7 1.7 3.1 1.7
60 As NEGATIVO (cm2) 17.39 10.50 10.50 10.50 17.39
As POSITIVO (cm2) 10.50 16.06 19.36 16.06 10.50
As - 2.49 3.98 4.95 3.98 2.49
As + 2.49 4.02 6.75 4.02 2.49
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.70 3.06 1.70 1.70 5.00 1.7 1.7 3.0625 1.7
As NEGATIVO (cm2) 20.29 11.34 10.65 11.34 20.29
As POSITIVO (cm2) 10.50 18.21 21.33 18.21 10.50
As - 2.49 3.98 4.94 3.98 2.49
As + 2.49 4.01 6.72 4.01 2.49
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.70 3.05 1.70 1.70 4.98 1.7 1.7 3.05 1.7
60 As NEGATIVO (cm2) 22.21 13.23 12.26 13.23 22.21
As POSITIVO (cm2) 11.11 20.27 22.93 20.27 11.11
As - 2.51 3.96 4.93 3.96 2.51
As + 2.51 3.99 6.70 3.99 2.51
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.70 3.03 1.70 1.70 4.95 1.7 1.7 3.025 1.7
60 As NEGATIVO (cm2) 24.71 14.92 12.90 14.92 24.71
As POSITIVO (cm2) 12.36 21.79 23.58 21.79 12.355
As - 2.53 3.96 4.93 3.96 2.53
As + 2.53 3.98 6.70 3.98 2.53
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30 15
1.70 3.01 1.70 1.70 4.95 1.7 1.7 3.01 1.7
60 As NEGATIVO (cm2) 24.09 15.60 13.48 15.60 24.09
As POSITIVO (cm2) 12.05 22.60 24.09 22.6 12.05
As - 2.52 3.94 4.89 3.94 2.52
As + 2.52 3.96 6.62 3.96 2.52
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30 15
1.70 2.98 1.70 1.70 4.88 1.7 1.7 2.975 1.7
PORTICO Z3S4.
7 9
55P
ISO
8
Ace
ro
Lon
gitu
dina
l 21.33
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
21.33
60
10.67 10.67
Long
.
(m) 4.31 4.31
2.73 2.73
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 24.79
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
24.79
85
12.40 12.40
Long
.
(m) 4.31 4.31
3.73 3.73
Arm
adur
a
Tra
nsve
rsal
PIS
O 6
Ace
ro
Long
itudi
nal 27.35 27.35
SEPARACIÓN (cm)
LONG. (m)
85
13.68 13.68
Long
.
(m) 4.31 4.31
3.73 3.73
Arm
adu
ra
Tra
nsve
rsal ESTRIBOS
PIS
O 5
Ace
ro
Long
itudi
nal
29.38 29.38
SEPARACIÓN (cm)
LONG. (m)
85
14.69 14.69
Long
.
(m) 4.32 4.32
3.75 3.75
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
60
PIS
O 4
Ace
ro
Long
itudi
nal 31.63
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
31.63
85
15.82 15.82
Long
.
(m) 4.33 4.33
3.78 3.78
Arm
adur
a
Tra
nsve
rsal
PIS
O 3
Ace
ro
Long
itudi
nal 33.59 33.59
SEPARACIÓN (cm)
LONG. (m)
85
16.80 16.80
Long
.
(m) 4.34 4.34
3.80 3.80
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 2
Ace
ro
Long
itudi
nal
34.35 34.35
SEPARACIÓN (cm)
LONG. (m)
85
17.18 17.18
Long
.
(m) 4.34 4.34
3.80 3.80
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 1
Ace
ro
Long
itudi
nal 34.99 34.99
SEPARACIÓN (cm)
LONG. (m)
85
17.50 17.50
Long
.
(m) 4.39 4.39
3.88 3.88
Arm
adur
a
Tra
nsv
ersa
l ESTRIBOS
7
202
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
LUZ =>
As NEGATIVO (cm2) 7.27 6.27 6.27 6.27 7.27
As POSITIVO (cm2) 6.27 7.72 10.82 7.72 6.27
As - 2.41 4.01 4.96 4.01 2.41
As + 2.41 4.57 7.77 4.57 2.41
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30 17.5
1.20 4.13 1.20 1.20 6.03 1.2 1.2 4.125 1.2
As NEGATIVO (cm2) 9.29 11.17 11.17 11.17 9.29
As POSITIVO (cm2) 11.17 11.08 15.58 11.08 11.17
As - 2.43 4.00 4.95 4.00 2.43
As + 2.43 3.95 6.55 3.95 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 15 15 15 30 15
1.80 2.90 1.80 1.80 4.80 1.8 1.8 2.9 1.8
60 As NEGATIVO (cm2) 14.59 11.17 11.17 11.17 14.59
As POSITIVO (cm2) 11.17 14.33 18.21 14.33 11.17
As - 2.49 3.98 4.95 3.98 2.49
As + 2.49 3.92 6.55 3.92 2.49
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30 15
1.80 2.86 1.80 1.80 4.80 1.8 1.8 2.8625 1.8
60 As NEGATIVO (cm2) 19.20 11.17 11.17 11.17 19.2
As POSITIVO (cm2) 11.17 17.54 20.87 17.54 11.17
As - 2.49 3.98 4.95 3.98 2.49
As + 2.49 3.92 6.55 3.92 2.49
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30 15
1.80 2.86 1.80 1.80 4.80 1.8 1.8 2.8625 1.8
As NEGATIVO (cm2) 22.91 14.14 13.02 14.14 22.91
As POSITIVO (cm2) 11.46 20.76 23.19 20.76 11.46
As - 2.53 3.96 4.93 3.96 2.53
As + 2.53 3.88 6.50 3.88 2.53
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.80 2.81 1.80 1.80 4.75 1.8 1.8 2.8125 1.8
60 As NEGATIVO (cm2) 25.76 16.54 14.85 16.54 25.76
As POSITIVO (cm2) 12.88 23.09 25.13 23.09 12.88
As - 2.53 3.95 4.91 3.95 2.53
As + 2.53 3.87 6.47 3.87 2.53
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.80 2.80 1.80 1.80 4.73 1.8 1.8 2.8 1.8
60 As NEGATIVO (cm2) 27.17 18.29 16.25 18.29 27.17
As POSITIVO (cm2) 13.59 24.99 26.39 24.99 13.585
As - 2.53 3.95 4.91 3.95 2.53
As + 2.53 3.87 6.47 3.87 2.53
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30 15
1.80 2.80 1.80 1.80 4.73 1.8 1.8 2.80 1.8
60 As NEGATIVO (cm2) 26.98 19.27 16.93 19.27 26.98
As POSITIVO (cm2) 14.19 25.95 27.12 25.95 14.19
As - 2.54 3.93 4.89 3.93 2.54
As + 2.54 3.85 6.42 3.85 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30 15
1.80 2.76 1.80 1.80 4.68 1.8 1.8 2.7625 1.8
PORTICO Z7S2.
7 9
55P
ISO
8
Ace
ro
Lon
gitu
dina
l 21.29
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
21.29
60
10.65 10.65
Long
.
(m) 4.31 4.31
2.73 2.73
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 24.71
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
24.71
90
12.36 12.36
Long
.
(m) 4.33 4.33
3.95 3.95
Arm
adur
a
Tra
nsve
rsal
PIS
O 6
Ace
ro
Long
itudi
nal 27.48 27.48
SEPARACIÓN (cm)
LONG. (m)
90
13.74 13.74
Long
.
(m) 4.32 4.32
3.95 3.95
Arm
adu
ra
Tra
nsve
rsal ESTRIBOS
PIS
O 5
Ace
ro
Long
itudi
nal
30.17 30.17
SEPARACIÓN (cm)
LONG. (m)
90
15.09 15.09
Long
.
(m) 4.32 4.32
3.95 3.95
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
60
PIS
O 4
Ace
ro
Long
itudi
nal 32.90
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
32.90
90
16.45 16.45
Long
.
(m) 4.34 4.34
4.00 4.00
Arm
adur
a
Tra
nsve
rsal
PIS
O 3
Ace
ro
Long
itudi
nal 35.10 35.10
SEPARACIÓN (cm)
LONG. (m)
90
17.55 17.55
Long
.
(m) 4.36 4.36
4.03 4.03
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 2
Ace
ro
Long
itudi
nal
36.76 36.76
SEPARACIÓN (cm)
LONG. (m)
90
18.38 18.38
Long
.
(m) 4.36 4.36
4.03 4.03
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 1
Ace
ro
Long
itudi
nal 37.49 37.49
SEPARACIÓN (cm)
LONG. (m)
90
18.75 18.75
Long
.
(m) 4.38 4.38
4.08 4.08
Arm
adur
a
Tra
nsv
ersa
l ESTRIBOS
7
203
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
LUZ =>
As NEGATIVO (cm2) 14.22 6.50 6.50 6.50 14.22
As POSITIVO (cm2) 7.11 9.72 13.41 9.72 7.11
As - 2.56 3.96 4.95 3.96 2.56
As + 2.56 4.59 7.95 4.59 2.56
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30 17.5
1.10 4.23 1.10 1.10 6.20 1.1 1.1 4.225 1.1
As NEGATIVO (cm2) 18.09 15.63 15.63 15.63 18.09
As POSITIVO (cm2) 15.63 7.05 20.25 7.05 15.63
As - 2.54 3.94 4.90 3.94 2.54
As + 2.54 3.66 6.05 3.66 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
50 15 30.00 15 15 15 15 15 30 15
2.00 2.38 2.00 2.00 4.30 2 2 2.375 2
70 As NEGATIVO (cm2) 25.49 15.86 16.54 15.86 25.49
As POSITIVO (cm2) 15.63 22.16 25.99 22.16 15.63
As - 2.57 3.93 4.90 3.93 2.57
As + 2.57 3.65 6.05 3.65 2.57
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
50 15 30.00 15 15 30.00 15 15 30 15
2.00 2.36 2.00 2.00 4.30 2 2 2.3625 2
70 As NEGATIVO (cm2) 33.75 23.57 21.36 23.57 33.75
As POSITIVO (cm2) 23.73 29.70 31.06 29.7 23.73
As - 2.61 3.92 4.90 3.92 2.61
As + 2.61 3.63 6.05 3.63 2.61
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
50 15 30.00 15 15 30.00 15 15 30 15
2.00 2.34 2.00 2.00 4.30 2 2 2.3375 2
As NEGATIVO (cm2) 41.85 30.48 25.03 30.48 41.85
As POSITIVO (cm2) 31.09 36.60 34.96 36.60 31.09
As - 2.63 3.91 4.90 3.91 2.63
As + 2.63 3.62 6.05 3.62 2.63
3R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 3R3/8"
50 17.5 30.00 10 12.5 30.00 12.5 10 30 17.5
2.00 2.33 2.00 2.00 4.30 2 2 2.325 2
70 As NEGATIVO (cm2) 47.03 35.69 28.71 35.69 47.03
As POSITIVO (cm2) 32.61 41.53 38.85 41.53 32.61
As - 2.65 3.89 4.88 3.89 2.65
As + 2.65 3.59 6.00 3.59 2.65
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
50 10 30.00 10 10 30.00 10 10 30 10
2.00 2.29 2.00 2.00 4.25 2 2 2.2875 2
70 As NEGATIVO (cm2) 49.94 38.67 30.17 38.67 49.94
As POSITIVO (cm2) 38.94 44.48 39.83 44.48 38.94
As - 2.66 3.86 4.83 3.86 2.66
As + 2.66 3.54 5.90 3.54 2.66
2R1/2" 2R3/8" 2R1/2" 2R3/8" 2R3/8" 2R3/8" 2R1/2" 2R3/8" 2R1/2"
50 15 30.00 15 10 30.00 10 15 30 15
2.00 2.23 2.00 2.00 4.15 2 2 2.23 2
70 As NEGATIVO (cm2) 45.80 35.43 27.70 35.43 45.8
As POSITIVO (cm2) 35.62 41.24 37.42 41.24 35.62
As - 2.73 3.81 4.78 3.81 2.73
As + 2.73 3.47 5.80 3.47 2.73
2R3/8" 2R3/8" 2R1/2" 2R3/8" 2R3/8" 2R3/8" 2R1/2" 2R3/8" 2R3/8"
50 10 30.00 15 10 30.00 10 15 30 10
2.00 2.13 2.00 2.00 4.05 2 2 2.125 2
PORTICO Z7S4.
7 9
60P
ISO
8
Ace
ro
Lon
gitu
dina
l 23.83
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
23.83
55
11.92 11.92
Long
.
(m) 4.31 4.31
2.55 2.55
Arm
adur
a
Tra
nsve
rsal
70
PIS
O 7
Ace
ro
Long
itudi
nal 28.20
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
28.20
100
15.63 15.63
Long
.
(m) 4.37 4.37
4.45 4.45
Arm
adur
a
Tra
nsve
rsal
PIS
O 6
Ace
ro
Long
itudi
nal 34.48 34.48
SEPARACIÓN (cm)
LONG. (m)
100
17.24 17.24
Long
.
(m) 4.37 4.37
4.45 4.45
Arm
adu
ra
Tra
nsve
rsal ESTRIBOS
PIS
O 5
Ace
ro
Long
itudi
nal
29.70 29.70
SEPARACIÓN (cm)
LONG. (m)
100
23.43 23.43
Long
.
(m) 4.36 4.36
4.45 4.45
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
70
PIS
O 4
Ace
ro
Long
itudi
nal 43.72
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
43.72
100
29.62 29.62
Long
.
(m) 4.36 4.36
4.45 4.45
Arm
adur
a
Tra
nsve
rsal
PIS
O 3
Ace
ro
Long
itudi
nal 47.89 47.89
SEPARACIÓN (cm)
LONG. (m)
100
34.95 34.95
Long
.
(m) 4.38 4.38
4.50 4.50
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 2
Ace
ro
Long
itudi
nal
51.32 51.32
SEPARACIÓN (cm)
LONG. (m)
100
38.05 38.05
Long
.
(m) 4.44 4.44
4.60 4.60
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 1
Ace
ro
Long
itudi
nal 48.51 48.51
SEPARACIÓN (cm)
LONG. (m)
100
35.04 35.04
Long
.
(m) 4.49 4.49
4.70 4.70
Arm
adur
a
Tra
nsv
ersa
l ESTRIBOS
7
204
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 8 PISOS R = 6.00
LUZ =>
As NEGATIVO (cm2) 5.04 6.27 6.27 6.27 5.04
As POSITIVO (cm2) 6.27 7.61 10.42 7.61 6.27
As - 2.37 4.03 4.98 4.03 2.37
As + 2.37 4.60 7.80 4.60 2.37
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30 17.5
1.20 4.16 1.20 1.20 6.05 1.2 1.2 4.1625 1.2
As NEGATIVO (cm2) 7.34 8.02 8.02 8.02 7.34
As POSITIVO (cm2) 8.02 9.78 13.06 9.78 8.02
As - 2.39 4.03 4.98 4.03 2.39
As + 2.39 4.29 7.20 4.29 2.39
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 15 30.00 15 12.5 12.5 12.5 15 30 15
1.50 3.55 1.50 1.50 5.45 1.5 1.5 3.55 1.5
55 As NEGATIVO (cm2) 7.97 8.02 8.02 8.02 7.97
As POSITIVO (cm2) 8.02 9.69 13.07 9.69 8.02
As - 2.39 4.03 4.98 4.03 2.39
As + 2.39 4.29 7.20 4.29 2.39
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 15 30.00 15 12.5 30.00 12.5 15 30 15
1.50 3.55 1.50 1.50 5.45 1.5 1.5 3.55 1.5
55 As NEGATIVO (cm2) 9.08 8.02 8.02 8.02 9.08
As POSITIVO (cm2) 8.02 10.14 13.70 10.14 8.02
As - 2.41 4.02 4.98 4.02 2.41
As + 2.41 4.28 7.20 4.28 2.41
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 15 30.00 15 12.5 30.00 12.5 15 30 15
1.50 3.54 1.50 1.50 5.45 1.5 1.5 3.5375 1.5
As NEGATIVO (cm2) 9.99 8.02 8.02 8.02 9.99
As POSITIVO (cm2) 8.02 10.57 14.21 10.57 8.02
As - 2.41 4.01 4.96 4.01 2.41
As + 2.41 4.27 7.17 4.27 2.41
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 15 30.00 15 12.5 30.00 12.5 15 30 15
1.50 3.53 1.50 1.50 5.43 1.5 1.5 3.525 1.5
55 As NEGATIVO (cm2) 10.87 8.02 8.02 8.02 10.87
As POSITIVO (cm2) 8.02 10.92 14.57 10.92 8.02
As - 2.43 4.01 4.96 4.01 2.43
As + 2.43 4.26 7.17 4.26 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 15 12.5 30.00 12.5 15 30 17.5
1.50 3.51 1.50 1.50 5.43 1.5 1.5 3.5125 1.5
55 As NEGATIVO (cm2) 11.74 8.02 8.02 8.02 11.74
As POSITIVO (cm2) 8.02 11.14 14.73 11.14 8.02433
As - 2.43 4.00 4.95 4.00 2.43
As + 2.43 4.25 7.15 4.25 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 15 12.5 30.00 12.5 15 30 17.5
1.50 3.50 1.50 1.50 5.40 1.5 1.5 3.50 1.5
55 As NEGATIVO (cm2) 10.40 8.02 8.02 8.02 10.4
As POSITIVO (cm2) 8.02 11.59 15.06 11.59 8.02
As - 2.42 3.99 4.93 3.99 2.42
As + 2.42 4.23 7.10 4.23 2.42
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 15 12.5 30.00 12.5 15 30 17.5
1.50 3.48 1.50 1.50 5.35 1.5 1.5 3.475 1.5
75
13.55 13.55
Long
.
(m) 4.36 4.36
3.40 3.40
Arm
adur
a
Tra
nsv
ersa
l ESTRIBOSPIS
O 1
Ace
ro
Long
itudi
nal 27.09 27.09
SEPARACIÓN (cm)
LONG. (m)
75
13.38 13.38
Long
.
(m) 4.33 4.33
3.35 3.35
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
2
Ace
ro
Long
itudi
nal
26.76 26.76
SEPARACIÓN (cm)
LONG. (m)
75
13.36 13.36
Long
.
(m) 4.31 4.31
3.33 3.33
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
3
Ace
ro
Long
itudi
nal 26.72 26.72
SEPARACIÓN (cm)
LONG. (m)
26.70
75
13.35 13.35
Long
.
(m) 4.31 4.31
3.33 3.33
Arm
adur
a
Tra
nsve
rsal
55
PIS
O 4
Ace
ro
Long
itudi
nal 26.70
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
75
13.34 13.34
Long
.
(m) 4.30 4.30
3.30 3.30
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
5
Ace
ro
Long
itudi
nal
26.67 26.67
SEPARACIÓN (cm)
LONG. (m)
75
13.35 13.35
Long
.
(m) 4.30 4.30
3.30 3.30
Arm
adu
ra
Tra
nsve
rsal ESTRIBOSP
ISO
6
Ace
ro
Long
itudi
nal 26.69 26.69
SEPARACIÓN (cm)
LONG. (m)
26.70
75
13.35 13.35
Long
.
(m) 4.30 4.30
3.30 3.30
Arm
adur
a
Tra
nsve
rsal
55
PIS
O 7
Ace
ro
Long
itudi
nal 26.70
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
21.35
60
10.68 10.68Lo
ng.
(m) 4.30 4.30
2.70 2.70
Arm
adur
a
Tra
nsve
rsal
55
PIS
O 8
Ace
ro
Lon
gitu
dina
l 21.35
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z3S2.
7 9 7
205
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
LUZ =>
As NEGATIVO (cm2) 6.00 6.27 6.27 6.27 6.00
As POSITIVO (cm2) 6.27 7.74 10.47 7.74 6.27
As - 2.39 4.03 4.98 4.03 2.39
As + 2.39 4.59 7.80 4.59 2.39
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30 17.5
1.20 4.15 1.20 1.20 6.05 1.2 1.2 4.15 1.2
As NEGATIVO (cm2) 9.13 9.50 9.50 9.50 9.13
As POSITIVO (cm2) 9.50 10.53 14.45 10.53 9.50
As - 2.41 4.02 4.98 4.02 2.41
As + 2.41 4.23 7.10 4.23 2.41
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 12.5 12.5 15 30 15
1.55 3.44 1.55 1.55 5.35 1.55 1.55 3.4375 1.55
60 As NEGATIVO (cm2) 11.83 9.50 9.50 9.50 11.83
As POSITIVO (cm2) 9.50 12.27 16.33 12.27 9.50
As - 2.43 4.01 4.96 4.01 2.43
As + 2.43 4.21 7.07 4.21 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.55 3.41 1.55 1.55 5.33 1.55 1.55 3.4125 1.55
60 As NEGATIVO (cm2) 14.75 9.50 9.50 9.50 14.75
As POSITIVO (cm2) 9.50 14.05 17.92 14.05 9.50
As - 2.45 4.00 4.96 4.00 2.45
As + 2.45 4.20 7.07 4.20 2.45
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.55 3.40 1.55 1.55 5.33 1.55 1.55 3.4 1.55
As NEGATIVO (cm2) 17.41 9.50 9.50 9.50 17.41
As POSITIVO (cm2) 9.50 15.90 19.38 15.90 9.50
As - 2.47 3.98 4.94 3.98 2.47
As + 2.47 4.17 7.02 4.17 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.55 3.36 1.55 1.55 5.28 1.55 1.55 3.3625 1.55
60 As NEGATIVO (cm2) 18.79 9.50 9.50 9.50 18.79
As POSITIVO (cm2) 9.50 17.02 20.61 17.02 9.50
As - 2.47 3.98 4.94 3.98 2.47
As + 2.47 4.17 7.02 4.17 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.55 3.36 1.55 1.55 5.28 1.55 1.55 3.3625 1.55
60 As NEGATIVO (cm2) 21.03 10.71 9.50 10.71 21.03
As POSITIVO (cm2) 10.52 18.08 21.03 18.08 10.515
As - 2.51 3.97 4.94 3.97 2.51
As + 2.51 4.15 7.02 4.15 2.51
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 17.5 30.00 17.5 12.5 30 15
1.55 3.34 1.55 1.55 5.28 1.55 1.55 3.34 1.55
60 As NEGATIVO (cm2) 20.63 11.11 9.55 11.11 20.63
As POSITIVO (cm2) 10.32 18.52 21.22 18.52 10.32
As - 2.51 3.96 4.93 3.96 2.51
As + 2.51 4.14 7.00 4.14 2.51
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 17.5 30.00 17.5 12.5 30 15
1.55 3.33 1.55 1.55 5.25 1.55 1.55 3.325 1.55
PORTICO Z3S4.
7 9
55
PIS
O 8
Ace
ro
Lon
gitu
dina
l 21.28
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
21.28
60
10.64 10.64
Long
.
(m) 4.30 4.30
2.70 2.70
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 25.37
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
25.37
77.5
12.69 12.69
Long
.
(m) 4.30 4.30
3.40 3.40
Arm
adur
a
Tra
nsve
rsal
PIS
O 6
Ace
ro
Long
itudi
nal 27.54 27.54
SEPARACIÓN (cm)
LONG. (m)
77.5
13.77 13.77
Long
.
(m) 4.31 4.31
3.43 3.43
Arm
adu
ra
Tra
nsve
rsal ESTRIBOS
PIS
O 5
Ace
ro
Long
itudi
nal
29.36 29.36
SEPARACIÓN (cm)
LONG. (m)
77.5
14.68 14.68
Long
.
(m) 4.31 4.31
3.43 3.43
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
60
PIS
O 4
Ace
ro
Long
itudi
nal 31.03
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
31.03
77.5
15.52 15.52
Long
.
(m) 4.33 4.33
3.48 3.48
Arm
adur
a
Tra
nsve
rsal
PIS
O 3
Ace
ro
Long
itudi
nal 32.48 32.48
SEPARACIÓN (cm)
LONG. (m)
77.5
16.24 16.24
Long
.
(m) 4.33 4.33
3.48 3.48
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 2
Ace
ro
Long
itudi
nal
32.91 32.91
SEPARACIÓN (cm)
LONG. (m)
77.5
16.46 16.46
Long
.
(m) 4.33 4.33
3.48 3.48
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 1
Ace
ro
Long
itudi
nal 33.01 33.01
SEPARACIÓN (cm)
LONG. (m)
77.5
16.51 16.51
Long
.
(m) 4.34 4.34
3.50 3.50
Arm
adur
a
Tra
nsv
ersa
l ESTRIBOS
7
206
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
LUZ =>
As NEGATIVO (cm2) 5.88 6.27 6.27 6.27 5.88
As POSITIVO (cm2) 6.27 7.76 10.47 7.76 6.27
As - 2.39 4.03 4.98 4.03 2.39
As + 2.39 4.59 7.80 4.59 2.39
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30 17.5
1.20 4.15 1.20 1.20 6.05 1.2 1.2 4.15 1.2
As NEGATIVO (cm2) 9.37 9.84 9.84 9.84 9.37
As POSITIVO (cm2) 9.84 10.44 14.41 10.44 9.84
As - 2.43 4.01 4.96 4.01 2.43
As + 2.43 4.16 6.97 4.16 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 15 15 15 30 15
1.60 3.31 1.60 1.60 5.23 1.6 1.6 3.3125 1.6
60 As NEGATIVO (cm2) 12.00 9.84 9.84 9.84 12.00
As POSITIVO (cm2) 9.84 12.33 16.41 12.33 9.84
As - 2.43 4.01 4.96 4.01 2.43
As + 2.43 4.16 6.97 4.16 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.60 3.31 1.60 1.60 5.23 1.6 1.6 3.3125 1.6
60 As NEGATIVO (cm2) 14.52 9.84 9.84 9.84 14.52
As POSITIVO (cm2) 9.84 14.49 18.29 14.49 9.84
As - 2.45 4.00 4.96 4.00 2.45
As + 2.45 4.15 6.97 4.15 2.45
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.60 3.30 1.60 1.60 5.23 1.6 1.6 3.3 1.6
As NEGATIVO (cm2) 17.24 9.84 9.84 9.84 17.24
As POSITIVO (cm2) 9.84 16.26 20.01 16.26 9.84
As - 2.47 3.98 4.94 3.98 2.47
As + 2.47 4.12 6.92 4.12 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.60 3.26 1.60 1.60 5.18 1.6 1.6 3.2625 1.6
60 As NEGATIVO (cm2) 19.62 10.47 9.84 10.47 19.62
As POSITIVO (cm2) 9.84 17.75 21.03 17.75 9.84
As - 2.49 3.98 4.94 3.98 2.49
As + 2.49 4.11 6.92 4.11 2.49
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 15 12.5 30.00 12.5 15 30 17.5
1.60 3.25 1.60 1.60 5.18 1.6 1.6 3.25 1.6
60 As NEGATIVO (cm2) 21.16 11.71 10.54 11.71 21.16
As POSITIVO (cm2) 10.58 18.96 21.79 18.96 10.58
As - 2.48 3.97 4.93 3.97 2.48
As + 2.48 4.10 6.90 4.10 2.48
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.60 3.24 1.60 1.60 5.15 1.6 1.6 3.24 1.6
60 As NEGATIVO (cm2) 19.84 12.05 11.27 12.05 19.84
As POSITIVO (cm2) 9.92 19.54 22.59 19.54 9.92
As - 2.48 3.97 4.93 3.97 2.48
As + 2.48 4.10 6.90 4.10 2.48
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30 15
1.60 3.24 1.60 1.60 5.15 1.6 1.6 3.2375 1.6
PORTICO Z7S2.
7 9
55
PIS
O 8
Ace
ro
Lon
gitu
dina
l 21.29
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
21.29
60
10.65 10.65Lo
ng.
(m) 4.30 4.30
2.70 2.70
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 24.89
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
24.89
80
12.45 12.45
Long
.
(m) 4.31 4.31
3.53 3.53
Arm
adur
a
Tra
nsve
rsal
PIS
O 6
Ace
ro
Long
itudi
nal 27.20 27.20
SEPARACIÓN (cm)
LONG. (m)
80
13.60 13.60
Long
.
(m) 4.31 4.31
3.53 3.53
Arm
adu
ra
Tra
nsve
rsal ESTRIBOS
PIS
O 5
Ace
ro
Long
itudi
nal
29.28 29.28
SEPARACIÓN (cm)
LONG. (m)
80
14.64 14.64
Long
.
(m) 4.31 4.31
3.53 3.53
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
60
PIS
O 4
Ace
ro
Long
itudi
nal 31.15
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
31.15
80
15.58 15.58
Long
.
(m) 4.33 4.33
3.58 3.58
Arm
adur
a
Tra
nsve
rsal
PIS
O 3
Ace
ro
Long
itudi
nal 32.40 32.40
SEPARACIÓN (cm)
LONG. (m)
80
16.20 16.20
Long
.
(m) 4.33 4.33
3.58 3.58
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 2
Ace
ro
Long
itudi
nal
33.32 33.32
SEPARACIÓN (cm)
LONG. (m)
80
16.66 16.66
Long
.
(m) 4.35 4.35
3.60 3.60
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 1
Ace
ro
Long
itudi
nal 34.17 34.17
SEPARACIÓN (cm)
LONG. (m)
80
17.09 17.09
Long
.
(m) 4.35 4.35
3.60 3.60
Arm
adur
a
Tra
nsv
ersa
l ESTRIBOS
7
207
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
LUZ =>
As NEGATIVO (cm2) 13.12 6.50 6.50 6.50 13.12
As POSITIVO (cm2) 6.56 8.74 12.46 8.74 6.56
As - 2.56 3.96 4.95 3.96 2.56
As + 2.56 4.59 7.95 4.59 2.56
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 17.5 17.5 30.00 17.5 17.5 30 17.5
1.10 4.23 1.10 1.10 6.20 1.1 1.1 4.225 1.1
As NEGATIVO (cm2) 15.67 15.63 15.63 15.63 15.67
As POSITIVO (cm2) 15.63 15.49 17.46 15.49 15.63
As - 2.54 3.94 4.90 3.94 2.54
As + 2.54 3.66 6.05 3.66 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
50 15 30.00 15 15 15 15 15 30 15
2.00 2.38 2.00 2.00 4.30 2 2 2.375 2
70 As NEGATIVO (cm2) 20.55 15.63 15.63 15.63 20.55
As POSITIVO (cm2) 15.63 17.96 21.70 17.96 15.63
As - 2.57 3.93 4.90 3.93 2.57
As + 2.57 3.65 6.05 3.65 2.57
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
50 15 30.00 15 15 30.00 15 15 30 15
2.00 2.36 2.00 2.00 4.30 2 2 2.3625 2
70 As NEGATIVO (cm2) 27.41 18.57 15.94 18.57 27.41
As POSITIVO (cm2) 15.63 23.66 25.45 23.66 15.63
As - 2.61 3.92 4.90 3.92 2.61
As + 2.61 3.63 6.05 3.63 2.61
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
50 15 30.00 15 15 30.00 15 15 30 15
2.00 2.34 2.00 2.00 4.30 2 2 2.3375 2
As NEGATIVO (cm2) 33.40 22.62 18.64 22.62 33.4
As POSITIVO (cm2) 17.53 28.46 28.20 28.46 17.53
As - 2.63 3.91 4.90 3.91 2.63
As + 2.63 3.62 6.05 3.62 2.63
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
50 15 30.00 15 15 30.00 15 15 30 15
2.00 2.33 2.00 2.00 4.30 2 2 2.325 2
70 As NEGATIVO (cm2) 37.09 26.40 21.34 26.40 37.09
As POSITIVO (cm2) 21.22 32.18 30.97 32.18 21.22
As - 2.65 3.89 4.88 3.89 2.65
As + 2.65 3.59 6.00 3.59 2.65
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
50 15 30.00 12.5 15 30.00 15 12.5 30 15
2.00 2.29 2.00 2.00 4.25 2 2 2.2875 2
70 As NEGATIVO (cm2) 39.11 28.55 22.40 28.55 39.11
As POSITIVO (cm2) 23.60 34.25 31.98 34.25 23.6
As - 2.66 3.86 4.83 3.86 2.66
As + 2.66 3.54 5.90 3.54 2.66
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
50 12.5 30.00 12.5 12.5 30.00 12.5 12.5 30 12.5
2.00 2.23 2.00 2.00 4.15 2 2 2.23 2
70 As NEGATIVO (cm2) 36.06 26.22 20.60 26.22 36.06
As POSITIVO (cm2) 21.10 32.10 30.05 32.1 21.10
As - 2.73 3.81 4.78 3.81 2.73
As + 2.73 3.47 5.80 3.47 2.73
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
50 15 30.00 12.5 15 30.00 15 12.5 30 15
2.00 2.13 2.00 2.00 4.05 2 2 2.125 2
100
19.61 19.61
Long
.
(m) 4.49 4.49
4.70 4.70
Arm
adur
a
Tra
nsv
ersa
l ESTRIBOSPIS
O 1
Ace
ro
Long
itudi
nal 39.22 39.22
SEPARACIÓN (cm)
LONG. (m)
100
20.55 20.55
Long
.
(m) 4.44 4.44
4.60 4.60
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
2
Ace
ro
Long
itudi
nal
41.09 41.09
SEPARACIÓN (cm)
LONG. (m)
100
19.93 19.93
Long
.
(m) 4.38 4.38
4.50 4.50
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
3
Ace
ro
Long
itudi
nal 39.86 39.86
SEPARACIÓN (cm)
LONG. (m)
36.80
100
18.40 18.40
Long
.
(m) 4.36 4.36
4.45 4.45
Arm
adur
a
Tra
nsve
rsal
70
PIS
O 4
Ace
ro
Long
itudi
nal 36.80
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
100
16.93 16.93
Long
.
(m) 4.36 4.36
4.45 4.45
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
5
Ace
ro
Long
itudi
nal
33.86 33.86
SEPARACIÓN (cm)
LONG. (m)
100
15.63 15.63
Long
.
(m) 4.37 4.37
4.45 4.45
Arm
adu
ra
Tra
nsve
rsal ESTRIBOSP
ISO
6
Ace
ro
Long
itudi
nal 30.02 30.02
SEPARACIÓN (cm)
LONG. (m)
25.32
100
15.63 15.63
Long
.
(m) 4.37 4.37
4.45 4.45
Arm
adur
a
Tra
nsve
rsal
70
PIS
O 7
Ace
ro
Long
itudi
nal 25.32
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
23.90
55
11.95 11.95
Long
.
(m) 4.31 4.31
2.55 2.55
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 8
Ace
ro
Lon
gitu
dina
l 23.90
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z7S4.
7 9
7
208
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 12 PISOS R = 3.32
LUZ =>
As NEGATIVO (cm2) 9.22 6.50 6.50 6.50 9.22
As POSITIVO (cm2) 6.50 7.67 11.54 7.67 6.50
As - 2.43 4.01 4.98 4.01 2.43
As + 2.43 4.67 8.00 4.67 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.10 4.33 1.10 1.10 6.25 1.1 1.1 4.33 1.10
As NEGATIVO (cm2) 11.06 9.84 9.84 9.84 11.06
As POSITIVO (cm2) 9.84 9.97 14.63 9.97 9.84
As - 2.43 4.01 4.98 4.01 2.43
As + 2.43 4.17 7.00 4.17 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.60 3.33 1.60 1.60 5.25 1.6 1.6 3.33 1.60
60 As NEGATIVO (cm2) 12.45 9.84 9.84 9.84 12.45
As POSITIVO (cm2) 9.84 11.89 16.48 11.89 9.84
As - 2.43 4.01 4.98 4.01 2.43
As + 2.43 4.17 7.00 4.17 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.60 3.33 1.60 1.60 5.25 1.6 1.6 3.33 1.60
60 As NEGATIVO (cm2) 15.49 9.84 9.84 9.84 15.49
As POSITIVO (cm2) 9.84 13.53 17.80 13.53 9.84
As - 2.48 4.00 4.98 4.00 2.48
As + 2.48 4.15 7.00 4.15 2.48
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.60 3.30 1.60 1.60 5.25 1.6 1.6 3.30 1.60
As NEGATIVO (cm2) 18.01 9.84 9.84 9.84 18.01
As POSITIVO (cm2) 9.84 14.97 19.09 14.97 9.84
As - 2.47 3.99 4.95 3.99 2.47
As + 2.47 4.13 6.95 4.13 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 15 12.5 30.00 12.5 15 30.00 17.5
1.60 3.28 1.60 1.60 5.20 1.6 1.6 3.28 1.60
As NEGATIVO (cm2) 18.35 9.84 9.84 9.84 18.35
As POSITIVO (cm2) 9.84 16.04 20.22 16.04 9.84
As - 2.47 3.99 4.95 3.99 2.47
As + 2.47 4.13 6.95 4.13 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 12.5 12.5 15 30.00 15
1.60 3.28 1.60 1.60 5.20 1.6 1.6 3.28 1.60
60 As NEGATIVO (cm2) 21.45 10.01 9.84 10.01 21.45
As POSITIVO (cm2) 10.73 17.00 20.43 17.00 10.73
As - 2.56 3.96 4.95 3.96 2.56
As + 2.56 4.09 6.95 4.09 2.56
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.60 3.23 1.60 1.60 5.20 1.6 1.6 3.23 1.60
60 As NEGATIVO (cm2) 23.23 11.06 9.84 11.06 23.23
As POSITIVO (cm2) 11.62 17.85 20.81 17.85 11.62
As - 2.55 3.95 4.93 3.95 2.55
As + 2.55 4.07 6.90 4.07 2.55
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.60 3.20 1.60 1.60 5.15 1.6 1.6 3.20 1.60
As NEGATIVO (cm2) 23.29 11.87 10.54 11.87 23.29
As POSITIVO (cm2) 11.65 18.79 21.76 18.79 11.65
As - 2.54 3.94 4.90 3.94 2.54
As + 2.54 4.06 6.85 4.06 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30.00 15
1.60 3.18 1.60 1.60 5.10 1.6 1.6 3.18 1.60
60 As NEGATIVO (cm2) 23.83 12.73 11.13 12.73 23.83
As POSITIVO (cm2) 11.92 19.84 22.35 19.84 11.92
As - 2.54 3.94 4.90 3.94 2.54
As + 2.54 4.06 6.85 4.06 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30.00 15
1.60 3.18 1.60 1.60 5.10 1.6 1.6 3.18 1.60
60 As NEGATIVO (cm2) 23.88 13.10 11.44 13.10 23.88
As POSITIVO (cm2) 11.94 20.22 22.60 20.22 11.94
As - 2.53 3.91 4.85 3.91 2.53
As + 2.53 4.02 6.75 4.02 2.53
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30.00 15
1.60 3.13 1.60 1.60 5.00 1.6 1.6 3.13 1.60
60 As NEGATIVO (cm2) 21.36 11.92 10.84 11.92 21.36
As POSITIVO (cm2) 10.68 19.12 21.97 19.12 10.68
As - 2.53 3.91 4.85 3.91 2.53
As + 2.53 4.02 6.75 4.02 2.53
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.60 3.13 1.60 1.60 5.00 1.6 1.6 3.13 1.60
80
16.93 16.93
Long
.
(m) 4.43 4.43
3.75 3.75
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
1
Ace
ro
Long
itudi
nal 33.85 33.85
SEPARACIÓN (cm)
LONG. (m)
80
17.29 17.29
Long
.
(m) 4.43 4.43
3.75 3.75
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
2
Ace
ro
Long
itudi
nal 34.57 34.57
SEPARACIÓN (cm)
LONG. (m)
80
17.06 17.06
Long
.
(m) 4.37 4.37
3.65 3.65
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
3
Ace
ro
Long
itudi
nal 34.11 34.11
SEPARACIÓN (cm)
LONG. (m)
33.37
80
16.69 16.69
Long
.
(m) 4.37 4.37
3.65 3.65
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 4
Ace
ro
Long
itudi
nal 33.37
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
80
15.98 15.98
Long
.
(m) 4.34 4.34
3.60 3.60
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
5
Ace
ro
Long
itudi
nal 31.96 31.96
SEPARACIÓN (cm)
LONG. (m)
80
15.63 15.63
Long
.
(m) 4.31 4.31
3.55 3.55
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
6
Ace
ro
Long
itudi
nal 31.26 31.26
SEPARACIÓN (cm)
LONG. (m)
31.08
80
15.54 15.54
Long
.
(m) 4.32 4.32
3.55 3.55
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 31.08
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
29.71
80
14.86 14.86
Long
.
(m) 4.32 4.32
3.55 3.55
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 8
Ace
ro
Long
itudi
nal 29.71
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z3S2.
7 9 7
60
PIS
O 1
2 Ace
ro
Long
itudi
nal 23.15
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
23.15
55
11.58 11.58
Long
.
(m) 4.29 4.29
2.50 2.50
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 1
1 Ace
ro
Long
itudi
nal 24.46
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
24.46
80
12.23 12.23
Long
.
(m) 4.29 4.29
3.50 3.50
Arm
adur
a
Tra
nsve
rsal
PIS
O 1
0 Ace
ro
Long
itudi
nal 26.60 26.60
SEPARACIÓN (cm)
LONG. (m)
80
13.30 13.30
Long
.
(m) 4.29 4.29
3.50 3.50
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 9
Ace
ro
Long
itudi
nal 27.94 27.94
SEPARACIÓN (cm)
LONG. (m)
80
13.97 13.97
Long
.
(m) 4.29 4.29
3.50 3.50
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
209
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
210
LUZ =>
As NEGATIVO (cm2) 10.77 6.50 6.50 6.50 10.77
As POSITIVO (cm2) 6.50 7.69 11.78 7.69 6.50
As - 2.48 4.00 4.98 4.00 2.48
As + 2.48 4.65 8.00 4.65 2.48
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.10 4.30 1.10 1.10 6.25 1.1 1.1 4.30 1.10
As NEGATIVO (cm2) 12.83 10.84 10.84 10.84 12.83
As POSITIVO (cm2) 10.84 10.72 15.95 10.72 10.84
As - 2.48 4.00 4.98 4.00 2.48
As + 2.48 4.00 6.70 4.00 2.48
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.75 3.00 1.75 1.75 4.95 1.75 1.75 3.00 1.75
60 As NEGATIVO (cm2) 16.93 10.84 10.84 10.84 16.93
As POSITIVO (cm2) 10.84 13.63 18.20 13.63 10.84
As - 2.51 3.98 4.95 3.98 2.51
As + 2.51 3.96 6.65 3.96 2.51
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.75 2.95 1.75 1.75 4.90 1.75 1.75 2.95 1.75
60 As NEGATIVO (cm2) 20.51 10.84 10.84 10.84 20.51
As POSITIVO (cm2) 10.84 16.47 20.68 16.47 10.84
As - 2.51 3.98 4.95 3.98 2.51
As + 2.51 3.96 6.65 3.96 2.51
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.75 2.95 1.75 1.75 4.90 1.75 1.75 2.95 1.75
As NEGATIVO (cm2) 23.91 12.61 12.44 12.61 23.91
As POSITIVO (cm2) 11.96 19.19 22.98 19.19 11.96
As - 2.55 3.95 4.93 3.95 2.55
As + 2.55 3.92 6.60 3.92 2.55
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.75 2.90 1.75 1.75 4.85 1.75 1.75 2.90 1.75
As NEGATIVO (cm2) 26.60 14.74 13.95 14.74 26.60
As POSITIVO (cm2) 13.30 21.33 24.35 21.33 13.30
As - 2.55 3.95 4.93 3.95 2.55
As + 2.55 3.92 6.60 3.92 2.55
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 12.5 12.5 12.5 30.00 15
1.75 2.90 1.75 1.75 4.85 1.75 1.75 2.90 1.75
60 As NEGATIVO (cm2) 28.38 16.78 15.27 16.78 28.38
As POSITIVO (cm2) 14.19 23.40 25.83 23.40 14.19
As - 2.55 3.95 4.93 3.95 2.55
As + 2.55 3.92 6.60 3.92 2.55
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30.00 15
1.75 2.90 1.75 1.75 4.85 1.75 1.75 2.90 1.75
60 As NEGATIVO (cm2) 29.31 18.43 17.01 18.43 29.31
As POSITIVO (cm2) 14.66 25.13 27.52 25.13 14.66
As - 2.54 3.94 4.90 3.94 2.54
As + 2.54 3.91 6.55 3.91 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 12.5 30.00 12.5 12.5 30.00 12.5
1.75 2.88 1.75 1.75 4.80 1.75 1.75 2.88 1.75
As NEGATIVO (cm2) 32.75 20.60 17.42 20.60 32.75
As POSITIVO (cm2) 16.38 27.06 27.95 27.06 16.38
As - 2.63 3.91 4.90 3.91 2.63
As + 2.63 3.87 6.55 3.87 2.63
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 17.5 30.00 17.5 12.5 30.00 12.5
1.75 2.83 1.75 1.75 4.80 1.75 1.75 2.83 1.75
60 As NEGATIVO (cm2) 34.08 21.87 16.21 21.87 34.08
As POSITIVO (cm2) 17.04 28.23 28.59 28.23 17.04
As - 2.62 3.89 4.85 3.89 2.62
As + 2.62 3.83 6.45 3.83 2.62
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 17.5 30.00 17.5 12.5 30.00 12.5
1.75 2.78 1.75 1.75 4.70 1.75 1.75 2.78 1.75
60 As NEGATIVO (cm2) 33.09 21.63 18.51 21.63 33.09
As POSITIVO (cm2) 16.55 28.07 28.83 28.07 16.55
As - 2.62 3.89 4.85 3.89 2.62
As + 2.62 3.83 6.45 3.83 2.62
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 17.5 30.00 17.5 12.5 30.00 12.5
1.75 2.78 1.75 1.75 4.70 1.75 1.75 2.78 1.75
60 As NEGATIVO (cm2) 29.77 19.11 15.97 19.11 29.77
As POSITIVO (cm2) 14.89 25.58 26.25 25.58 14.89
As - 2.65 3.85 4.80 3.85 2.65
As + 2.65 3.77 6.35 3.77 2.65
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 12.5 30.00 12.5 12.5 30.00 12.5
87.5
18.68 18.68
Long
.
(m) 4.48 4.48
4.15 4.15
dura
sver
sal ESTRIBOSPIS
O 1
Ace
ro
Long
itudi
nal 37.36 37.36
SEPARACIÓN (cm)
87.5
20.18 20.18
Long
.
(m) 4.42 4.42
4.05 4.05
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
2
Ace
ro
Long
itudi
nal 40.35 40.35
SEPARACIÓN (cm)
LONG. (m)
87.
5
19.98 19.98
Long
.
(m) 4.42 4.42
4.05 4.05
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
3
Ace
ro
Long
itudi
nal 39.95 39.95
SEPARACIÓN (cm)
LONG. (m)
38.85
87.
5
19.43 19.43
Long
.
(m) 4.36 4.36
3.95 3.95
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 4
Ace
ro
Long
itudi
nal 38.85
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
87.
5
19.18 19.18
Long
.
(m) 4.37 4.37
3.95 3.95
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
5
Ace
ro
Long
itudi
nal 38.36 38.36
SEPARACIÓN (cm)
LONG. (m)
87.5
18.10 18.10
Long
.
(m) 4.34 4.34
3.90 3.90
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
6
Ace
ro
Long
itudi
nal 36.20 36.20
SEPARACIÓN (cm)
LONG. (m)
34.65
87.5
17.33 17.33
Long
.
(m) 4.34 4.34
3.90 3.90
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 34.65
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
32.83
87.5
16.42 16.42
Long
.
(m) 4.34 4.34
3.90 3.90
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 8
Ace
ro
Long
itudi
nal 32.83
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z3S4.
7 9 7
60
PIS
O 1
2 Ace
ro
Long
itudi
nal 23.18
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
23.18
55
11.59 11.59
Long
.
(m) 4.29 4.29
2.50 2.50Arm
adur
a
Tra
nsve
rsal
60
PIS
O 1
1 Ace
ro
Long
itudi
nal 24.60
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
24.60
87.
5
12.30 12.30
Long
.
(m) 4.29 4.29
3.80 3.80
Arm
adur
a
Tra
nsve
rsal
PIS
O 1
0 Ace
ro
Long
itudi
nal 27.08 27.08
SEPARACIÓN (cm)
LONG. (m)
87.
5
13.54 13.54
Long
.
(m) 4.31 4.31
3.85 3.85
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 9
Ace
ro
Long
itudi
nal 29.68 29.68
SEPARACIÓN (cm)
LONG. (m)
87.
5
14.84 14.84
Long
.
(m) 4.31 4.31
3.85 3.85
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
1.75 2.70 1.75 1.75 4.60 1.75 1.75 2.70 1.75Arm
a
Tra
n
LONG. (m)
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
211
LUZ =>
As NEGATIVO (cm2) 11.06 7.17 7.17 7.17 11.06
As POSITIVO (cm2) 7.17 7.14 11.26 7.14 7.17
As - 2.54 3.94 4.90 3.94 2.54
As + 2.54 4.46 7.65 4.46 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.20 3.98 1.20 1.20 5.90 1.2 1.2 3.98 1.20
As NEGATIVO (cm2) 12.87 13.84 13.84 13.84 12.87
As POSITIVO (cm2) 13.84 13.72 17.09 13.72 13.84
As - 2.54 3.94 4.90 3.94 2.54
As + 2.54 3.46 5.65 3.46 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
2.20 1.98 2.20 2.20 3.90 2.2 2.2 1.98 2.20
60 As NEGATIVO (cm2) 16.58 13.84 13.84 13.84 16.58
As POSITIVO (cm2) 13.84 14.43 20.87 14.43 13.84
As - 2.54 3.94 4.90 3.94 2.54
As + 2.54 3.46 5.65 3.46 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
2.20 1.98 2.20 2.20 3.90 2.2 2.2 1.98 2.20
60 As NEGATIVO (cm2) 22.00 13.84 16.45 13.84 22.00
As POSITIVO (cm2) 13.84 19.19 24.92 19.19 13.84
As - 2.58 3.91 4.88 3.91 2.58
As + 2.58 3.42 5.60 3.42 2.58
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
2.20 1.93 2.20 2.20 3.85 2.2 2.2 1.93 2.20
As NEGATIVO (cm2) 27.06 18.34 20.25 18.34 27.06
As POSITIVO (cm2) 17.94 23.81 28.69 23.81 17.94
As - 2.58 3.91 4.88 3.91 2.58
As + 2.58 3.42 5.60 3.42 2.58
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 12.5 15 30.00 15 12.5 30.00 17.5
2.20 1.93 2.20 2.20 3.85 2.2 2.2 1.93 2.20
As NEGATIVO (cm2) 33.07 23.17 23.11 23.17 33.07
As POSITIVO (cm2) 23.07 28.42 31.53 28.42 23.07
As - 2.66 3.88 4.85 3.88 2.66
As + 2.66 3.36 5.55 3.36 2.66
2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 17.5 12.5 12.5 12.5 17.5 30.00 12.5
2.20 1.85 2.20 2.20 3.80 2.2 2.2 1.85 2.20
60 As NEGATIVO (cm2) 37.99 27.24 25.18 27.24 37.99
As POSITIVO (cm2) 27.35 32.41 33.72 32.41 27.35
As - 2.66 3.88 4.85 3.88 2.66
As + 2.66 3.36 5.55 3.36 2.66
3R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 3R3/8"
40 17.5 30.00 10 12.5 30.00 12.5 10 30.00 17.5
2.20 1.85 2.20 2.20 3.80 2.2 2.2 1.85 2.20
60 As NEGATIVO (cm2) 40.14 30.41 28.49 30.41 40.14
As POSITIVO (cm2) 29.83 35.61 36.91 35.61 29.83
As - 2.65 3.85 4.80 3.85 2.65
As + 2.65 3.32 5.45 3.32 2.65
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 10 30.00 10 10 30.00 10 10 30.00 10
2.20 1.80 2.20 2.20 3.70 2.2 2.2 1.80 2.20
As NEGATIVO (cm2) 43.02 33.19 30.11 33.19 43.02
As POSITIVO (cm2) 32.57 38.50 38.70 38.50 32.57
As - 2.69 3.84 4.80 3.84 2.69
As + 2.69 3.31 5.45 3.31 2.69
2R3/8" 2R3/8" 2R1/2" 2R3/8" 2R3/8" 2R3/8" 2R1/2" 2R3/8" 2R3/8"
40 10 30.00 15 10 30.00 10 15 30.00 10
2.20 1.78 2.20 2.20 3.70 2.2 2.2 1.78 2.20
60 As NEGATIVO (cm2) 44.78 35.12 30.99 35.12 44.78
As POSITIVO (cm2) 34.35 40.39 39.52 40.39 34.35
As - 2.68 3.81 4.75 3.81 2.68
As + 2.68 3.27 5.35 3.27 2.68
2R1/2" 2R3/8" 2R1/2" 2R3/8" 2R3/8" 2R3/8" 2R1/2" 2R3/8" 2R1/2"
40 15 30.00 15 10 30.00 10 15 30.00 15
2.20 1.73 2.20 2.20 3.60 2.2 2.2 1.73 2.20
60 As NEGATIVO (cm2) 44.78 35.12 30.99 35.12 44.78
As POSITIVO (cm2) 34.35 40.39 39.52 40.39 34.35
As - 2.73 3.80 4.75 3.80 2.73
As + 2.73 3.25 5.35 3.25 2.73
2R1/2" 2R3/8" 2R1/2" 2R3/8" 2R3/8" 2R3/8" 2R1/2" 2R3/8" 2R1/2"
40 15 30.00 15 10 30.00 10 15 30.00 15
2.20 1.70 2.20 2.20 3.60 2.2 2.2 1.70 2.20
60 As NEGATIVO (cm2) 44.78 35.12 30.99 35.12 44.78
As POSITIVO (cm2) 34.35 40.39 39.52 40.39 34.35
As - 2.71 3.78 4.70 3.78 2.71
As + 2.71 3.21 5.25 3.21 2.71
2R1/2" 2R3/8" 2R1/2" 2R3/8" 2R3/8" 2R3/8" 2R1/2" 2R3/8" 2R1/2"
40 15 30.00 15 10 30.00 10 15 30.00 15
110
35.01 35.01
Long
.
(m) 4.59 4.59
5.25 5.25
dura
sver
sal ESTRIBOSPIS
O 1
Ace
ro
Long
itudi
nal 48.88 48.88
SEPARACIÓN (cm)
110
35.01 35.01
Long
.
(m) 4.53 4.53
5.15 5.15
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
2
Ace
ro
Long
itudi
nal 48.88 48.88
SEPARACIÓN (cm)
LONG. (m)
110
35.01 35.01
Long
.
(m) 4.53 4.53
5.15 5.15
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
3
Ace
ro
Long
itudi
nal 48.88 48.88
SEPARACIÓN (cm)
LONG. (m)
47.85
110
33.10 33.10
Long
.
(m) 4.47 4.47
5.05 5.05
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 4
Ace
ro
Long
itudi
nal 47.85
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
110
30.24 30.24
Long
.
(m) 4.48 4.48
5.05 5.05
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
5
Ace
ro
Long
itudi
nal 46.00 46.00
SEPARACIÓN (cm)
LONG. (m)
110
26.63 26.63
Long
.
(m) 4.41 4.41
4.95 4.95
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
6
Ace
ro
Long
itudi
nal 42.21 42.21
SEPARACIÓN (cm)
LONG. (m)
39.89
110
23.01 23.01
Long
.
(m) 4.41 4.41
4.95 4.95
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 39.89
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
36.72
110
18.46 18.46
Long
.
(m) 4.39 4.39
4.90 4.90
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 8
Ace
ro
Long
itudi
nal 36.72
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z7S2.
7 9 7
60PIS
O 1
2 Ace
ro
Long
itudi
nal 21.02
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
21.02
60
10.51 10.51
Long
.
(m) 4.37 4.37
2.85 2.85
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 1
1 Ace
ro
Long
itudi
nal 23.98
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
23.98
110
13.84 13.84
Long
.
(m) 4.37 4.37
4.85 4.85
Arm
adur
a
Tra
nsve
rsal
PIS
O 1
0 Ace
ro
Long
itudi
nal 27.90 27.90
SEPARACIÓN (cm)
LONG. (m)
110
13.95 13.95
Long
.
(m) 4.37 4.37
4.85 4.85
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 9
Ace
ro
Long
itudi
nal 32.15 32.15
SEPARACIÓN (cm)
LONG. (m)
110
16.37 16.37
Long
.
(m) 4.39 4.39
4.90 4.90
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
2.20 1.65 2.20 2.20 3.50 2.2 2.2 1.65 2.20Arm
a
Tra
n
LONG. (m)
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
212
LUZ =>
As NEGATIVO (cm2) 10.17 7.17 7.17 7.17 10.17
As POSITIVO (cm2) 7.17 9.94 15.01 9.94 7.17
As - 2.62 3.89 4.85 3.89 2.62
As + 2.62 4.38 7.55 4.38 2.62
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.20 3.88 1.20 1.20 5.80 1.2 1.2 3.88 1.20
As NEGATIVO (cm2) 7.24 23.26 23.26 23.26 7.24
As POSITIVO (cm2) 23.26 22.92 29.72 22.92 23.26
As - 2.62 3.89 4.85 3.89 2.62
As + 2.62 3.13 5.05 3.13 2.62
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
60 15 30.00 15 15 30.00 15 15 30.00 15
2.45 1.38 2.45 2.45 3.30 2.45 2.45 1.38 2.45
80 As NEGATIVO (cm2) 19.23 23.26 27.54 23.26 19.23
As POSITIVO (cm2) 23.26 22.92 36.10 22.92 23.26
As - 2.61 3.88 4.83 3.88 2.61
As + 2.61 3.11 5.00 3.11 2.61
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
60 15 30.00 15 15 30.00 15 15 30.00 15
2.45 1.35 2.45 2.45 3.25 2.45 2.45 1.35 2.45
80 As NEGATIVO (cm2) 33.69 23.26 32.82 23.26 33.69
As POSITIVO (cm2) 23.26 28.96 41.31 28.96 23.26
As - 2.70 3.85 4.83 3.85 2.70
As + 2.70 3.07 5.00 3.07 2.70
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
60 15 30.00 12.5 15 30.00 15 12.5 30.00 15
2.45 1.30 2.45 2.45 3.25 2.45 2.45 1.30 2.45
As NEGATIVO (cm2) 44.81 32.56 39.32 32.56 44.81
As POSITIVO (cm2) 25.93 38.16 48.05 38.16 25.93
As - 2.69 3.83 4.78 3.83 2.69
As + 2.69 3.04 4.90 3.04 2.69
2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8"
60 12.5 30.00 17.5 12.5 30.00 12.5 17.5 30.00 12.5
2.45 1.25 2.45 2.45 3.15 2.45 2.45 1.25 2.45
As NEGATIVO (cm2) 55.14 41.32 44.81 41.32 55.14
As POSITIVO (cm2) 35.05 46.80 53.5 46.80 35.05
As - 2.78 3.80 4.78 3.80 2.78
As + 2.78 3.00 4.90 3.00 2.78
2R3/8" 2R3/8" 2R1/2" 2R3/8" 2R3/8" 2R3/8" 2R1/2" 2R3/8" 2R3/8"
60 10 30.00 15 10 10 10 15 30.00 10
2.45 1.20 2.45 2.45 3.15 2.45 2.45 1.20 2.45
80 As NEGATIVO (cm2) 64.16 49.54 49.36 49.54 64.16
As POSITIVO (cm2) 43.12 54.61 58.50 54.61 43.12
As - 2.76 3.78 4.73 3.78 2.76
As + 2.76 2.96 4.80 2.96 2.76
2R1/2" 2R3/8" 2R1/2" 2R3/8" 2R3/8" 2R3/8" 2R1/2" 2R3/8" 2R1/2"
60 15 30.00 12.5 10 30.00 10 12.5 30.00 15
2.45 1.15 2.45 2.45 3.05 2.45 2.45 1.15 2.45
80 As NEGATIVO (cm2) 70.21 56.35 54.62 56.35 70.21
As POSITIVO (cm2) 49.94 61.54 63.32 61.54 49.94
As - 2.76 3.78 4.73 3.78 2.76
As + 2.76 2.96 4.80 2.96 2.76
2R1/2" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 2R1/2"
60 12.5 30.00 12.5 15 30.00 15 12.5 30.00 12.5
2.45 1.15 2.45 2.45 3.05 2.45 2.45 1.15 2.45
As NEGATIVO (cm2) 75.63 62.33 58.29 62.33 75.63
As POSITIVO (cm2) 55.52 67.39 66.87 67.39 55.52
As - 2.79 3.74 4.68 3.74 2.79
As + 2.79 2.91 4.70 2.91 2.79
3R3/8" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 3R3/8"
60 10 30.00 10 15 30.00 15 10 30.00 10
2.45 1.08 2.45 2.45 2.95 2.45 2.45 1.08 2.45
80 As NEGATIVO (cm2) 80.49 67.56 60.29 67.56 80.49
As POSITIVO (cm2) 61.05 72.41 68.77 72.41 61.05
As - 2.79 3.74 4.68 3.74 2.79
As + 2.79 2.91 4.70 2.91 2.79
2R1/2" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 2R1/2"
60 10 30.00 10 12.5 30.00 12.5 10 30.00 10
2.45 1.08 2.45 2.45 2.95 2.45 2.45 1.08 2.45
80 As NEGATIVO (cm2) 82.86 70.97 61.27 70.97 82.86
As POSITIVO (cm2) 64.37 76.10 69.66 76.10 64.37
As - 2.87 3.69 4.63 3.69 2.87
As + 2.87 2.83 4.60 2.83 2.87
2R1/2" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 2R1/2"
60 10 30.00 10 12.5 30.00 12.5 10 30.00 10
2.45 0.98 2.45 2.45 2.85 2.45 2.45 0.98 2.45
80 As NEGATIVO (cm2) 81.95 71.79 58.76 71.79 81.95
As POSITIVO (cm2) 66.14 76.98 67.19 76.98 66.14
As - 2.87 3.69 4.63 3.69 2.87
As + 2.87 2.83 4.60 2.83 2.87
2R1/2" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 2R1/2" 2R1/2" 2R3/8" 2R1/2"
60 10 30.00 10 15 30.00 15 10 30.00 10
122.
5
24.48 24.48
Long
.
(m) 4.44 4.44
5.50 5.50
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
9
Ace
ro
Long
itudi
nal 47.83 47.83
SEPARACIÓN (cm)
LONG. (m)
122.
5
23.26 23.26
Long
.
(m) 4.45 4.45
5.50 5.50
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
10 Ace
ro
Long
itudi
nal 42.50 42.50
SEPARACIÓN (cm)
LONG. (m)
36.21
122
.5
23.26 23.26
Long
.
(m) 4.42 4.42
5.45 5.45
Arm
adur
a
Tra
nsve
rsal
80
PIS
O 1
1 Ace
ro
Long
itudi
nal 36.21
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
24.36
60
12.18 12.18
Long
.
(m) 4.42 4.42
2.95 2.95Arm
adur
a
Tra
nsve
rsal
60PIS
O 1
2 Ace
ro
Long
itudi
nal 24.36
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z7S4.
7 9 7
80
PIS
O 8
Ace
ro
Long
itudi
nal 55.01
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
55.01
122.
5
30.50 30.50
Long
.
(m) 4.50 4.50
5.60 5.60
Arm
adur
a
Tra
nsve
rsal
80
PIS
O 7
Ace
ro
Long
itudi
nal 60.84
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
60.84
122
.5
36.05 36.05
Long
.
(m) 4.49 4.49
5.60 5.60
Arm
adur
a
Tra
nsve
rsal
PIS
O 6
Ace
ro
Long
itudi
nal 65.71 65.71
SEPARACIÓN (cm)
LONG. (m)
122
.5
40.09 40.09
Long
.
(m) 4.55 4.55
5.70 5.70
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 5
Ace
ro
Long
itudi
nal 71.42 71.42
SEPARACIÓN (cm)
LONG. (m)
122
.5
45.15 45.15
Long
.
(m) 4.55 4.55
5.70 5.70
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
80
PIS
O 4
Ace
ro
Long
itudi
nal 75.41
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
75.41
122
.5
48.76 48.76
Long
.
(m) 4.61 4.61
5.80 5.80
Arm
adur
a
Tra
nsve
rsal
PIS
O 3
Ace
ro
Long
itudi
nal 77.64 77.64
SEPARACIÓN (cm)
LONG. (m)
122.
5
50.41 50.41
Long
.
(m) 4.61 4.61
5.80 5.80
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 2
Ace
ro
Long
itudi
nal 78.76 78.76
SEPARACIÓN (cm)
LONG. (m)
122.
5
51.29 51.29
Long
.
(m) 4.66 4.66
5.90 5.90
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 1
Ace
ro
Long
itudi
nal 76.06 76.06
SEPARACIÓN (cm)
122.
5
49.12 49.12
Long
.
(m) 4.66 4.66
5.90 5.90
dura
sver
sal ESTRIBOS
2.45 0.98 2.45 2.45 2.85 2.45 2.45 0.98 2.45LONG. (m)Arm
a
Tra
n
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 12 PISOS R = 4.50
LUZ =>
As NEGATIVO (cm2) 8.23 6.50 6.50 6.50 8.23
As POSITIVO (cm2) 6.50 7.86 11.50 7.86 6.50
As - 2.41 4.02 4.98 4.02 2.41
As + 2.41 4.68 8.00 4.68 2.41
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.10 4.34 1.10 1.10 6.25 1.1 1.1 4.34 1.10
As NEGATIVO (cm2) 10.10 9.17 9.17 9.17 10.10
As POSITIVO (cm2) 9.17 9.80 14.22 9.80 9.17
As - 2.41 4.02 4.98 4.02 2.41
As + 2.41 4.28 7.20 4.28 2.41
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.50 3.54 1.50 1.50 5.45 1.5 1.5 3.54 1.50
60 As NEGATIVO (cm2) 10.93 9.17 9.17 9.17 10.93
As POSITIVO (cm2) 9.17 11.20 15.62 11.20 9.17
As - 2.41 4.02 4.98 4.02 2.41
As + 2.41 4.28 7.20 4.28 2.41
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.50 3.54 1.50 1.50 5.45 1.5 1.5 3.54 1.50
60 As NEGATIVO (cm2) 14.17 9.17 9.17 9.17 14.17
As POSITIVO (cm2) 9.17 12.29 16.54 12.29 9.17
As - 2.48 4.00 4.98 4.00 2.48
As + 2.48 4.25 7.20 4.25 2.48
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.50 3.50 1.50 1.50 5.45 1.5 1.5 3.50 1.50
As NEGATIVO (cm2) 16.68 9.17 9.17 9.17 16.68
As POSITIVO (cm2) 9.17 13.19 17.39 13.19 9.17
As - 2.47 3.99 4.96 3.99 2.47
As + 2.47 4.24 7.17 4.24 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 15 12.5 30.00 12.5 15 30.00 17.5
1.50 3.49 1.50 1.50 5.43 1.5 1.5 3.49 1.50
As NEGATIVO (cm2) 16.89 9.17 9.17 9.17 16.89
As POSITIVO (cm2) 9.17 14.01 18.11 14.01 9.17
As - 2.47 3.99 4.96 3.99 2.47
As + 2.47 4.24 7.17 4.24 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 12.5 12.5 15 30.00 15
1.50 3.49 1.50 1.50 5.43 1.5 1.5 3.49 1.50
60 As NEGATIVO (cm2) 18.44 9.17 9.17 9.17 18.44
As POSITIVO (cm2) 9.22 14.73 18.49 14.73 9.22
As - 2.51 3.98 4.95 3.98 2.51
As + 2.51 4.21 7.15 4.21 2.51
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.50 3.45 1.50 1.50 5.40 1.5 1.5 3.45 1.50
60 As NEGATIVO (cm2) 19.52 9.17 9.17 9.17 19.52
As POSITIVO (cm2) 9.76 15.37 19.00 15.37 9.76
As - 2.51 3.96 4.93 3.96 2.51
As + 2.51 4.19 7.10 4.19 2.51
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 17.5 30.00 17.5 15 30.00 15
1.50 3.43 1.50 1.50 5.35 1.5 1.5 3.43 1.50
As NEGATIVO (cm2) 19.61 9.17 9.17 9.17 19.61
As POSITIVO (cm2) 9.81 16.04 19.76 16.04 9.81
As - 2.50 3.95 4.90 3.95 2.50
As + 2.50 4.17 7.05 4.17 2.50
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 17.5 30.00 17.5 12.5 30.00 15
1.50 3.40 1.50 1.50 5.30 1.5 1.5 3.40 1.50
60 As NEGATIVO (cm2) 20.47 9.21 9.17 9.21 20.47
As POSITIVO (cm2) 10.24 16.65 20.10 16.65 10.24
As - 2.52 3.94 4.90 3.94 2.52
As + 2.52 4.17 7.05 4.17 2.52
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 17.5 30.00 17.5 12.5 30.00 15
1.50 3.39 1.50 1.50 5.30 1.5 1.5 3.39 1.50
60 As NEGATIVO (cm2) 20.92 9.51 9.17 9.51 20.92
As POSITIVO (cm2) 10.46 16.88 20.13 16.88 10.46
As - 2.51 3.93 4.86 3.93 2.51
As + 2.51 4.14 6.97 4.14 2.51
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 17.5 30.00 17.5 12.5 30.00 15
1.50 3.35 1.50 1.50 5.23 1.5 1.5 3.35 1.50
60 As NEGATIVO (cm2) 18.70 9.17 9.17 9.17 18.70
As POSITIVO (cm2) 9.35 16.17 19.48 16.17 9.35
As - 2.51 3.93 4.86 3.93 2.51
As + 2.51 4.14 6.97 4.14 2.51
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 17.5 30.00 17.5 15 30.00 15
1.50 3.35 1.50 1.50 5.23 1.5 1.5 3.35 1.50
75
13.83 13.83
Long
.
(m) 4.29 4.29
3.30 3.30
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
9
Ace
ro
Long
itudi
nal 27.66 27.66
SEPARACIÓN (cm)
LONG. (m)
75
13.40 13.40
Long
.
(m) 4.30 4.30
3.30 3.30
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
10 Ace
ro
Long
itudi
nal 26.80 26.80
SEPARACIÓN (cm)
LONG. (m)
25.84
75
12.92 12.92
Long
.
(m) 4.30 4.30
3.30 3.30
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 1
1 Ace
ro
Long
itudi
nal 25.84
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
23.20
55
11.60 11.60
Long
.
(m) 4.30 4.30
2.50 2.50
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 1
2 Ace
ro
Long
itudi
nal 23.20
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z3S2
7 9 7
60
PIS
O 8
Ace
ro
Long
itudi
nal 29.06
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
29.06
75
14.53 14.53
Long
.
(m) 4.30 4.30
3.33 3.33
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 30.06
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
30.06
75
15.03 15.03
Long
.
(m) 4.30 4.30
3.33 3.33
Arm
adur
a
Tra
nsve
rsal
PIS
O 6
Ace
ro
Long
itudi
nal 30.52 30.52
SEPARACIÓN (cm)
LONG. (m)
75
15.26 15.26
Long
.
(m) 4.31 4.31
3.35 3.35
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 5
Ace
ro
Long
itudi
nal 31.24 31.24
SEPARACIÓN (cm)
LONG. (m)
75
15.62 15.62
Long
.
(m) 4.34 4.34
3.40 3.40
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
60
PIS
O 4
Ace
ro
Long
itudi
nal 32.24
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
32.24
75
16.12 16.12
Long
.
(m) 4.38 4.38
3.45 3.45
Arm
adur
a
Tra
nsve
rsal
PIS
O 3
Ace
ro
Long
itudi
nal 32.68 32.68
SEPARACIÓN (cm)
LONG. (m)
75
16.34 16.34
Long
.
(m) 4.37 4.37
3.45 3.45
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 2
Ace
ro
Long
itudi
nal 32.82 32.82
SEPARACIÓN (cm)
LONG. (m)
75
16.41 16.41
Long
.
(m) 4.42 4.42
3.53 3.53
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 1
Ace
ro
Long
itudi
nal 32.18 32.18
SEPARACIÓN (cm)
LONG. (m)
75
16.09 16.09
Long
.
(m) 4.42 4.42
3.53 3.53
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
213
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
214
LUZ =>
As NEGATIVO (cm2) 9.08 6.50 6.50 6.50 9.08
As POSITIVO (cm2) 6.50 7.67 11.53 7.67 6.50
As - 2.43 4.01 4.98 4.01 2.43
As + 2.43 4.67 8.00 4.67 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.10 4.33 1.10 1.10 6.25 1.1 1.1 4.33 1.10
As NEGATIVO (cm2) 10.24 10.50 10.50 10.50 10.24
As POSITIVO (cm2) 10.50 10.39 14.9 10.39 10.50
As - 2.43 4.01 4.98 4.01 2.43
As + 2.43 4.07 6.80 4.07 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.70 3.13 1.70 1.70 5.05 1.7 1.7 3.13 1.70
60 As NEGATIVO (cm2) 13.30 10.50 10.50 10.50 13.30
As POSITIVO (cm2) 10.50 12.28 17.07 12.28 10.50
As - 2.47 3.99 4.95 3.99 2.47
As + 2.47 4.03 6.75 4.03 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.70 3.08 1.70 1.70 5.00 1.7 1.7 3.08 1.70
60 As NEGATIVO (cm2) 16.20 10.50 10.50 10.50 16.20
As POSITIVO (cm2) 10.50 14.34 19.01 14.34 10.50
As - 2.47 3.99 4.95 3.99 2.47
As + 2.47 4.03 6.75 4.03 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.70 3.08 1.70 1.70 5.00 1.7 1.7 3.08 1.70
As NEGATIVO (cm2) 19.57 10.50 10.50 10.50 19.57
As POSITIVO (cm2) 10.50 16.48 20.71 16.48 10.50
As - 2.51 3.98 4.95 3.98 2.51
As + 2.51 4.01 6.75 4.01 2.51
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 15 12.5 30.00 12.5 15 30.00 17.5
1.70 3.05 1.70 1.70 5.00 1.7 1.7 3.05 1.70
As NEGATIVO (cm2) 21.94 11.36 11.27 11.36 21.94
As POSITIVO (cm2) 11.15 18.12 22.02 18.12 11.15
As - 2.51 3.96 4.93 3.96 2.51
As + 2.51 3.99 6.70 3.99 2.51
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 12.5 12.5 15 30.00 15
1.70 3.03 1.70 1.70 4.95 1.7 1.7 3.03 1.70
60 As NEGATIVO (cm2) 22.77 12.70 12.69 12.70 22.77
As POSITIVO (cm2) 12.27 19.63 23.41 19.63 12.27
As - 2.51 3.96 4.93 3.96 2.51
As + 2.51 3.99 6.70 3.99 2.51
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.70 3.03 1.70 1.70 4.95 1.7 1.7 3.03 1.70
60 As NEGATIVO (cm2) 25.03 14.33 13.57 14.33 25.03
As POSITIVO (cm2) 13.91 21.23 24.16 21.23 13.91
As - 2.54 3.94 4.90 3.94 2.54
As + 2.54 3.96 6.65 3.96 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30.00 15
1.70 2.98 1.70 1.70 4.90 1.7 1.7 2.98 1.70
As NEGATIVO (cm2) 26.88 15.75 14.25 15.75 26.88
As POSITIVO (cm2) 15.41 22.55 25.09 22.55 15.41
As - 2.54 3.94 4.90 3.94 2.54
As + 2.54 3.96 6.65 3.96 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30.00 15
1.70 2.98 1.70 1.70 4.90 1.7 1.7 2.98 1.70
60 As NEGATIVO (cm2) 27.20 16.71 15.16 16.71 27.20
As POSITIVO (cm2) 15.41 23.57 25.82 23.57 15.41
As - 2.54 3.93 4.88 3.93 2.54
As + 2.54 3.94 6.60 3.94 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 12.5 30.00 12.5 12.5 30.00 12.5
1.70 2.95 1.70 1.70 4.85 1.7 1.7 2.95 1.70
60 As NEGATIVO (cm2) 28.45 17.45 15.16 17.45 28.45
As POSITIVO (cm2) 16.96 24.07 25.82 24.07 16.96
As - 2.58 3.91 4.88 3.91 2.58
As + 2.58 3.92 6.60 3.92 2.58
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 12.5 30.00 12.5 12.5 30.00 12.5
1.70 2.93 1.70 1.70 4.85 1.7 1.7 2.93 1.70
60 As NEGATIVO (cm2) 28.45 17.45 15.16 17.45 28.45
As POSITIVO (cm2) 16.96 24.07 25.82 24.07 16.96
As - 2.58 3.90 4.85 3.90 2.58
As + 2.58 3.90 6.55 3.90 2.58
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 12.5 30.00 12.5 12.5 30.00 12.5
85
14.33 14.33
Long
.
(m) 4.32 4.32
3.75 3.75
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
9
Ace
ro
Long
itudi
nal 28.66 28.66
SEPARACIÓN (cm)
LONG. (m)
85
13.23 13.23
Long
.
(m) 4.32 4.32
3.75 3.75
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
10 Ace
ro
Long
itudi
nal 26.46 26.46
SEPARACIÓN (cm)
LONG. (m)
24.00
85
12.00 12.00
Long
.
(m) 4.29 4.29
3.70 3.70
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 1
1 Ace
ro
Long
itudi
nal 24.00
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
23.16
55
11.58 11.58
Long
.
(m) 4.29 4.29
2.50 2.50Arm
adur
a
Tra
nsve
rsal
60PIS
O 1
2 Ace
ro
Long
itudi
nal 23.16
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z3S4.
7 9 7
60
PIS
O 8
Ace
ro
Long
itudi
nal 30.66
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
30.66
85
15.33 15.33
Long
.
(m) 4.31 4.31
3.75 3.75
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 32.30
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
32.30
85
16.15 16.15
Long
.
(m) 4.34 4.34
3.80 3.80
Arm
adur
a
Tra
nsve
rsal
PIS
O 6
Ace
ro
Long
itudi
nal 34.06 34.06
SEPARACIÓN (cm)
LONG. (m)
85
17.03 17.03
Long
.
(m) 4.34 4.34
3.80 3.80
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 5
Ace
ro
Long
itudi
nal 35.14 35.14
SEPARACIÓN (cm)
LONG. (m)
85
17.57 17.57
Long
.
(m) 4.37 4.37
3.85 3.85
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
60
PIS
O 4
Ace
ro
Long
itudi
nal 35.98
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
35.98
85
17.99 17.99
Long
.
(m) 4.37 4.37
3.85 3.85
Arm
adur
a
Tra
nsve
rsal
PIS
O 3
Ace
ro
Long
itudi
nal 37.14 37.14
SEPARACIÓN (cm)
LONG. (m)
85
18.57 18.57
Long
.
(m) 4.40 4.40
3.90 3.90
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 2
Ace
ro
Long
itudi
nal 37.14 37.14
SEPARACIÓN (cm)
LONG. (m)
85
18.57 18.57
Long
.
(m) 4.39 4.39
3.90 3.90
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 1
Ace
ro
Long
itudi
nal 37.14 37.14
SEPARACIÓN (cm)
85
18.57 18.57
Long
.
(m) 4.43 4.43
3.95 3.95
dura
sver
sal ESTRIBOS
1.70 2.90 1.70 1.70 4.80 1.7 1.7 2.90 1.70LONG. (m)Arm
a
Tra
n
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
215
LUZ =>
As NEGATIVO (cm2) 8.75 6.27 6.27 6.27 8.75
As POSITIVO (cm2) 6.27 6.88 10.78 6.88 6.27
As - 2.47 3.99 4.95 3.99 2.47
As + 2.47 4.53 7.75 4.53 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
35 15 30.00 15 15 30.00 15 15 30.00 15
1.20 4.08 1.20 1.20 6.00 1.2 1.2 4.08 1.20
As NEGATIVO (cm2) 9.54 12.50 12.50 12.50 9.54
As POSITIVO (cm2) 12.50 12.36 14.96 12.36 12.50
As - 2.47 3.99 4.95 3.99 2.47
As + 2.47 3.73 6.15 3.73 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
2.00 2.48 2.00 2.00 4.40 2 2 2.48 2.00
60 As NEGATIVO (cm2) 13.41 12.50 12.50 12.50 13.41
As POSITIVO (cm2) 12.50 12.40 17.42 12.40 12.50
As - 2.51 3.98 4.95 3.98 2.51
As + 2.51 3.71 6.15 3.71 2.51
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
2.00 2.45 2.00 2.00 4.40 2 2 2.45 2.00
60 As NEGATIVO (cm2) 16.68 12.50 12.50 12.50 16.68
As POSITIVO (cm2) 12.50 15.25 20.76 15.25 12.50
As - 2.50 3.95 4.90 3.95 2.50
As + 2.50 3.67 6.05 3.67 2.50
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
2.00 2.40 2.00 2.00 4.30 2 2 2.40 2.00
As NEGATIVO (cm2) 20.52 12.59 14.29 12.59 20.52
As POSITIVO (cm2) 12.50 18.57 23.43 18.57 12.50
As - 2.54 3.94 4.90 3.94 2.54
As + 2.54 3.66 6.05 3.66 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 15 15 30.00 15 15 30.00 17.5
2.00 2.38 2.00 2.00 4.30 2 2 2.38 2.00
As NEGATIVO (cm2) 23.79 15.50 16.63 15.50 23.79
As POSITIVO (cm2) 14.90 21.52 25.79 21.52 14.90
As - 2.54 3.93 4.88 3.93 2.54
As + 2.54 3.64 6.00 3.64 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 12.5 12.5 15 30.00 15
2.00 2.35 2.00 2.00 4.25 2 2 2.35 2.00
60 As NEGATIVO (cm2) 27.17 18.31 18.33 18.31 27.17
As POSITIVO (cm2) 17.76 24.14 27.48 24.14 17.76
As - 2.58 3.91 4.88 3.91 2.58
As + 2.58 3.62 6.00 3.62 2.58
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30.00 15
2.00 2.33 2.00 2.00 4.25 2 2 2.33 2.00
60 As NEGATIVO (cm2) 29.50 20.58 20.18 20.58 29.50
As POSITIVO (cm2) 19.93 26.44 29.27 26.44 19.93
As - 2.57 3.89 4.83 3.89 2.57
As + 2.57 3.58 5.90 3.58 2.57
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 12.5 30.00 12.5 12.5 30.00 12.5
2.00 2.28 2.00 2.00 4.15 2 2 2.28 2.00
As NEGATIVO (cm2) 31.67 22.44 21.29 22.44 31.67
As POSITIVO (cm2) 21.70 28.23 30.35 28.23 21.70
As - 2.61 3.88 4.83 3.88 2.61
As + 2.61 3.56 5.90 3.56 2.61
2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 17.5 12.5 30.00 12.5 17.5 30.00 12.5
2.00 2.25 2.00 2.00 4.15 2 2 2.25 2.00
60 As NEGATIVO (cm2) 33.34 23.92 21.81 23.92 33.34
As POSITIVO (cm2) 23.20 29.62 30.84 29.62 23.20
As - 2.61 3.86 4.80 3.86 2.61
As + 2.61 3.54 5.85 3.54 2.61
2R3/8" 2R3/8" 3R3/8" 3R3/8" 2R3/8" 3R3/8" 3R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 17.5 17.5 30.00 17.5 17.5 30.00 12.5
2.00 2.23 2.00 2.00 4.10 2 2 2.23 2.00
60 As NEGATIVO (cm2) 34.03 24.42 21.45 24.42 34.03
As POSITIVO (cm2) 23.76 30.04 30.47 30.04 23.76
As - 2.65 3.85 4.80 3.85 2.65
As + 2.65 3.52 5.85 3.52 2.65
2R3/8" 2R3/8" 3R3/8" 3R3/8" 2R3/8" 3R3/8" 3R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 17.5 17.5 30.00 17.5 17.5 30.00 12.5
2.00 2.20 2.00 2.00 4.10 2 2 2.20 2.00
60 As NEGATIVO (cm2) 34.03 24.42 21.45 24.42 34.03
As POSITIVO (cm2) 23.76 30.04 30.47 30.04 23.76
As - 2.64 3.84 4.78 3.84 2.64
As + 2.64 3.51 5.80 3.51 2.64
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 10 17.5 30.00 17.5 10 30.00 12.5
2.00 2.18 2.00 2.00 4.05 2 2 2.18 2.00
100
24.82 24.82
Long
.
(m) 4.51 4.51
4.70 4.70
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
1
Ace
ro
Long
itudi
nal 40.75 40.75
SEPARACIÓN (cm)
LONG. (m)
100
24.82 24.82
Long
.
(m) 4.48 4.48
4.65 4.65
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
2
Ace
ro
Long
itudi
nal 40.75 40.75
SEPARACIÓN (cm)
LONG. (m)
100
24.19 24.19
Long
.
(m) 4.48 4.48
4.65 4.65
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
3
Ace
ro
Long
itudi
nal 40.75 40.75
SEPARACIÓN (cm)
LONG. (m)
40.14
100
22.93 22.93
Long
.
(m) 4.45 4.45
4.60 4.60
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 4
Ace
ro
Long
itudi
nal 40.14
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
100
21.08 21.08
Long
.
(m) 4.46 4.46
4.60 4.60
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
5
Ace
ro
Long
itudi
nal 38.83 38.83
SEPARACIÓN (cm)
LONG. (m)
100
18.56 18.56
Long
.
(m) 4.39 4.39
4.50 4.50
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
6
Ace
ro
Long
itudi
nal 36.66 36.66
SEPARACIÓN (cm)
LONG. (m)
34.73
100
17.37 17.37
Long
.
(m) 4.40 4.40
4.50 4.50
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 34.73
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
32.06
100
16.03 16.03
Long
.
(m) 4.37 4.37
4.45 4.45
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 8
Ace
ro
Long
itudi
nal 32.06
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z7S2.
7 9 7
55PIS
O 1
2 Ace
ro
Long
itudi
nal 20.81
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
20.81
60
10.41 10.41
Long
.
(m) 4.32 4.32
2.75 2.75Arm
adur
a
Tra
nsve
rsal
60
PIS
O 1
1 Ace
ro
Long
itudi
nal 22.49
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
22.49
100
12.50 12.50
Long
.
(m) 4.32 4.32
4.35 4.35
Arm
adur
a
Tra
nsve
rsal
PIS
O 1
0 Ace
ro
Long
itudi
nal 24.98 24.98
SEPARACIÓN (cm)
LONG. (m)
100
12.50 12.50
Long
.
(m) 4.31 4.31
4.35 4.35
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 9
Ace
ro
Long
itudi
nal 28.74 28.74
SEPARACIÓN (cm)
LONG. (m)
100
14.37 14.37
Long
.
(m) 4.38 4.38
4.45 4.45
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
216
LUZ =>
As NEGATIVO (cm2) 9.04 7.17 7.17 7.17 9.04
As POSITIVO (cm2) 15.03 9.04 13.53 9.04 15.03
As - 2.50 3.95 4.90 3.95 2.50
As + 2.50 4.47 7.65 4.47 2.50
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.20 4.00 1.20 1.20 5.90 1.2 1.2 4.00 1.20
As NEGATIVO (cm2) 9.04 15.17 15.17 15.17 9.04
As POSITIVO (cm2) 15.17 15.03 19.3 15.03 15.17
As - 2.50 3.95 4.90 3.95 2.50
As + 2.50 3.27 5.25 3.27 2.50
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
2.40 1.60 2.40 2.40 3.50 2.4 2.4 1.60 2.40
60 As NEGATIVO (cm2) 13.44 15.17 15.83 15.17 13.44
As POSITIVO (cm2) 15.17 15.03 23.66 15.03 15.17
As - 2.50 3.95 4.90 3.95 2.50
As + 2.50 3.27 5.25 3.27 2.50
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
2.40 1.60 2.40 2.40 3.50 2.4 2.4 1.60 2.40
60 As NEGATIVO (cm2) 22.36 15.17 18.97 15.17 22.36
As POSITIVO (cm2) 15.17 19.24 26.97 19.24 15.17
As - 2.58 3.91 4.88 3.91 2.58
As + 2.58 3.22 5.20 3.22 2.58
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
2.40 1.53 2.40 2.40 3.45 2.4 2.4 1.53 2.40
As NEGATIVO (cm2) 29.27 19.13 22.48 19.13 29.27
As POSITIVO (cm2) 15.17 24.27 30.59 24.27 15.17
As - 2.58 3.91 4.88 3.91 2.58
As + 2.58 3.22 5.20 3.22 2.58
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 15 15 30.00 15 15 30.00 17.5
2.40 1.53 2.40 2.40 3.45 2.4 2.4 1.53 2.40
As NEGATIVO (cm2) 36.24 24.49 25.24 24.49 36.24
As POSITIVO (cm2) 18.99 29.40 33.45 29.40 18.99
As - 2.66 3.88 4.85 3.88 2.66
As + 2.66 3.16 5.15 3.16 2.66
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 12.5 12.5 12.5 12.5 30.00 12.5
2.40 1.45 2.40 2.40 3.40 2.4 2.4 1.45 2.40
60 As NEGATIVO (cm2) 41.68 28.97 27.73 28.97 41.68
As POSITIVO (cm2) 23.46 33.74 35.85 33.74 23.46
As - 2.66 3.88 4.85 3.88 2.66
As + 2.66 3.16 5.15 3.16 2.66
2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 17.5 12.5 30.00 12.5 17.5 30.00 12.5
2.40 1.45 2.40 2.40 3.40 2.4 2.4 1.45 2.40
60 As NEGATIVO (cm2) 44.39 32.62 30.99 32.62 44.39
As POSITIVO (cm2) 26.88 37.40 39.16 37.40 26.88
As - 2.65 3.85 4.80 3.85 2.65
As + 2.65 3.12 5.05 3.12 2.65
3R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 3R3/8"
40 17.5 30.00 10 12.5 30.00 12.5 10 30.00 17.5
2.40 1.40 2.40 2.40 3.30 2.4 2.4 1.40 2.40
As NEGATIVO (cm2) 47.36 35.98 33.16 35.98 47.36
As POSITIVO (cm2) 30.11 40.85 41.24 40.85 30.11
As - 2.69 3.84 4.80 3.84 2.69
As + 2.69 3.11 5.05 3.11 2.69
2R3/8" 2R3/8" 2R1/2" 3R3/8" 2R3/8" 3R3/8" 2R1/2" 2R3/8" 2R3/8"
40 10 30.00 17.5 17.5 30.00 17.5 17.5 30.00 10
2.40 1.38 2.40 2.40 3.30 2.4 2.4 1.38 2.40
60 As NEGATIVO (cm2) 49.92 38.88 34.28 38.88 49.92
As POSITIVO (cm2) 33.26 43.63 42.29 43.63 33.26
As - 2.68 3.81 4.75 3.81 2.68
As + 2.68 3.07 4.95 3.07 2.68
2R3/8" 2R3/8" 2R1/2" 3R3/8" 2R3/8" 3R3/8" 2R1/2" 2R3/8" 2R3/8"
40 10 30.00 15 17.5 30.00 17.5 15 30.00 10
2.40 1.33 2.40 2.40 3.20 2.4 2.4 1.33 2.40
60 As NEGATIVO (cm2) 50.92 40.88 35.09 40.88 50.92
As POSITIVO (cm2) 35.29 45.56 43.03 45.56 35.29
As - 2.73 3.80 4.75 3.80 2.73
As + 2.73 3.05 4.95 3.05 2.73
2R3/8" 2R3/8" 2R1/2" 3R3/8" 2R3/8" 3R3/8" 2R1/2" 2R3/8" 2R3/8"
40 10 30.00 15 17.5 30.00 17.5 15 30.00 10
2.40 1.30 2.40 2.40 3.20 2.4 2.4 1.30 2.40
60 As NEGATIVO (cm2) 50.92 41.86 35.09 41.86 50.92
As POSITIVO (cm2) 36.95 46.58 43.09 46.58 36.95
As - 2.71 3.78 4.70 3.78 2.71
As + 2.71 3.01 4.85 3.01 2.71
2R3/8" 2R3/8" 2R1/2" 2R3/8" 2R3/8" 2R3/8" 2R1/2" 2R3/8" 2R3/8"
40 10 30.00 15 10 30.00 10 15 30.00 10
120
26.36 26.36
Long
.
(m) 4.59 4.59
5.65 5.65
dura
sver
sal ESTRIBOSPIS
O 1
Ace
ro
Long
itudi
nal 51.31 51.31
SEPARACIÓN (cm)
120
26.36 26.36
Long
.
(m) 4.53 4.53
5.55 5.55
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
2
Ace
ro
Long
itudi
nal 51.31 51.31
SEPARACIÓN (cm)
LONG. (m)
120
25.64 25.64
Long
.
(m) 4.53 4.53
5.55 5.55
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
3
Ace
ro
Long
itudi
nal 50.35 50.35
SEPARACIÓN (cm)
LONG. (m)
49.06
120
24.72 24.72
Long
.
(m) 4.47 4.47
5.45 5.45
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 4
Ace
ro
Long
itudi
nal 49.06
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
120
23.31 23.31
Long
.
(m) 4.48 4.48
5.45 5.45
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
5
Ace
ro
Long
itudi
nal 46.61 46.61
SEPARACIÓN (cm)
LONG. (m)
120
21.46 21.46
Long
.
(m) 4.41 4.41
5.35 5.35
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
6
Ace
ro
Long
itudi
nal 42.92 42.92
SEPARACIÓN (cm)
LONG. (m)
40.13
120
20.07 20.07
Long
.
(m) 4.41 4.41
5.35 5.35
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 40.13
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
37.13
120
18.57 18.57
Long
.
(m) 4.39 4.39
5.30 5.30
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 8
Ace
ro
Long
itudi
nal 37.13
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z7S4.
7 9 7
60
PIS
O 1
2 Ace
ro
Long
itudi
nal 23.31
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
23.31
60
11.66 11.66
Long
.
(m) 4.38 4.38
2.85 2.85Arm
adur
a
Tra
nsve
rsal
60
PIS
O 1
1 Ace
ro
Long
itudi
nal 25.10
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
25.10
120
15.17 15.17
Long
.
(m) 4.38 4.38
5.25 5.25
Arm
adur
a
Tra
nsve
rsal
PIS
O 1
0 Ace
ro
Long
itudi
nal 29.88 29.88
SEPARACIÓN (cm)
LONG. (m)
120
15.17 15.17
Long
.
(m) 4.38 4.38
5.25 5.25
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 9
Ace
ro
Long
itudi
nal 33.05 33.05
SEPARACIÓN (cm)
LONG. (m)
120
16.53 16.53
Long
.
(m) 4.39 4.39
5.30 5.30
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
2.40 1.25 2.40 2.40 3.10 2.4 2.4 1.25 2.40Arm
a
Tra
n
LONG. (m)
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 12 PISOS R = 6.00
LUZ =>
As NEGATIVO (cm2) 7.06 6.50 6.50 6.50 7.06
As POSITIVO (cm2) 6.50 8.11 11.47 8.11 6.50
As - 2.39 4.03 4.98 4.03 2.39
As + 2.39 4.69 8.00 4.69 2.39
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.10 4.35 1.10 1.10 6.25 1.1 1.1 4.35 1.10
As NEGATIVO (cm2) 9.27 8.50 8.50 8.50 9.27
As POSITIVO (cm2) 8.50 10.17 14.39 10.17 8.50
As - 2.39 4.03 4.98 4.03 2.39
As + 2.39 4.39 7.40 4.39 2.39
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 17.5 30.00 17.5 15 30.00 15
1.40 3.75 1.40 1.40 5.65 1.4 1.4 3.75 1.40
60 As NEGATIVO (cm2) 9.95 8.50 8.50 8.50 9.95
As POSITIVO (cm2) 8.50 11.10 15.52 11.10 8.50
As - 2.39 4.03 4.98 4.03 2.39
As + 2.39 4.39 7.40 4.39 2.39
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 17.5 30.00 17.5 15 30.00 15
1.40 3.75 1.40 1.40 5.65 1.4 1.4 3.75 1.40
60 As NEGATIVO (cm2) 12.26 8.50 8.50 8.50 12.26
As POSITIVO (cm2) 8.50 11.91 16.36 11.91 8.50
As - 2.43 4.01 4.98 4.01 2.43
As + 2.43 4.37 7.40 4.37 2.43
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 17.5 30.00 17.5 15 30.00 15
1.40 3.73 1.40 1.40 5.65 1.4 1.4 3.73 1.40
As NEGATIVO (cm2) 14.05 8.50 8.50 8.50 14.05
As POSITIVO (cm2) 8.50 12.67 17.18 12.67 8.50
As - 2.43 4.01 4.96 4.01 2.43
As + 2.43 4.36 7.37 4.36 2.43
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 12.5 17.5 30.00 17.5 12.5 30.00 17.5
1.40 3.71 1.40 1.40 5.63 1.4 1.4 3.71 1.40
As NEGATIVO (cm2) 15.58 8.50 8.50 8.50 15.58
As POSITIVO (cm2) 8.50 13.20 17.57 13.20 8.50
As - 2.47 3.99 4.96 3.99 2.47
As + 2.47 4.34 7.37 4.34 2.47
2R3/8" 2R3/8" 2R3/8" 3R3/8" 3R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 17.5 17.5 17.5 12.5 30.00 15
1.40 3.69 1.40 1.40 5.63 1.4 1.4 3.69 1.40
60 As NEGATIVO (cm2) 16.92 8.50 8.50 8.50 16.92
As POSITIVO (cm2) 8.50 13.66 17.85 13.66 8.50
As - 2.47 3.99 4.96 3.99 2.47
As + 2.47 4.34 7.37 4.34 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 10 30.00 10 12.5 30.00 15
1.40 3.69 1.40 1.40 5.63 1.4 1.4 3.69 1.40
60 As NEGATIVO (cm2) 16.97 8.50 8.50 8.50 16.97
As POSITIVO (cm2) 8.50 14.36 18.39 14.36 8.50
As - 2.46 3.97 4.91 3.97 2.46
As + 2.46 4.30 7.27 4.30 2.46
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 10 30.00 10 12.5 30.00 15
1.40 3.64 1.40 1.40 5.53 1.4 1.4 3.64 1.40
As NEGATIVO (cm2) 17.18 8.50 8.50 8.50 17.18
As POSITIVO (cm2) 8.59 14.76 18.83 14.76 8.59
As - 2.46 3.97 4.91 3.97 2.46
As + 2.46 4.30 7.27 4.30 2.46
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 10 30.00 10 12.5 30.00 15
1.40 3.64 1.40 1.40 5.53 1.4 1.4 3.64 1.40
60 As NEGATIVO (cm2) 18.48 8.50 8.50 8.50 18.48
As POSITIVO (cm2) 9.24 15.18 19.11 15.18 9.24
As - 2.49 3.93 4.86 3.93 2.49
As + 2.49 4.25 7.17 4.25 2.49
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 10 30.00 10 12.5 30.00 15
1.40 3.56 1.40 1.40 5.43 1.4 1.4 3.56 1.40
60 As NEGATIVO (cm2) 19.45 8.50 8.50 8.50 19.45
As POSITIVO (cm2) 9.73 15.23 19.00 15.23 9.73
As - 2.49 3.93 4.86 3.93 2.49
As + 2.49 4.25 7.17 4.25 2.49
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 10 30.00 10 12.5 30.00 15
1.40 3.56 1.40 1.40 5.43 1.4 1.4 3.56 1.40
60 As NEGATIVO (cm2) 17.34 8.50 8.50 8.50 17.34
As POSITIVO (cm2) 8.67 14.65 18.32 14.65 8.67
As - 2.49 3.93 4.86 3.93 2.49
As + 2.49 4.25 7.17 4.25 2.49
70
16.12 16.12
ng.
(m) 4.42 4.42
3.33 3.33
1
Ace
ro
Long
itudi
nal 32.24 32.24
70
16.53 16.53
Long
.
(m) 4.42 4.42
3.33 3.33
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
2
Ace
ro
Long
itudi
nal 33.06 33.06
SEPARACIÓN (cm)
LONG. (m)
70
16.56 16.56
Long
.
(m) 4.42 4.42
3.33 3.33
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
3
Ace
ro
Long
itudi
nal 33.12 33.12
SEPARACIÓN (cm)
LONG. (m)
32.79
70
16.40 16.40
Long
.
(m) 4.37 4.37
3.23 3.23
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 4
Ace
ro
Long
itudi
nal 32.79
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
70
16.06 16.06
Long
.
(m) 4.37 4.37
3.23 3.23
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
5
Ace
ro
Long
itudi
nal 32.11 32.11
SEPARACIÓN (cm)
LONG. (m)
70
15.57 15.57
Long
.
(m) 4.30 4.30
3.13 3.13
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
6
Ace
ro
Long
itudi
nal 31.14 31.14
SEPARACIÓN (cm)
LONG. (m)
30.88
70
15.44 15.44
Long
.
(m) 4.30 4.30
3.13 3.13
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 30.88
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
30.38
70
15.19 15.19
Long
.
(m) 4.31 4.31
3.13 3.13
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 8
Ace
ro
Long
itudi
nal 30.38
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z3S2.
7 9 7
60
PIS
O 1
2 Ace
ro
Long
itudi
nal 23.33
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
23.33
55
11.67 11.67
Long
.
(m) 4.30 4.30
2.50 2.50
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 1
1 Ace
ro
Long
itudi
nal 28.42
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
28.42
70
14.21 14.21
Long
.
(m) 4.30 4.30
3.10 3.10
Arm
adur
a
Tra
nsve
rsal
PIS
O 1
0 Ace
ro
Long
itudi
nal 28.44 28.44
SEPARACIÓN (cm)
LONG. (m)
70
14.22 14.22
Long
.
(m) 4.30 4.30
3.10 3.10
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 9
Ace
ro
Long
itudi
nal 28.88 28.88
SEPARACIÓN (cm)
LONG. (m)
70
14.44 14.44
Long
.
(m) 4.29 4.29
3.10 3.10
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
217
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 10 30.00 10 12.5 30.00 15
1.40 3.56 1.40 1.40 5.43 1.4 1.4 3.56 1.40
Lo
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
SEPARACIÓN (cm)
LONG. (m)
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
218
LUZ =>
As NEGATIVO (cm2) 9.08 6.50 6.50 6.50 9.08
As POSITIVO (cm2) 6.50 7.65 11.53 7.65 6.50
As - 2.43 4.01 4.98 4.01 2.43
As + 2.43 4.67 8.00 4.67 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.10 4.33 1.10 1.10 6.25 1.1 1.1 4.33 1.10
As NEGATIVO (cm2) 11.60 9.17 9.17 9.17 11.60
As POSITIVO (cm2) 9.17 10.04 14.79 10.04 9.17
As - 2.43 4.01 4.98 4.01 2.43
As + 2.43 4.27 7.20 4.27 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.50 3.53 1.50 1.50 5.45 1.5 1.5 3.53 1.50
60 As NEGATIVO (cm2) 12.96 9.17 9.17 9.17 12.96
As POSITIVO (cm2) 9.17 11.86 16.55 11.86 9.17
As - 2.43 4.01 4.98 4.01 2.43
As + 2.43 4.27 7.20 4.27 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.50 3.53 1.50 1.50 5.45 1.5 1.5 3.53 1.50
60 As NEGATIVO (cm2) 15.95 9.17 9.17 9.17 15.95
As POSITIVO (cm2) 9.17 13.48 17.86 13.48 9.17
As - 2.47 3.99 4.95 3.99 2.47
As + 2.47 4.23 7.15 4.23 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.50 3.48 1.50 1.50 5.40 1.5 1.5 3.48 1.50
As NEGATIVO (cm2) 18.46 9.17 9.17 9.17 18.46
As POSITIVO (cm2) 9.23 15.01 19.33 15.01 9.23
As - 2.47 3.99 4.95 3.99 2.47
As + 2.47 4.23 7.15 4.23 2.47
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 17.5 30.00 17.5 15 30.00 15
1.50 3.48 1.50 1.50 5.40 1.5 1.5 3.48 1.50
As NEGATIVO (cm2) 19.06 9.17 9.17 9.17 19.06
As POSITIVO (cm2) 9.53 16.17 20.58 16.17 9.53
As - 2.47 3.99 4.95 3.99 2.47
As + 2.47 4.23 7.15 4.23 2.47
2R3/8" 2R3/8" 2R3/8" 3R3/8" 3R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 17.5 17.5 17.5 12.5 30.00 15
1.50 3.48 1.50 1.50 5.40 1.5 1.5 3.48 1.50
60 As NEGATIVO (cm2) 21.33 9.75 9.17 9.75 21.33
As POSITIVO (cm2) 10.67 17.32 21.16 17.32 10.67
As - 2.51 3.96 4.93 3.96 2.51
As + 2.51 4.19 7.10 4.19 2.51
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 17.5 30.00 17.5 12.5 30.00 15
1.50 3.43 1.50 1.50 5.35 1.5 1.5 3.43 1.50
60 As NEGATIVO (cm2) 22.85 10.83 9.74 10.83 22.85
As POSITIVO (cm2) 11.43 18.30 21.82 18.30 11.43
As - 2.51 3.96 4.93 3.96 2.51
As + 2.51 4.19 7.10 4.19 2.51
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 17.5 30.00 17.5 12.5 30.00 15
1.50 3.43 1.50 1.50 5.35 1.5 1.5 3.43 1.50
As NEGATIVO (cm2) 23.17 11.66 10.54 11.66 23.17
As POSITIVO (cm2) 11.59 9.28 22.60 9.28 11.59
As - 2.51 3.96 4.93 3.96 2.51
As + 2.51 4.19 7.10 4.19 2.51
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 10 30.00 10 12.5 30.00 12.5
1.50 3.43 1.50 1.50 5.35 1.5 1.5 3.43 1.50
60 As NEGATIVO (cm2) 24.38 12.48 10.92 12.48 24.38
As POSITIVO (cm2) 12.19 20.14 22.99 20.14 12.19
As - 2.54 3.93 4.88 3.93 2.54
As + 2.54 4.14 7.00 4.14 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 10 30.00 10 12.5 30.00 12.5
1.50 3.35 1.50 1.50 5.25 1.5 1.5 3.35 1.50
60 As NEGATIVO (cm2) 25.03 12.70 10.92 12.70 25.03
As POSITIVO (cm2) 12.52 20.26 22.99 20.26 12.52
As - 2.54 3.93 4.88 3.93 2.54
As + 2.54 4.14 7.00 4.14 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 10 30.00 10 12.5 30.00 12.5
1.50 3.35 1.50 1.50 5.25 1.5 1.5 3.35 1.50
60 As NEGATIVO (cm2) 25.03 12.70 10.92 12.70 25.03
As POSITIVO (cm2) 12.52 20.26 22.99 20.26 12.52
As - 2.53 3.91 4.85 3.91 2.53
As + 2.53 4.12 6.95 4.12 2.53
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 10 30.00 10 12.5 30.00 12.5
75
14.56 14.56
Long
.
(m) 4.32 4.32
3.35 3.35
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
9
Ace
ro
Long
itudi
nal 29.11 29.11
SEPARACIÓN (cm)
LONG. (m)
75
13.88 13.88
Long
.
(m) 4.29 4.29
3.30 3.30
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
10 Ace
ro
Long
itudi
nal 27.76 27.76
SEPARACIÓN (cm)
LONG. (m)
25.80
75
12.90 12.90
Long
.
(m) 4.29 4.29
3.30 3.30
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 1
1 Ace
ro
Long
itudi
nal 25.80
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
23.17
55
11.59 11.59
Long
.
(m) 4.29 4.29
2.50 2.50Arm
adur
a
Tra
nsve
rsal
60PIS
O 1
2 Ace
ro
Long
itudi
nal 23.17
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z3S4.
7 9 7
60
PIS
O 8
Ace
ro
Long
itudi
nal 31.29
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
31.29
75
15.65 15.65
Long
.
(m) 4.32 4.32
3.35 3.35
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 32.84
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
32.84
75
16.42 16.42
Long
.
(m) 4.32 4.32
3.35 3.35
Arm
adur
a
Tra
nsve
rsal
PIS
O 6
Ace
ro
Long
itudi
nal 33.41 33.41
SEPARACIÓN (cm)
LONG. (m)
75
16.71 16.71
Long
.
(m) 4.34 4.34
3.40 3.40
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 5
Ace
ro
Long
itudi
nal 34.35 34.35
SEPARACIÓN (cm)
LONG. (m)
75
17.18 17.18
Long
.
(m) 4.34 4.34
3.40 3.40
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
60
PIS
O 4
Ace
ro
Long
itudi
nal 35.41
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
35.41
75
17.71 17.71
Long
.
(m) 4.34 4.34
3.40 3.40
Arm
adur
a
Tra
nsve
rsal
PIS
O 3
Ace
ro
Long
itudi
nal 36.05 36.05
SEPARACIÓN (cm)
LONG. (m)
75
18.03 18.03
Long
.
(m) 4.40 4.40
3.50 3.50
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 2
Ace
ro
Long
itudi
nal 36.05 36.05
SEPARACIÓN (cm)
LONG. (m)
75
18.03 18.03
Long
.
(m) 4.40 4.40
3.50 3.50
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 1
Ace
ro
Long
itudi
nal 36.05 36.05
SEPARACIÓN (cm)
75
18.03 18.03
Long
.
(m) 4.43 4.43
3.55 3.55
dura
sver
sal ESTRIBOS
1.50 3.33 1.50 1.50 5.20 1.5 1.5 3.33 1.50LONG. (m)Arm
a
Tra
n
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
219
LUZ =>
As NEGATIVO (cm2) 8.64 5.38 5.38 5.38 8.64
As POSITIVO (cm2) 5.38 6.8 10.14 6.80 5.38
As - 2.43 4.00 4.95 4.00 2.43
As + 2.43 4.55 7.75 4.55 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
30 15 30.00 15 15 30.00 15 15 30.00 15
1.20 4.10 1.20 1.20 6.00 1.2 1.2 4.10 1.20
As NEGATIVO (cm2) 10.69 10.50 10.50 10.50 10.69
As POSITIVO (cm2) 10.50 10.72 15.87 10.72 10.50
As - 2.43 4.00 4.95 4.00 2.43
As + 2.43 4.05 6.75 4.05 2.43
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.70 3.10 1.70 1.70 5.00 1.7 1.7 3.10 1.70
60 As NEGATIVO (cm2) 14.08 10.50 10.50 10.50 14.08
As POSITIVO (cm2) 10.50 13.14 17.91 13.14 10.50
As - 2.47 3.99 4.95 3.99 2.47
As + 2.47 4.03 6.75 4.03 2.47
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.70 3.08 1.70 1.70 5.00 1.7 1.7 3.08 1.70
60 As NEGATIVO (cm2) 16.99 10.50 10.50 10.50 16.99
As POSITIVO (cm2) 10.50 15.31 20.22 15.31 10.50
As - 2.46 3.98 4.93 3.98 2.46
As + 2.46 4.01 6.70 4.01 2.46
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 30.00 12.5 15 30.00 15
1.70 3.05 1.70 1.70 4.95 1.7 1.7 3.05 1.70
As NEGATIVO (cm2) 20.10 10.50 11.15 10.50 20.10
As POSITIVO (cm2) 10.50 17.3 21.85 17.30 10.50
As - 2.51 3.96 4.93 3.96 2.51
As + 2.51 3.99 6.70 3.99 2.51
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 15 12.5 30.00 12.5 15 30.00 17.5
1.70 3.03 1.70 1.70 4.95 1.7 1.7 3.03 1.70
As NEGATIVO (cm2) 22.44 11.92 12.04 11.92 22.44
As POSITIVO (cm2) 11.54 18.78 22.85 18.78 11.54
As - 2.51 3.96 4.93 3.96 2.51
As + 2.51 3.99 6.70 3.99 2.51
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 12.5 12.5 12.5 15 30.00 15
1.70 3.03 1.70 1.70 4.95 1.7 1.7 3.03 1.70
60 As NEGATIVO (cm2) 24.72 13.54 12.76 13.54 24.72
As POSITIVO (cm2) 13.31 20.43 23.55 20.43 13.31
As - 2.55 3.95 4.93 3.95 2.55
As + 2.55 3.97 6.70 3.97 2.55
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30.00 15
1.70 3.00 1.70 1.70 4.95 1.7 1.7 3.00 1.70
60 As NEGATIVO (cm2) 26.48 14.99 13.64 14.99 26.48
As POSITIVO (cm2) 14.78 21.77 24.27 21.77 14.78
As - 2.54 3.94 4.90 3.94 2.54
As + 2.54 3.96 6.65 3.96 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30.00 15
1.70 2.98 1.70 1.70 4.90 1.7 1.7 2.98 1.70
As NEGATIVO (cm2) 27.12 16.21 14.78 16.21 27.12
As POSITIVO (cm2) 15.91 23.08 25.50 23.08 15.91
As - 2.54 3.94 4.90 3.94 2.54
As + 2.54 3.96 6.65 3.96 2.54
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 12.5 30.00 12.5 12.5 30.00 15
1.70 2.98 1.70 1.70 4.90 1.7 1.7 2.98 1.70
60 As NEGATIVO (cm2) 28.86 17.63 15.39 17.63 28.86
As POSITIVO (cm2) 17.22 24.28 26.09 24.28 17.22
As - 2.58 3.91 4.88 3.91 2.58
As + 2.58 3.92 6.60 3.92 2.58
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 17.5 30.00 17.5 12.5 30.00 12.5
1.70 2.93 1.70 1.70 4.85 1.7 1.7 2.93 1.70
60 As NEGATIVO (cm2) 29.75 18.33 15.39 18.33 29.75
As POSITIVO (cm2) 17.98 25.13 26.07 25.13 17.98
As - 2.58 3.91 4.88 3.91 2.58
As + 2.58 3.92 6.60 3.92 2.58
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 17.5 30.00 17.5 12.5 30.00 12.5
1.70 2.93 1.70 1.70 4.85 1.7 1.7 2.93 1.70
60 As NEGATIVO (cm2) 29.75 18.33 15.39 18.33 29.75
As POSITIVO (cm2) 17.98 25.13 26.07 25.13 17.98
As - 2.57 3.89 4.83 3.89 2.57
As + 2.57 3.88 6.50 3.88 2.57
2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 17.5 30.00 17.5 12.5 30.00 12.5
85
18.75 18.75
Long
.
(m) 4.46 4.46
4.00 4.00
dura
sver
sal ESTRIBOSPIS
O 1
Ace
ro
Long
itudi
nal 37.49 37.49
SEPARACIÓN (cm)
85
18.75 18.75
Long
.
(m) 4.39 4.39
3.90 3.90
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
2
Ace
ro
Long
itudi
nal 37.49 37.49
SEPARACIÓN (cm)
LONG. (m)
85
18.73 18.73
Long
.
(m) 4.39 4.39
3.90 3.90
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
3
Ace
ro
Long
itudi
nal 37.45 37.45
SEPARACIÓN (cm)
LONG. (m)
36.69
85
18.35 18.35
Long
.
(m) 4.37 4.37
3.85 3.85
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 4
Ace
ro
Long
itudi
nal 36.69
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
85
17.63 17.63
Long
.
(m) 4.37 4.37
3.85 3.85
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
5
Ace
ro
Long
itudi
nal 35.26 35.26
SEPARACIÓN (cm)
LONG. (m)
85
17.08 17.08
Long
.
(m) 4.34 4.34
3.80 3.80
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
6
Ace
ro
Long
itudi
nal 34.15 34.15
SEPARACIÓN (cm)
LONG. (m)
33.38
85
16.69 16.69
Long
.
(m) 4.34 4.34
3.80 3.80
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 33.38
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
32.29
85
16.15 16.15
Long
.
(m) 4.34 4.34
3.80 3.80
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 8
Ace
ro
Long
itudi
nal 32.29
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z7S2.
7 9 7
50PIS
O 1
2 Ace
ro
Long
itudi
nal 21.01
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
21.01
60
10.51 10.51
Long
.
(m) 4.33 4.33
2.75 2.75
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 1
1 Ace
ro
Long
itudi
nal 25.29
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
25.29
85
12.65 12.65
Long
.
(m) 4.33 4.33
3.75 3.75
Arm
adur
a
Tra
nsve
rsal
PIS
O 1
0 Ace
ro
Long
itudi
nal 27.54 27.54
SEPARACIÓN (cm)
LONG. (m)
85
13.77 13.77
Long
.
(m) 4.32 4.32
3.75 3.75
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 9
Ace
ro
Long
itudi
nal 30.03 30.03
SEPARACIÓN (cm)
LONG. (m)
85
15.02 15.02
Long
.
(m) 4.35 4.35
3.80 3.80
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
1.70 2.88 1.70 1.70 4.75 1.7 1.7 2.88 1.70Arm
a
Tra
n
LONG. (m)
APENDICE A. GEOMETRIA Y ARMADO DE VIGAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
220
LUZ =>
As NEGATIVO (cm2) 10.11 7.17 7.17 7.17 10.11
As POSITIVO (cm2) 7.17 7.39 11.61 7.39 7.17
As - 2.50 3.95 4.90 3.95 2.50
As + 2.50 4.47 7.65 4.47 2.50
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
1.20 4.00 1.20 1.20 5.90 1.2 1.2 4.00 1.20
As NEGATIVO (cm2) 9.85 15.17 15.17 15.17 9.85
As POSITIVO (cm2) 15.17 15.03 16.38 15.03 15.17
As - 2.50 3.95 4.90 3.95 2.50
As + 2.50 3.27 5.25 3.27 2.50
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
2.40 1.60 2.40 2.40 3.50 2.4 2.4 1.60 2.40
60 As NEGATIVO (cm2) 12.61 15.17 15.17 15.17 12.61
As POSITIVO (cm2) 15.17 15.03 20.36 15.03 15.17
As - 2.50 3.95 4.90 3.95 2.50
As + 2.50 3.27 5.25 3.27 2.50
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
2.40 1.60 2.40 2.40 3.50 2.4 2.4 1.60 2.40
60 As NEGATIVO (cm2) 18.75 15.17 15.83 15.17 18.75
As POSITIVO (cm2) 15.17 17.23 23.63 17.23 15.17
As - 2.58 3.91 4.88 3.91 2.58
As + 2.58 3.22 5.20 3.22 2.58
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 30.00 15 15 30.00 15
2.40 1.53 2.40 2.40 3.45 2.4 2.4 1.53 2.40
As NEGATIVO (cm2) 24.19 16.27 18.86 16.27 24.19
As POSITIVO (cm2) 15.17 21.43 26.72 21.43 15.17
As - 2.58 3.91 4.88 3.91 2.58
As + 2.58 3.22 5.20 3.22 2.58
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 17.5 30.00 15 17.5 30.00 17.5 15 30.00 17.5
2.40 1.53 2.40 2.40 3.45 2.4 2.4 1.53 2.40
As NEGATIVO (cm2) 29.49 20.54 21.37 20.54 29.49
As POSITIVO (cm2) 15.79 25.48 29.2 25.48 15.79
As - 2.66 3.88 4.85 3.88 2.66
As + 2.66 3.16 5.15 3.16 2.66
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 15 15 15 15 15 30.00 15
2.40 1.45 2.40 2.40 3.40 2.4 2.4 1.45 2.40
60 As NEGATIVO (cm2) 33.99 24.22 23.13 24.22 33.99
As POSITIVO (cm2) 19.51 28.94 30.91 28.94 19.51
As - 2.66 3.88 4.85 3.88 2.66
As + 2.66 3.16 5.15 3.16 2.66
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 15 30.00 12.5 15 30.00 15 12.5 30.00 15
2.40 1.45 2.40 2.40 3.40 2.4 2.4 1.45 2.40
60 As NEGATIVO (cm2) 35.56 26.95 26.20 26.95 35.56
As POSITIVO (cm2) 21.91 31.71 33.97 31.71 21.91
As - 2.65 3.85 4.80 3.85 2.65
As + 2.65 3.12 5.05 3.12 2.65
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 12.5 12.5 30.00 12.5 12.5 30.00 12.5
2.40 1.40 2.40 2.40 3.30 2.4 2.4 1.40 2.40
As NEGATIVO (cm2) 38.07 29.46 27.68 29.46 38.07
As POSITIVO (cm2) 24.16 34.26 35.39 34.26 24.16
As - 2.69 3.84 4.80 3.84 2.69
As + 2.69 3.11 5.05 3.11 2.69
2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 17.5 12.5 30.00 12.5 17.5 30.00 12.5
2.40 1.38 2.40 2.40 3.30 2.4 2.4 1.38 2.40
60 As NEGATIVO (cm2) 39.73 31.77 28.57 31.77 39.73
As POSITIVO (cm2) 26.10 36.08 36.21 36.08 26.10
As - 2.68 3.81 4.75 3.81 2.68
As + 2.68 3.07 4.95 3.07 2.68
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 10 12.5 30.00 12.5 10 30.00 12.5
2.40 1.33 2.40 2.40 3.20 2.4 2.4 1.33 2.40
60 As NEGATIVO (cm2) 39.46 31.72 28.60 31.72 39.46
As POSITIVO (cm2) 26.27 36.43 36.21 36.43 26.27
As - 2.73 3.80 4.75 3.80 2.73
As + 2.73 3.05 4.95 3.05 2.73
2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 10 12.5 30.00 12.5 10 30.00 12.5
2.40 1.30 2.40 2.40 3.20 2.4 2.4 1.30 2.40
60 As NEGATIVO (cm2) 34.57 28.28 25.59 28.28 34.57
As POSITIVO (cm2) 23.24 33.17 33.18 33.17 23.24
As - 2.71 3.78 4.70 3.78 2.71
As + 2.71 3.01 4.85 3.01 2.71
2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8" 2R3/8" 3R3/8" 2R3/8" 2R3/8"
40 12.5 30.00 17.5 12.5 30.00 12.5 17.5 30.00 12.5
2.40 1.25 2.40 2.40 3.10 2.4 2.4 1.25 2.40
120
20.63 20.63
Long
.
(m) 4.59 4.59
5.65 5.65
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
1
Ace
ro
Long
itudi
nal 41.26 41.26
SEPARACIÓN (cm)
LONG. (m)
120
22.25 22.25
Long
.
(m) 4.53 4.53
5.55 5.55
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
2
Ace
ro
Long
itudi
nal 44.50 44.50
SEPARACIÓN (cm)
LONG. (m)
120
22.22 22.22
Long
.
(m) 4.53 4.53
5.55 5.55
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
3
Ace
ro
Long
itudi
nal 44.44 44.44
SEPARACIÓN (cm)
LONG. (m)
43.40
120
21.70 21.70
Long
.
(m) 4.47 4.47
5.45 5.45
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 4
Ace
ro
Long
itudi
nal 43.40
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
120
20.87 20.87
Long
.
(m) 4.48 4.48
5.45 5.45
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
5
Ace
ro
Long
itudi
nal 41.74 41.74
SEPARACIÓN (cm)
LONG. (m)
120
19.13 19.13
Long
.
(m) 4.41 4.41
5.35 5.35
Arm
adur
a
Tra
nsve
rsal ESTRIBOSP
ISO
6
Ace
ro
Long
itudi
nal 38.26 38.26
SEPARACIÓN (cm)
LONG. (m)
36.32
120
18.16 18.16
Long
.
(m) 4.41 4.41
5.35 5.35
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 7
Ace
ro
Long
itudi
nal 36.32
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
33.55
120
16.78 16.78
Long
.
(m) 4.39 4.39
5.30 5.30
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 8
Ace
ro
Long
itudi
nal 33.55
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PORTICO Z7S4.
7 9 7
60
PIS
O 1
2 Ace
ro
Long
itudi
nal 20.97
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
20.97
60
10.49 10.49
Long
.
(m) 4.38 4.38
2.85 2.85
Arm
adur
a
Tra
nsve
rsal
60
PIS
O 1
1 Ace
ro
Long
itudi
nal 22.44
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
22.44
120
15.17 15.17
Long
.
(m) 4.38 4.38
5.25 5.25
Arm
adur
a
Tra
nsve
rsal
PIS
O 1
0 Ace
ro
Long
itudi
nal 26.57 26.57
SEPARACIÓN (cm)
LONG. (m)
120
15.17 15.17
Long
.
(m) 4.38 4.38
5.25 5.25
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
PIS
O 9
Ace
ro
Long
itudi
nal 29.98 29.98
SEPARACIÓN (cm)
LONG. (m)
120
15.17 15.17
Long
.
(m) 4.39 4.39
5.30 5.30
Arm
adur
a
Tra
nsve
rsal ESTRIBOS
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 4 PISOS R = 3.32
B1 B2
31.11 60.50
7.78 15.13
3R1/2" 3R3/8"
10 10
0.50 0.55
3R1/2" 3R3/8"
12.50 22.50
2.00 1.90
35.04 67.00
8.76 16.75
3R1/2" 2R3/8"
10 10
0.50 0.6
3R1/2" 2R3/8"
15.00 10.00
1.83 1.63
40.82 66.00
10.21 16.50
3R1/2" 2R3/8"
10 10
0.50 0.6
3R1/2" 2R3/8"
17.50 12.50
1.83 1.63
37.03 75.00
9.26 18.75
3R1/2" 2R3/8"
10 10
0.70 0.7
3R1/2" 2R3/8"
17.50 25.00
2.58 2.58
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
42.50LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra T
ran
sve
rsal
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
60.00 60.00 42.50
4.7
53.
60
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
42.50 57.50 57.50 42.50
40.00 57.50 57.50 40.00
3.6
0
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
3.6
0
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
35.00 55.00 55.00 35.00
PORTICO Z3S2
B1 B2 B3 B4
B1 B2
44.34 60.00
11.09 15.00
3R1/2" 3R3/8"
10 10
0.50 0.55
3R1/2" 3R3/8"
17.50 22.50
2.00 1.90
49.41 75.00
12.35 18.75
3R1/2" 3R3/8"
10 10
0.50 0.6
3R1/2" 3R3/8"
20.00 15.00
1.78 1.58
50.99 75.00
12.75 18.75
3R1/2" 2R3/8"
10 10
0.50 0.6
3R1/2" 2R3/8"
20.00 10.00
1.78 1.58
74.71 118.91
18.68 29.73
3R1/2" 2R3/8"
10 10
0.70 0.7
3R1/2" 2R3/8"
22.50 10.00
2.53 2.53
PORTICO Z3S4
B1 B2 B3 B4
45.00 55.00 55.00 45.00
3.6
0
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
3.6
0
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)47.50 60.00 60.00 47.50
47.50 60.00 60.00 47.50
3.60
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
67.50 67.50 55.00
4.7
5
55.00LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
ran
sve
rsa
l
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
221
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2
57.78 51.12
14.45 12.78
3R1/2" 2R1/2"
10 10
0.55 0.6
3R1/2" 2R1/2"
22.50 25.00
1.93 1.83
64.13 115.00
16.03 28.75
3R1/2" 2R1/2"
10 10
0.55 0.65
3R1/2" 2R1/2"
22.50 10.00
1.60 1.40
77.03 115.00
19.26 28.75
3R1/2" 2R1/2"
10 10
0.60 0.65
3R1/2" 2R1/2"
22.50 10.00
1.50 1.40
134.86 166.50
33.72 41.63
3R1/2" 2R1/2"
10 10
0.70 0.75
3R1/2" 2R1/2"
22.50 12.50
2.45 2.35
PORTICO Z7S2
B1 B2 B3 B4
55.00 60.00 60.00 55.00
3.60
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
3.6
0
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)55.00 65.00 65.00 55.00
57.50 65.00 65.00 57.50
3.60
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
75.00 75.00 67.50
4.7
5
67.50LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
B1 B2
72.60 73.80
18.15 18.45
3R1/2" 2R1/2"
10 10
0.55 0.6
3R1/2" 2R1/2"
22.50 17.50
1.88 1.78
71.28 90.00
17.82 22.50
3R1/2" 3R3/8"
10 10
0.60 0.65
3R1/2" 3R3/8"
22.50 10.00
1.43 1.33
96.59 134.75
24.15 33.69
3R1/2" 3R1/2"
10 10
0.70 0.7
3R1/2" 3R1/2"
15.00 12.50
1.23 1.23
171.52 234.00
42.88 58.50
4R1/2" 3R1/2"
10 10
0.80 0.9
4R1/2" 3R1/2"
20.00 10.00
2.18 1.98
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
80.00LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
ran
sve
rsa
l
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
90.00 90.00 80.00
4.75
3.60
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
67.50 70.00 70.00 67.50
60.00 65.00 65.00 60.00
3.6
0
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
3.6
0
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
55.00 60.00 60.00 55.00
PORTICO Z7S4
B1 B2 B3 B4
222
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 4 PISOS R = 4.50
B1 B2
25.97 62.00
6.49 15.50
3R1/2" 3R3/8"
10 10
0.50 0.55
3R1/2" 3R3/8"
12.50 20.00
2.00 1.90
25.88 62.00
6.47 15.50
3R1/2" 2R3/8"
10 10
0.50 0.55
3R1/2" 2R3/8"
15.00 12.50
1.85 1.75
32.80 62.00
8.20 15.50
3R1/2" 2R3/8"
10 10
0.50 0.55
3R1/2" 2R3/8"
15.00 15.00
1.85 1.75
24.96 53.00
6.24 13.25
3R1/2" 2R3/8"
10 10
0.70 0.7
3R1/2" 2R3/8"
15.00 25.00
2.60 2.60
PORTICO Z3S2
B1 B2 B3 B4
35.00 55.00 55.00 35.00
3.6
0
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
3.6
0
Arm
adur
a T
ran
sver
sal
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)37.50 55.00 55.00 37.50
40.00 55.00 55.00 40.00
3.6
0 LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
60.00 60.00 40.004.
75
40.00LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
B1 B2
36.26 62.00
9.07 15.50
3R1/2" 2R1/2"
10 10
0.50 0.6
3R1/2" 2R1/2"
12.50 22.50
2.00 1.80
42.08 62.00
10.52 15.50
3R1/2" 2R3/8"
10 10
0.50 0.6
3R1/2" 2R3/8"
17.50 12.50
1.80 1.60
43.35 62.00
10.84 15.50
3R1/2" 2R3/8"
10 10
0.50 0.6
3R1/2" 2R3/8"
17.50 12.50
1.80 1.60
52.58 88.92
13.15 22.23
3R1/2" 2R3/8"
10 10
0.70 0.7
3R1/2" 2R3/8"
17.50 22.50
2.55 2.55
PORTICO Z3S4
B1 B2 B3 B4
35.00 57.50 57.50 35.00
3.60
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
3.6
0
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)42.50 57.50 57.50 42.50
42.50 57.50 57.50 42.50
3.60
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
60.00 60.00 45.00
4.7
5
45.00LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
223
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2
45.77 68.00
11.44 17.00
3R1/2" 2R1/2"
10 10
0.50 0.6
3R1/2" 2R1/2"
17.50 20.00
2.00 1.80
49.50 68.00
12.38 17.00
3R1/2" 2R3/8"
10 10
0.50 0.6
3R1/2" 2R3/8"
20.00 10.00
1.75 1.55
58.25 73.00
14.56 18.25
3R1/2" 3R3/8"
10 10
0.50 0.65
3R1/2" 3R3/8"
20.00 15.00
1.75 1.45
73.87 122.10
18.47 30.53
3R1/2" 2R3/8"
10 10
0.65 0.7
3R1/2" 2R3/8"
22.50 10.00
2.60 2.50
PORTICO Z7S2
B1 B2 B3 B4
45.00 60.00 60.00 45.00
3.6
0
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
3.6
0
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)50.00 60.00 60.00 50.00
50.00 62.50 62.50 50.00
3.60
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
67.50 67.50 52.50
4.7
5
52.50LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
ran
sve
rsa
l
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
B1 B2
61.75 70.50
15.44 17.63
3R1/2" 2R1/2"
10 10
0.50 0.6
3R1/2" 2R1/2"
20.00 20.00
2.00 1.80
61.75 70.50
15.44 17.63
3R1/2" 3R3/8"
10 10
0.60 0.65
3R1/2" 3R3/8"
25.00 12.50
1.50 1.40
67.78 95.50
16.95 23.88
3R1/2" 3R3/8"
10 10
0.60 0.65
3R1/2" 3R3/8"
25.00 10.00
1.50 1.40
118.91 180.48
29.73 45.12
3R1/2" 2R1/2"
10 10
0.70 0.8
3R1/2" 2R1/2"
25.00 10.00
2.45 2.25
PORTICO Z7S4
B1 B2 B3 B4
50.00 60.00 60.00 50.00
3.60
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
3.6
0
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)57.50 65.00 65.00 57.50
57.50 65.00 65.00 57.50
3.60
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
80.00 80.00 67.50
4.7
5
67.50LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
224
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 4 PISOS R = 6.00
B1 B2
24.50 60.50
6.13 15.13
3R1/2" 3R3/8"
10 10
0.50 0.55
3R1/2" 3R3/8"
12.50 22.50
2.00 1.90
24.50 60.50
6.13 15.13
3R1/2" 2R3/8"
10 10
0.50 0.55
3R1/2" 2R3/8"
12.50 15.00
1.88 1.78
26.08 60.50
6.52 15.13
3R1/2" 2R3/8"
10 10
0.50 0.55
3R1/2" 2R3/8"
15.00 15.00
1.88 1.78
26.08 60.50
6.52 15.13
3R1/2" 2R3/8"
10 10
0.70 0.7
3R1/2" 2R3/8"
15.00 25.00
2.63 2.63
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
ELONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
40.00LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
57.50 57.50 40.00
4.7
53
.60 LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
40.00 55.00 55.00 40.00
35.00 55.00 55.00 35.00
3.6
0
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
3.6
0
Arm
adu
ra T
ran
sver
sal
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
35.00 55.00 55.00 35.00
PORTICO Z3S2
B1 B2 B3 B4
B1 B2
30.25 60.50
7.56 15.13
3R1/2" 3R3/8"
10 10
0.50 0.55
3R1/2" 3R3/8"
12.50 22.50
2.00 1.90
31.68 60.50
7.92 15.13
3R1/2" 2R3/8"
10 10
0.50 0.6
3R1/2" 2R3/8"
15.00 12.50
1.80 1.60
34.50 60.50
8.63 15.13
3R1/2" 2R3/8"
10 10
0.50 0.6
3R1/2" 2R3/8"
17.50 12.50
1.80 1.60
35.76 66.24
8.94 16.56
3R1/2" 2R3/8"
10 10
0.70 0.7
3R1/2" 2R3/8"
17.50 25.00
SEPARACIÓN (cm)
LONG. (m)
TE ESTRIBOS
SEPARACIÓN (cm)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
42.50LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
60.00 60.00 42.50
4.75
3.6
0 LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
42.50 57.50 57.50 42.50
40.00 57.50 57.50 40.00
3.60
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
35.00 55.00 55.00 35.00
PORTICO Z3S4
B1 B2 B3 B4
2.55 2.55CO
R
LONG. (m)Arm
adur
225
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2
36.70 66.13
9.18 16.53
3R1/2" 2R1/2"
10 10
0.50 0.6
3R1/2" 2R1/2"
15.00 22.50
2.00 1.80
41.51 66.13
10.38 16.53
3R1/2" 2R3/8"
10 10
0.50 0.6
3R1/2" 2R3/8"
17.50 10.00
1.80 1.60
42.93 66.13
10.73 16.53
3R1/2" 2R3/8"
10 10
0.50 0.6
3R1/2" 2R3/8"
17.50 10.00
1.80 1.60
52.57 83.88
13.14 20.97
3R1/2" 2R3/8"
10 10
0.70 0.7
3R1/2" 2R3/8"
20.00 25.00
2.55 2.55
PORTICO Z7S2
B1 B2 B3 B4
37.50 57.50 57.50 37.50
3.60
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)45.00 57.50 57.50 45.00
45.00 60.00 60.00 45.00
3.6
0 LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
60.00 60.00 47.50
4.7547.50
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
B1 B2
51.43 66.00
12.86 16.50
3R1/2" 2R1/2"
10 10
0.50 0.6
3R1/2" 2R1/2"
17.50 20.00
2.00 1.80
54.57 72.00
13.64 18.00
3R1/2" 3R3/8"
10 10
0.55 0.6
3R1/2" 3R3/8"
22.50 15.00
1.65 1.55
52.64 72.00
13.16 18.00
3R1/2" 3R3/8"
10 10
0.55 0.65
3R1/2" 3R3/8"
22.50 15.00
1.65 1.45
88.92 137.18
22.23 34.30
3R1/2" 3R3/8"
10 10
0.65 0.75
3R1/2" 3R3/8"
25.00 12.50
2.60 2.40
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
60.00LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
ran
sve
rsa
l
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
72.50 72.50 60.00
4.75
3.60
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
52.50 62.50 62.50 52.50
52.50 60.00 60.00 52.50
3.6
0
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
3.6
0
Arm
adu
ra T
rans
vers
al
CO
NF
IN. ESTRIBOS
SEPARACIÓN (cm)
45.00 60.00 60.00 45.00
PORTICO Z7S4
B1 B2 B3 B4
226
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 8 PISOS R = 3.32
B1 B2
23.13 60.505.78 15.125
3R1/2" 3R3/8"10 10
0.50 0.55
3R1/2" 3R3/8"
12.50 22.502.00 1.90
23.13 60.505.78 15.13
3R1/2" 2R3/8"10 10
0.50 0.55
3R1/2" 2R3/8"
12.50 12.501.80 1.70
23.1 60.50
5.78 15.13
3R1/2" 2R3/8"
10 100.50 0.55
3R1/2" 2R3/8"
12.50 15.001.80 1.70
24.96 60.506.240 15.13
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
15.00 15.001.80 1.60
35 69.00
8.750 17.25
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
15.00 15.001.80 1.60
37.02 72.009.26 18.00
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
17.50 12.501.80 1.60
48.41 72.00
12.10 18.00
3R1/2" 2R3/8"
10 100.50 0.65
3R1/2" 2R3/8"
17.50 12.501.80 1.50
48.41 99.3212.10 24.83
3R1/2" 2R3/8"
10 100.70 0.7
3R1/2" 2R3/8"
17.50 27.502.55 2.55
42.5
PORTICO Z3S2
B1 B2 B3 B4
32.5 55.0 55.0 32.5
3.60
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
3.6
0
Arm
adura
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)35.0 55.0 55.0 35.0
35.0 55.0 55.0 35.0
3.60
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)3.
60LONG. (m)
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adura
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
40.0 57.5 57.5 40.03.
60
42.5 60.0 60.0 42.5
3.60
40.0 57.5 57.5 40.0
3.6042.5 62.5 62.5 42.5
62.5 62.5 42.5
4.75
227
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2
35.76 66.128.94 16.530
3R1/2" 2R1/2"10 10
0.50 0.6
3R1/2" 2R1/2"
17.50 22.502.00 1.80
38.29 72.009.57 18.00
3R1/2" 3R3/8"10 10
0.45 0.6
3R1/2" 3R3/8"
17.50 15.001.80 1.50
48.6 72.00
12.15 18.00
3R1/2" 2R3/8"
10 100.45 0.6
3R1/2" 2R3/8"
17.50 10.001.80 1.50
60 72.0015.000 18.00
3R1/2" 2R3/8"
10 100.50 0.65
3R1/2" 2R3/8"
20.00 10.001.70 1.40
60 86.00
15.000 21.50
3R1/2" 3R3/8"
10 100.55 0.65
3R1/2" 3R3/8"
22.50 12.501.60 1.40
62.29 91.0015.57 22.75
3R1/2" 3R3/8"
10 100.55 0.7
3R1/2" 3R3/8"
22.50 12.501.60 1.30
83.00 91.00
20.75 22.75
3R1/2" 3R3/8"
10 100.55 0.7
3R1/2" 3R3/8"
22.50 10.001.60 1.30
83.00 158.0020.75 39.50
3R1/2" 3R3/8"
10 100.65 0.8
3R1/2" 3R3/8"
22.50 10.002.55 2.25
80 80 55
4.75
3.6055 70 70 55
67.5 52.53.
60
52.5 65 65 52.5
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
50 62.5 62.5 50
3.60
52.5 67.5
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.ESTRIBOS
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
3.60
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
3.60
LONG. (m)
45 60 60 45
42.5 60 60 42.5
3.60
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
55
PORTICO Z3S4
B1 B2 B3 B4
42.5 57.5 57.5 42.5
228
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2
37.26 72.009.32 18.000
3R1/2" 2R1/2"10 10
0.50 0.6
3R1/2" 2R1/2"
17.50 20.002.00 1.80
47.18 76.0011.80 19.00
3R1/2" 3R3/8"10 10
0.45 0.65
3R1/2" 3R3/8"
17.50 12.501.70 1.30
56.5 76.00
14.13 19.00
3R1/2" 3R3/8"
10 100.55 0.65
3R1/2" 3R3/8"
22.50 12.501.50 1.30
62.01 80.7015.503 20.18
3R1/2" 3R3/8"
10 100.55 0.65
3R1/2" 3R3/8"
22.50 12.501.50 1.30
68 90.16
17.000 22.54
3R1/2" 2R1/2"
10 100.60 0.7
3R1/2" 2R1/2"
25.00 12.501.40 1.20
76.32 97.0219.08 24.26
3R1/2" 2R1/2"
10 100.60 0.7
3R1/2" 2R1/2"
22.50 10.001.40 1.20
85.56 95.63
21.39 23.91
3R1/2" 2R1/2"
10 100.65 0.75
3R1/2" 2R1/2"
17.50 10.001.30 1.10
115.73 183.5228.93 45.88
3R1/2" 4R3/8"
10 100.65 0.85
3R1/2" 4R3/8"
27.50 10.002.45 2.05
85 85 62.5
4.75
3.6062.5 75 75 62.5
70 60
3.6
057.5 70 70 57.5
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
55 65 65 55
3.60
60 70
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adura
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
3.60
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
3.60
LONG. (m)
52.5 65 65 52.5
45 62.5 62.5 45
3.60
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
62.5
PORTICO Z7S2
B1 B2 B3 B4
45 60 60 45
229
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2
83.88 85.5420.97 21.385
3R1/2" 4R3/8"10 10
0.60 0.65
3R1/2" 4R3/8"
25.00 17.501.83 1.73
107.40 110.0026.85 27.50
3R1/2" 4R1/2"10 10
0.65 0.8
3R1/2" 4R1/2"
15.00 17.501.30 1.00
118.9 118.92
29.73 29.73
4R1/2" 3R1/2"
10 100.70 0.8
4R1/2" 3R1/2"
17.50 12.501.20 1.00
122.11 148.3530.528 37.09
4R1/2" 3R1/2"
10 100.70 0.8
4R1/2" 3R1/2"
17.50 10.001.20 1.00
122.47 160.96
30.618 40.24
4R1/2" 4R1/2"
10 100.75 0.8
4R1/2" 4R1/2"
15.00 12.501.10 1.00
143.66 239.7635.92 59.94
3R5/8" 4R5/8"
10 100.85 0.9
3R5/8" 4R5/8"
15.00 12.500.90 0.80
193.63 315.81
48.41 78.95
6R5/8" 6R5/8"
10 100.85 1.1
6R5/8" 6R5/8"
22.50 12.500.90 0.40
268.00 451.5667.00 112.89
6R5/8" 6R5/8"
10 101.00 1.25
6R5/8" 6R5/8"
27.50 15.001.75 1.25
100
PORTICO Z7S4
B1 B2 B3 B4
60 62.5 62.5 60
3.60
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)62.5 77.5 77.5 62.5
67.5 77.5 77.5 67.5
3.60
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
3.60
LONG. (m)
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adura
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
67.5 77.5 77.5 67.5
3.60
85 90 90 853.6
0
72.5 77.5 77.5 72.5
3.6085 110 110 85
125 125 100
4.75
230
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 8 PISOS R = 4.50
B1 B2
24.50 62.006.13 15.500
3R1/2" 3R3/8"10 10
0.50 0.55
3R1/2" 3R3/8"
12.50 20.002.00 1.90
24.50 62.006.13 15.50
3R1/2" 2R3/8"10 10
0.50 0.55
3R1/2" 2R3/8"
12.50 12.501.83 1.73
24.5 62.00
6.13 15.50
3R1/2" 2R3/8"
10 100.50 0.55
3R1/2" 2R3/8"
12.50 15.001.83 1.73
24.5 62.006.125 15.50
3R1/2" 2R3/8"
10 100.50 0.55
3R1/2" 2R3/8"
15.00 17.501.83 1.73
24.5 73.00
6.125 18.25
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
15.00 12.501.83 1.63
34.00 73.008.50 18.25
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
15.00 12.501.83 1.63
43.35 73.00
10.84 18.25
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
17.50 15.001.83 1.63
43.40 98.4510.85 24.61
3R1/2" 2R3/8"
10 100.70 0.7
3R1/2" 2R3/8"
17.50 27.502.58 2.58
42.5
PORTCO Z3S2
B1 B2 B3 B4
32.5 55 55 32.5
3.60
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adu
ra
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)35 55 55 35
35 55 55 35
3.60
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
3.6
0
LONG. (m)P
ISO
7Acero
LongitudinalAs TOTAL
As por caraA
rmad
ura
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)C
OR
TE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adura
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
40 55 55 40
3.60
40 60 60 40
3.60
40 60 60 40
3.6042.5 60 60 42.5
62.5 62.5 42.5
4.75
231
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2
26.86 66.136.72 16.533
3R1/2" 2R1/2"10 10
0.50 0.6
3R1/2" 2R1/2"
15.00 22.502.00 1.80
33.75 66.138.44 16.53
3R1/2" 2R3/8"10 10
0.50 0.6
3R1/2" 2R3/8"
15.00 10.001.75 1.55
40.8 66.13
10.21 16.53
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
17.50 12.501.75 1.55
45.1 72.0011.275 18.00
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
20.00 10.001.75 1.55
45.1 78.13
11.275 19.53
3R1/2" 2R3/8"
10 100.50 0.65
3R1/2" 2R3/8"
20.00 10.001.75 1.45
50.00 84.5012.50 21.13
3R1/2" 3R3/8"
10 100.50 0.65
3R1/2" 3R3/8"
20.00 12.501.75 1.45
56.50 84.50
14.13 21.13
3R1/2" 3R3/8"
10 100.55 0.65
3R1/2" 3R3/8"
22.50 15.001.65 1.45
68.08 122.4717.02 30.62
3R1/2" 2R3/8"
10 100.65 0.75
3R1/2" 2R3/8"
22.50 12.502.60 2.40
72.5 72.5 52.5
4.75
3.6052.5 65 65 52.5
65 50
3.60
47.5 62.5 62.5 47.5
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
47.5 60 60 47.5
3.60
50 65
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adura
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NFIN
.
ESTRIBOS
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
3.60
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)3.6
0
LONG. (m)
42.5 57.5 57.5 42.5
37.5 57.5 57.5 37.5
3.60
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adu
ra
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
52.5
PORTICO Z3S4
B1 B2 B3 B4
37.5 57.5 57.5 37.5
232
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2
36.70 66.139.18 16.533
3R1/2" 2R1/2"10 10
0.50 0.6
3R1/2" 2R1/2"
15.00 22.502.00 1.80
33.92 73.008.48 18.25
3R1/2" 3R3/8"10 10
0.45 0.6
3R1/2" 3R3/8"
15.00 12.501.80 1.50
46.3 73.00
11.56 18.25
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
20.00 10.001.70 1.50
46.25 73.0011.563 18.25
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
20.00 10.001.70 1.50
55.1 87.50
13.775 21.88
3R1/2" 3R3/8"
10 100.55 0.65
3R1/2" 3R3/8"
22.50 12.501.60 1.40
55.10 91.1313.78 22.78
3R1/2" 3R3/8"
10 100.55 0.7
3R1/2" 3R3/8"
22.50 12.501.60 1.30
70.00 91.13
17.50 22.78
3R1/2" 3R3/8"
10 100.55 0.7
3R1/2" 3R3/8"
22.50 12.501.60 1.30
83.19 140.8720.80 35.22
3R1/2" 2R3/8"
10 100.65 0.75
3R1/2" 2R3/8"
22.50 10.002.55 2.35
72.5 72.5 55
4.75
3.6052.5 67.5 67.5 52.5
67.5 52.5
3.60
52.5 65 65 52.5
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
47.5 60 60 47.5
3.60
52.5 67.5
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adura
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NFIN
.
ESTRIBOS
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
3.60
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
3.6
0LONG. (m)
47.5 60 60 47.5
40 60 60 40
3.60
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adu
ra
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
55
PORTICO Z7S2
B1 B2 B3 B4
37.5 57.5 57.5 37.5
233
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2
60.50 72.0015.13 18.000
3R1/2" 2R1/2"10 10
0.55 0.6
3R1/2" 2R1/2"
22.50 20.001.95 1.85
70.48 100.4517.62 25.11
3R1/2" 4R3/8"10 10
0.55 0.7
3R1/2" 4R3/8"
22.50 10.001.50 1.20
84.0 100.45
21.00 25.11
3R1/2" 2R1/2"
10 100.60 0.7
3R1/2" 2R1/2"
20.00 10.001.40 1.20
93.75 100.4523.438 25.11
3R1/2" 2R1/2"
10 100.65 0.7
3R1/2" 2R1/2"
17.50 10.001.30 1.20
95.44 140.00
23.860 35.00
3R1/2" 3R1/2"
10 100.65 0.7
3R1/2" 3R1/2"
15.00 12.501.30 1.20
103.00 136.0025.75 34.00
4R1/2" 3R1/2"
10 100.70 0.75
4R1/2" 3R1/2"
20.00 12.501.20 1.10
131.30 158.23
32.83 39.56
4R1/2" 4R1/2"
10 100.70 0.85
4R1/2" 4R1/2"
15.00 12.501.20 0.90
171.52 254.5142.88 63.63
3R1/2" 4R1/2"
10 100.80 0.95
3R1/2" 4R1/2"
15.00 12.502.15 1.85
95 95 80
4.75
3.6070 85 85 70
75 67.5
3.60
65 70 70 65
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
62.5 70 70 62.53.
60
67.5 75P
ISO
1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adura
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NFIN
.
ESTRIBOS
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
3.60
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
3.6
0LONG. (m)
57.5 70 70 57.5
55 70 70 55
3.60
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adu
ra
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
80
PORTICO Z7S4
B1 B2 B3 B4
55 60 60 55
234
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 8 PISOS R = 6.00
B1 B2
21.65 60.505.41 15.125
3R1/2" 3R3/8"10 10
0.50 0.55
3R1/2" 3R3/8"
12.50 22.502.00 1.90
21.65 60.505.41 15.13
3R1/2" 2R3/8"10 10
0.50 0.55
3R1/2" 2R3/8"
12.50 15.001.85 1.75
21.7 60.50
5.41 15.13
3R1/2" 2R3/8"
10 100.50 0.55
3R1/2" 2R3/8"
12.50 15.001.85 1.75
21.65 60.505.413 15.13
3R1/2" 2R3/8"
10 100.50 0.55
3R1/2" 2R3/8"
15.00 17.501.85 1.75
26 72.00
6.500 18.00
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
15.00 15.001.85 1.65
26.00 68.006.50 17.00
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
15.00 17.501.85 1.65
41.76 72.89
10.44 18.22
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
15.00 15.001.85 1.65
41.76 81.5310.44 20.38
3R1/2" 2R3/8"
10 100.70 0.7
3R1/2" 2R3/8"
15.00 27.502.60 2.60
40
PORTICO Z3S2
B1 B2 B3 B4
32.5 55 55 32.5
3.60
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adu
ra
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)35 55 55 35
35 55 55 353.
60LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
3.6
0
LONG. (m)
PIS
O 7
Acero Longitudinal
As TOTAL
As por caraA
rmad
ura
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)C
OR
TE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adura
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
37.5 55 55 37.5
3.60
40 57.5 57.5 40
3.60
37.5 57.5 57.5 37.5
3.6040 60 60 40
65 65 40
4.75
235
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2
25.97 62.006.49 15.500
3R1/2" 3R3/8"10 10
0.50 0.55
3R1/2" 3R3/8"
12.50 20.002.00 1.90
25.97 62.006.49 15.50
3R1/2" 2R3/8"10 10
0.50 0.55
3R1/2" 2R3/8"
15.00 12.501.83 1.73
29.0 60.50
7.25 15.13
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
15.00 12.501.83 1.63
30.71 60.507.678 15.13
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
17.50 15.001.83 1.63
34.43 72.00
8.608 18.00
3R1/2" 2R3/8"
10 100.50 0.65
3R1/2" 2R3/8"
17.50 10.001.83 1.53
41.51 72.0010.38 18.00
3R1/2" 2R3/8"
10 100.50 0.65
3R1/2" 2R3/8"
17.50 12.501.83 1.53
44.75 75.00
11.19 18.75
3R1/2" 2R3/8"
10 100.50 0.65
3R1/2" 2R3/8"
20.00 12.501.83 1.53
44.75 75.0011.19 18.75
3R1/2" 2R3/8"
10 100.70 0.7
3R1/2" 2R3/8"
20.00 27.502.58 2.58
65 65 50
4.75
3.6050 62.5 62.5 50
62.5 45
3.60
45 62.5 62.5 45
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
42.5 57.5 57.5 42.5
3.60
45 62.5
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adura
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NFIN
.
ESTRIBOS
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
3.60
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
3.6
0
LONG. (m)
40 57.5 57.5 40
37.5 55 55 37.5
3.60
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adu
ra
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
50
PORTICO Z3S4
B1 B2 B3 B4
35 55 55 35
236
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2
25.97 60.506.49 15.125
3R1/2" 3R3/8"10 10
0.50 0.55
3R1/2" 3R3/8"
12.50 22.502.00 1.90
25.97 60.506.49 15.13
3R1/2" 2R3/8"10 10
0.50 0.6
3R1/2" 2R3/8"
15.00 12.501.80 1.60
32.0 60.50
8.00 15.13
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
15.00 12.501.80 1.60
32 72.008.000 18.00
3R1/2" 2R3/8"
10 100.50 0.6
3R1/2" 2R3/8"
17.50 12.501.80 1.60
35 72.00
8.750 18.00
3R1/2" 2R3/8"
10 100.50 0.65
3R1/2" 2R3/8"
17.50 10.001.80 1.50
38.36 72.009.59 18.00
3R1/2" 2R3/8"
10 100.50 0.65
3R1/2" 2R3/8"
20.00 12.501.80 1.50
47.83 72.00
11.96 18.00
3R1/2" 2R3/8"
10 100.50 0.65
3R1/2" 2R3/8"
20.00 12.501.80 1.50
52.57 117.8913.14 29.47
3R1/2" 2R3/8"
10 100.70 0.7
3R1/2" 2R3/8"
20.00 17.502.55 2.55
65 65 47.5
4.75
3.6047.5 65 65 47.5
62.5 47.5
3.60
45 62.5 62.5 45
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
42.5 57.5 57.5 42.5
3.60
47.5 62.5
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adura
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NFIN
.
ESTRIBOS
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
3.60
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
3.6
0
LONG. (m)
40 57.5 57.5 40
40 57.5 57.5 40
3.60
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adu
ra
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
47.5
PORTICO Z7S2
B1 B2 B3 B4
35 55 55 35
237
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2
44.35 66.1311.09 16.533
3R1/2" 2R1/2"10 10
0.55 0.6
3R1/2" 2R1/2"
22.50 22.501.95 1.85
48.60 78.0012.15 19.50
3R1/2" 2R1/2"10 10
0.55 0.7
3R1/2" 2R1/2"
22.50 12.501.50 1.20
60.4 78.00
15.09 19.50
3R1/2" 3R3/8"
10 100.60 0.7
3R1/2" 3R3/8"
25.00 10.001.40 1.20
60.36 78.0015.090 19.50
3R1/2" 3R3/8"
10 100.65 0.7
3R1/2" 3R3/8"
25.00 10.001.30 1.20
63.15 88.00
15.788 22.00
3R1/2" 3R3/8"
10 100.65 0.7
3R1/2" 3R3/8"
22.50 10.001.30 1.20
76.32 100.0019.08 25.00
3R1/2" 2R1/2"
10 100.70 0.75
3R1/2" 2R1/2"
17.50 10.001.20 1.10
81.36 111.43
20.34 27.86
3R1/2" 3R1/2"
10 100.70 0.85
3R1/2" 3R1/2"
17.50 12.501.20 0.90
124.46 168.1131.12 42.03
3R1/2" 4R3/8"
10 100.80 0.95
3R1/2" 4R3/8"
20.00 10.002.15 1.85
80
PORTICO Z7S4
B1 B2 B3 B4
55 60 60 55
3.60
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)55 70 70 55
57.5 70 70 57.5
3.60
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
3.60
LONG. (m)
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adura
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NFIN
.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RTE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
62.5 70 70 62.5
3.60
67.5 75 75 67.5
3.6
065 70 70 65
3.6070 85 85 70
95 95 80
4.75
238
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 12 PISOS R = 3.32
B1 B2 B1 B2
37.28 62.00 50.0 90.00
9.32 15.500 12.50 22.50
3R1/2" 3R3/8" 3R1/2" 2R3/8"10 10 10 10
0.55 0.55 0.55 0.6
3R1/2" 3R3/8" 3R1/2" 2R3/8"
15.00 22.50 22.50 10.001.95 1.95 1.70 1.60
37.30 62.00 50 90.009.33 15.50 12.5 22.50
3R1/2" 2R3/8" 3R1/2" 2R3/8"10 10 10 10
0.50 0.55 0.55 0.65
3R1/2" 2R3/8" 3R1/2" 2R3/8"
15.00 12.50 22.50 10.001.80 1.70 1.70 1.50
37.3 78.00 50 90.00
9.32 19.50 12.5 22.50
3R1/2" 2R3/8" 3R1/2" 3R3/8"10 10 10 10
0.50 0.55 0.55 0.7
3R1/2" 2R3/8" 3R1/2" 3R3/8"
15.00 10.00 22.50 12.501.80 1.70 1.70 1.40
37.28 78.00 51.42 118.959.32 19.50 12.86 29.74
3R1/2" 2R3/8" 3R1/2" 3R3/8"
10 10 10 100.50 0.55 0.55 0.7
3R1/2" 2R3/8" 3R1/2" 3R3/8"
17.50 12.50 22.50 10.001.80 1.70 1.70 1.40
41.3 90.00 72.59 118.95
10.33 22.500 18.15 29.74
3R1/2" 3R3/8" 3R1/2" 2R1/2"
10 10 10 100.50 0.6 0.55 0.8
3R1/2" 3R3/8" 3R1/2" 2R1/2"
17.50 15.00 22.50 10.001.80 1.60 1.70 1.20
50.00 90.00 76.32 136.9112.50 22.50 19.08 34.23
3R1/2" 2R3/8" 3R1/2" 2R3/8"
10 10 10 100.50 0.6 0.70 0.8
3R1/2" 2R3/8" 3R1/2" 2R3/8"
17.50 10.00 22.50 10.001.80 1.60 2.55 2.35
PORTICO Z3S2
55.0
55.0
55.0
55.0
55.0
55.0
55.0
80.0 80.0 55.0
70.0
80.0 80.0
70.0
3.6
03.
603.
603.
604.
75
B1 B2 B3 B4
65.0
70.0 70.0 55.0
LONG. (m)
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por caraA
rmad
ura
T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)C
OR
TE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
40.0 55.0 55.0 40.0
3.6
03.
6040.0 55.0 55.0
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)40.0
40.0 55.0 55.0 40.0
3.60
LONG. (m)
CO
RT
E ESTRIBOS
3.60 SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
2
Acero Longitudinal
As TOTAL
45.0 55.0 55.0 45.0
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
3.60
LONG. (m)55.0
45.0
3.60
PIS
O 1
1
45.0 45.060.060.0
45.060.0
As por cara
PIS
O 1
0
Acero Longitudinal
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
CO
RT
E
As TOTAL
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 9
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
55.065.0
60.0
55.060.060.0
239
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2 B1 B2
44.35 72.00 62.0 96.00
11.09 18.000 15.50 24.00
3R1/2" 2R1/2" 3R1/2" 3R3/8"10 10 10 10
0.55 0.55 0.55 0.65
3R1/2" 2R1/2" 3R1/2" 3R3/8"
17.50 22.50 22.50 12.501.95 1.95 1.63 1.43
44.35 72.00 66.25 96.0011.09 18.00 16.5625 24.00
3R1/2" 2R3/8" 3R1/2" 3R3/8"10 10 10 10
0.50 0.55 0.55 0.7
3R1/2" 2R3/8" 3R1/2" 3R3/8"
17.50 10.00 22.50 10.001.73 1.63 1.63 1.33
53.0 72.00 66.25 96.00
13.25 18.00 16.5625 24.00
3R1/2" 2R3/8" 3R1/2" 3R3/8"10 10 10 10
0.50 0.6 0.65 0.7
3R1/2" 2R3/8" 3R1/2" 3R3/8"
20.00 10.00 25.00 12.501.73 1.53 1.43 1.33
53 72.00 66.25 96.0013.25 18.00 16.56 24.00
3R1/2" 2R3/8" 3R1/2" 2R1/2"
10 10 10 100.50 0.6 0.65 0.8
3R1/2" 2R3/8" 3R1/2" 2R1/2"
20.00 10.00 25.00 10.001.73 1.53 1.43 1.13
55.66 80.00 71.85 112.75
13.92 20.000 17.96 28.19
3R1/2" 3R3/8" 3R1/2" 2R1/2"
10 10 10 100.55 0.65 0.65 0.8
3R1/2" 3R3/8" 3R1/2" 2R1/2"
22.50 12.50 25.00 10.001.63 1.43 1.43 1.13
55.66 96.00 114.17 200.0713.92 24.00 28.54 50.02
3R1/2" 3R3/8" 3R1/2" 4R3/8"
10 10 10 100.55 0.65 0.70 0.9
3R1/2" 3R3/8" 3R1/2" 4R3/8"
22.50 12.50 30.00 10.001.63 1.43 2.48 2.08
PORTICO Z3S4
65.0
70.0
65.0
55.0
65.0
65.0
65.0
90.0 90.0 70.0
80.0
80.0 80.0
80.0
3.6
03.
603.
603.
604.
75
B1 B2 B3 B4
70.0
70.0 70.0 65.0
LONG. (m)
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
45.0 55.0 55.0 45.0
3.6
03.
6045.0 55.0 55.0
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)45.0
50.0 60.0 60.0 50.0
3.60
LONG. (m)
CO
RT
E ESTRIBOS
3.60 SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
2
Acero Longitudinal
As TOTAL
50.0 60.0 60.0 50.0
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
3.60
LONG. (m)55.0
55.0
3.60
PIS
O 1
1
55.0 55.065.065.0
55.065.0
As por cara
PIS
O 1
0
Acero Longitudinal
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
CO
RT
E
As TOTAL
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 9
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
55.070.0
65.0
55.065.065.0
240
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2 B1 B2
60.50 98.00 98.0 128.00
15.13 24.500 24.50 32.00
3R1/2" 3R1/2" 3R1/2" 3R1/2"10 10 10 10
0.55 0.7 0.70 0.8
3R1/2" 3R1/2" 3R1/2" 3R1/2"
22.50 17.50 15.00 10.001.90 1.60 1.10 0.90
60.50 98.00 98 162.0015.13 24.50 24.5 40.50
3R1/2" 4R3/8" 3R1/2" 4R1/2"10 10 10 10
0.55 0.7 0.70 0.9
3R1/2" 4R3/8" 3R1/2" 4R1/2"
22.50 10.00 15.00 10.001.40 1.10 1.10 0.70
62.0 98.00 112.5 162.00
15.50 24.50 28.125 40.50
3R1/2" 4R3/8" 3R1/2" 4R1/2"10 10 10 10
0.55 0.7 0.75 0.9
3R1/2" 4R3/8" 3R1/2" 4R1/2"
22.50 10.00 12.50 10.001.40 1.10 1.00 0.70
73 112.50 112.50 200.0018.25 28.13 28.13 50.00
3R1/2" 3R1/2" 3R1/2" 4R5/8"
10 10 10 100.60 0.75 0.75 1
3R1/2" 3R1/2" 3R1/2" 4R5/8"
22.50 12.50 12.50 12.501.30 1.00 1.00 0.50
73 112.50 128.00 212.00
18.25 28.125 32.00 53.00
3R1/2" 3R1/2" 3R1/2" 4R5/8"
10 10 10 100.60 0.75 0.80 1
3R1/2" 3R1/2" 3R1/2" 4R5/8"
22.50 12.50 10.00 12.501.30 1.00 0.90 0.50
98.00 128.00 167.00 324.0024.50 32.00 41.75 81.00
3R1/2" 3R1/2" 3R1/2" 3R5/8"
10 10 10 100.70 0.8 0.80 1.1
3R1/2" 3R1/2" 3R1/2" 3R5/8"
15.00 10.00 15.00 10.001.10 0.90 2.05 1.45
PORTICO Z7S2
80.0
80.0
75.0
70.0
75.0
75.0
80.0
110.0 110.0 80.0
100.0
100.0 100.0
100.0
3.60
3.60
3.60
3.60
4.75
B1 B2 B3 B4
90.0
90.0 90.0 75.0
LONG. (m)
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
55.0 70.0 70.0 55.0
3.60
3.6055.0 70.0 70.0
As por caraA
rmad
ura
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)55.0
55.0 70.0 70.0 55.0
3.60
LONG. (m)C
OR
TE ESTRIBOS
3.60 SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
2Acero
Longitudinal
As TOTAL
60.0 75.0 75.0 60.0
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
3.60
LONG. (m)70.0
70.0
3.60
PIS
O 1
1
60.0 60.075.075.0
70.080.0
As por cara
PIS
O 1
0
Acero Longitudinal
Arm
adur
a T
rans
vers
al
CO
NF
IN.
CO
RT
E
As TOTAL
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 9
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
70.090.0
80.0
70.080.080.0
241
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2 B1 B2
84.50 128.00 144.5 220.50
21.13 32.000 36.13 55.13
3R1/2" 4R1/2" 4R5/8" 4R5/8"10 10 10 10
0.65 0.8 0.85 1.05
3R1/2" 4R1/2" 4R5/8" 4R5/8"
22.50 17.50 17.50 10.001.70 1.40 0.68 0.28
84.50 128.00 163 220.5021.13 32.00 40.75 55.13
3R1/2" 3R5/8" 4R5/8" 4R5/8"10 10 10 10
0.65 0.8 0.85 1.05
3R1/2" 3R5/8" 4R5/8" 4R5/8"
15.00 15.00 15.00 10.001.08 0.78 0.68 0.28
84.5 144.50 163 264.50
21.13 36.13 40.75 66.13
3R1/2" 4R1/2" 6R5/8" 6R5/8"10 10 10 10
0.65 0.85 0.90 1.15
3R1/2" 4R1/2" 6R5/8" 6R5/8"
15.00 10.00 22.50 12.501.08 0.68 0.58 0.07
112.5 144.50 166.00 264.5028.125 36.13 41.50 66.13
4R1/2" 4R1/2" 6R5/8" 6R5/8"
10 10 10 100.75 0.85 0.90 1.15
4R1/2" 4R1/2" 6R5/8" 6R5/8"
15.00 10.00 22.50 12.500.88 0.68 0.58 0.07
115 180.50 200.00 312.50
28.75 45.125 50.00 78.13
4R1/2" 4R5/8" 6R5/8" 6R5/8"
10 10 10 100.75 0.95 1.00 1.25
4R1/2" 4R5/8" 6R5/8" 6R5/8"
15.00 12.50 17.50 10.000.88 0.48 0.38 -0.13
144.50 180.50 296.00 430.0036.13 45.13 74.00 107.50
4R5/8" 4R5/8" 6R5/8" 6R5/8"
10 10 10 100.85 0.95 1.00 1.25
4R5/8" 4R5/8" 6R5/8" 6R5/8"
17.50 12.50 22.50 15.000.68 0.48 1.53 1.03
PORTICO Z7S4
85.0105.0
95.0
85.0105.0105.0
PIS
O 9
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
As por cara
PIS
O 1
0
Acero Longitudinal
Arm
adur
a T
rans
vers
al
CO
NF
IN.
CO
RT
E
As TOTAL
85.0
85.0
3.60
PIS
O 1
1
75.0 75.095.095.0
85.095.0
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
3.60
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
75.0 85.0 85.0 75.0
3.6
0 LONG. (m)C
OR
TE ESTRIBOS
3.6
0 SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
2Acero
Longitudinal
As TOTAL
65.0
65.0 85.0 85.0 65.0
As por caraA
rmad
ura
T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
65.0 80.0 80.0 65.0
3.60
3.6065.0 80.0 80.0
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
LONG. (m)
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
4.7
5B1 B2 B3 B4
105.0
115.0 115.0 90.0
3.60
3.60
3.60
3.60
115.0
125.0 125.0
115.0
100.0
100.0
90.0
85.0
90.0
90.0
100.0
125.0 125.0 100.0
242
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 12 PISOS R = 4.50
B1 B2 B1 B2
32.76 60.50 33.0 86.00
8.19 15.125 8.25 21.50
3R1/2" 3R3/8" 3R1/2" 2R3/8"10 10 10 10
0.55 0.55 0.50 0.6
3R1/2" 3R3/8" 3R1/2" 2R3/8"
15.00 22.50 20.00 12.501.95 1.95 1.85 1.65
32.76 60.50 33 86.008.19 15.13 8.25 21.50
3R1/2" 2R3/8" 3R1/2" 2R3/8"10 10 10 10
0.50 0.55 0.50 0.65
3R1/2" 2R3/8" 3R1/2" 2R3/8"
15.00 12.50 20.00 10.001.85 1.75 1.85 1.55
32.8 60.50 39 86.00
8.19 15.13 9.75 21.50
3R1/2" 2R3/8" 3R1/2" 3R3/8"10 10 10 10
0.50 0.55 0.50 0.7
3R1/2" 2R3/8" 3R1/2" 3R3/8"
15.00 15.00 20.00 15.001.85 1.75 1.85 1.45
32.76 72.00 42.99 118.558.19 18.00 10.75 29.64
3R1/2" 2R3/8" 3R1/2" 3R3/8"
10 10 10 100.50 0.55 0.55 0.7
3R1/2" 2R3/8" 3R1/2" 3R3/8"
17.50 12.50 22.50 10.001.85 1.75 1.75 1.45
32.76 82.00 63.46 118.55
8.19 20.500 15.87 29.64
3R1/2" 2R3/8" 3R1/2" 2R1/2"
10 10 10 100.50 0.6 0.55 0.8
3R1/2" 2R3/8" 3R1/2" 2R1/2"
17.50 12.50 22.50 10.001.85 1.65 1.75 1.25
33.00 82.00 63.46 143.558.25 20.50 15.87 35.89
3R1/2" 2R3/8" 3R1/2" 2R3/8"
10 10 10 100.50 0.6 0.70 0.8
3R1/2" 2R3/8" 3R1/2" 2R3/8"
17.50 12.50 22.50 12.501.85 1.65 2.60 2.40
PORTICO Z3S2
50.065.0
57.5
50.060.060.0
PIS
O 9
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
As por cara
PIS
O 1
0
Acero Longitudinal
Arm
adur
a T
rans
vers
al
CO
NF
IN.
CO
RT
E
As TOTAL
50.0
45.0
3.60
PIS
O 1
1
45.0 45.057.557.5
45.057.5
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
3.60
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
45.0 55.0 55.0 45.0
3.60
LONG. (m)
CO
RT
E ESTRIBOS
3.60 SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
2
Acero Longitudinal
As TOTAL
37.5
37.5 55.0 55.0 37.5
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
37.5 55.0 55.0 37.5
3.60
3.6037.5 55.0 55.0
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
LONG. (m)
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
4.75
B1 B2 B3 B4
65.0
70.0 70.0 50.0
3.60
3.60
3.60
3.60
70.0
77.5 77.5
70.0
52.5
52.5
52.5
50.0
50.0
52.5
52.5
77.5 77.5 52.5
243
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2 B1 B2
40.00 60.50 57.0 85.00
10.00 15.125 14.25 21.25
3R1/2" 3R3/8" 3R1/2" 3R3/8"10 10 10 10
0.55 0.55 0.50 0.65
3R1/2" 3R3/8" 3R1/2" 3R3/8"
15.00 22.50 20.00 15.001.95 1.95 1.75 1.45
40.00 72.00 60.5 98.0010.00 18.00 15.125 24.50
3R1/2" 2R3/8" 3R1/2" 3R3/8"10 10 10 10
0.50 0.55 0.55 0.7
3R1/2" 2R3/8" 3R1/2" 3R3/8"
15.00 10.00 22.50 10.001.75 1.65 1.65 1.35
42.0 72.00 60.5 98.00
10.50 18.00 15.125 24.50
3R1/2" 2R3/8" 3R1/2" 3R3/8"10 10 10 10
0.50 0.6 0.55 0.7
3R1/2" 2R3/8" 3R1/2" 3R3/8"
17.50 10.00 22.50 12.501.75 1.55 1.65 1.35
42 72.00 74.00 112.5010.5 18.00 18.50 28.13
3R1/2" 2R3/8" 3R1/2" 2R1/2"
10 10 10 100.50 0.6 0.55 0.75
3R1/2" 2R3/8" 3R1/2" 2R1/2"
17.50 10.00 22.50 10.001.75 1.55 1.65 1.25
50 85.00 74.00 126.00
12.50 21.250 18.50 31.50
3R1/2" 2R3/8" 3R1/2" 2R1/2"
10 10 10 100.50 0.6 0.60 0.75
3R1/2" 2R3/8" 3R1/2" 2R1/2"
20.00 10.00 25.00 10.001.75 1.55 1.55 1.25
50.00 85.00 92.00 189.0012.50 21.25 23.00 47.25
3R1/2" 3R3/8" 3R1/2" 3R3/8"
10 10 10 100.50 0.65 0.65 0.8
3R1/2" 3R3/8" 3R1/2" 3R3/8"
20.00 12.50 25.00 10.001.75 1.45 2.60 2.30
PORTICO Z3S4
55.070.0
65.0
50.065.065.0
PIS
O 9
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
As por cara
PIS
O 1
0
Acero Longitudinal
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
CO
RT
E
As TOTAL
50.0
50.0
3.60
PIS
O 1
1
50.0 50.060.060.0
50.065.0
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
3.60
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
45.0 60.0 60.0 45.0
3.60
LONG. (m)
CO
RT
E ESTRIBOS
3.60 SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
2
Acero Longitudinal
As TOTAL
40.0
45.0 60.0 60.0 45.0
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
40.0 55.0 55.0 40.0
3.6
03.
6040.0 55.0 55.0
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
LONG. (m)
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
4.75
B1 B2 B3 B4
70.0
70.0 70.0 55.0
3.6
03.
603.
603.
60
75.0
75.0 75.0
75.0
60.0
60.0
55.0
55.0
55.0
55.0
60.0
80.0 80.0 60.0
244
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2 B1 B2
42.00 72.00 72.0 112.50
10.50 18.000 18.00 28.13
3R1/2" 2R1/2" 3R1/2" 4R3/8"10 10 10 10
0.50 0.6 0.60 0.75
3R1/2" 2R1/2" 3R1/2" 4R3/8"
17.50 20.00 25.00 10.002.00 1.80 1.40 1.10
42.00 72.00 72 144.5010.50 18.00 18 36.13
3R1/2" 3R3/8" 3R1/2" 4R1/2"10 10 10 10
0.45 0.6 0.60 0.85
3R1/2" 3R3/8" 3R1/2" 4R1/2"
17.50 12.50 25.00 12.501.70 1.40 1.40 0.90
51.0 72.00 84.5 144.50
12.75 18.00 21.125 36.13
3R1/2" 3R3/8" 3R1/2" 3R1/2"10 10 10 10
0.50 0.6 0.65 0.85
3R1/2" 3R3/8" 3R1/2" 3R1/2"
20.00 12.50 17.50 10.001.60 1.40 1.30 0.90
51 98.00 84.50 162.0012.75 24.50 21.13 40.50
3R1/2" 2R1/2" 3R1/2" 4R1/2"
10 10 10 100.50 0.7 0.65 0.9
3R1/2" 2R1/2" 3R1/2" 4R1/2"
20.00 10.00 17.50 12.501.60 1.20 1.30 0.80
60.5 98.00 98.00 162.00
15.13 24.500 24.50 40.50
3R1/2" 2R1/2" 3R1/2" 4R1/2"
10 10 10 100.55 0.7 0.70 0.9
3R1/2" 2R1/2" 3R1/2" 4R1/2"
22.50 10.00 15.00 12.501.50 1.20 1.20 0.80
60.50 112.50 114.00 210.0015.13 28.13 28.50 52.50
3R1/2" 4R3/8" 3R1/2" 3R1/2"
10 10 10 100.55 0.75 0.70 0.95
3R1/2" 4R3/8" 3R1/2" 3R1/2"
22.50 10.00 25.00 12.501.50 1.10 2.35 1.85
PORTICO Z7S2
70.0
70.0
65.0
60.0
65.0
65.0
70.0
95.0 95.0 70.0
90.0
90.0 90.0
90.0
3.60
3.60
3.60
3.60
4.75
B1 B2 B3 B4
85.0
85.0 85.0 65.0
LONG. (m)
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)C
OR
TE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
45.0 60.0 60.0 45.0
3.60
3.6045.0 60.0 60.0
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)45.0
50.0 60.0 60.0 50.0
3.60
LONG. (m)
CO
RT
E ESTRIBOS
3.60 SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
2
Acero Longitudinal
As TOTAL
50.0 70.0 70.0 50.0
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
3.6
0 LONG. (m)60.0
55.0
3.60
PIS
O 1
1
55.0 55.070.070.0
55.075.0
As por cara
PIS
O 1
0
Acero Longitudinal
Arm
adur
a T
rans
vers
al
CO
NF
IN.
CO
RT
E
As TOTAL
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 9
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
60.085.0
75.0
60.075.075.0
245
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2 B1 B2
50.00 98.00 110.0 136.00
12.50 24.500 27.50 34.00
3R1/2" 3R1/2" 4R1/2" 4R1/2"10 10 10 10
0.50 0.7 0.70 0.8
3R1/2" 3R1/2" 4R1/2" 4R1/2"
20.00 17.50 15.00 12.502.00 1.60 1.00 0.80
50.00 98.00 110 162.0012.50 24.50 27.5 40.50
3R1/2" 3R1/2" 4R1/2" 3R5/8"10 10 10 10
0.50 0.7 0.70 0.9
3R1/2" 3R1/2" 4R1/2" 3R5/8"
20.00 12.50 15.00 12.501.40 1.00 1.00 0.60
58.3 98.00 131 162.00
14.56 24.50 32.75 40.50
3R1/2" 4R3/8" 3R5/8" 4R1/2"10 10 10 10
0.50 0.7 0.75 0.9
3R1/2" 4R3/8" 3R5/8" 4R1/2"
20.00 10.00 15.00 10.001.40 1.00 0.90 0.60
76.5 112.50 137.00 200.0019.125 28.13 34.25 50.00
3R1/2" 3R1/2" 3R5/8" 4R5/8"
10 10 10 100.60 0.75 0.75 1
3R1/2" 3R1/2" 3R5/8" 4R5/8"
20.00 12.50 15.00 12.501.20 0.90 0.90 0.40
86.4 123.00 145.00 200.00
21.60 30.750 36.25 50.00
3R1/2" 3R1/2" 4R5/8" 4R5/8"
10 10 10 100.60 0.75 0.80 1
3R1/2" 3R1/2" 4R5/8" 4R5/8"
17.50 10.00 17.50 12.501.20 0.90 0.80 0.40
100.00 128.00 145.00 324.0025.00 32.00 36.25 81.00
4R1/2" 3R1/2" 4R1/2" 4R5/8"
10 10 10 100.70 0.8 0.80 1.1
4R1/2" 3R1/2" 4R1/2" 4R5/8"
17.50 10.00 20.00 12.501.00 0.80 1.95 1.35
PORTICO Z7S4
80.0
80.0
75.0
70.0
75.0
75.0
80.0
110.0 110.0 80.0
100.0
100.0 100.0
100.0
3.6
03.
603.
603.
604.
75B1 B2 B3 B4
90.0
90.0 90.0 75.0
LONG. (m)
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
50.0 70.0 70.0 50.0
3.6
03.
6050.0 70.0 70.0
As por caraA
rmad
ura
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)50.0
50.0 70.0 70.0 50.0
3.60
LONG. (m)C
OR
TE ESTRIBOS
3.60 SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
2Acero
Longitudinal
As TOTAL
60.0 75.0 75.0 60.0
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
3.60
LONG. (m)70.0
70.0
3.60
PIS
O 1
1
60.0 60.075.075.0
70.080.0
As por cara
PIS
O 1
0
Acero Longitudinal
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
CO
RT
E
As TOTAL
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 9
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
70.090.0
80.0
70.080.080.0
246
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
PORTICOS DE 12 PISOS R = 6.00
B1 B2 B1 B2
29.40 60.50 32.0 84.40
7.35 15.125 8.00 21.10
3R1/2" 3R3/8" 3R1/2" 2R3/8"10 10 10 10
0.55 0.55 0.50 0.6
3R1/2" 3R3/8" 3R1/2" 2R3/8"
12.50 22.50 17.50 15.001.95 1.95 1.90 1.70
29.40 60.50 42.93 84.407.35 15.13 10.7325 21.10
3R1/2" 2R3/8" 3R1/2" 2R3/8"10 10 10 10
0.50 0.55 0.50 0.7
3R1/2" 2R3/8" 3R1/2" 2R3/8"
12.50 15.00 17.50 10.001.90 1.80 1.90 1.50
29.4 60.50 51.68 98.80
7.35 15.13 12.92 24.70
3R1/2" 2R3/8" 3R1/2" 3R3/8"10 10 10 10
0.50 0.55 0.50 0.7
3R1/2" 2R3/8" 3R1/2" 3R3/8"
12.50 15.00 17.50 15.001.90 1.80 1.90 1.50
29.4 72.00 51.68 98.807.35 18.00 12.92 24.70
3R1/2" 2R3/8" 3R1/2" 3R3/8"
10 10 10 100.50 0.55 0.50 0.8
3R1/2" 2R3/8" 3R1/2" 3R3/8"
15.00 15.00 20.00 10.001.90 1.80 1.90 1.30
32 72.00 62.83 104.02
8.00 18.000 15.71 26.01
3R1/2" 2R3/8" 3R1/2" 3R3/8"
10 10 10 100.50 0.6 0.50 0.8
3R1/2" 2R3/8" 3R1/2" 3R3/8"
15.00 15.00 20.00 10.001.90 1.70 1.90 1.30
32.00 84.40 62.83 146.648.00 21.10 15.71 36.66
3R1/2" 2R3/8" 3R1/2" 2R3/8"
10 10 10 100.50 0.6 0.70 0.8
3R1/2" 2R3/8" 3R1/2" 2R3/8"
17.50 12.50 20.00 12.501.90 1.70 2.65 2.45
PORTICO Z3S2
50.0
50.0
50.0
45.0
45.0
50.0
50.0
77.5 77.5 50.0
77.5
77.5 77.5
77.5
3.60
3.60
3.60
3.60
4.75
B1 B2 B3 B4
67.5
67.5 67.5 45.0
LONG. (m)
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por caraA
rmad
ura
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)C
OR
TE ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
35.0 55.0 55.0 35.0
3.60
3.6035.0 55.0 55.0
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)35.0
35.0 55.0 55.0 35.0
3.60
LONG. (m)
CO
RT
E ESTRIBOS
3.60 SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
2
Acero Longitudinal
As TOTAL
40.0 55.0 55.0 40.0
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
Acero Longitudinal
As TOTAL
As por cara
3.6
0
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
3.60
LONG. (m)45.0
45.0
3.60
PIS
O 1
1
40.0 40.057.557.5
45.057.5
As por cara
PIS
O 1
0
Acero Longitudinal
Arm
adur
a T
rans
vers
al
CO
NF
IN.
CO
RT
E
As TOTAL
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 9
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
45.067.5
57.5
45.057.557.5
247
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
B1 B2 B1 B2
36.00 60.50 50.0 84.50
9.00 15.125 12.50 21.13
3R1/2" 3R3/8" 3R1/2" 2R3/8"10 10 10 10
0.55 0.55 0.50 0.65
3R1/2" 3R3/8" 3R1/2" 2R3/8"
15.00 22.50 20.00 10.001.95 1.95 1.85 1.55
36.00 60.50 50 84.509.00 15.13 12.5 21.13
3R1/2" 2R3/8" 3R1/2" 2R3/8"10 10 10 10
0.50 0.55 0.50 0.65
3R1/2" 2R3/8" 3R1/2" 2R3/8"
15.00 15.00 20.00 10.001.85 1.75 1.85 1.55
36.0 60.50 58 112.50
9.00 15.13 14.5 28.13
3R1/2" 2R3/8" 3R1/2" 3R3/8"10 10 10 10
0.50 0.55 0.50 0.65
3R1/2" 2R3/8" 3R1/2" 3R3/8"
15.00 15.00 20.00 12.501.85 1.75 1.85 1.55
40.5 72.00 60.50 112.5010.125 18.00 15.13 28.13
3R1/2" 2R3/8" 3R1/2" 3R3/8"
10 10 10 100.50 0.6 0.55 0.75
3R1/2" 2R3/8" 3R1/2" 3R3/8"
17.50 12.50 22.50 10.001.85 1.65 1.75 1.35
40.5 72.00 69.00 120.00
10.13 18.000 17.25 30.00
3R1/2" 2R3/8" 3R1/2" 2R1/2"
10 10 10 100.50 0.6 0.55 0.75
3R1/2" 2R3/8" 3R1/2" 2R1/2"
17.50 12.50 22.50 12.501.85 1.65 1.75 1.35
48.00 72.00 69.00 128.0012.00 18.00 17.25 32.00
3R1/2" 2R3/8" 3R1/2" 2R3/8"
10 10 10 100.50 0.6 0.70 0.8
3R1/2" 2R3/8" 3R1/2" 2R3/8"
PORTICO Z3S4
50.065.0
60.0
50.065.065.0
PIS
O 9
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
As por cara
PIS
O 1
0
Acero Longitudinal
Arm
adur
a T
rans
vers
al
CO
NF
IN.
CO
RT
E
As TOTAL
50.0
45.0
3.60
PIS
O 1
1
45.0 45.060.060.0
45.060.0
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
3.60
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
45.0 60.0 60.0 45.0
3.60
LONG. (m)
CO
RT
E ESTRIBOS
3.60 SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
2Acero
Longitudinal
As TOTAL
40.0
40.0 55.0 55.0 40.0
As por caraA
rmad
ura
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
40.0 55.0 55.0 40.0
3.60
3.6040.0 55.0 55.0
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
LONG. (m)
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
4.75
B1 B2 B3 B4
65.0
65.0 65.0 50.0
3.60
3.60
3.60
3.60
75.0
75.0 75.0
75.0
55.0
55.0
55.0
50.0
50.0
55.0
55.0
80.0 80.0 55.0
17.50 12.50 22.50 12.501.85 1.65 2.60 2.40C
OR
TE
SEPARACIÓN (cm)
LONG. (m)CO
RT
E
SEPARACIÓN (cm)
LONG. (m)
248
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
20.00 12.50 25.00 12.501.75 1.45 2.60 2.20C
O
SEPARACIÓN (cm)
LONG. (m) CO
SEPARACIÓN (cm)
LONG. (m)
B1 B2 B1 B2
40.00 72.00 60.5 84.50
10.00 18.000 15.13 21.13
3R1/2" 2R1/2" 3R1/2" 3R3/8"10 10 10 10
0.50 0.6 0.55 0.65
3R1/2" 2R1/2" 3R1/2" 3R3/8"
15.00 20.00 22.50 15.002.00 1.80 1.65 1.45
40.00 72.00 60.5 98.0010.00 18.00 15.125 24.50
3R1/2" 3R3/8" 3R1/2" 3R3/8"10 10 10 10
0.50 0.6 0.55 0.7
3R1/2" 3R3/8" 3R1/2" 3R3/8"
15.00 15.00 22.50 10.001.75 1.55 1.65 1.35
44.0 72.00 64 98.00
11.00 18.00 16 24.50
3R1/2" 2R3/8" 3R1/2" 3R3/8"10 10 10 10
0.50 0.6 0.55 0.7
3R1/2" 2R3/8" 3R1/2" 3R3/8"
17.50 10.00 22.50 12.501.75 1.55 1.65 1.35
44 84.50 72.00 112.5011 21.13 18.00 28.13
3R1/2" 3R3/8" 3R1/2" 2R1/2"
10 10 10 100.50 0.65 0.60 0.75
3R1/2" 3R3/8" 3R1/2" 2R1/2"
17.50 12.50 25.00 10.001.75 1.45 1.55 1.25
50 84.50 79.00 127.00
12.50 21.125 19.75 31.75
3R1/2" 3R3/8" 3R1/2" 2R1/2"
10 10 10 100.50 0.65 0.60 0.75
3R1/2" 3R3/8" 3R1/2" 2R1/2"
20.00 12.50 25.00 10.001.75 1.45 1.55 1.25
50.00 84.50 88.00 158.0012.50 21.13 22.00 39.50
3R1/2" 3R3/8" 3R1/2" 3R3/8"
10 10 10 100.50 0.65 0.65 0.85
3R1/2" 3R3/8" 3R1/2" 3R3/8"
PORTICO Z7S2
60.0
60.0
60.0
55.0
55.0
60.0
60.0
85.0 85.0 60.0
75.0
75.0 75.0
75.0
3.6
03.
603.
603.
604.
75
B1 B2 B3 B4
70.0
70.0 70.0 55.0
LONG. (m)
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
RT
E ESTRIBOS
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
RT
E ESTRIBOS
40.0 60.0 60.0 40.0
3.60
3.6040.0 60.0 60.0
As por caraA
rmad
ura
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)40.0
45.0 60.0 60.0 45.0
3.60
LONG. (m)
CO
RT
E ESTRIBOS
3.60 SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
2Acero
Longitudinal
As TOTAL
45.0 65.0 65.0 45.0
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
Acero Longitudinal
As TOTAL
As por cara
3.60
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
3.60
LONG. (m)55.0
50.0
3.6
0
PIS
O 1
1
50.0 50.065.065.0
50.065.0
As por cara
PIS
O 1
0
Acero Longitudinal
Arm
adur
a T
rans
vers
al
CO
NF
IN.
CO
RT
E
As TOTAL
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 9
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
55.070.0
65.0
55.065.065.0
249
APENDICE B. GEOMETRIA Y ARMADO DE COLUMNAS Ing. Ada Moreno
LA UNIVERSIDAD DEL ZULIA
250
B1 B2 B1 B2
40.50 72.00 74.0 112.50
10.13 18.000 18.50 28.13
3R1/2" 3R1/2" 3R1/2" 3R1/2"10 10 10 10
0.50 0.7 0.70 0.8
3R1/2" 3R1/2" 3R1/2" 3R1/2"
20.00 22.50 15.00 10.002.00 1.60 1.00 0.80
42.00 75.00 74 144.5010.50 18.75 18.5 36.13
3R1/2" 2R1/2" 3R1/2" 4R1/2"10 10 10 10
0.50 0.7 0.70 0.9
3R1/2" 2R1/2" 3R1/2" 4R1/2"
20.00 10.00 15.00 10.001.40 1.00 1.00 0.60
62.0 75.00 84.5 144.50
15.50 18.75 21.125 36.13
3R1/2" 2R1/2" 4R1/2" 4R1/2"10 10 10 10
0.50 0.7 0.75 0.9
3R1/2" 2R1/2" 4R1/2" 4R1/2"
20.00 10.00 17.50 10.001.40 1.00 0.90 0.60
62 98.00 87.00 162.0015.5 24.50 21.75 40.50
3R1/2" 3R1/2" 4R1/2" 3R5/8"
10 10 10 100.60 0.75 0.75 1
3R1/2" 3R1/2" 4R1/2" 3R5/8"
22.50 12.50 17.50 10.001.20 0.90 0.90 0.40
71 98.00 98.00 161.00
17.75 24.500 24.50 40.25
3R1/2" 3R1/2" 4R1/2" 3R5/8"
10 10 10 100.60 0.75 0.80 1
3R1/2" 3R1/2" 4R1/2" 3R5/8"
20.00 12.50 15.00 10.001.20 0.90 0.80 0.40
71.00 112.50 124.00 217.0017.75 28.13 31.00 54.25
3R1/2" 3R1/2" 3R1/2" 4R1/2"
10 10 10 100.70 0.8 0.80 1.1
3R1/2" 3R1/2" 3R1/2" 4R1/2"
PORTICO Z7S4
80.0
80.0
75.0
70.0
75.0
75.0
80.0
110.0 110.0 80.0
100.0
100.0 100.0
100.0
3.6
03.
603.
60
3.60
4.75
B1 B2 B3 B4
90.0
90.0 90.0 75.0
LONG. (m)
PIS
O 8
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
PIS
O 7
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
E ESTRIBOS
PIS
O 6
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 5
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 4
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 3
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 2
Acero Longitudinal
As TOTAL
As por cara
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
E ESTRIBOS
50.0 70.0 70.0 50.0
3.6
03.
6050.0 70.0 70.0
As por caraA
rmad
ura
Tra
nsve
rsal
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)50.0
50.0 70.0 70.0 50.0
3.6
0 LONG. (m)
CO
RT
E ESTRIBOS
3.60 SEPARACIÓN (cm)
LONG. (m)
PIS
O 1
2Acero
Longitudinal
As TOTAL
60.0 75.0 75.0 60.0
CO
RT
E ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
Acero Longitudinal
As TOTAL
As por cara
3.6
0
Arm
adur
a T
rans
vers
al
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
3.60
LONG. (m)70.0
70.0
3.60
PIS
O 1
1
60.0 60.075.075.0
70.080.0
As por cara
PIS
O 1
0
Acero Longitudinal
Arm
adu
ra
Tra
nsve
rsal
CO
NF
IN.
CO
RT
E
As TOTAL
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
PIS
O 9
Acero Longitudinal
As TOTAL
As por cara
Arm
adur
a
Tra
nsv
ersa
l
CO
NF
IN.
ESTRIBOS
SEPARACIÓN (cm)
LONG. (m)
CO
RT
E
70.090.0
80.0
70.080.080.0
15.00 10.00 17.50 12.501.00 0.80 1.95 1.35C
OR
T
SEPARACIÓN (cm)
LONG. (m) CO
RT
SEPARACIÓN (cm)
LONG. (m)