Excel - Concreto Armado i - Joshe Luis

INGENIERIA CIVIL CONCRETO ARMADO I UNPRG

PROYECTO VIVIENDA MULTIFAMILIAR - 3 PSIOS

ESPECIFICACIONES TÉCNICAS: PROYECTO DEPARTAMENTOS 3 NIVELES Tab. Equiv. 2º pisoDATOS GEOMÉTRICOS : PESO POR METRO CUADRADO Longitudes muros

Largo: 20.00 m Vivienda (S/C) 200 Kg/m² NORMA E-020 10.35 m

Ancho: 11.00 m Aligerado (0.20cm) 300 Kg/m² 10.59 m

Nº Porticos X-X 6 Espesor de P. Muerto: 0.075 m Ceramica, contrapiso y cielo raso 1.90 m

Nº Porticos Y-Y 4 Ancho tabiqueria: 0.15 m 14.36 m

Nº Pisos 3 Pisos P. Tab.Eq. 2º piso: 319 Kg/m² 5.61 m

Altura Entrepiso 2.60 m P. Tab.Eq. 3º piso: 324 Kg/m² 7.27 m

CARACTERISTICAS DE MATERIALES Azotea: S/C 100 Kg/m² Total

P. Esp. Muro de Albañileria: 1800 Kg/m³ CARACTERISTICAS DE LA ZONA 319 Kg/m²

Resistencia a la compresion : f'c 210 Kg/cm² Uso: Edificaciones Comunes

P. Esp. Del Cº: Γc 2400 Kg/m³ Suelo: Suelos Intermedios

Esfuerzo de fluencia del acero 4200 Kg/cm² P. Esp. Del Cº: simple 2000 Kg/m³

PREDIMENSIONAMIENTO DE ELEMENTOS ESTRUCTURALES

1. PREDIMENSIONAMIENTO DE LOSA ALIGERADA Se utilizará la dimensión de la mayor luz

Luz Libre: 3.73 mPeralte de Los Luz Libre / 25 CUADRO RESUMEN - PREDIMENSIONAMIENTO DE VIGAS

0.149 m VIGAS PRINCIPALES

Usamos 0.200 m VIGAS h = Ln/12

2. PREDIMENSIONAMIENTO DE VIGAS A - A 0.35 m

B - B 0.35 m2.1 VIGAS PRINCIPALES (EJES 2-3-4-5-6-7) Portico X-X C - C 0.35 m

b min = 0.25 m D - D 0.35 mLuz Libre: 4.25 m VIGAS SECUNDARIAS

Altura de Viga Luz Libre / 12VIGAS h = Ln/14

0.354 mUsamos h = 0.35 m 2 - 2 0.27 m

b = 0.25 m 3 - 3 0.27 m

4 - 4 0.27 m2.2 VIGAS SECUNDARIAS (EJES A-B-C-D) Portico Y-Y 5 - 5 0.27 m

b min = 0.25 m 6 - 6 0.27 mLuz Libre: 3.73 m 7 - 7 0.27 mAltura de Viga Luz Libre / 14 VIGAS EN VOLADO

0.266 m VIGAS h = Ln/10Usamos h = 0.30 m

b = 0.25 m A - A 0.09 m

B - B 0.09 m2.3 VIGAS EN VOLADO C - C 0.09 m

b min = 0.25 m D - D 0.09 mLuz Libre: 0.93 mAltura de Viga Luz Libre / 10

Valor minimo 0.09 m


Usamos h = 0.30 m

b = 0.25 m

3. PREDIMENSIONAMIENTO DE COLUMNAS Dimensiones minimas para columnas es 25 cm.

Area minima C. Pu ф = 0.7

ф (0.85. f'c + Р. fy) f'c = 210 Kg/cm²

fy = 4200 Kg/cm³

Р = 0.01

Ejes Area Tributaria Tipo P. Aligerado Long. Vigas P. Vigas P. Muerto P. Muro2 - A 5.625 m² C4 5062.50 Kg 4.50 m 2610.00 Kg 2531.25 Kg 7897.50 Kg2 - B 6.675 m² C3 6007.50 Kg 5.50 m 2830.50 Kg 3003.75 Kg 2808.00 Kg2 - C 6.675 m² C3 6007.50 Kg 5.50 m 3397.50 Kg 3003.75 Kg 2808.00 Kg2 - D 5.625 m² C4 5062.50 Kg 4.50 m 2610.00 Kg 2531.25 Kg 7897.50 Kg3 - A 6.806 m² C3 6125.40 Kg 5.03 m 2896.20 Kg 3062.70 Kg 17058.60 Kg3 - B 8.381 m² C1 7542.90 Kg 3.03 m 3683.70 Kg 3771.45 Kg 5089.50 Kg3 - C 8.381 m² C1 7542.90 Kg 3.03 m 3683.70 Kg 3771.45 Kg 5089.50 Kg3 - D 6.806 m² C3 6125.40 Kg 5.03 m 2896.20 Kg 3062.70 Kg 17058.60 Kg4 - A 6.019 m² C3 5417.10 Kg 4.68 m 2707.20 Kg 2708.55 Kg 2843.10 Kg4 - B 8.694 m² C1 7824.60 Kg 5.68 m 3494.70 Kg 3912.30 Kg 8529.30 Kg4 - C 8.328 m² C1 7495.20 Kg 5.68 m 3494.70 Kg 3747.60 Kg 0.00 Kg4 - D 5.051 m² C3 4545.90 Kg 4.25 m 2475.00 Kg 2272.95 Kg 7020.00 Kg5 - A 3.038 m² C3 2734.20 Kg 3.35 m 1989.00 Kg 1367.10 Kg 10881.00 Kg5 - B 8.348 m² C1 7513.20 Kg 6.22 m 3786.30 Kg 3756.60 Kg 15163.20 Kg5 - C 9.514 m² C1 8562.60 Kg 6.22 m 3786.30 Kg 4281.30 Kg 10249.20 Kg5 - D 4.759 m² C3 4283.10 Kg 4.12 m 2404.80 Kg 2141.55 Kg 10494.90 Kg6 - A 6.728 m² C3 6055.20 Kg 4.99 m 2874.60 Kg 3027.60 Kg 9617.40 Kg6 - B 10.641 m² C1 9576.90 Kg 6.43 m 3899.70 Kg 4788.45 Kg 7897.50 Kg6 - C 11.148 m² C1 10033.20 Kg 6.68 m 3899.70 Kg 5016.60 Kg 3510.00 Kg6 - D 7.706 m² C3 6935.40 Kg 5.43 m 3112.20 Kg 3467.70 Kg 11583.00 Kg7 - A 4.073 m² C4 3665.70 Kg 3.81 m 2237.40 Kg 1832.85 Kg 12495.60 Kg7 - B 5.883 m² C3 5294.70 Kg 4.81 m 3024.90 Kg 2647.35 Kg 10530.00 Kg7 - C 5.883 m² C3 5294.70 Kg 4.81 m 3024.90 Kg 2647.35 Kg 10530.00 Kg7 - D 4.073 m² C4 3665.70 Kg 3.81 m 2237.40 Kg 1832.85 Kg 12495.60 Kg


Tab. Equiv. 2º piso Tab. Equiv. 3º piso

Longitudes muros Areas Libres Longitudes muros Areas Libres5.45 m 24.96 m² 9.41 m 2.28 m 24.96 m²

5.95 m 34.72 m² 4.00 m 1.02 m 34.72 m²

17.64 m² 7.96 m 7.15 m 17.64 m²

26.50 m² 1.90 m 6.10 m 26.50 m²

23.20 m² 12.16 m 5.86 m 23.20 m²

8.08 m² 4.48 m 8.08 m²

61.48 m 135.09 m² Total 62.32 m 135.09 m²319 Kg/m² 324 Kg/m²

CUADRO RESUMEN - PREDIMENSIONAMIENTO DE VIGAS

VIGAS PRINCIPALES

TERCER PISO

0.20 m 0.25 m 0.25 x 0.35 0.25 x 0.35 0.25 x 0.35

0.20 m 0.25 m 0.25 x 0.35 0.25 x 0.35 0.25 x 0.35

0.20 m 0.25 m 0.25 x 0.35 0.25 x 0.35 0.25 x 0.35

0.20 m 0.25 m 0.25 x 0.35 0.25 x 0.35 0.25 x 0.35

VIGAS SECUNDARIAS

TERCER PISO

0.18 m 0.25 m 0.25 x 0.30 0.25 x 0.30 0.25 x 0.30

0.18 m 0.25 m 0.25 x 0.30 0.25 x 0.30 0.25 x 0.30

0.18 m 0.25 m 0.25 x 0.30 0.25 x 0.30 0.25 x 0.30

0.18 m 0.25 m 0.25 x 0.30 0.25 x 0.30 0.25 x 0.30

0.18 m 0.25 m 0.25 x 0.30 0.25 x 0.30 0.25 x 0.30

0.18 m 0.25 m 0.25 x 0.30 0.25 x 0.30 0.25 x 0.30

VIGAS EN VOLADO

TERCER PISO

0.12 m 0.25 m 0.25 x 0.30 0.25 x 0.30 0.25 x 0.30

0.12 m 0.25 m 0.25 x 0.30 0.25 x 0.30 0.25 x 0.30

0.12 m 0.25 m 0.25 x 0.30 0.25 x 0.30 0.25 x 0.30

0.12 m 0.25 m 0.25 x 0.30 0.25 x 0.30 0.25 x 0.30

UNIFORMIZANDO

CONTROL DE DEFLEXIONES h = L/21 b ≥0.25 m PRIMER

PISOSEGUNDO

PISO


PISOSEGUNDO

PISO


PISOSEGUNDO

PISO


P. Tabiqueria P. Columna Cm Cv Pu Area Min. Secc. Cuadrada Usamos

3618.62 Kg 1170.00 Kg 22889.87 Kg 2812.50 Kg 36827.06 Kg 477.189 cm² 21.84 cm 0.25 m

























m


METRADO DE CARGA

DIMENSIONES

Viga Principales b = 0.25 m h = 0.35 mVigas Secundarias : b = 0.25 m h = 0.30 mColumna: 0.25 m 0.25 m

PESO POR METRO CUADRADO

P. Esp. Del Cº: Γc 2.40 T/m³ Acabado 0.15 T/m²Azotea: S/C 0.10 T/m³ P. Tab.Eq. 2º piso 0.32 T/m²Vivienda (S/C) 0.20 T/m² P. Tab.Eq. 3º piso 0.32 T/m²Aligerado (0.20cm) 0.30 T/m² Ancho Tributario BP. Esp. Muro de Albañileria 1800 Kg/m³Altura Entrepiso 2.60 mParapeto 1.00 m

1. PRIMER PISO

1.1. VIGAS PRNCIPALES

Eje Eje Longuitud (m)

2A - B 4.00 m 2.50 m 0.21 T/m 0.67 T/m 0.38 T/m 0.00 m 0.00 T/mB - C 2.00 m 2.50 m 0.21 T/m 0.67 T/m 0.38 T/m 0.00 m 0.00 T/mC - D 4.00 m 2.50 m 0.21 T/m 0.67 T/m 0.38 T/m 0.00 m 0.00 T/m






Para las vigas secundarias ya no se considera la carga viva, solo la carga muerta, por lo tanto no habra combinacion de carga1.2. VIGAS SECUNDARIAS Carga Ubicada en 2º Piso

Eje Eje Longuitud (m) P. Propio Viga 1.4 * Wm

A

2 - 3 2.90 m 0.18 T/m 2.90 m 0.70 T/m 0.88 T/m no 1.23 T/m 3 - 4 2.65 m 0.18 T/m 2.65 m 0.70 T/m 0.88 T/m no 1.23 T/m 4 - 5 2.20 m 0.18 T/m 2.20 m 0.70 T/m 0.88 T/m no 1.23 T/m 5 - 6 3.48 m 0.18 T/m 1.18 m 0.24 T/m 0.42 T/m no 0.59 T/m 6 - 7 3.12 m 0.18 T/m 3.12 m 0.70 T/m 0.88 T/m no 1.23 T/m

B

2 - 3 2.90 m 0.18 T/m 2.25 m 0.54 T/m 0.72 T/m no 1.01 T/m 3 - 4 2.65 m 0.18 T/m 1.40 m 0.37 T/m 0.55 T/m no 0.77 T/m

Ancho Tributario B (m)

P. Propio Viga

Peso Aligerado

Peso Acabado

Longitud muro (m)

Peso de Muro

Longitud muro (m)

Peso de Muro

Carga Muerta (Wm)

Carga Viva (Wv)

B 4 - 5 2.20 m 0.18 T/m 2.20 m 0.70 T/m 0.88 T/m no 1.23 T/m 5 - 6 3.48 m 0.18 T/m 1.22 m 0.25 T/m 0.43 T/m no 0.60 T/m 6 - 7 3.12 m 0.18 T/m 0.00 m 0.00 T/m 0.18 T/m no 0.25 T/m

C


D


2. SEGUNDO PISO









Para las vigas secundarias ya no se considera la carga viva, solo la carga muerta, por lo tanto no habra combinacion de carga2.2. VIGAS SECUNDARIAS Carga Ubicada en 3º Piso

Eje Eje Longuitud (m) P. Propio Viga Peso Muro 1.4 * Wm

A


B

2 - 3 2.90 m 0.18 T/m 2.10 m 0.51 T/m 0.69 T/m no 0.96 T/m 3 - 4 2.65 m 0.18 T/m 1.40 m 0.37 T/m 0.55 T/m no 0.77 T/m 4 - 5 2.20 m 0.18 T/m 2.20 m 0.70 T/m 0.88 T/m no 1.23 T/m 5 - 6 3.48 m 0.18 T/m 1.22 m 0.25 T/m 0.43 T/m no 0.60 T/m


P. Propio Viga

Peso Aligerado

Peso Acabado

Longitud muro (m) Peso Muro

Longitud muro (m)

Carga Muerta (Wm)

Carga Viva (Wv)

B

6 - 7 3.12 m 0.18 T/m 0.00 m 0.00 T/m 0.18 T/m no 0.25 T/m

C


D


3. TERCER PISO









Para las vigas secundarias ya no se considera la carga viva, solo la carga muerta, por lo tanto no habra combinacion de carga2.2. VIGAS SECUNDARIAS Carga Ubicada en la Azotea

Eje Eje Longuitud (m) P. Propio Viga Peso Muro 1.4 * Wm

A


B


C

2 - 3 2.90 m 0.18 T/m 0.00 m 0.00 T/m 0.18 T/m no 0.25 T/m


P. Propio Viga

Peso Aligerado

Peso Acabado

Longitud muro (m)

Peso Parapeto

Longitud muro (m)

Carga Muerta (Wm)

Carga Viva (Wv)

C 3 - 4 2.65 m 0.18 T/m 0.00 m 0.00 T/m 0.18 T/m no 0.25 T/m 4 - 5 2.20 m 0.18 T/m 0.00 m 0.00 T/m 0.18 T/m no 0.25 T/m 5 - 6 3.48 m 0.18 T/m 0.00 m 0.00 T/m 0.18 T/m no 0.25 T/m 6 - 7 3.12 m 0.18 T/m 0.00 m 0.00 T/m 0.18 T/m no 0.25 T/m

D


Carga Ubicada en 2º Piso

1.4 * Wm 1.7 * Wv

0.80 T/m 2.059 T/m 0.500 T/m 2.88 T/m 0.85 T/m 3.73 T/m0.80 T/m 2.059 T/m 0.500 T/m 2.88 T/m 0.85 T/m 3.73 T/m0.80 T/m 2.059 T/m 0.500 T/m 2.88 T/m 0.85 T/m 3.73 T/m0.97 T/m 2.832 T/m 0.606 T/m 3.96 T/m 1.03 T/m 4.99 T/m0.97 T/m 2.467 T/m 0.606 T/m 3.45 T/m 1.03 T/m 4.48 T/m0.97 T/m 2.832 T/m 0.606 T/m 3.96 T/m 1.03 T/m 4.99 T/m0.86 T/m 2.197 T/m 0.536 T/m 3.08 T/m 0.91 T/m 3.99 T/m0.86 T/m 2.197 T/m 0.536 T/m 3.08 T/m 0.91 T/m 3.99 T/m0.86 T/m 2.197 T/m 0.536 T/m 3.08 T/m 0.91 T/m 3.99 T/m1.03 T/m 3.315 T/m 0.644 T/m 4.64 T/m 1.09 T/m 5.74 T/m1.03 T/m 2.936 T/m 0.644 T/m 4.11 T/m 1.09 T/m 5.20 T/m1.03 T/m 3.171 T/m 0.644 T/m 4.44 T/m 1.09 T/m 5.53 T/m1.10 T/m 2.994 T/m 0.686 T/m 4.19 T/m 1.17 T/m 5.36 T/m1.10 T/m 3.476 T/m 0.686 T/m 4.87 T/m 1.17 T/m 6.03 T/m1.10 T/m 2.774 T/m 0.686 T/m 3.88 T/m 1.17 T/m 5.05 T/m0.58 T/m 2.230 T/m 0.362 T/m 3.12 T/m 0.62 T/m 3.74 T/m0.58 T/m 2.230 T/m 0.362 T/m 3.12 T/m 0.62 T/m 3.74 T/m0.58 T/m 2.230 T/m 0.362 T/m 3.12 T/m 0.62 T/m 3.74 T/m

Para las vigas secundarias ya no se considera la carga viva, solo la carga muerta, por lo tanto no habra combinacion de cargaCarga Ubicada en 2º Piso

1.7 * Wv

0.00 T/m 1.23 T/m0.00 T/m 1.23 T/m0.00 T/m 1.23 T/m0.00 T/m 0.59 T/m0.00 T/m 1.23 T/m0.00 T/m 1.01 T/m0.00 T/m 0.77 T/m

Peso Tabiqueria

Carga Muerta (Wm)

Carga Viva (Wv)

Wu = 1.4 (Wm) + 1.7 (Wv)

Wu = 1.4 (Wm) + 1.7 (Wv)

0.00 T/m 1.23 T/m0.00 T/m 0.60 T/m0.00 T/m 0.25 T/m0.00 T/m 1.01 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 1.23 T/m0.00 T/m 1.23 T/m0.00 T/m 0.55 T/m0.00 T/m 1.23 T/m0.00 T/m 1.23 T/m

Carga Ubicada en 3º Piso

1.4 * Wm 1.7 * Wv


Para las vigas secundarias ya no se considera la carga viva, solo la carga muerta, por lo tanto no habra combinacion de cargaCarga Ubicada en 3º Piso

1.7 * Wv

0.00 T/m 1.23 T/m0.00 T/m 1.23 T/m0.00 T/m 1.23 T/m0.00 T/m 0.59 T/m0.00 T/m 1.23 T/m0.00 T/m 0.96 T/m0.00 T/m 0.77 T/m0.00 T/m 1.23 T/m0.00 T/m 0.60 T/m

Peso Tabiqueria

Carga Muerta (Wm)

Carga Viva (Wv)

Wu = 1.4 (Wm) + 1.7 (Wv)

Wu = 1.4 (Wm) + 1.7 (Wv)

0.00 T/m 0.25 T/m0.00 T/m 0.96 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 1.23 T/m0.00 T/m 1.23 T/m0.00 T/m 0.55 T/m0.00 T/m 1.23 T/m0.00 T/m 1.23 T/m

Carga Ubicada en Azotea

1.4 * Wm 1.7 * Wv


Para las vigas secundarias ya no se considera la carga viva, solo la carga muerta, por lo tanto no habra combinacion de cargaCarga Ubicada en la Azotea

1.7 * Wv

0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m

Peso Tabiqueria

Carga Muerta (Wm)

Carga Viva (Wv)

Wu = 1.4 (Wm) + 1.7 (Wv)

Wu = 1.4 (Wm) + 1.7 (Wv)

0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m0.00 T/m 0.25 T/m


PORTICOS A ANALIZAR - COMBINACIONES DE CARGA

PORTICO PRINCIPAL 2-2

Carga Viva ESTADO 1

Carga Muerta0.43 T/m 0.43 T/m 0.43 T/m

ESTADO 1: ESTADO PARA CARGA MUERTA 1.76 T/m 1.76 T/m 1.76 T/m2.19 T/m 2.19 T/m 2.19 T/m

1.76 T/m 1.76 T/m 1.76 T/m

2.80 m

0.85 T/m 0.85 T/m 0.85 T/m

2.80 m 2.90 T/m 2.90 T/m 2.90 T/m

3.75 T/m 3.75 T/m 3.75 T/m

2.90 T/m 2.90 T/m 2.90 T/m

2.80 m

0.85 T/m 0.85 T/m 0.85 T/m

2.80 m 2.88 T/m 2.88 T/m 2.88 T/m

3.73 T/m 3.73 T/m 3.73 T/m

2.88 T/m 2.88 T/m 2.88 T/m 3.90 m

3.90 m

A B C D

4.25 m 2.25 m 4.25 m

A B C D4.25 m 2.25 m 4.25 m ESTADO 2

ESTADO 2: ESTADO PARA CARGA VIVA 0.43 T/m 0.43 T/m

1.76 T/m 1.76 T/m 1.76 T/m

0.43 T/m 0.43 T/m 2.19 T/m 1.76 T/m 2.19 T/m

2.80 m 2.80 m

2.80 m 0.85 T/m

2.90 T/m 2.90 T/m 2.90 T/m

0.85 T/m 3.75 T/m

2.80 m 2.80 m

2.80 m 0.85 T/m 0.85 T/m

2.88 T/m 2.88 T/m 2.88 T/m

0.85 T/m 0.85 T/m 3.73 T/m 3.73 T/m3.90 m 3.90 m

3.90 mA B C D

A B C D 4.25 m 2.25 m 4.25 m4.25 m 2.25 m 4.25 m

ESTADO 3

ESTADO 3: ESTADO PARA CARGA VIVA

0.43 T/m0.43 T/m 1.76 T/m 1.76 T/m 1.76 T/m

2.19 T/m

2.80 m 2.80 m 2.80 m0.85 T/m 0.85 T/m

0.85 T/m 0.85 T/m 2.90 T/m 2.90 T/m 2.90 T/m3.75 T/m 3.75 T/m

2.80 m 2.80 m 2.80 m0.85 T/m

0.85 T/m 2.88 T/m 2.88 T/m 2.88 T/m3.73 T/m

3.90 m 3.90 m3.90 m

A B C D A B C D4.25 m 2.25 m 4.25 m 4.25 m 2.25 m 4.25 m


0.43 T/m 0.43 T/m

2.80 m

0.85 T/m 0.85 T/m

2.80 m

0.85 T/m 0.85 T/m

3.90 m

A B C D4.25 m 2.25 m 4.25 m


0.43 T/m 0.43 T/m

2.80 m

0.85 T/m 0.85 T/m

2.80 m

0.85 T/m 0.85 T/m

3.90 m

A B C D4.25 m 2.25 m 4.25 m

ESTADO 4

0.43 T/m 0.43 T/m

1.76 T/m 1.76 T/m 1.76 T/m

2.19 T/m 2.19 T/m

0.85 T/m 0.85 T/m

2.90 T/m 2.90 T/m 2.90 T/m

3.75 T/m 3.75 T/m

0.85 T/m 0.85 T/m

2.88 T/m 2.88 T/m 2.88 T/m

3.73 T/m 3.73 T/m

A B C D4.25 m 2.25 m 4.25 m

ESTADO 5

0.43 T/m 0.43 T/m1.76 T/m 1.76 T/m 1.76 T/m

2.19 T/m 2.19 T/m

0.85 T/m 0.85 T/m2.90 T/m 2.90 T/m 2.90 T/m3.75 T/m 3.75 T/m

0.85 T/m 0.85 T/m2.88 T/m 2.88 T/m 2.88 T/m

3.73 T/m 3.73 T/m

A B C D4.25 m 2.25 m 4.25 m


ELEMENTOS INERCIAS ESTADO 1 MOMENTOS DE EMPOTRAMIENTO

VP 89322.9167 M111 -5.62 Tn-m M1112 -1.57 Tn-m M124 -5.62 Tn-mVS 56250.0000 M111 5.62 Tn-m M1211 1.57 Tn-m M412 5.62 Tn-m

COLUMNA 32552.0833 M29 -5.64 Tn-m M910 -1.58 Tn-m M105 -5.64 Tn-m M92 5.64 Tn-m M109 1.58 Tn-m M510 5.64 Tn-m

NUDO 3 = 6 I / L FD M37 -3.29 Tn-m M78 -0.92 Tn-m M86 -3.29 Tn-mK37 210.1716 0.6439 M73 3.29 Tn-m M87 0.92 Tn-m M68 3.29 Tn-mK32 116.2574 0.3561

Σ 326.4290 1.00003 0.3561 0.6439 0.2905

NUDO 2 = 5 I / L FD 0.6361 -3.2949 3.2949K21 116.2574 0.2626 0.9469 1.7119 0.8559K29 210.1716 0.4748 0.0186 -0.4688 -0.9376K23 116.2574 0.2626 0.1604 0.2899 0.1449

Σ 442.6864 1.0000 0.0029 -0.1352 -0.27040.0471 0.0852 0.0426

NUDO 1 = 4 I / L FD -0.0057 0.0033 0.0067K12 116.2574 0.2836 0.0008 0.0015 0.0008

K111 210.1716 0.5127 -0.0009 -0.0019 -0.0038K113 83.4669 0.2036 0.0010 0.0018 0.0009

Σ 409.8959 1.0000 -0.0002 -0.0010 -0.00210.0005 0.0008 0.0004

NUDO 7 = 8 I / L FD -0.0003 -0.0006

K73 210.1716 0.2905 1.8074 -1.8077

K79 116.2574 0.1607 3.1326

K78 396.9907 0.5488

Σ 723.4197 1.0000 2.80 m

NUDO 9 - 10 I / L FD -1.1338

K97 116.2574 0.1385

K92 210.1716 0.2503 1.8795 0.0003

K911 116.2574 0.1385 -0.0005 -0.0002

K910 396.9907 0.4728 0.0005 0.0012Σ 839.6772 1.0000 -0.0019 -0.0006

0.0004 0.0062NUDO 11 - 12 I / L FD -0.0114 -0.0011

K111 210.1716 0.2605 0.0236 0.0190K119 116.2574 0.1441 0.0059 0.0018K1112 396.9907 0.4920 0.0802 -0.1410K1114 83.4669 0.1034 0.0371 -0.0748

Σ 806.8866 1.0000 0.4735 -0.68541.2721 -0.2593

2 0.2626 0.2626 9 0.1385

0.4748 0.2503

0.7967 -5.6407 5.64071.2721 2.2998 1.14990.0047 -0.6195 -1.23910.0371 0.0671 0.0335

PORTICO PRINCIPAL 2-2 - DESARROLLO DE 3 COMBINACIONES POR CROSS

0.0250 -0.1275 -0.25490.0059 0.0106 0.00530.0025 0.0172 0.0344-0.0114 -0.0205 -0.01030.0012 0.0056 0.0112-0.0019 -0.0034 -0.00170.0002 0.0010 0.0021-0.0005 -0.0009 -0.0004

0.0002 0.0005

2.1317 -4.0109

5.3712

2.80 m

2.3114 -1.3829

-0.0002 -0.0002

0.0005 0.0001-0.0009 -0.00080.0024 0.0006-0.0057 -0.00290.0051 0.00310.0029 -0.02300.0500 0.00950.0186 -0.21540.0095 -0.07050.6361 -0.74071.5933 -0.3427

1 0.2036 0.2836 11 0.1441

0.5127 0.2605

-5.6177 5.61771.1439 2.8804 1.4402

-0.6695 -1.33900.0068 0.0171 0.0086

-0.1947 -0.38940.0359 0.0903 0.0452

-0.0208 -0.04160.0036 0.0092 0.0046

-0.0026 -0.00530.0017 0.0043 0.0021

-0.0007 -0.00150.0003 0.0009 0.0004

-0.0002 -0.0003

1.1923 -3.5040 5.3416

3.90 m

0.5961

0.0002

0.0008

0.00180.01790.00340.5720

13 14

4.25 m

7 80.5488 0.5488 0.2905

0.1607 -0.9235 0.9235 0.1607 -3.2949-0.8559

-0.5187 -1.7711 -0.8855-0.3427 1.1285 2.2570 0.6610 1.1949-0.1496 -0.5108 -0.2554 0.4188 -0.1815-0.0705 0.0050 0.0099 0.0029 0.00530.0037 0.0126 0.0063 -0.0108 -0.00600.0095 0.0029 0.0058 0.0017 0.0031-0.0021 -0.0072 -0.0036 -0.0065 -0.00130.0031 0.0031 0.0062 0.0018 0.0033-0.0011 -0.0039 -0.0020 -0.0014 -0.00070.0006 0.0011 0.0022 0.0006 0.0012

-0.0003 -0.0011 -0.0006 -0.0003 -0.0002

0.0001 0.0003 0.0006 0.0002 0.0003

-1.0680 -2.0645 -0.0001

2.0645 1.0680 -3.1326

-2.9465 2.9462 1.1338

-0.0002 -0.0005 -0.0001

0.0009 0.0005 0.0001

-0.0010 -0.0019 -0.0006

0.0040 0.0020 0.0003-0.0046 -0.0092 -0.00270.0212 0.0106 0.0009-0.0220 -0.0441 -0.01290.0649 0.0325 0.0008-0.0368 -0.0736 -0.0216-0.4815 -0.2408 0.00151.4300 2.8601 0.8376-2.3404 -1.1702-1.5809 1.5809 0.33050.4728 0.4728 0.1385 100.1385 0.1385 0.2503

-5.6407-1.1499

-0.6854-0.3703 0.8376 1.5142

-0.1410 0.4560 -0.0610-0.1077 -0.0216 -0.03900.0190 0.0307 0.0292-0.0115 -0.0129 -0.02330.0062 0.0037 0.0043-0.0015 -0.0027 -0.00490.0012 0.0009 0.0009-0.0004 -0.0006 -0.0010

0.0003 0.0002 0.0002

-0.0001 -0.0001 -0.0002

-1.2912 1.2912 -5.3712

-3.2530 3.2527 1.3828

-0.0006 -0.0003 -0.0001

0.0007 0.0013 0.0004-0.0028 -0.0014 -0.00030.0030 0.0060 0.0018-0.0100 -0.0050 -0.00140.0126 0.0253 0.0074-0.0786 -0.0393 -0.00650.1050 0.2100 0.0615-0.7356 -0.3678 -0.01081.5570 3.1140 0.9119-2.5292 -1.2646-1.5745 1.5745 0.41880.4920 0.4920 0.1441 120.1034 0.1034 0.2605

-5.6177-1.4402

-0.53180.6547 1.6486

-0.1547 -0.04830.0442 0.1112

-0.0165 -0.00560.0053 0.0134

-0.0021 -0.00590.0013 0.0032

-0.0006 -0.00100.0003 0.0007

-0.0001 -0.0002

-0.7058 0.7057 -5.3418

-0.3529

-0.0001 0.3529-0.0003 0.0001

-0.0011 0.0006-0.0083 0.0027-0.0773 0.0221-0.2659 0.3274

15

2.25 m 4.25 m

ESTADO 2 MOMENTOS DE EMPOTRAMIENTO

M111 -5.62 Tn-m M1112M111 5.62 Tn-m M1211M29 -4.36 Tn-m M910 M92 4.36 Tn-m M109M37 -3.29 Tn-m M78M73 3.29 Tn-m M87

0.6439 0.3561 6 3 0.3561 0.6439

3.2949 -0.6361 0.4681 -3.2949-1.7119 -0.9469 1.0068 1.8201

-0.0160 -0.50270.5975 -0.0337 0.1847 0.3340-0.3629 -0.2008 -0.0095 -0.16640.0026 0.0161 0.0626 0.1132-0.0121 -0.0067 -0.0090 -0.01350.0015 0.0024 0.0080 0.0144-0.0025 -0.0014 -0.0019 -0.00650.0016 0.0005 0.0030 0.0055-0.0014 -0.0008 -0.0005 -0.00220.0006 0.0001 0.0010 0.0018

-0.0005 -0.0003 -0.0006

0.0002 1.6973 -1.6979

1.8076 -1.8074

-1.8797

-0.0001

0.0003 1.4949

-0.0004 -0.0010

0.0010 0.0015-0.0007 -0.00390.0048 0.0040-0.0033 -0.01790.0323 0.0313-0.1004 -0.0190-0.0675 0.0924

-0.0319-0.4735 0.5034-1.2721 0.93610.2626 0.2626 5 2 0.2626 0.2626

0.4748 0.4748

5.6407 -0.7967 0.7967 -4.3612-2.2998 -1.2721 0.9361 1.6923

0.0372 -0.41900.7571 -0.0267 -0.0319 -0.0577

-0.1220 -0.0675 0.0345 -0.0545-0.0195 -0.0031 -0.0190 -0.03430.0584 0.0323 0.0054 0.0315-0.0117 -0.0032 -0.0179 -0.03240.0087 0.0048 0.0019 0.0089-0.0024 -0.0006 -0.0039 -0.00700.0018 0.0010 0.0005 0.0019-0.0005 -0.0001 -0.0010 -0.0018

0.0005 0.0003 0.0005

-0.0001 1.7385 -3.2330

4.0111 -2.1316

-2.3115 2.1835

-0.0002 -0.0005

0.0005 0.0009-0.0011 -0.00190.0024 0.0039-0.0065 -0.00900.0161 0.0108-0.0062 -0.0095-0.0337 0.0690-0.0534 -0.0160

0.0745-0.6361 0.4681-1.5933 1.59330.2836 0.2036 4 1 0.2036 0.2836

0.5127 0.5127

5.6177 -5.6177-2.8804 -1.1439 1.1439 2.8804

-0.73060.8243 0.0535 0.1346-0.0965 -0.0383 -0.22720.0556 0.0495 0.1247-0.0112 -0.0044 -0.02870.0067 0.0078 0.0196-0.0117 -0.0046 -0.00470.0016 0.0028 0.0070-0.0020 -0.0008 -0.00120.0004 0.0006 0.0016

-0.0004 -0.0002 -0.0003

3.5039 -1.1923 1.2581 -3.4424

-0.5962 0.6291

-0.0001 0.0003

-0.0004 0.0014

-0.0023 0.0039-0.0022 0.0248-0.0192 0.0267-0.5720 0.5720

16 13

MOMENTOS DE EMPOTRAMIENTO

-1.22 Tn-m M124 -5.62 Tn-m1.22 Tn-m M412 5.62 Tn-m-1.58 Tn-m M105 -4.36 Tn-m1.58 Tn-m M510 4.36 Tn-m-0.74 Tn-m M86 -3.29 Tn-m0.74 Tn-m M68 3.29 Tn-m

7 80.2905 0.5488 0.5488 0.2905

3.2949 0.1607 -0.7442 0.7442 0.1607 -3.29490.9100 -0.9100-1.0054 -0.5562 -1.8992 -0.94960.1670 -0.2318 1.2101 2.4202 0.7088 1.2813-0.3327 -0.1841 -0.6285 -0.3143 0.2813 -0.20860.0566 -0.0302 0.0663 0.1326 0.0388 0.0702-0.0269 -0.0149 -0.0509 -0.0254 -0.0298 -0.01890.0072 0.0174 0.0203 0.0407 0.0119 0.0215-0.0131 -0.0072 -0.0247 -0.0123 -0.0104 -0.00490.0027 0.0049 0.0076 0.0152 0.0044 0.0080-0.0044 -0.0024 -0.0084 -0.0042 -0.0023 -0.00160.0009 0.0011 0.0022 0.0044 0.0013 0.0024

-0.0012 -0.0007 -0.0023 -0.0011 -0.0005 -0.0005

0.0003 0.0006 0.0012 0.0003 0.0006

3.0555 -1.0038 -2.0515 -0.0001

2.0515 1.0038 -3.0555

-0.8593 -2.3948 2.3943 0.8593

-0.0004 -0.0009 -0.0003

0.0005 0.0018 0.0009 0.0002

-0.0003 -0.0018 -0.0036 -0.0010

0.0021 0.0072 0.0036 0.0007-0.0012 -0.0079 -0.0157 -0.00460.0098 0.0336 0.0168 0.0022-0.0036 -0.0354 -0.0707 -0.02070.0349 0.1191 0.0596 0.0060-0.0075 -0.1016 -0.2033 -0.0595-0.0603 -0.2059 -0.1030 0.0194-0.0920 0.9606 1.9212 0.5626-0.4636 -1.5831 -0.7915-0.2781 -1.5809 1.5809 0.3544

9 0.1385 0.4728 0.4728 0.1385

0.2503 0.1385 0.1385 0.2503

4.3612 -4.36120.8462 -0.8462-0.8381 -0.4636-0.0289 -0.4042 0.5626 1.0171

-0.1090 -0.0603 0.5000 0.0134-0.0172 -0.1257 -0.0595 -0.10760.0631 0.0349 0.0411 0.0429-0.0162 -0.0159 -0.0207 -0.03740.0178 0.0098 0.0062 0.0081-0.0035 -0.0026 -0.0046 -0.00830.0038 0.0021 0.0014 0.0019-0.0009 -0.0007 -0.0010 -0.0019

0.0009 0.0005 0.0003 0.0005

-0.0002 -0.0003 -0.0005

4.2792 -1.0257 1.0256 -4.2792

-1.3365 -3.0912 3.0907 1.3364

-0.0003 -0.0011 -0.0005 -0.0001

0.0003 0.0011 0.0023 0.0007-0.0014 -0.0047 -0.0023 -0.00050.0011 0.0049 0.0099 0.0029-0.0051 -0.0176 -0.0088 -0.00230.0049 0.0210 0.0421 0.0123-0.0317 -0.1083 -0.0542 -0.01040.0174 0.1404 0.2808 0.0822-0.2514 -0.8584 -0.4292 -0.0298-0.0302 1.7074 3.4149 1.0000-0.8083 -2.7602 -1.3801-0.2318 -1.2159 1.2159 0.2813

11 0.1441 0.4920 0.4920 0.1441

0.2605 0.1034 0.1034 0.2605

5.6177 -5.61771.4402 -1.4402-1.4613 -0.58030.0673 0.7180 1.8079-0.4544 -0.1805 -0.11170.0623 0.0590 0.1486-0.0573 -0.0228 -0.02100.0098 0.0088 0.0223-0.0093 -0.0037 -0.00890.0035 0.0021 0.0052-0.0025 -0.0010 -0.00180.0008 0.0005 0.0012

-0.0006 -0.0002 -0.0004

5.2162 -0.7885 0.7884 -5.2165

-0.3942

-0.0001 0.3942

-0.0005 0.0002

-0.0018 0.0010-0.0114 0.0044-0.0902 0.0295-0.2902 0.3590

14

4.25 m 2.25 m

ESTADO 4

0.6439 0.3561 6 33.2949 -0.4681-1.8201 -1.0068

0.6407 0.0074-0.4173 -0.23080.0351 0.0237-0.0379 -0.02100.0108 0.0045-0.0098 -0.00540.0040 0.0010-0.0032 -0.00180.0012 0.0003

-0.0009 -0.0005

0.0003

1.6977 -1.6974

-1.4953

-0.0003

0.0005

-0.0009

0.0021-0.00270.0090-0.01050.0475-0.11540.0149

-0.5034-0.9361

10 0.2626 0.2626 5 20.4748

4.3612 -0.7967-1.6923 -0.9361

0.5086 -0.0618

0.0269 0.0149-0.0538 -0.01160.0858 0.0475-0.0187 -0.00490.0162 0.0090-0.0042 -0.00100.0037 0.0021-0.0009 -0.0002

0.0010 0.0005

-0.0002

3.2333 -1.7384

-2.1839

-0.0005

0.0010-0.00200.0045-0.00990.0237-0.02320.0074-0.1236

-0.4681-1.5933

12 0.2836 0.2036 4 10.5127

5.6177-2.8804 -1.1439

0.9039-0.2235 -0.08880.0743-0.0419 -0.01660.0111-0.0179 -0.00710.0026-0.0036 -0.00140.0006

-0.0008 -0.0003

3.4421 -1.2582

-0.6291

-0.0002

-0.0007

-0.0036-0.0083-0.0444-0.5720

15 16 13

4.25 m

MOMENTOS DE EMPOTRAMIENTO

M111 -4.34 Tn-m M1112 -1.57 Tn-m M124 -4.34 Tn-mM111 4.34 Tn-m M1211 1.57 Tn-m M412 4.34 Tn-mM29 -5.64 Tn-m M910 -1.22 Tn-m M105 -5.64 Tn-m M92 5.64 Tn-m M109 1.22 Tn-m M510 5.64 Tn-mM37 -2.66 Tn-m M78 -0.92 Tn-m M86 -2.66 Tn-mM73 2.66 Tn-m M87 0.92 Tn-m M68 2.66 Tn-m

70.3561 0.6439 0.2905 0.5488

0.6599 -2.6552 2.6552 0.1607 -0.92350.7106 1.2847 0.64230.0462 -0.3449 -0.6897 -0.3815 -1.30280.1064 0.1923 0.0961 -0.3752 0.83010.0140 -0.0800 -0.1601 -0.0886 -0.30240.0235 0.0425 0.0213 -0.0941 -0.0517-0.0014 0.0181 0.0362 0.0200 0.0683-0.0060 -0.0108 -0.0054 -0.0003 -0.01400.0002 0.0029 0.0057 0.0032 0.0108-0.0011 -0.0020 -0.0010 0.0007 -0.00180.0001 0.0003 0.0006 0.0003 0.0012-0.0001 -0.0002 -0.0001 0.0000 -0.0002

0.0000 0.0001 0.0001 0.0002

1.5523 -1.5523 0.0000 0.0000

2.6012 -0.9155 -1.6858

-1.1612 -2.8237

0.0000

1.8548 0.0000 -0.0001

0.0001 0.0000 0.0000

-0.0005 0.0000 0.00000.0004 0.0002 -0.0005-0.0030 0.0014 0.0047-0.0027 0.0016 -0.00440.0118 -0.0006 -0.00210.0280 0.0100 0.03430.0532 -0.1882 -0.64250.0924 -0.0443 1.57190.3553 -0.7505 -2.56281.3198 -0.1908 -1.2224

0.2626 0.2626 9 0.1385 0.4728

0.4748 0.2503 0.1385

0.6152 -5.6407 5.64071.3198 2.3859 1.1929-0.0289 -0.6784 -1.3568 -0.75050.0924 0.1671 0.0836 -0.2522

0.0102 -0.1701 -0.3402 -0.18820.0280 0.0507 0.0253 -0.0652-0.0008 -0.0005 -0.0011 -0.0006-0.0027 -0.0049 -0.0025 -0.00460.0002 0.0012 0.0025 0.00140.0004 0.0007 0.0004 -0.00010.0000 0.0000 0.0000 0.00000.0001 0.0003 0.0001 -0.0001

0.0000 0.0000 0.0000

2.0339 -3.8887 0.0000

5.2450 -1.2601

1.9107 -1.1133 -2.6747

0.0001 0.0000 0.0000

0.0000 0.0000 0.00010.0002 -0.0001 -0.00040.0004 0.0000 0.0005-0.0014 -0.0001 -0.0004-0.0016 0.0007 0.00160.0140 -0.0092 -0.03150.0203 -0.0003 0.04590.0462 -0.1305 -0.4456-0.0579 -0.0941 1.05210.6599 -0.5044 -1.72241.2304 -0.3752 -1.5745

0.2036 0.2836 11 0.1441 0.4920

0.5127 0.2605 0.1034

-4.3382 4.33820.8834 2.2244 1.1122

-0.4559 -0.9118 -0.3621-0.0415 -0.1046 -0.0523

-0.1180 -0.2359 -0.09370.0146 0.0368 0.0184

-0.0083 -0.0167 -0.0066-0.0012 -0.0029 -0.0015

-0.0001 -0.0002 -0.00010.0003 0.0008 0.0004

-0.0001 -0.0002 -0.00010.0000 0.0000 0.0000

0.0000 0.0000 0.0000

0.8556 -2.7663 4.2506 -0.4626

0.4278 -0.2313

0.0000 0.0000

0.0002 0.0000

-0.0006 0.00000.0073 -0.0033-0.0208 -0.04680.4417 -0.1811

14

4.25 m 2.25 m

80.5488 0.2905 0.6439 0.3561 6

0.9235 0.1607 -2.6552 2.6552 -0.6599-0.6423 -1.2847 -0.7106

-0.65141.6603 0.4862 0.8790 0.4395 -0.0645-0.1512 0.4603 -0.1207 -0.2414 -0.1335-0.1034 -0.0303 -0.0547 -0.0274 0.00560.0342 0.0100 0.0070 0.0140 0.0077-0.0281 -0.0082 -0.0149 -0.0074 -0.00010.0054 -0.0013 0.0024 0.0048 0.0027-0.0036 -0.0011 -0.0019 -0.0010 -0.00010.0006 -0.0001 0.0004 0.0007 0.0004-0.0004 -0.0001 -0.0002 -0.0001 0.0000

0.0001 0.0000 0.0000 0.0001 0.0001

-0.0001 0.0000 0.0000 0.0000

0.0000 1.5523 -1.5523

1.6858 0.9154 -2.6012

2.8237 1.1612 -1.8547

0.0000 0.0000 0.0000

0.0000 0.0000 -0.0001

0.0001 0.0000 0.0002

0.0000 -0.0001 -0.0003-0.0010 -0.0003 0.00130.0023 -0.0005 -0.0002-0.0087 -0.0026 0.0039-0.0010 -0.0041 0.01130.0685 0.0201 -0.0668-0.3213 -0.0151 -0.12913.1438 0.9207-1.2814 -0.35531.2224 0.2431 -1.31980.4728 0.1385 10 0.2626 0.2626 50.1385 0.2503 0.4748

-5.6407 5.6407 -0.6152-1.1929 -2.3859 -1.3198

0.9207 1.6644 0.8322 0.0146

0.3081 -0.1167 -0.2333 -0.12910.0201 0.0363 0.0181 0.00570.0134 0.0102 0.0204 0.0113-0.0026 -0.0046 -0.0023 -0.00090.0005 -0.0002 -0.0003 -0.0002-0.0003 -0.0005 -0.0003 0.00000.0001 -0.0002 -0.0005 -0.00030.0000 0.0000 0.0000 0.0000

0.0000 -0.0001 -0.0001 -0.0001

0.0000 0.0000 0.0000

1.2601 -5.2450 3.8887 -2.0339

2.6747 1.1133 -1.9107

0.0000 0.0000 0.0000

0.0001 0.0000 -0.0001-0.0002 0.0000 -0.00010.0010 0.0003 -0.0001-0.0002 -0.0001 -0.00180.0033 0.0010 0.0056-0.0157 -0.0013 0.01140.0917 0.0269 -0.0645-0.2228 0.0100 0.02922.1042 0.6162-0.8612 -0.65991.5745 0.4603 -1.23040.4920 0.1441 12 0.2836 0.2036 40.1034 0.2605 0.5127

-4.3382 4.3382-1.1122 -2.2244 -0.8834

0.4424 1.1140 0.55700.0264 0.0528 0.0210

0.0193 0.0486 0.02430.0103 0.0206 0.0082

0.0007 0.0017 0.0009-0.0017 -0.0033 -0.0013

0.0002 0.0005 0.00030.0000 -0.0001 0.0000

0.0000 0.0001 0.0000

0.0000 0.0001 0.0000

0.4626 -4.2506 2.7663 -0.8556

-0.4278

0.2313 0.0000

0.0000 0.0000

0.0001 -0.00070.0003 0.00410.0096 0.01050.2212 -0.4417

15 16

4.25 m



M111 -5.62 Tn-m M1112 ### M124 ###M111 5.62 Tn-m M1211 1.57 Tn-m M412 4.34 Tn-mM29 -4.36 Tn-m M910 ### M105 ### M92 4.36 Tn-m M109 1.58 Tn-m M510 5.64 Tn-mM37 -3.29 Tn-m M78 ### M86 ###M73 3.29 Tn-m M87 0.92 Tn-m M68 2.66 Tn-m

COEFICIENTES DE GIRO SIMETRIA COEF. DE DESPLAZAMIENTO

NUDO 1 NUDO 4 K δ

K K I (cm4) L (cm) µ µ µ µ δ113 83.47 -0.375 δ21210.17 89322.92 cm4 425.00 cm µ111 -0.256 µ412 -0.256 δ1114 83.47 -0.375 δ91183.47 32552.08 cm4 390.00 cm µ113 -0.102 µ416 -0.102 δ1215 83.47 -0.375 δ1012116.26 32552.08 cm4 280.00 cm µ12 -0.142 µ45 -0.142 δ416 83.47 -0.375 δ54

ΣK 409.90 -0.500 -0.500 Σ 333.87 ΣNUDO 2 NUDO 5

K K I (cm4) L (cm) µ µ µ µ

K21 116.26 32552.08 cm4 280.00 cm µ21 -0.131 µ54 -0.131

K29 210.17 89322.92 cm4 425.00 cm µ29 -0.237 µ510 -0.237

-0.3

219

K23 116.26 32552.08 cm4 280.00 cm µ23 -0.131 µ56 -0.131 5º 3 -3.2949

ΣK 442.69 -0.500 -0.500 -0.1781

NUDO 3 NUDO 6 0.5034 0.9100K K I (cm4) L (cm) µ µ µ µ 0.6010 1.0866

K32 116.26 32552.08 cm4 280.00 cm µ32 -0.178 µ65 -0.178 0.6208 1.1224K37 210.17 89322.92 cm4 425.00 cm µ37 -0.322 µ68 -0.322 0.6253 1.1305ΣK 326.43 -0.500 -0.500 0.6263 1.1321

NUDO 7 NUDO 8 0.6264 1.1324K K I (cm4) L (cm) µ µ µ µ 0.6264 1.1325

K73 210.17 89322.92 cm4 425.00 cm µ73 -0.145 µ86 -0.145 0.6265 1.1325K79 116.26 32552.08 cm4 280.00 cm µ79 -0.080 µ810 -0.080 0.6265 1.1325K78 396.99 89322.92 cm4 225.00 cm µ78 -0.274 µ87 -0.274 1.5865 -1.5865

ΣK 723.42 -0.500 -0.500NUDO 9 NUDO 10

K K I (cm4) L (cm) µ µ µ µ -0.3750 -0.0966K911 116.26 32552.08 cm4 280.00 cm µ911 -0.069 µ1012 -0.069 -0.1145K92 210.17 89322.92 cm4 425.00 cm µ92 -0.125 µ105 -0.125 -0.1181K97 116.26 32552.08 cm4 280.00 cm µ97 -0.069 µ108 -0.069 -0.1191K910 396.99 89322.92 cm4 225.00 cm µ910 -0.236 µ109 -0.236 -0.1194ΣK 839.68 -0.500 -0.500 -0.1194

NUDO 11 NUDO 12 -0.1195K K I (cm4) L (cm) µ µ µ µ -0.1195

K111 210.17 89322.92 cm4 425.00 cm µ111 -0.130 µ124 -0.130 -0.1195K119 116.26 32552.08 cm4 280.00 cm µ119 -0.072 µ1210 -0.072K1112 396.99 89322.92 cm4 225.00 cm µ1112 -0.246 µ1211 -0.246K1114 83.47 32552.08 cm4 390.00 cm µ1114 -0.052 µ1215 -0.052

ΣK 806.89 -0.500 -0.500 0.46810.46050.4574

PORTICO PRINCIPAL 2-2 - DESARROLLO DE LAS 2 COMBINACIONES POR KANI CON DESPLAZAMIENTO

K111K113K12

0.45460.45350.45320.45310.45310.45311.5326

-0.1313

-0.2

374

3º 2 -4.3612

-0.1313

0.4681 0.84620.4605 0.83250.4574 0.82680.4546 0.82180.4535 0.81980.4532 0.81920.4531 0.81910.4531 0.81910.4531 0.81911.7082 -3.2408

-0.3750 -0.0916-0.0651-0.0632-0.0628-0.0626-0.0625-0.0625-0.0625-0.0625

0.79670.84690.86090.86370.86430.86450.86460.86460.86462.1822

-0.1418

-0.2

564

1º 1 -5.6177

-0.1018

0.5720 1.44020.6080 1.53100.6181 1.55640.6201 1.56140.6205 1.5625

0.6207 1.56280.6207 1.56300.6207 1.56300.6207 1.56301.1310 -3.3133

-0.3750 -0.1081-0.1080-0.1096-0.1102-0.1104-0.1104-0.1104-0.1104-0.1104

0.5655

13

COEF. DE DESPLAZAMIENTO

K δ K δ

116.26 -0.375 δ32 116.26 -0.375116.26 -0.375 δ79 116.26 -0.375116.26 -0.375 δ810 116.26 -0.375116.26 -0.375 δ65 116.26 -0.375465.03 Σ 465.03

7

-0.1

453

-0.2

744

-0.2

744

-3.2949 6º 3.2949 2.3714 -0.9235 0.9235 -1.7317

-0.0804 -0.0804

-0.4442 -0.2457 -0.8390 0.6788 0.1988-0.5344 -0.2956 -1.0094 0.8067 0.2362-0.5532 -0.3060 -1.0450 0.8226 0.2409-0.5562 -0.3077 -1.0506 0.8242 0.2414-0.5566 -0.3079 -1.0513 0.8243 0.2414-0.5566 -0.3079 -1.0514 0.8243 0.2414-0.5566 -0.3079 -1.0514 0.8243 0.2414-0.5566 -0.3079 -1.0514 0.8243 0.2414-0.5566 -0.3079 -1.0514 0.8243 0.24143.3141 -1.1122 -2.2020 1.5207 1.0523

-0.3750 -0.1712 -0.3750-0.2031-0.2084-0.2096-0.2099-0.2100-0.2100-0.2100-0.2100

-0.2237 0.3584-0.2870 0.3847-0.2888 0.3820

-0.2870 0.3808-0.2865 0.3806-0.2864 0.3806-0.2864 0.3806-0.2864 0.3806-0.2864 0.3806-0.8806 1.0026

9

-0.1

252 -0.0692

-0.2

364

-0.2

364 -0.0692

-4.3612 4º 4.3612 2.7803 -1.5809 1.5809 -4.0597

-0.0692 -0.0692

-0.4044 -0.2237 -0.7639 1.2237 0.3584-0.5188 -0.2870 -0.9799 1.3138 0.3847-0.5221 -0.2888 -0.9861 1.3045 0.3820-0.5189 -0.2870 -0.9802 1.3005 0.3808-0.5179 -0.2865 -0.9783 1.2998 0.3806-0.5177 -0.2864 -0.9780 1.2997 0.3806-0.5177 -0.2864 -0.9779 1.2997 0.3806-0.5177 -0.2864 -0.9779 1.2997 0.3806-0.5177 -0.2864 -0.9779 1.2997 0.38064.1449 -1.0272 -2.2370 3.2025 1.3413

-4.1449-0.3750 -0.2260 -0.3750

-0.2094-0.2065-0.2056-0.2054-0.2053-0.2052-0.2052-0.2052

-0.3950 0.2997-0.4456 0.3486-0.4539 0.3495-0.4543 0.3494-0.4544 0.3495-0.4545 0.3495-0.4545 0.3496-0.4545 0.3496-0.4545 0.3496-1.1954 1.0797

11

-0.1

302 -0.0720

-0.2

460

-0.2

460 -0.0720

-5.6177 2º 5.6177 4.0432 -1.5745 1.5745 -2.7637

-0.0517 -0.0517

-0.7141 -0.28361 -1.3489 1.0233 0.2151-0.8055 -0.3199 -1.5215 1.1905 0.2503-0.8206 -0.3259 -1.5501 1.1935 0.2509-0.8212 -0.3261 -1.5512 1.1930 0.2508-0.8214 -0.3262 -1.5516 1.1934 0.2509

-0.8216 -0.3263 -1.5519 1.1936 0.2510-0.8216 -0.3263 -1.5520 1.1936 0.2510-0.8216 -0.3263 -1.5520 1.1936 0.2510-0.8217 -0.3263 -1.5520 1.1936 0.25105.5374 -0.8571 -3.4849 2.4098 0.6956

-0.3750 -0.1888 -0.3750-0.2019-0.2037-0.2043-0.2045-0.2045-0.2045-0.2045-0.2045

-0.4286 0.3478

14 15

8

-0.1

453

-0.3

219

-2.6552 12º 2.6552 2.6552 6 11º-0.1781

0.3594 -0.8548 -0.47280.4271 -0.7787 -0.43080.4355 -0.7872 -0.43540.4363 -0.7900 -0.43700.4364 -0.7905 -0.43730.4364 -0.7906 -0.43730.4364 -0.7906 -0.43730.4364 -0.7906 -0.43730.4364 -0.7906 -0.4373-2.5730 1.5103 -1.5103

0.1949 -0.3750 0.10280.1838 0.07290.1877 0.07290.1887 0.07340.1889 0.07350.1889 0.07350.1889 0.07350.1889 0.07350.1889 0.0735

-0.6599-0.6983-0.7101

-0.7097-0.7092-0.7091-0.7091-0.7091-0.7091-1.8555

10

-0.1

252

-0.2

374 -0.1313

-5.6407 10º 5.6407 5.6407 5 9º-0.1313

0.6479 -1.1929 -0.65990.6956 -1.2625 -0.69830.6906 -1.2836 -0.71010.6885 -1.2830 -0.70970.6881 -1.2822 -0.70920.6881 -1.2819 -0.70910.6881 -1.2819 -0.70910.6881 -1.2819 -0.70910.6881 -1.2819 -0.7091-5.5464 3.7649 -1.9094

0.1970 -0.3750 0.11310.2252 0.11760.2313 0.12300.2310 0.12330.2307 0.12320.2306 0.12320.2306 0.12320.2306 0.12320.2306 0.1232

-0.6152-0.6105-0.6156-0.6143-0.6143-0.6144-0.6144-0.6144-0.6144-1.9379

12

-0.1

302

-0.2

564 -0.1418

-4.3382 8º 4.3382 4.3382 4 7º-0.1018

0.5417 -1.1122 -0.44170.6302 -1.1037 -0.43830.6318 -1.1128 -0.44190.6316 -1.1105 -0.44100.6318 -1.1105 -0.4410

0.6319 -1.1106 -0.44110.6319 -1.1107 -0.44110.6319 -1.1107 -0.44110.6319 -1.1107 -0.4411-4.1851 2.7488 -0.8109

0.1913 -0.3750 0.08500.1905 0.07050.1938 0.07160.1936 0.07130.1936 0.07130.1937 0.07130.1937 0.07130.1937 0.07130.1937 0.0713

-0.4054

16



M111 -4.34 Tn-m M1112 -1.57 Tn-m M124 -5.62 Tn-m

M111 4.34 Tn-m M1211 1.57 Tn-m M412 5.62 Tn-m

M29 -5.64 Tn-m M910 -1.58 Tn-m M105 -4.36 Tn-m

M92 5.64 Tn-m M109 1.58 Tn-m M510 4.36 Tn-m

M37 -2.66 Tn-m M78 -0.92 Tn-m M86 -3.29 Tn-m

M73 2.66 Tn-m M87 0.92 Tn-m M68 3.29 Tn-m

COEFICIENTES DE GIRO SIMETRIA COEF. DE DESPLAZAMIENTO

NUDO 1 NUDO 4 K δ

K K I (cm4) L (cm) µ µ µ µ δ113 83.47 -0.375 δ21

210.17 89322.92 cm4 425.00 cm µ111 -0.256 µ412 -0.256 δ1114 83.47 -0.375 δ911

83.47 32552.08 cm4 390.00 cm µ113 -0.102 µ416 -0.102 δ1215 83.47 -0.375 δ1012

116.26 32552.08 cm4 280.00 cm µ12 -0.142 µ45 -0.142 δ416 83.47 -0.375 δ54

ΣK 409.90 -0.500 -0.500 Σ 333.87 Σ

NUDO 2 NUDO 5

K K I (cm4) L (cm) µ µ µ µ

K21 116.26 32552.08 cm4 280.00 cm µ21 -0.131 µ54 -0.131

K29 210.17 89322.92 cm4 425.00 cm µ29 -0.237 µ510 -0.237

-0.3

219

K23 116.26 32552.08 cm4 280.00 cm µ23 -0.131 µ56 -0.131 5º 3 -2.6552

ΣK 442.69 -0.500 -0.500 -0.1781

NUDO 3 NUDO 6 0.3553 0.6423

K K I (cm4) L (cm) µ µ µ µ 0.4114 0.7438

K32 116.26 32552.08 cm4 280.00 cm µ32 -0.178 µ65 -0.178 0.4309 0.7789

K37 210.17 89322.92 cm4 425.00 cm µ37 -0.322 µ68 -0.322 0.4355 0.7873

ΣK 326.43 -0.500 -0.500 0.4364 0.7889

NUDO 7 NUDO 8 0.4365 0.7891

K K I (cm4) L (cm) µ µ µ µ 0.4365 0.7891

K73 210.17 89322.92 cm4 425.00 cm µ73 -0.145 µ86 -0.145 0.4365 0.7891

K79 116.26 32552.08 cm4 280.00 cm µ79 -0.080 µ810 -0.080 0.4365 0.7891

K78 396.99 89322.92 cm4 225.00 cm µ78 -0.274 µ87 -0.274 1.5115 -1.5115

ΣK 723.42 -0.500 -0.500

NUDO 9 NUDO 10

K K I (cm4) L (cm) µ µ µ µ -0.3750 -0.0721

K911 116.26 32552.08 cm4 280.00 cm µ911 -0.069 µ1012 -0.069 -0.0691

K92 210.17 89322.92 cm4 425.00 cm µ92 -0.125 µ105 -0.125 -0.0720

K97 116.26 32552.08 cm4 280.00 cm µ97 -0.069 µ108 -0.069 -0.0732

K910 396.99 89322.92 cm4 225.00 cm µ910 -0.236 µ109 -0.236 -0.0735

ΣK 839.68 -0.500 -0.500 -0.0735

NUDO 11 NUDO 12 -0.0736

K K I (cm4) L (cm) µ µ µ µ -0.0736

K111 210.17 89322.92 cm4 425.00 cm µ111 -0.130 µ124 -0.130 -0.0736

PORTICO PRINCIPAL 2-2 - DESARROLLO DE LAS 2 COMBINACIONES POR KANI CON DESPLAZAMIENTO

K111

K113

K12

K119 116.26 32552.08 cm4 280.00 cm µ119 -0.072 µ1210 -0.072

K1112 396.99 89322.92 cm4 225.00 cm µ1112 -0.246 µ1211 -0.246

K1114 83.47 32552.08 cm4 390.00 cm µ1114 -0.052 µ1215 -0.052

ΣK 806.89 -0.500 -0.500 0.6599

0.7117

0.7154

0.7134

0.7123

0.7121

0.7120

0.7120

0.7120

1.8605

-0.1313

-0.2

374

3º 2 -5.6407

-0.1313

0.6599 1.1929

0.7117 1.2866

0.7154 1.2934

0.7134 1.2897

0.7123 1.2878

0.7121 1.2873

0.7120 1.2872

0.7120 1.2871

0.7120 1.2871

1.9186 -3.7791

-0.3750 -0.1183

-0.1193

-0.1197

-0.1195

-0.1193

-0.1192

-0.1192

-0.1192

-0.1192

0.6152

0.6061

0.6115

0.6131

0.6135

0.6137

0.6137

0.6138

0.6138

1.9395

-0.1418

-0.2

564

1º 1 -4.3382

-0.1018

0.4417 1.1122

0.4351 1.0956

0.4390 1.1055

0.4402 1.1084

0.4405 1.1091

0.4406 1.1094

0.4406 1.1095

0.4406 1.1096

0.4406 1.1096

0.8099 -2.7494

-0.3750 -0.0905

-0.0718

-0.0709

-0.0713

-0.0713

-0.0714

-0.0714

-0.0714

-0.0714

0.4050

13

COEF. DE DESPLAZAMIENTO

K δ K δ

116.26 -0.375 δ32 116.26 -0.375

116.26 -0.375 δ79 116.26 -0.375

116.26 -0.375 δ810 116.26 -0.375

116.26 -0.375 δ65 116.26 -0.375

465.03 Σ 465.03

7

-0.1

453

-0.2

744

-2.6552 6º 2.6552 1.7317 -0.9235 0.9235

-0.0804

-0.2948 -0.1631 -0.5569 0.9188

-0.4108 -0.2272 -0.7759 1.0425

-0.4319 -0.2389 -0.8158 1.0538

-0.4344 -0.2403 -0.8205 1.0543

-0.4346 -0.2404 -0.8208 1.0542

-0.4346 -0.2404 -0.8208 1.0542

-0.4346 -0.2404 -0.8208 1.0542

-0.4346 -0.2404 -0.8208 1.0542

-0.4346 -0.2404 -0.8208 1.0542

2.5752 -1.0643 -1.5109 2.2111

-0.3750 -0.1730

-0.1836

-0.1877

-0.1890

-0.1893

-0.1893

-0.1893

-0.1893

-0.1893

-0.3443

-0.3936

-0.3963

-0.3948

-0.3943

-0.3942

-0.3942

-0.3942

-0.3942

-1.0288

9-0

.125

2 -0.0692

-0.2

364

-5.6407 4º 5.6407 4.0597 -1.5809 1.5809

-0.0692

-0.6224 -0.344299 -1.1757 0.8419

-0.7116 -0.3936 -1.3441 0.9475

-0.7165 -0.3963 -1.3534 0.9406

-0.7137 -0.3948 -1.3481 0.9373

-0.7129 -0.3943 -1.3465 0.9369

-0.7127 -0.3942 -1.3462 0.9368

-0.7127 -0.3942 -1.3462 0.9369

-0.7127 -0.3942 -1.3462 0.9369

-0.7127 -0.3942 -1.3462 0.9369

5.5024 -1.1371 -3.3365 2.1085

-5.5024

-0.3750 -0.2108

-0.2233

-0.2230

-0.2224

-0.2221

-0.2221

-0.2220

-0.2220

-0.2220

-0.2792

-0.3395

-0.3483

-0.3485

-0.3486

-0.3486

-0.3486

-0.3487

-0.3487

-1.0915

11

-0.1

302 -0.0720

-0.2

460

-4.3382 2º 4.3382 2.7637 -1.5745 1.5745

-0.0517

-0.5048 -0.20047 -0.9535 1.3982

-0.6138 -0.2437 -1.1593 1.5531

-0.6296 -0.2500 -1.1893 1.5545

-0.6299 -0.2502 -1.1899 1.5540

-0.6301 -0.2502 -1.1902 1.5544

-0.6303 -0.2503 -1.1905 1.5545

-0.6303 -0.2503 -1.1905 1.5545

-0.6303 -0.2503 -1.1906 1.5545

-0.6303 -0.2503 -1.1906 1.5545

4.1872 -0.6946 -2.4011 3.4930

-0.3750 -0.2007

-0.1942

-0.1934

-0.1938

-0.1939

-0.1939

-0.1939

-0.1939

-0.1939

-0.3473

14

8

-0.2

744

-0.1

453

-0.3

219

-2.3714 -3.2949 12º 3.2949 3.2949 6 11º-0.0804 -0.1781

0.2691 0.4864 -1.0607 -0.5867

0.3053 0.5519 -1.1097 -0.6138

0.3086 0.5579 -1.1297 -0.6249

0.3088 0.5582 -1.1332 -0.6269

0.3087 0.5581 -1.1337 -0.6271

0.3087 0.5581 -1.1338 -0.6272

0.3087 0.5581 -1.1338 -0.6272

0.3087 0.5581 -1.1338 -0.6272

0.3087 0.5581 -1.1338 -0.6272

1.1014 -3.3125 1.5854 -1.5854

-0.3750 0.1803 -0.3750 0.1191

0.2009 0.1157

0.2082 0.1186

0.2094 0.1193

0.2095 0.1194

0.2096 0.1194

0.2096 0.1194

0.2096 0.1194

0.2096 0.1194

0.2465 -0.4681

0.2775 -0.4534

0.2754 -0.4531

0.2745 -0.4512

0.2744 -0.4506

0.2744 -0.4505

0.2744 -0.4505

0.2744 -0.4505

0.2744 -0.4505

0.8574 -1.5282

10

-0.2

364 -0.0692

-0.1

252

-0.2

374 -0.1313

-2.7803 -4.3612 10º 4.3612 4.3612 5 9º-0.0692 -0.1313

0.2465 0.4457 -0.8462 -0.4681

0.2775 0.5016 -0.8197 -0.4534

0.2754 0.4979 -0.8192 -0.4531

0.2745 0.4962 -0.8157 -0.4512

0.2744 0.4960 -0.8147 -0.4506

0.2744 0.4960 -0.8145 -0.4505

0.2744 0.4960 -0.8145 -0.4505

0.2744 0.4960 -0.8145 -0.4505

0.2744 0.4960 -0.8145 -0.4505

1.2178 -4.1837 3.2283 -1.7001

-0.3750 0.2122 -0.3750 0.0831

0.2136 0.0660

0.2153 0.0666

0.2143 0.0663

0.2140 0.0661

0.2139 0.0661

0.2139 0.0661

0.2139 0.0661

0.2139 0.0661

0.4095 -0.7967

0.4548 -0.8500

0.4552 -0.8640

0.4551 -0.8647

0.4552 -0.8650

0.4552 -0.8651

0.4552 -0.8651

0.4552 -0.8651

0.4552 -0.8651

1.1848 -2.1808

12

-0.2

460 -0.0720

-0.1

302

-0.2

564 -0.1418

-4.0432 -5.6177 8º 5.6177 5.6177 4 7º-0.0517 -0.1018

0.2940 0.7402 -1.4402 -0.5720

0.3265 0.8222 -1.5367 -0.6103

0.3268 0.8230 -1.5620 -0.6203

0.3267 0.8227 -1.5632 -0.6208

0.3268 0.8229 -1.5637 -0.6210

0.3268 0.8230 -1.5639 -0.6211

0.3268 0.8230 -1.5640 -0.6211

0.3268 0.8230 -1.5640 -0.6211

0.3268 0.8230 -1.5640 -0.6211

0.8579 -5.5357 3.3127 -1.131882

-0.3750 0.1794 -0.3750 0.1042

0.1978 0.1064

0.2038 0.1101

0.2041 0.1103

0.2042 0.1103

0.2042 0.1103

0.2042 0.1104

0.2042 0.1104

0.2042 0.1104

0.4289 -0.5659

15 16


MOMENTOS VIGAS - PORTICOS X-X

MOMENTOS CALCULADOS CON EL SAP - PORTICO 2-2 MOMENTOS CALCULADOS CON EL SAP - PORTICO 3-3

ESTADO 1Mº Max. Negativos

ENVOLVENTEMº Max. Negativos

Izquierda Derecha Izquierda Derecha

VIGAS

Viga 1 - 11 3.800 Tn-m 5.493 Tn-m 4.230 Tn-m

VIGAS

Viga 1 - 11 5.138 Tn-m 7.619 Tn-m3.389 Tn-m 3.389 Tn-m 0.000 Tn-m 4.781 Tn-m 4.781 Tn-m

Viga 12 - 4 5.493 Tn-m 3.800 Tn-m 4.230 Tn-m Viga 12 - 4 7.619 Tn-m 5.138 Tn-mViga 2 - 9 4.412 Tn-m 5.458 Tn-m 3.950 Tn-m Viga 2 - 9 5.843 Tn-m 7.591 Tn-m

Viga 9 - 10 3.048 Tn-m 3.048 Tn-m 0.000 Tn-m Viga 9 - 10 4.464 Tn-m 4.464 Tn-mViga 10 - 5 5.458 Tn-m 4.412 Tn-m 3.950 Tn-m Viga 10 - 5 7.591 Tn-m 5.843 Tn-mViga 3 - 7 2.083 Tn-m 3.245 Tn-m 2.750 Tn-m Viga 3 - 7 2.547 Tn-m 4.177 Tn-mViga 7 - 8 2.180 Tn-m 2.180 Tn-m 0.000 Tn-m Viga 7 - 8 2.935 Tn-m 2.935 Tn-mViga 8 - 6 3.245 Tn-m 2.083 Tn-m 2.750 Tn-m Viga 8 - 6 4.177 Tn-m 2.547 Tn-m


Izquierda Derecha MOMENTOS CALCULADOS CON EL SAP - PORTICO 4-4

VIGAS

Viga 1 - 11 3.928 Tn-m 5.675 Tn-m 3.180 Tn-m3.414 Tn-m 3.414 Tn-m 0.000 Tn-m


Viga 12 - 4 5.675 Tn-m 3.928 Tn-m 4.550 Tn-m Izquierda Derecha

Viga 2 - 9 3.866 Tn-m 4.677 Tn-m 3.180 Tn-m

VIGAS

Viga 1 - 11 4.173 Tn-m 6.256 Tn-mViga 9 - 10 2.656 Tn-m 2.656 Tn-m 0.000 Tn-m 4.034 Tn-m 4.034 Tn-mViga 10 - 5 4.677 Tn-m 3.866 Tn-m 3.180 Tn-m Viga 12 - 4 6.256 Tn-m 4.173 Tn-mViga 3 - 7 2.125 Tn-m 3.474 Tn-m 3.100 Tn-m Viga 2 - 9 4.789 Tn-m 6.217 Tn-mViga 7 - 8 2.379 Tn-m 2.379 Tn-m 0.000 Tn-m Viga 9 - 10 3.752 Tn-m 3.752 Tn-mViga 8 - 6 3.474 Tn-m 2.125 Tn-m 3.100 Tn-m Viga 10 - 5 6.217 Tn-m 4.789 Tn-m

ESTADO 3Mº Max. Negativos Viga 3 - 7 2.254 Tn-m 3.787 Tn-m

Izquierda Derecha Viga 7 - 8 2.706 Tn-m 2.706 Tn-m

VIGAS

Viga 1 - 11 3.256 Tn-m 4.708 Tn-m 3.460 Tn-m Viga 8 - 6 3.787 Tn-m 2.254 Tn-m2.995 Tn-m 2.995 Tn-m 0.000 Tn-m

Viga 12 - 4 4.708 Tn-m 3.256 Tn-m 3.460 Tn-m MOMENTOS CALCULADOS CON EL SAP - PORTICO 5-5

Viga 2 - 9 4.519 Tn-m 5.641 Tn-m 4.280 Tn-mViga 9 - 10 3.086 Tn-m 3.086 Tn-m 0.000 Tn-m



Viga 3 - 7 1.975 Tn-m 3.014 Tn-m 3.430 Tn-m

VIGAS

Viga 1 - 11 5.848 Tn-m 8.654 Tn-mViga 7 - 8 2.011 Tn-m 2.011 Tn-m 0.000 Tn-m 5.408 Tn-m 5.459 Tn-mViga 8 - 6 3.014 Tn-m 1.975 Tn-m 3.430 Tn-m Viga 12 - 4 8.667 Tn-m 5.826 Tn-m

ESTADO 4Mº Max. Negativos Viga 2 - 9 6.603 Tn-m 8.634 Tn-m

Izquierda Derecha Viga 9 - 10 5.077 Tn-m 4.920 Tn-m

VIGAS

Viga 1 - 11 3.870 Tn-m 5.886 Tn-m 4.490 Tn-m Viga 10 - 5 8.342 Tn-m 6.436 Tn-m3.794 Tn-m 2.850 Tn-m 0.000 Tn-m Viga 3 - 7 2.736 Tn-m 4.360 Tn-m

Viga 12 - 4 4.577 Tn-m 3.305 Tn-m 3.490 Tn-m Viga 7 - 8 3.015 Tn-m 3.082 Tn-mViga 2 - 9 3.923 Tn-m 4.509 Tn-m 3.220 Tn-m Viga 8 - 6 4.382 Tn-m 2.709 Tn-m

Viga 9 - 10 2.450 Tn-m 3.536 Tn-m 0.000 Tn-mViga 10 - 5 5.864 Tn-m 4.465 Tn-m 4.210 Tn-m MOMENTOS CALCULADOS CON EL SAP - PORTICO 6-6





VIGAS

Viga 1 - 11 5.443 Tn-m 8.292 Tn-mIzquierda Derecha 4.828 Tn-m 4.663 Tn-m

VIGAS

Viga 1 - 11 3.305 Tn-m 4.577 Tn-m 3.490 Tn-m Viga 12 - 4 7.841 Tn-m 5.177 Tn-m2.850 Tn-m 3.794 Tn-m 0.000 Tn-m Viga 2 - 9 6.231 Tn-m 8.230 Tn-m

Mº Max. Posiitivo

PRIMER PISO

PRIMER PISOViga 11 - 12 Viga 11 - 12

SEGUNDO PISO

SEGUNDO PISO

TERCER PISO

TERCER PISO

Mº Max. Posiitivo

PRIMER PISO Viga 11 - 12

SEGUNDO PISO


TERCER PISO

SEGUNDO PISO

Mº Max. Posiitivo TERCER

PISO


SEGUNDO PISO

TERCER PISO


Mº Max. Posiitivo SEGUNDO

PISO


TERCER PISO

SEGUNDO PISO

TERCER PISO

Mº Max. Posiitivo PRIMER

PISO Viga 11 - 12


SEGUNDO PISO

VIGAS

Viga 12 - 4 5.886 Tn-m 3.870 Tn-m 4.490 Tn-m VIGAS Viga 9 - 10 5.124 Tn-m 4.966 Tn-mViga 2 - 9 4.465 Tn-m 5.864 Tn-m 4.210 Tn-m Viga 10 - 5 7.798 Tn-m 5.937 Tn-m

Viga 9 - 10 3.536 Tn-m 2.450 Tn-m 0.000 Tn-m Viga 3 - 7 2.805 Tn-m 4.531 Tn-mViga 10 - 5 4.509 Tn-m 3.923 Tn-m 3.220 Tn-m Viga 7 - 8 3.207 Tn-m 3.337 Tn-mViga 3 - 7 1.979 Tn-m 2.929 Tn-m 2.460 Tn-m Viga 8 - 6 4.589 Tn-m 2.757 Tn-mViga 7 - 8 1.933 Tn-m 2.558 Tn-m 0.000 Tn-mViga 8 - 6 3.581 Tn-m 2.131 Tn-m 3.050 Tn-m MOMENTOS CALCULADOS CON EL SAP - PORTICO 7-7

ENVOLVENTEMº Maximos NegativosIzquierda Derecha


VIGAS


3.794 Tn-m 3.794 Tn-m 0.000 Tn-m

VIGAS

Viga 1 - 11 3.954 Tn-m 5.867 Tn-mViga 12 - 4 5.886 Tn-m 3.928 Tn-m 4.550 Tn-m 3.746 Tn-m 3.746 Tn-mViga 2 - 9 4.519 Tn-m 5.864 Tn-m 4.280 Tn-m Viga 12 - 4 5.867 Tn-m 3.954 Tn-m

Viga 9 - 10 3.536 Tn-m 3.536 Tn-m 0.000 Tn-m Viga 2 - 9 4.628 Tn-m 5.821 Tn-mViga 10 - 5 5.864 Tn-m 4.519 Tn-m 4.280 Tn-m Viga 9 - 10 3.403 Tn-m 3.403 Tn-mViga 3 - 7 2.131 Tn-m 3.581 Tn-m 3.430 Tn-m Viga 10 - 5 5.821 Tn-m 4.628 Tn-mViga 7 - 8 2.558 Tn-m 2.558 Tn-m 0.000 Tn-m Viga 3 - 7 2.437 Tn-m 4.169 Tn-mViga 8 - 6 3.581 Tn-m 2.131 Tn-m 3.430 Tn-m Viga 7 - 8 2.965 Tn-m 2.965 Tn-m

Viga 8 - 6 4.169 Tn-m 2.437 Tn-mMOMENTOS CALCULADOS CON HARDY CROSS Y KANI - PORTICO 2-2


Izquierda Derecha

VIGAS

Viga 1 - 11 ### 5.342 Tn-m 4.230 Tn-m### 3.253 Tn-m 0.000 Tn-m

Viga 12 - 4 ### 3.504 Tn-m 4.230 Tn-mViga 2 - 9 ### 5.371 Tn-m 3.950 Tn-m

Viga 9 - 10 ### 2.946 Tn-m 0.000 Tn-mViga 10 - 5 ### 4.011 Tn-m 3.950 Tn-mViga 3 - 7 ### 3.133 Tn-m 2.750 Tn-mViga 7 - 8 ### 2.064 Tn-m 0.000 Tn-mViga 8 - 6 ### 1.808 Tn-m 2.750 Tn-m


Izquierda Derecha

VIGAS





Izquierda Derecha

VIGAS





PRIMER PISO SEGUNDO

PISO

SEGUNDO PISO TERCER

PISO

TERCER PISO

Mº Max. Posiitivo



SEGUNDO PISO SEGUNDO

PISO

TERCER PISO TERCER

PISO

Mº Max. Posiitivo


SEGUNDO PISO

TERCER PISO

Mº Max. Posiitivo


SEGUNDO PISO

TERCER PISO

Mº Max. Posiitivo


SEGUNDO PISO

TERCER PISO

Mº Max. Posiitivo

ESTADO 4Izquierda Derecha

VIGAS





Izquierda Derecha

VIGAS




ENVOLVENTEMº Maximos NegativosIzquierda Derecha

VIGAS

Viga 1 - 11 2.749 Tn-m 5.537 Tn-m 4.490 Tn-m2.401 Tn-m 3.493 Tn-m 0.000 Tn-m


Viga 9 - 10 2.237 Tn-m 3.202 Tn-m 0.000 Tn-mViga 10 - 5 4.184 Tn-m 4.011 Tn-m 4.280 Tn-mViga 3 - 7 1.511 Tn-m 3.314 Tn-m 3.430 Tn-mViga 7 - 8 1.511 Tn-m 2.211 Tn-m 0.000 Tn-mViga 8 - 6 2.573 Tn-m 1.808 Tn-m 3.430 Tn-m

Mº Max. Posiitivo


SEGUNDO PISO

TERCER PISO

Mº Max. Posiitivo


SEGUNDO PISO

TERCER PISO

Mº Max. Posiitivo


SEGUNDO PISO

TERCER PISO

MOMENTOS CALCULADOS CON EL SAP - PORTICO 3-3

5.940 Tn-m0.000 Tn-m5.940 Tn-m5.610 Tn-m0.000 Tn-m5.610 Tn-m3.570 Tn-m0.000 Tn-m3.570 Tn-m






6.310 Tn-m0.000 Tn-m5.970 Tn-m5.950 Tn-m

Mº Max. Posiitivo

Mº Max. Posiitivo

Mº Max. Posiitivo

Mº Max. Posiitivo

0.120 Tn-m5.620 Tn-m3.970 Tn-m0.000 Tn-m3.970 Tn-m



Mº Max. Posiitivo


MOMENTOS VIGAS - PORTICOS Y-Y

MOMENTOS CALCULADOS CON EL SAP - PORTICO A-A MOMENTOS CALCULADOS CON EL SAP - PORTICO B-B


Mº Max. Posiitivo ENVOLVENTEMº Max. Negativos

Izquierda Derecha Izquierda

VIGAS

Volado 0.610 Tn-m ###

VIGAS

Volado 0.515 Tn-m

1.119 Tn-m ### 0.640 Tn-m 0.933 Tn-m

Viga 3 - 4 0.955 Tn-m ### 0.480 Tn-m Viga 3 - 4 0.617 Tn-m


1.021 Tn-m ### 0.410 Tn-m 0.809 Tn-m


Volado 0.610 Tn-m ### Volado 0.493 Tn-m

1.102 Tn-m ### 0.610 Tn-m 0.858 Tn-m


Volado 0.982 Tn-m ### Viga 4 - 5 0.729 Tn-m

0.871 Tn-m ### 0.350 Tn-m 0.793 Tn-m


Volado 0.186 Tn-m ### Volado 0.186 Tn-m

0.265 Tn-m ### 0.200 Tn-m 0.340 Tn-m


Volado 0.300 Tn-m ### Viga 4 - 5 0.275 Tn-m

0.400 Tn-m ### 0.300 Tn-m 0.540 Tn-m


No hay la necesidad de hacer conmbinaciones, ya que no intervienen la carga viva

PRIMER PISO

PRIMER PISO

Viga 2 - 3 Viga 2 - 3

Viga 5 - 6 Viga 5 - 6

SEGUNDO PISO

SEGUNDO PISO

Viga 2 - 3 Viga 2 - 3

Viga 5 - 6 Viga 5 - 6

TRCER PISO

TRCER PISO

Viga 2 - 3 Viga 2 - 3

Viga 5 - 6 Viga 5 - 6

MOMENTOS CALCULADOS CON EL SAP - PORTICO B-B MOMENTOS CALCULADOS CON EL SAP - PORTICO C-C MOMENTOS CALCULADOS CON EL SAP - PORTICO D-D

Mº Max. NegativosMº Max. Posiitivo ENVOLVENTE

Mº Max. NegativosMº Max. Posiitivo ENVOLVENTE

Derecha Izquierda Derecha

0.000 Tn-m

VIGAS

Volado ### 0.000 Tn-m

VIGAS

0.859 Tn-m 0.560 Tn-m ### 0.876 Tn-m 0.590 Tn-m

0.793 Tn-m 0.290 Tn-m Viga 3 - 4 ### 0.524 Tn-m 0.090 Tn-m


0.902 Tn-m 0.500 Tn-m ### 0.452 Tn-m 0.270 Tn-m


0.000 Tn-m Volado ### 0.000 Tn-m

0.876 Tn-m 0.520 Tn-m ### 0.890 Tn-m 0.560 Tn-m



0.920 Tn-m 0.500 Tn-m ### 0.483 Tn-m 0.270 Tn-m


0.000 Tn-m Volado ### 0.000 Tn-m

0.327 Tn-m 0.190 Tn-m ### 0.317 Tn-m 0.190 Tn-m



0.400 Tn-m 0.280 Tn-m ### 0.430 Tn-m 0.280 Tn-m


PRIMER PISO

PRIMER PISO

Viga 2 - 3

Viga 5 - 6

SEGUNDO PISO

SEGUNDO PISO

Viga 2 - 3

Viga 5 - 6

TRCER PISO

TRCER PISO

Viga 2 - 3

Viga 5 - 6

MOMENTOS CALCULADOS CON EL SAP - PORTICO D-D


Mº Max. PosiitivoIzquierda Derecha

Volado 0.610 Tn-m 0.000 Tn-m

1.148 Tn-m 1.020 Tn-m 0.640 Tn-m

Viga 3 - 4 0.777 Tn-m 1.115 Tn-m 0.540 Tn-m

Volado 0.673 Tn-m 0.468 Tn-m 0.000 Tn-m

1.674 Tn-m 1.412 Tn-m 0.910 Tn-m

Viga 6 - 7 0.900 Tn-m 1.675 Tn-m 0.880 Tn-m


1.131 Tn-m 1.073 Tn-m 0.620 Tn-m

Viga 3 - 4 0.673 Tn-m 1.124 Tn-m 0.580 Tn-m


1.193 Tn-m 1.726 Tn-m 0.990 Tn-m

Viga 6 - 7 1.025 Tn-m 1.628 Tn-m 0.830 Tn-m


0.281 Tn-m 0.362 Tn-m 0.210 Tn-m

Viga 3 - 4 0.257 Tn-m 0.290 Tn-m 0.180 Tn-m


0.407 Tn-m 0.458 Tn-m 0.320 Tn-m

Viga 6 - 7 0.362 Tn-m 0.407 Tn-m 0.260 Tn-m

Viga 2 - 3

Viga 5 - 6

Viga 2 - 3

Viga 5 - 6

Viga 2 - 3

Viga 5 - 6

COMBINACIONES RECOMENDADAS

PROYECTO VIVIENDA MULTIFAMILIAR - 3 PSIOS 1/2 - 3/8" Area b min

1.420 cm² 14.34 cmDISEÑO DE VIGAS PRINCIPALES 1 Φ 1/2 + 1 Φ 3/8 2.000 cm² 14.66 cm

2.130 cm² 17.83 cmVIGAS PRINCIPALES EJE 2-2 2 Φ 1/2 2.580 cm² 14.98 cm

PISO VIGASMº Max. Negativos 1 Φ 1/2 + 2 Φ 3/8 2.710 cm² 18.15 cm

Izquierda Derecha 4 Φ 3/8 2.840 cm² 21.32 cmViga A - B 2.749 Tn-m 5.537 Tn-m 4.490 Tn-m 2 Φ 1/2 + 1 Φ 3/8 3.290 cm² 18.47 cmViga B - C 2.401 Tn-m 3.493 Tn-m 0.000 Tn-m 3 Φ 1/2 3.870 cm² 18.79 cmViga C - D 4.185 Tn-m 3.504 Tn-m 4.550 Tn-m 2 Φ 1/2 + 2 Φ 3/8 4.000 cm² 21.96 cmViga A - B 3.233 Tn-m 5.502 Tn-m 4.280 Tn-m 3 Φ 1/2 + 1 Φ 3/8 4.580 cm² 22.28 cmViga B - C 2.237 Tn-m 3.202 Tn-m 0.000 Tn-m 4 Φ 1/2 5.160 cm² 22.60 cmViga C - D 4.184 Tn-m 4.011 Tn-m 4.280 Tn-m 5/8 - 1" Area b min

Viga A - B 1.511 Tn-m 3.314 Tn-m 3.430 Tn-m 1 Φ 1 + 1 Φ 5/8 7.080 cm² 16.57 cmViga B - C 1.511 Tn-m 2.211 Tn-m 0.000 Tn-m 10.200 cm² 17.52 cmViga C - D 2.573 Tn-m 1.808 Tn-m 3.430 Tn-m 2 Φ 1+ 1 Φ 5/8 12.180 cm² 21.65 cm

2 Φ 1+ 2 Φ 5/8 14.160 cm² 25.78 cm

1. DIMENSION Y PROPIEDADES DE LA VIGA 15.300 cm² 22.60 cm

b = 25.00 cm Peralte Efectivo de la seccion: 3/4 - 1" Area b min

h = 35.00 cm Ф Asumo : 3/4" 1.91 cm 1 Φ 3/4 + 1 Φ 1 7.950 cm² 16.89 cmf'c = 210 Kg/cm² Ф Estribos : 3/8" 0.95 cm 1 Φ 1 + 2 Φ 3/4 10.800 cm² 21.34 cmfy = 4200 Kg/cm² d: h - Recub - Фestrib - Фasumo/2 2 Φ 1 + 1 Φ 3/4 13.050 cm² 21.97 cmβ = 0.85 d: 29.10 cm 2 Φ 1+ 2 Φ 3/4 15.900 cm² 26.42 cm

Recub = 4.00 cm

2. DETERMINACION DEL ACERO MINIMO

As min = Pmin.b.dPmin = 0.0024

As min = 1.757 cm² 2 Φ 3/8 As =1.420 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²

3. DETERMINACION DEL ACERO MAXIMO

Pb = (0.723.f'c/fy)*(6300/(6300+fy))Pb = 0.0217

Pmax = 0.75.Pb 0.0163As max = 11.833 cm² 4 Φ 3/4 ###

2 Φ 1+ 1 Φ 5/8 ###

4. DETERMINACION DEL REFUERZO EN LA VIGA

A. ACEROS POSITIVOS FORMULAS B. ACEROS NEGATIVOS

M max 4.490 Tn-m M maxM max 0.000 Tn-m 0 = colocar acero minimo M maxM max 4.550 Tn-m M maxM max 4.280 Tn-m M maxM max 0.000 Tn-m M maxM max 4.280 Tn-m M max

M max 3.430 Tn-m M max

M max 0.000 Tn-m M maxM max 3.430 Tn-m M max

PRIMER PISO PRIMER PISO PRIMER PISO

2 Φ 3/8

3 Φ 3/8

Mº Max. Posiitivo

PRIMER PISO

SEGUNDO PISO

TERCER PISO 2 Φ 1

3 Φ 1

PRIMER PISO

PRIMER PISO

SEGUNDO PISO

SEGUNDO PISO

TERCER PISO

TERCER PISO

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

Mmax (+) 4.490 Tn-m Mmax (+) ### Mmax (-) ###

b = 25.00 cm b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9 Ф = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.dAs = 4.297 cm² a =4.04 cm REPETIR As = 4.355 cm² a =4.10 cm REPETIR As = 2.632 cm²As = 4.388 cm² a =4.13 cm REPETIR As = 4.451 cm² a =4.19 cm REPETIR As = 2.611 cm²As = 4.394 cm² a =4.14 cm OK As = 4.458 cm² a =4.20 cm OK As = 2.610 cm²As = 4.395 cm² As = 4.459 cm² As = 2.610 cm²

Usar 2 Φ 1/2 + 1 Φ 5/8 ### Usar 2 Φ 1/2 + 1 Φ 5/8 As =4.560 cm²Usar 1 Φ 1/2 + 2 Φ 3/8

SEGUNDO PISO Mmax (-) ###

Mmax 4.280 Tn-m b = 25.00 cmb = 25.00 cm d = 29.10 cmd = 29.10 cm Ф = 0.9Ф = 0.9

Asumir: a = 0.10.dAsumir: a = 0.10.d a =2.91 cm As = 3.343 cm²

As = 4.096 cm² a =3.86 cm REPETIR As = 3.358 cm²As = 4.168 cm² a =3.92 cm REPETIR As = 3.358 cm²As = 4.173 cm² a =3.93 cm OK As = 3.358 cm²

As = 4.173 cm² Usar 3 Φ 1/2 Usar 2 Φ 1/2 + 1 Φ 5/8 ###

SEGUNDO PISO

TERCER PISO Mmax (-) ###

Mmax 3.430 Tn-m b = 25.00 cmb = 25.00 cm d = 29.10 cmd = 29.10 cm Ф = 0.9Ф = 0.9

Asumir: a = 0.10.dAsumir: a = 0.10.d 2.91 cm As = 3.094 cm²

As = 3.283 cm² 3.09 cm REPETIR As = 3.095 cm²As = 3.294 cm² 3.10 cm REPETIR As = 3.095 cm²As = 3.294 cm² 3.10 cm OK As = 3.095 cm²As = 3.294 cm² As = 3.095 cm²

Usar 1 Φ 1/2 + 1 Φ 5/8Usar 3 Φ 1/2 ### Mmax (-) ###

b = 25.00 cmd = 29.10 cmФ = 0.9

Asumir: a = 0.10.dAs = 3.065 cm²As = 3.064 cm²As = 3.064 cm²As = 3.064 cm²As = 3.064 cm²

Usar 1 Φ 1/2 + 1 Φ 5/8

TERCER PISO

Mmax (-) ###

b = 25.00 cmd = 29.10 cm

Ф = 0.9

Asumir: a = 0.10.dAs = 1.447 cm²As = 1.407 cm²As = 1.406 cm²As = 1.406 cm²

Usar 2 Φ 1/2Mmax (-) ###

b = 25.00 cmd = 29.10 cmФ = 0.9


Usar 3 Φ 3/8


1/2 - 5/8" Area b min ACEROS COMERCIALES

1 Φ 1/2 + 1 Φ 5/8 3.270 cm² 15.30 cm BARRA DIAMETRO Peso Area

3.960 cm² 15.62 cm numero pulg cm Kg/m cm2

2 Φ 1/2 + 1 Φ 5/8 4.560 cm² 19.11 cm 3 3/8 0.95 0.559 0.71

1 Φ 1/2 + 2 Φ 5/8 5.250 cm² 19.43 cm 4 1/2 1.27 0.993 1.29

3 Φ 1/2 + 1 Φ 5/8 5.850 cm² 22.92 cm 5 5/8 1.59 1.552 1.98

3 Φ 5/8 5.940 cm² 19.75 cm 6 3/4 1.91 2.235 2.85

2 Φ 1/2 + 2 Φ 5/8 6.540 cm² 23.24 cm 7 7/8 2.22 3.042 3.88

1 Φ 1/2 + 3 Φ 5/8 7.230 cm² 23.56 cm 8 1 2.54 3.973 5.1

4 Φ 5/8 7.920 cm² 23.88 cm 9 1 1/8 2.86 5.028 6.45

1/2 - 3/4" Area b min 10 1 1/4 3.18 6.207 8.19

1 Φ 1/2 + 1 Φ 3/4 4.140 cm² 15.62 cm 11 1 3/8 3.49 7.511 9.58

2 Φ 1/2 + 1 Φ 3/4 5.430 cm² 19.43 cm 12 1 1/2 3.81 8.938 11.45.700 cm² 15.62 cm

1 Φ 1/2 + 2 Φ 3/4 6.990 cm² 20.07 cm

3 Φ 3/4 8.550 cm² 20.71 cm

2 Φ 1/2 + 2 Φ 3/4 8.280 cm² 23.88 cm

4 Φ 3/4 11.400 cm² 25.16 cm

Izquierda Derecha FORMULAS2.749 Tn-m 5.537 Tn-m2.401 Tn-m 3.493 Tn-m4.185 Tn-m 3.504 Tn-m3.233 Tn-m 5.502 Tn-m2.237 Tn-m 3.202 Tn-m4.184 Tn-m 4.011 Tn-m

1.511 Tn-m 3.314 Tn-m

1.511 Tn-m 2.211 Tn-m2.573 Tn-m 1.808 Tn-m


2 Φ 5/8

2 Φ 3/4

NOTA: Las celdas que estan de fondo blanco son combinaciones que no se pueden tomar porque son

menores que el acerro minimo o mayores que el acero maximo, tambien cuando estan sobrepasando en

ancho b = 0.25 m

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

Mmax (-) 5.537 Tn-m Mmax (-) 2.401 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9

a =2.91 cm Asumir: a = 0.10.d ### Asumir: a = 0.10.d a =2.91 cma =2.48 cm REPETIR As = 5.300 cm² ### REPETIR As = 2.298 cm² a =2.16 cm REPETIRa =2.46 cm REPETIR As = 5.507 cm² ### REPETIR As = 2.268 cm² a =2.13 cm REPETIRa =2.46 cm OK As = 5.527 cm² ### REPETIR As = 2.266 cm² a =2.13 cm OK

As = 5.529 cm² ### OK As = 2.266 cm²

As = 5.529 cm²

1 Φ 1/2 + 2 Φ 3/8 As =2.710 cm² Usar 2 Φ 3/4 ### Usar 2 Φ 1/2 As =2.580 cm²Mmax (-) 4.185 Tn-m Mmax (-) 3.504 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9

a =2.91 cm Asumir: a = 0.10.d ### Asumir: a = 0.10.d a =2.91 cma =3.15 cm REPETIR As = 4.006 cm² ### REPETIR As = 3.354 cm² a =3.16 cm REPETIRa =3.16 cm REPETIR As = 4.069 cm² ### REPETIR As = 3.369 cm² a =3.17 cm REPETIRa =3.16 cm OK As = 4.073 cm² ### OK As = 3.370 cm² a =3.17 cm OK

As = 4.074 cm² As = 3.370 cm²

3 Φ 1/2 As =3.870 cm² Usar 1 Φ 1/2 + 1 Φ 3/4 ### Usar 3 Φ 1/2 As =3.870 cm²

SEGUNDO PISO SEGUNDO PISO SEGUNDO PISO

Mmax (-) 5.502 Tn-m Mmax (-) 2.237 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9

a =2.91 cm Asumir: a = 0.10.d ### Asumir: a = 0.10.d a =2.91 cma =2.91 cm OK As = 5.266 cm² ### REPETIR As = 2.141 cm² a =2.02 cm REPETIRa =2.91 cm OK As = 5.469 cm² ### REPETIR As = 2.107 cm² a =1.98 cm REPETIRa =2.91 cm OK As = 5.489 cm² ### REPETIR As = 2.106 cm² a =1.98 cm OKa =2.91 cm OK As = 5.491 cm² ### OK As = 2.106 cm²

As = 5.491 cm²

1 Φ 1/2 + 1 Φ 5/8 As =3.270 cm² Usar 2 Φ 3/4 ### Usar 3 Φ 3/8 As =2.130 cm²Mmax (-) 4.184 Tn-m Mmax (-) 4.011 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9

a =2.91 cm Asumir: a = 0.10.d ### Asumir: a = 0.10.d a =2.91 cma =2.88 cm REPETIR As = 4.004 cm² ### REPETIR As = 3.839 cm² a =3.61 cm REPETIRa =2.88 cm OK As = 4.068 cm² ### REPETIR As = 3.889 cm² a =3.66 cm REPETIRa =2.88 cm OK As = 4.072 cm² ### OK As = 3.892 cm² a =3.66 cm OKa =2.88 cm OK As = 4.072 cm² ### OK As = 3.892 cm²

As = 4.072 cm²

1 Φ 1/2 + 1 Φ 5/8 As =3.270 cm² Usar 1 Φ 1/2 + 1 Φ 3/4 ### Usar 2 Φ 5/8 As =3.960 cm²

TERCER PISO TERCER PISO TERCER PISO

Mmax (-) 3.314 Tn-m Mmax (-) 1.511 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cm

Ф = 0.9 Ф = 0.9

a =2.91 cm Asumir: a = 0.10.d ### Asumir: a = 0.10.d a =2.91 cma =1.36 cm REPETIR As = 3.172 cm² ### REPETIR As = 1.446 cm² a =1.36 cm REPETIRa =1.32 cm REPETIR As = 3.176 cm² ### OK As = 1.407 cm² a =1.32 cm REPETIRa =1.32 cm OK As = 3.177 cm² As = 1.406 cm² a =1.32 cm OK

As = 1.406 cm²

2 Φ 1/2 As =2.580 cm² Usar 3 Φ 1/2 ### Usar 2 Φ 1/2 As =2.580 cm²Mmax (-) 2.573 Tn-m Mmax (-) 1.808 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9

a =2.91 cm Asumir: a = 0.10.d ### Asumir: a = 0.10.d a =2.91 cma =1.99 cm REPETIR As = 2.463 cm² ### REPETIR As = 1.730 cm² a =1.63 cm REPETIRa =1.96 cm REPETIR As = 2.437 cm² ### REPETIR As = 1.691 cm² a =1.59 cm REPETIRa =1.96 cm OK As = 2.436 cm² ### OK As = 1.690 cm² a =1.59 cm OK

As = 2.436 cm² As = 1.690 cm²

3 Φ 3/8 As =2.130 cm² Usar 2 Φ 1/2 ### Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²

VIGAS PRINCIPALES EJE 3-3

PISO VIGASMº Max. Negativos

Mº Max. PosiitivoIzquierda Derecha

Viga A - B 5.138 Tn-m 7.619 Tn-m 5.940 Tn-mViga B - C 4.781 Tn-m 4.781 Tn-m 0.000 Tn-mViga C - D 7.619 Tn-m 5.138 Tn-m 5.940 Tn-mViga A - B 5.843 Tn-m 7.591 Tn-m 5.610 Tn-mViga B - C 4.464 Tn-m 4.464 Tn-m 0.000 Tn-mViga C - D 7.591 Tn-m 5.843 Tn-m 5.610 Tn-mViga A - B 2.547 Tn-m 4.177 Tn-m 3.570 Tn-mViga B - C 2.935 Tn-m 2.935 Tn-m 0.000 Tn-mViga C - D 4.177 Tn-m 2.547 Tn-m 3.570 Tn-m

1. DIMENSION Y PROPIEDADES DE LA VIGA

b = 25.00 cm Peralte Efectivo de la seccion:h = 35.00 cm Ф Asumo : 3/4" 1.91 cmf'c = 210 Kg/cm² Ф Estribos : 3/8" 0.95 cmfy = ### d: h - Recub - Фestrib - Фasumo/2β = 0.85 d: 29.10 cm

Recub = 4.00 cm



As min = 1.757 cm² 2 Φ 3/8 1.420 cm²

1 Φ 1/2 + 1 Φ 3/8 2.000 cm²


Pb = (0.723.f'c/fy)*(6300/(6300+fy))Pb = 0.0217

Pmax = 0.75.Pb 0.0163As max = 11.833 cm² 4 Φ 3/4 11.400 cm²

2 Φ 1+ 1 Φ 5/8 12.180 cm²

4. DETERMINACION DEL REFUERZO EN LA VIGA B. ACEROS NEGATIVOS Izquierda Derecha FORMULASA. ACEROS POSITIVOS FORMULAS M max 5.138 Tn-m 7.619 Tn-m

M max 5.940 Tn-m M max 4.781 Tn-m 4.781 Tn-mM max 0.000 Tn-m 0 = colocar acero minimo M max 7.619 Tn-m 5.138 Tn-mM max 5.940 Tn-m M max 5.843 Tn-m 7.591 Tn-mM max 5.610 Tn-m M max 4.464 Tn-m 4.464 Tn-mM max 0.000 Tn-m M max 7.591 Tn-m 5.843 Tn-mM max 5.610 Tn-m M max 2.547 Tn-m 4.177 Tn-m

M max 3.570 Tn-m M max 2.935 Tn-m 2.935 Tn-m

M max 0.000 Tn-m M max 4.177 Tn-m 2.547 Tn-mM max 3.570 Tn-m


PRIMER PISO

SEGUNDO PISO

TERCER PISO

PRIMER PISO

PRIMER PISO

SEGUNDO PISOSEGUNDO

PISO

TERCER PISOTERCER

PISO

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Mmax (+) 5.940 Tn-m Mmax (-) 5.138 Tn-m Mmax (-)

b = 25.00 cm b = 25.00 cm b =d = 29.10 cm d = 29.10 cm d =Ф = 0.9 Ф = 0.9 Ф =

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm Asumir:As = 5.685 cm² a =5.35 cm REPETIR As = 4.917 cm² a =4.63 cm REPETIR As =As = 5.948 cm² a =5.60 cm REPETIR As = 5.075 cm² a =4.78 cm REPETIR As =As = 5.976 cm² a =5.62 cm REPETIR As = 5.089 cm² a =4.79 cm REPETIR As =As = 5.979 cm² a =5.63 cm OK As = 5.091 cm² a =4.79 cm OK As =As = 5.979 cm² As = 5.091 cm² As =Usar 2 Φ 1/2 + 2 Φ 5/8 ### As =

Usar 4 Φ 1/2 As =5.160 cm² Usar

SEGUNDO PISO

Mmax 5.610 Tn-m SEGUNDO PISO SEGUNDO PISO

b = 25.00 cm Mmax (-) 5.843 Tn-m Mmax (-)

d = 29.10 cm b = 25.00 cm b =Ф = 0.9 d = 29.10 cm d =

Ф = 0.9 Ф =Asumir: a = 0.10.d a =2.91 cm

As = 5.369 cm² a =5.05 cm REPETIR Asumir: a = 0.10.d a =2.91 cm Asumir:As = 5.586 cm² a =5.26 cm REPETIR As = 5.592 cm² a =5.26 cm REPETIR As =As = 5.608 cm² a =5.28 cm REPETIR As = 5.841 cm² a =5.50 cm REPETIR As =As = 5.610 cm² a =5.28 cm OK As = 5.867 cm² a =5.52 cm REPETIR As =As = 5.610 cm² As = 5.870 cm² a =5.52 cm OK As =Usar 3 Φ 1/2 + 1 Φ 5/8 ### As = 5.870 cm² As =

As =

TERCER PISO Usar 3 Φ 5/8 As =5.940 cm² Usar

Mmax 3.570 Tn-m

b = 25.00 cm TERCER PISO TERCER PISO

d = 29.10 cm Mmax (-) 2.547 Tn-m Mmax (-)

Ф = 0.9 b = 25.00 cm b =d = 29.10 cm d =

Asumir: a = 0.10.d 2.91 cm Ф = 0.9 Ф =As = 3.417 cm² 3.22 cm REPETIRAs = 3.436 cm² 3.23 cm REPETIR Asumir: a = 0.10.d a =2.91 cm Asumir:As = 3.437 cm² As = 2.438 cm² a =2.29 cm REPETIR As =Usar 3 Φ 1/2 ### As = 2.411 cm² a =2.27 cm REPETIR As =

As = 2.410 cm² a =2.27 cm OK As =As = 2.410 cm² As =




Izquierda

PRIMER PISOViga A - B 4.173 Tn-mViga B - C 4.034 Tn-mViga C - D 6.256 Tn-mViga A - B 4.789 Tn-mViga B - C 3.752 Tn-mViga C - D 6.217 Tn-m

TERCER PISOViga A - B 2.254 Tn-mViga B - C 2.706 Tn-mViga C - D 3.787 Tn-m


b = 25.00 cm Peralte Efectivo de la seccion:h = 35.00 cm Ф Asumo :f'c = 210 Kg/cm² Ф Estribos :fy = 4200 Kg/cm² d:β = 0.85 d:

Recub = 4.00 cm



As min = 1.757 cm² 2 Φ 3/81 Φ 1/2 + 1 Φ 3/8


Pb = (0.723.f'c/fy)*(6300/(6300+fy))Pb = 0.0217

Pmax = 0.75.Pb 0.0163As max = 11.833 cm² 4 Φ 3/4

2 Φ 1+ 1 Φ 5/8

FORMULAS 4. DETERMINACION DEL REFUERZO EN LA VIGA

A. ACEROS POSITIVOS

PRIMER PISOM max 4.840 Tn-mM max 0.000 Tn-mM max 4.840 Tn-mM max 4.540 Tn-mM max 0.000 Tn-mM max 4.540 Tn-m

TERCER PISOM max 3.280 Tn-m

M max 0.000 Tn-mM max 3.280 Tn-m


SEGUNDO PISO

SEGUNDO PISO

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7.619 Tn-m Mmax (-) 4.781 Tn-m Mmax (+) 4.840 Tn-m

25.00 cm b = 25.00 cm b = 25.00 cm29.10 cm d = 29.10 cm d = 29.10 cm

0.9 Ф = 0.9 Ф = 0.9

a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm7.292 cm² a =6.86 cm REPETIR As = 4.576 cm² a =4.31 cm REPETIR As = 4.632 cm² a =4.36 cm7.854 cm² a =7.39 cm REPETIR As = 4.695 cm² a =4.42 cm REPETIR As = 4.757 cm² a =4.48 cm7.935 cm² a =7.47 cm REPETIR As = 4.704 cm² a =4.43 cm OK As = 4.768 cm² a =4.49 cm7.947 cm² a =7.48 cm REPETIR As = 4.705 cm² As = 4.769 cm²

7.949 cm² a =7.48 cm OK Usar 4 Φ 1/2 7.949 cm²

1 Φ 3/4 + 1 Φ 1 ### Usar 4 Φ 1/2 As =5.160 cm² SEGUNDO PISO

Mmax 4.540 Tn-m

SEGUNDO PISO SEGUNDO PISO b = 25.00 cm7.591 Tn-m Mmax (-) 4.464 Tn-m d = 29.10 cm

25.00 cm b = 25.00 cm Ф = 0.929.10 cm d = 29.10 cm

0.9 Ф = 0.9 Asumir: a = 0.10.d a =2.91 cmAs = 4.345 cm² a =4.09 cm

a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm As = 4.440 cm² a =4.18 cm7.266 cm² a =6.84 cm REPETIR As = 4.273 cm² a =4.02 cm REPETIR As = 4.447 cm² a =4.19 cm7.822 cm² a =7.36 cm REPETIR As = 4.360 cm² a =4.10 cm REPETIR As = 4.448 cm²

7.902 cm² a =7.44 cm REPETIR As = 4.367 cm² a =4.11 cm OK Usar 3 Φ 1/2 + 1 Φ 3/87.914 cm² a =7.45 cm REPETIR As = 4.368 cm²

7.916 cm² a =7.45 cm OK TERCER PISO

7.916 cm² Mmax 3.280 Tn-m

4 Φ 5/8 ### Usar 2 Φ 1/2 + 1 Φ 5/8 As =4.560 cm² b = 25.00 cmd = 29.10 cm

TERCER PISO TERCER PISO Ф = 0.94.177 Tn-m Mmax (-) 2.935 Tn-m

25.00 cm b = 25.00 cm Asumir: a = 0.10.d 2.91 cm29.10 cm d = 29.10 cm As = 3.139 cm² 2.95 cm

0.9 Ф = 0.9 As = 3.142 cm² 2.96 cmAs = 3.142 cm²

a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm Usar 1 Φ 1/2 + 1 Φ 5/83.998 cm² a =3.76 cm REPETIR As = 2.809 cm² a =2.64 cm REPETIR4.061 cm² a =3.82 cm REPETIR As = 2.796 cm² a =2.63 cm REPETIR4.065 cm² a =3.83 cm OK As = 2.795 cm² a =2.63 cm OK4.065 cm² As = 2.795 cm²

1 Φ 1/2 + 1 Φ 3/4 ### Usar 4 Φ 3/8 As =2.840 cm²


Mº Max. Negativos

Derecha

6.256 Tn-m 4.840 Tn-m4.034 Tn-m 0.000 Tn-m4.173 Tn-m 4.840 Tn-m6.217 Tn-m 4.540 Tn-m3.752 Tn-m 0.000 Tn-m4.789 Tn-m 4.540 Tn-m3.787 Tn-m 3.280 Tn-m2.706 Tn-m 0.000 Tn-m2.254 Tn-m 3.280 Tn-m


Peralte Efectivo de la seccion:

3/4" 1.91 cm

3/8" 0.95 cm

h - Recub - Фestrib - Фasumo/229.10 cm


2 Φ 3/8 1.420 cm²

1 Φ 1/2 + 1 Φ 3/8 2.000 cm²


(0.723.f'c/fy)*(6300/(6300+fy))

4 Φ 3/4 11.400 cm²

2 Φ 1+ 1 Φ 5/8 12.180 cm²

4. DETERMINACION DEL REFUERZO EN LA VIGA B. ACEROS NEGATIVOS Izquierda Derecha FORMULAS

FORMULAS M max 4.173 Tn-m 6.256 Tn-m

M max 4.034 Tn-m 4.034 Tn-m

0 = colocar acero minimo M max 6.256 Tn-m 4.173 Tn-mM max 4.789 Tn-m 6.217 Tn-mM max 3.752 Tn-m 3.752 Tn-mM max 6.217 Tn-m 4.789 Tn-mM max 2.254 Tn-m 3.787 Tn-m

M max 2.706 Tn-m 2.706 Tn-m

M max 3.787 Tn-m 2.254 Tn-m


Mº Max. Posiitivo

PRIMER PISO

SEGUNDO PISO

TERCER PISO

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Mmax (-) 4.173 Tn-m Mmax (-) 6.256 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

REPETIR As = 3.994 cm² a =3.76 cm REPETIR As = 5.988 cm² a =5.64 cm


OK As = 4.060 cm² a =3.82 cm OK As = 6.334 cm² a =5.96 cmAs = 4.061 cm² As = 6.338 cm² a =5.96 cm

As =5.160 cm² As = 6.338 cm²

Usar 1 Φ 1/2 + 1 Φ 3/4 As =4.140 cm² Usar 2 Φ 1/2 + 2 Φ 5/8SEGUNDO PISO

SEGUNDO PISO SEGUNDO PISO

Mmax (-) 4.789 Tn-m Mmax (-) 6.217 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9

REPETIR Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm


OK As = 4.703 cm² a =4.43 cm REPETIR As = 6.255 cm² a =5.89 cmAs = 4.713 cm² a =4.44 cm OK As = 6.289 cm² a =5.92 cm

As =4.580 cm² As = 4.714 cm² As = 6.293 cm² a =5.92 cmAs = 6.293 cm²

TERCER PISO Usar 4 Φ 1/2 As =5.160 cm² Usar 2 Φ 1/2 + 2 Φ 5/8

TERCER PISO TERCER PISO

Mmax (-) 2.254 Tn-m Mmax (-) 3.787 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9

REPETIROK Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = 2.157 cm² a =2.03 cm REPETIR As = 3.625 cm² a =3.41 cmAs =3.270 cm² As = 2.123 cm² a =2.00 cm REPETIR As = 3.658 cm² a =3.44 cm

As = 2.122 cm² a =2.00 cm OK As = 3.660 cm² a =3.44 cmAs = 2.122 cm² As = 3.660 cm²

Usar 2 Φ 1/2 As =2.580 cm² Usar 3 Φ 1/2



Izquierda Derecha

Viga A - B 5.848 Tn-m 8.654 Tn-mViga B - C 5.408 Tn-m 5.459 Tn-mViga C - D 8.667 Tn-m 5.826 Tn-mViga A - B 6.603 Tn-m 8.634 Tn-mViga B - C 5.077 Tn-m 4.920 Tn-mViga C - D 8.342 Tn-m 6.436 Tn-mViga A - B 2.736 Tn-m 4.360 Tn-mViga B - C 3.015 Tn-m 3.082 Tn-mViga C - D 4.382 Tn-m 2.709 Tn-m


b = 25.00 cm Peralte Efectivo de la seccion:h = 35.00 cm Ф Asumo : 3/4"f'c = 210 Kg/cm² Ф Estribos : 3/8"fy = 4200 Kg/cm² d: h - Recub - Фestrib - Фasumo/2β = 0.85 d: 29.10 cm

Recub = 4.00 cm



As min = 1.757 cm² 2 Φ 3/81 Φ 1/2 + 1 Φ 3/8


Pb = (0.723.f'c/fy)*(6300/(6300+fy))Pb = 0.0217

Pmax = 0.75.Pb 0.0163As max = 11.833 cm² 4 Φ 3/4

2 Φ 1+ 1 Φ 5/8


A. ACEROS POSITIVOS FORMULASM max 6.740 Tn-mM max 0.000 Tn-m 0 = colocar acero minimoM max 6.750 Tn-mM max 6.380 Tn-mM max 0.000 Tn-mM max 6.160 Tn-m

AZOTEAM max 3.720 Tn-m



PRIMER PISO

SEGUNDO PISO

TERCER PISO

SEGUNDO PISO

TERCER PISO

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Mmax (-) 4.034 Tn-m Mmax (+) 6.740 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9


REPETIR As = 3.861 cm² a =3.63 cm REPETIR As = 6.451 cm² a =6.07 cm REPETIRREPETIR As = 3.913 cm² a =3.68 cm REPETIR As = 6.842 cm² a =6.44 cm REPETIRREPETIR As = 3.916 cm² a =3.69 cm OK As = 6.891 cm² a =6.49 cm REPETIR

OK As = 3.916 cm² As = 6.897 cm² a =6.49 cm OKAs = 6.898 cm²

As =6.540 cm² Usar 2 Φ 1/2 + 2 Φ 3/8 As =4.000 cm² Usar 1 Φ 1/2 + 2 Φ 3/4 As =6.990 cm²


Mmax (-) 3.752 Tn-m Mmax 6.380 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9


REPETIR As = 3.591 cm² a =3.38 cm REPETIR As = 6.106 cm² a =5.75 cm REPETIRREPETIR As = 3.621 cm² a =3.41 cm REPETIR As = 6.437 cm² a =6.06 cm REPETIRREPETIR As = 3.623 cm² a =3.41 cm OK As = 6.475 cm² a =6.09 cm REPETIR

OK As = 3.624 cm² As = 6.480 cm² a =6.10 cm OKAs = 6.480 cm²

As =6.540 cm² Usar 3 Φ 1/2 As =3.870 cm² Usar 2 Φ 1/2 + 2 Φ 5/8 As =6.540 cm²


Mmax (-) 2.706 Tn-m Mmax 3.720 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d 2.91 cm

REPETIR As = 2.590 cm² a =2.44 cm REPETIR As = 3.560 cm² 3.35 cm REPETIRREPETIR As = 2.568 cm² a =2.42 cm REPETIR As = 3.589 cm² 3.38 cm REPETIR

OK As = 2.567 cm² a =2.42 cm OK As = 3.591 cm² 3.38 cm OKAs = 2.567 cm² As = 3.591 cm²

As =3.870 cm² Usar 2 Φ 1/2 As =2.580 cm² Usar 3 Φ 1/2 As =3.870 cm²




Peralte Efectivo de la seccion:1.91 cm0.95 cm

h - Recub - Фestrib - Фasumo/2


1.420 cm²2.000 cm²


11.400 cm²12.180 cm²

4. DETERMINACION DEL REFUERZO EN LA VIGA B. ACEROS NEGATIVOS Izquierda Derecha FORMULAS

FORMULAS M max 5.848 Tn-m 8.654 Tn-m

M max 5.408 Tn-m 5.459 Tn-m

0 = colocar acero minimo M max 8.667 Tn-m 5.826 Tn-mM max 6.603 Tn-m 8.634 Tn-mM max 5.077 Tn-m 4.920 Tn-mM max 8.342 Tn-m 6.436 Tn-m

AZOTEA

M max 2.736 Tn-m 4.360 Tn-m

M max 3.015 Tn-m 3.082 Tn-m

M max 4.382 Tn-m 2.709 Tn-m


Mº Max. Posiitivo

SEGUNDO PISO

TERCER PISO

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Mmax (+) 6.750 Tn-m Mmax (-) 5.848 Tn-m Mmax (-)


Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm Asumir:As = 6.461 cm² a =6.08 cm REPETIR As = 5.597 cm² a =5.27 cm REPETIR As =As = 6.854 cm² a =6.45 cm REPETIR As = 5.846 cm² a =5.50 cm REPETIR As =As = 6.903 cm² a =6.50 cm REPETIR As = 5.872 cm² a =5.53 cm REPETIR As =As = 6.909 cm² a =6.50 cm OK As = 5.875 cm² a =5.53 cm OK As =As = 6.910 cm² As = 5.875 cm² As =Usar 1 Φ 1/2 + 2 Φ 3/4 As =6.990 cm² As =


SEGUNDO PISO Mmax (-) 5.459 Tn-m Mmax (-)

Mmax 6.160 Tn-m b = 25.00 cm b =b = 25.00 cm d = 29.10 cm d =d = 29.10 cm Ф = 0.9 Ф =Ф = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir:Asumir: a = 0.10.d a =2.91 cm As = 5.225 cm² a =4.92 cm REPETIR As =

As = 5.896 cm² a =5.55 cm REPETIR As = 5.422 cm² a =5.10 cm REPETIR As =As = 6.191 cm² a =5.83 cm REPETIR As = 5.441 cm² a =5.12 cm REPETIR As =As = 6.224 cm² a =5.86 cm REPETIR As = 5.443 cm² a =5.12 cm OK As =As = 6.228 cm² a =5.86 cm OK As = 5.443 cm² As =As = 6.228 cm² As =

Usar 2 Φ 1/2 + 2 Φ 5/8 As =6.540 cm² Usar 2 Φ 3/4 As =5.700 cm² Usar

TERCER PISO SEGUNDO PISO SEGUNDO PISO

Mmax 3.730 Tn-m Mmax (-) 6.603 Tn-m Mmax (-)


Asumir: a = 0.10.d 2.91 cm Asumir: a = 0.10.d a =2.91 cm Asumir:As = 3.570 cm² 3.36 cm REPETIR As = 6.320 cm² a =5.95 cm REPETIR As =As = 3.599 cm² 3.39 cm REPETIR As = 6.687 cm² a =6.29 cm REPETIR As =As = 3.601 cm² 3.39 cm OK As = 6.732 cm² a =6.34 cm REPETIR As =As = 3.601 cm² As = 6.737 cm² a =6.34 cm OK As =Usar 3 Φ 1/2 As =3.870 cm² As = 6.738 cm² As =

As =

Usar 1 Φ 1/2 + 2 Φ 3/4 As =6.990 cm² Usar

Mmax (-) 4.920 Tn-m Mmax (-)

b = 25.00 cm b =d = 29.10 cm d =Ф = 0.9 Ф =

Asumir: a = 0.10.d a =2.91 cm Asumir:As = 4.709 cm² a =4.43 cm REPETIR As =As = 4.842 cm² a =4.56 cm REPETIR As =As = 4.853 cm² a =4.57 cm REPETIR As =As = 4.854 cm² a =4.57 cm OK As =As = 4.855 cm² As =

As =



Mmax (-) 2.736 Tn-m Mmax (-)

b = 25.00 cm b =d = 29.10 cm d =Ф = 0.9 Ф =

Asumir: a = 0.10.d a =2.91 cm Asumir:As = 2.619 cm² a =2.46 cm REPETIR As =As = 2.598 cm² a =2.44 cm REPETIR As =As = 2.597 cm² a =2.44 cm OK As =As = 2.597 cm² As =

Usar 1 Φ 1/2 + 2 Φ 3/8 As =2.710 cm² Usar

Mmax (-) 3.082 Tn-m Mmax (-)

b = 25.00 cm b =d = 29.10 cm d =Ф = 0.9 Ф =

Asumir: a = 0.10.d a =2.91 cm Asumir:As = 2.950 cm² a =2.78 cm REPETIR As =As = 2.943 cm² a =2.77 cm OK As =As = 2.942 cm² As =

As =

Usar 1 Φ 1/2 + 1 Φ 5/8 As =3.270 cm² Usar


PISO VIGAS

Viga A - BViga B - CViga C - DViga A - BViga B - CViga C - DViga A - BViga B - CViga C - D


b = 25.00 cmh = 35.00 cmf'c = 210 Kg/cm²fy = ###β = 0.85

Recub = 4.00 cm



As min = 1.757 cm²


Pb = (0.723.f'c/fy)*(6300/(6300+fy))Pb = 0.0217

Pmax = 0.75.PbAs max = 11.833 cm²

FORMULAS 4. DETERMINACION DEL REFUERZO EN LA VIGA

A. ACEROS POSITIVOS

M maxM maxM maxM maxM maxM max

M max

M maxM max


PRIMER PISO

SEGUNDO PISO

TERCER PISO

PRIMER PISO

SEGUNDO PISO

TERCER PISO

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8.654 Tn-m Mmax (-) 5.408 Tn-m Mmax (+) 6.310 Tn-m


0.9 Ф = 0.9 Ф = 0.9

a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d8.283 cm² a =7.80 cm REPETIR As = 5.176 cm² a =4.87 cm REPETIR As = 6.039 cm²9.086 cm² a =8.55 cm REPETIR As = 5.366 cm² a =5.05 cm REPETIR As = 6.359 cm²9.224 cm² a =8.68 cm REPETIR As = 5.384 cm² a =5.07 cm REPETIR As = 6.395 cm²9.248 cm² a =8.70 cm REPETIR As = 5.386 cm² a =5.07 cm OK As = 6.399 cm²9.253 cm² a =8.71 cm OK As = 5.386 cm² As = 6.400 cm²

9.253 cm² Usar 2 Φ 1/2 + 2 Φ 5/82 Φ 1 As =10.200 cm² Usar 2 Φ 1/2 + 1 Φ 3/4 As =5.430 cm²

8.667 Tn-m Mmax (-) 5.826 Tn-m SEGUNDO PISO

25.00 cm b = 25.00 cm Mmax 5.950 Tn-m

29.10 cm d = 29.10 cm b = 25.00 cm0.9 Ф = 0.9 d = 29.10 cm

Ф = 0.9a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm8.295 cm² a =7.81 cm REPETIR As = 5.576 cm² a =5.25 cm REPETIR Asumir: a = 0.10.d9.101 cm² a =8.57 cm REPETIR As = 5.823 cm² a =5.48 cm REPETIR As = 5.695 cm²9.240 cm² a =8.70 cm REPETIR As = 5.848 cm² a =5.50 cm REPETIR As = 5.959 cm²9.265 cm² a =8.72 cm REPETIR As = 5.851 cm² a =5.51 cm OK As = 5.987 cm²9.269 cm² a =8.72 cm OK As = 5.851 cm² As = 5.990 cm²9.270 cm² As = 5.991 cm²

2 Φ 1 As =10.200 cm² Usar 3 Φ 5/8 As =5.940 cm² Usar 2 Φ 1/2 + 2 Φ 5/8

SEGUNDO PISO SEGUNDO PISO TERCER PISO

8.634 Tn-m Mmax (-) 5.077 Tn-m Mmax 3.970 Tn-m


0.9 Ф = 0.9 Ф = 0.9

a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d8.264 cm² a =7.78 cm REPETIR As = 4.859 cm² a =4.57 cm REPETIR As = 3.800 cm²9.062 cm² a =8.53 cm REPETIR As = 5.010 cm² a =4.71 cm REPETIR As = 3.846 cm²9.199 cm² a =8.66 cm REPETIR As = 5.023 cm² a =4.73 cm REPETIR As = 3.849 cm²9.223 cm² a =8.68 cm REPETIR As = 5.024 cm² a =4.73 cm OK As = 3.849 cm²

9.227 cm² a =8.68 cm OK As = 5.024 cm² Usar 3 Φ 1/2 9.228 cm²

2 Φ 1 As =10.200 cm² Usar 4 Φ 1/2 As =5.160 cm²8.342 Tn-m Mmax (-) 6.436 Tn-m

25.00 cm b = 25.00 cm29.10 cm d = 29.10 cm

0.9 Ф = 0.9

a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm7.984 cm² a =7.51 cm REPETIR As = 6.160 cm² a =5.80 cm REPETIR8.710 cm² a =8.20 cm REPETIR As = 6.499 cm² a =6.12 cm REPETIR8.829 cm² a =8.31 cm REPETIR As = 6.539 cm² a =6.15 cm REPETIR8.849 cm² a =8.33 cm REPETIR As = 6.544 cm² a =6.16 cm OK8.852 cm² a =8.33 cm OK As = 6.544 cm²

8.853 cm²

2 Φ 1 As =10.200 cm² Usar 1 Φ 1/2 + 2 Φ 3/4 As =6.990 cm²


4.360 Tn-m Mmax (-) 3.015 Tn-m

25.00 cm b = 25.00 cm29.10 cm d = 29.10 cm

0.9 Ф = 0.9

a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm4.173 cm² a =3.93 cm REPETIR As = 2.886 cm² a =2.72 cm REPETIR4.251 cm² a =4.00 cm REPETIR As = 2.876 cm² a =2.71 cm OK4.257 cm² a =4.01 cm OK As = 2.875 cm²

4.257 cm²

2 Φ 1/2 + 1 Φ 5/8 As =4.560 cm² Usar 1 Φ 1/2 + 1 Φ 5/8 As =3.270 cm²4.382 Tn-m Mmax (-) 2.709 Tn-m

25.00 cm b = 25.00 cm29.10 cm d = 29.10 cm

0.9 Ф = 0.9

a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm4.195 cm² a =3.95 cm REPETIR As = 2.593 cm² a =2.44 cm REPETIR4.275 cm² a =4.02 cm REPETIR As = 2.571 cm² a =2.42 cm REPETIR4.281 cm² a =4.03 cm OK As = 2.570 cm² a =2.42 cm OK4.281 cm² As = 2.570 cm²

2 Φ 1/2 + 1 Φ 5/8 As =4.560 cm² Usar 2 Φ 1/2 As =2.580 cm²


Mº Max. Negativos

Izquierda Derecha

5.443 Tn-m 8.292 Tn-m 6.310 Tn-m4.828 Tn-m 4.663 Tn-m 0.000 Tn-m7.841 Tn-m 5.177 Tn-m 5.970 Tn-m6.231 Tn-m 8.230 Tn-m 5.950 Tn-m5.124 Tn-m 4.966 Tn-m 0.120 Tn-m7.798 Tn-m 5.937 Tn-m 5.620 Tn-m2.805 Tn-m 4.531 Tn-m 3.970 Tn-m3.207 Tn-m 3.337 Tn-m 0.000 Tn-m4.589 Tn-m 2.757 Tn-m 3.970 Tn-m



Ф Asumo : 3/4" 1.91 cm

Ф Estribos : 3/8" 0.95 cmd: h - Recub - Фestrib - Фasumo/2d: 29.10 cm


2 Φ 3/8 1.420 cm²

1 Φ 1/2 + 1 Φ 3/8 2.000 cm²


(0.723.f'c/fy)*(6300/(6300+fy))

0.0163

4 Φ 3/4 11.400 cm²

2 Φ 1+ 1 Φ 5/8 12.180 cm²


A. ACEROS POSITIVOS FORMULAS6.310 Tn-m0.000 Tn-m 0 = colocar acero minimo5.970 Tn-m5.950 Tn-m0.120 Tn-m5.620 Tn-m

3.970 Tn-m

0.000 Tn-m3.970 Tn-m

PRIMER PISO PRIMER PISO

Mº Max. Posiitivo

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Mmax (+) 5.970 Tn-m

b = 25.00 cmd = 29.10 cmФ = 0.9

a =2.91 cm Asumir: a = 0.10.d a =2.91 cma =5.68 cm REPETIR As = 5.714 cm² a =5.38 cm REPETIRa =5.98 cm REPETIR As = 5.981 cm² a =5.63 cm REPETIRa =6.02 cm REPETIR As = 6.010 cm² a =5.66 cm REPETIRa =6.02 cm OK As = 6.013 cm² a =5.66 cm OK

As = 6.013 cm²

2 Φ 1/2 + 2 Φ 5/8 As =6.540 cm² Usar 2 Φ 1/2 + 2 Φ 5/8 ###


Mmax 5.620 Tn-m Mmax 0.120 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9

a =2.91 cm Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cma =5.36 cm REPETIR As = 5.379 cm² a =5.06 cm REPETIR As = 0.115 cm² a =0.11 cm REPETIRa =5.61 cm REPETIR As = 5.597 cm² a =5.27 cm REPETIR As = 0.109 cm² a =0.10 cm OKa =5.63 cm REPETIR As = 5.619 cm² a =5.29 cm REPETIR As = 0.109 cm²

a =5.64 cm OK As = 5.621 cm² a =5.29 cm OKAs = 5.621 cm²

2 Φ 1/2 + 2 Φ 5/8 As =6.540 cm² Usar 2 Φ 3/4 ### Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²

TERCER PISO

2.91 cm3.58 cm REPETIR3.62 cm REPETIR3.62 cm OK

3 Φ 1/2 As =3.870 cm²

B. ACEROS NEGATIVOS Izquierda Derecha FORMULASM max 5.443 Tn-m 8.292 Tn-m

M max 4.828 Tn-m 4.663 Tn-mM max 7.841 Tn-m 5.177 Tn-mM max 6.231 Tn-m 8.230 Tn-mM max 5.124 Tn-m 4.966 Tn-mM max 7.798 Tn-m 5.937 Tn-mM max 2.805 Tn-m 4.531 Tn-m

M max 3.207 Tn-m 3.337 Tn-m

M max 4.589 Tn-m 2.757 Tn-m


PRIMER PISO

SEGUNDO PISO

TERCER PISO

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Mmax (-) 5.443 Tn-m Mmax (-) 8.292 Tn-m Mmax (-)


Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm Asumir:As = 5.209 cm² a =4.90 cm REPETIR As = 7.936 cm² a =7.47 cm REPETIR As =As = 5.404 cm² a =5.09 cm REPETIR As = 8.650 cm² a =8.14 cm REPETIR As =As = 5.423 cm² a =5.10 cm REPETIR As = 8.766 cm² a =8.25 cm REPETIR As =As = 5.425 cm² a =5.11 cm OK As = 8.785 cm² a =8.27 cm REPETIR As =

As = 5.425 cm² As = 8.788 cm² a =8.27 cm OKAs = 8.789 cm²

Usar 2 Φ 1/2 + 1 Φ 3/4 As =5.430 cm² Usar 2 Φ 1 ### Usar



Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm Asumir:As = 4.463 cm² a =4.20 cm REPETIR As = 7.505 cm² a =7.06 cm REPETIR As =As = 4.570 cm² a =4.30 cm REPETIR As = 8.114 cm² a =7.64 cm REPETIR As =As = 4.579 cm² a =4.31 cm OK As = 8.206 cm² a =7.72 cm REPETIR As =As = 4.579 cm² As = 8.221 cm² a =7.74 cm REPETIR As =

As = 8.223 cm² a =7.74 cm OK As =

As = 8.223 cm²

Usar 3 Φ 1/2 + 1 Φ 3/8 As =4.580 cm² Usar 3 Φ 3/4 As =8.550 cm² Usar




Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm Asumir:As = 5.963 cm² a =5.61 cm REPETIR As = 7.877 cm² a =7.41 cm REPETIR As =As = 6.270 cm² a =5.90 cm REPETIR As = 8.576 cm² a =8.07 cm REPETIR As =As = 6.305 cm² a =5.93 cm REPETIR As = 8.689 cm² a =8.18 cm REPETIR As =As = 6.309 cm² a =5.94 cm OK As = 8.707 cm² a =8.19 cm REPETIR As =As = 6.309 cm² As = 8.710 cm² a =8.20 cm OK As =

As = 8.710 cm²

Usar 2 Φ 1/2 + 2 Φ 5/8 As =6.540 cm² Usar 2 Φ 1 ### Usar



Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm Asumir:As = 4.753 cm² a =4.47 cm REPETIR As = 7.463 cm² a =7.02 cm REPETIR As =As = 4.892 cm² a =4.60 cm REPETIR As = 8.064 cm² a =7.59 cm REPETIR As =As = 4.904 cm² a =4.62 cm REPETIR As = 8.154 cm² a =7.67 cm REPETIR As =As = 4.905 cm² a =4.62 cm OK As = 8.167 cm² a =7.69 cm REPETIR As =As = 4.905 cm² As = 8.170 cm² a =7.69 cm OK As =

As = 8.170 cm²

Usar 4 Φ 1/2 As =5.160 cm² Usar 2 Φ 1/2 + 2 Φ 3/4 As =8.280 cm² Usar




Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm Asumir:As = 2.685 cm² a =2.53 cm REPETIR As = 4.337 cm² a =4.08 cm REPETIR As =As = 2.667 cm² a =2.51 cm REPETIR As = 4.431 cm² a =4.17 cm REPETIR As =As = 2.666 cm² a =2.51 cm OK As = 4.438 cm² a =4.18 cm OK As =

As = 2.666 cm² As = 4.439 cm²

Usar 1 Φ 1/2 + 2 Φ 3/8 As =2.710 cm² Usar 2 Φ 1/2 + 1 Φ 5/8 As =4.560 cm² Usar



Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm Asumir:As = 3.194 cm² a =3.01 cm REPETIR As = 4.392 cm² a =4.13 cm REPETIR As =As = 3.199 cm² a =3.01 cm OK As = 4.492 cm² a =4.23 cm REPETIR As =As = 3.200 cm² As = 4.499 cm² a =4.23 cm OK As =

As = 4.500 cm² As =

Usar 1 Φ 1/2 + 1 Φ 5/8 As =3.270 cm² Usar 2 Φ 1/2 + 1 Φ 5/8 As =4.560 cm² Usar



Izquierda Derecha

Viga A - B 3.954 Tn-m 5.867 Tn-m ###Viga B - C 3.746 Tn-m 3.746 Tn-m ###Viga C - D 5.867 Tn-m 3.954 Tn-m ###Viga A - B 4.628 Tn-m 5.821 Tn-m ###Viga B - C 3.403 Tn-m 3.403 Tn-m ###Viga C - D 5.821 Tn-m 4.628 Tn-m ###Viga A - B 2.437 Tn-m 4.169 Tn-m ###Viga B - C 2.965 Tn-m 2.965 Tn-m ###Viga C - D 4.169 Tn-m 2.437 Tn-m ###


b = 25.00 cm Peralte Efectivo de la seccion:h = 35.00 cm Ф Asumo : 3/4" 1.91 cmf'c = 210 Kg/cm² Ф Estribos : 3/8" 0.95 cmfy = ### d: h - Recub - Фestrib - Фasumo/2β = 0.85 d: 29.10 cm

Recub = 4.00 cm



As min = 1.757 cm² 2 Φ 3/8 1.420 cm²

1 Φ 1/2 + 1 Φ 3/8 2.000 cm²


Pb = (0.723.f'c/fy)*(6300/(6300+fy))Pb = 0.0217

Pmax = 0.75.Pb 0.0163As max = 11.833 cm² 4 Φ 3/4 11.400 cm²

2 Φ 1+ 1 Φ 5/8 12.180 cm²


A. ACEROS POSITIVOS FORMULASM max 4.540 Tn-mM max 0.000 Tn-m 0 = colocar acero minimoM max 4.540 Tn-mM max 4.210 Tn-mM max 0.000 Tn-mM max 4.210 Tn-m

M max 3.610 Tn-m



Mº Max. Posiitivo

PRIMER PISO

SEGUNDO PISO

TERCER PISO

PRIMER PISO

SEGUNDO PISO

TERCER PISO

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4.828 Tn-m Mmax (+) ###

25.00 cm b = 25.00 cm29.10 cm d = 29.10 cm

0.9 Ф = 0.9


Usar 2 Φ 1/2 + 1 Φ 5/8 As =4.560 cm²

4 Φ 1/2 As =5.160 cm² SEGUNDO PISO

5.177 Tn-m Mmax ###

25.00 cm b = 25.00 cm29.10 cm d = 29.10 cm

0.9 Ф = 0.9

a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm4.955 cm² a =4.66 cm REPETIR As = 4.029 cm² a =3.79 cm REPETIR5.117 cm² a =4.82 cm REPETIR As = 4.095 cm² a =3.85 cm REPETIR5.132 cm² a =4.83 cm REPETIR As = 4.100 cm² a =3.86 cm OK5.133 cm² a =4.83 cm OK As = 4.100 cm²

5.133 cm² Usar 1 Φ 1/2 + 1 Φ 3/4 As =4.140 cm²

4 Φ 1/2 As =5.160 cm² TERCER PISO

Mmax ###

SEGUNDO PISO b = 25.00 cm5.124 Tn-m d = 29.10 cm

25.00 cm Ф = 0.929.10 cm

0.9 Asumir: a = 0.10.d 2.91 cmAs = 3.455 cm² 3.25 cm REPETIR

a = 0.10.d a =2.91 cm As = 3.477 cm² 3.27 cm REPETIR4.904 cm² a =4.62 cm REPETIR As = 3.478 cm²

5.060 cm² a =4.76 cm REPETIR Usar 3 Φ 1/2 As =3.870 cm²5.074 cm² a =4.78 cm REPETIR5.075 cm² a =4.78 cm OK5.075 cm²

4 Φ 1/2 As =5.160 cm²5.937 Tn-m

25.00 cm29.10 cm

0.9

a = 0.10.d a =2.91 cm5.682 cm² a =5.35 cm REPETIR5.944 cm² a =5.59 cm REPETIR5.972 cm² a =5.62 cm REPETIR5.975 cm² a =5.62 cm OK5.975 cm²

2 Φ 1/2 + 2 Φ 5/8 As =6.540 cm²

TERCER PISO

3.207 Tn-m

25.00 cm29.10 cm

0.9

a = 0.10.d a =2.91 cm3.070 cm² a =2.89 cm REPETIR3.068 cm² a =2.89 cm OK3.068 cm²

1 Φ 1/2 + 1 Φ 5/8 As =3.270 cm²2.757 Tn-m

25.00 cm29.10 cm

0.9

a = 0.10.d a =2.91 cm2.639 cm² a =2.48 cm REPETIR2.618 cm² a =2.46 cm REPETIR2.617 cm² a =2.46 cm OK2.617 cm²

1 Φ 1/2 + 2 Φ 3/8 As =2.710 cm²

B. ACEROS NEGATIVOS Izquierda Derecha FORMULASM max 3.954 Tn-m 5.867 Tn-m

M max 3.746 Tn-m 3.746 Tn-mM max 5.867 Tn-m 3.954 Tn-mM max 4.628 Tn-m 5.821 Tn-mM max 3.403 Tn-m 3.403 Tn-mM max 5.821 Tn-m 4.628 Tn-mM max 2.437 Tn-m 4.169 Tn-m

M max 2.965 Tn-m 2.965 Tn-m

M max 4.169 Tn-m 2.437 Tn-m


PRIMER PISO

SEGUNDO PISO

TERCER PISO

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MuAs

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Mmax (-) 3.954 Tn-m Mmax (-) 5.867 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cmAs = 3.784 cm² a =3.56 cm REPETIR As = 5.615 cm² a =5.28 cmAs = 3.830 cm² a =3.60 cm REPETIR As = 5.867 cm² a =5.52 cmAs = 3.832 cm² a =3.61 cm OK As = 5.894 cm² a =5.55 cmAs = 3.833 cm² As = 5.897 cm² a =5.55 cm

As = 5.897 cm²

Usar 3 Φ 1/2 ### Usar 3 Φ 5/8


Mmax (-) 4.628 Tn-m Mmax (-) 5.821 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cmAs = 4.430 cm² a =4.17 cm REPETIR As = 5.571 cm² a =5.24 cmAs = 4.533 cm² a =4.27 cm REPETIR As = 5.817 cm² a =5.47 cmAs = 4.541 cm² a =4.27 cm OK As = 5.842 cm² a =5.50 cmAs = 4.542 cm² As = 5.845 cm² a =5.50 cm

As = 5.845 cm²

Usar 2 Φ 1/2 + 1 Φ 5/8 ### Usar 3 Φ 1/2 + 1 Φ 5/8


Mmax (-) 2.437 Tn-m Mmax (-) 4.169 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cmФ = 0.9 Ф = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cmAs = 2.333 cm² a =2.20 cm REPETIR As = 3.990 cm² a =3.76 cmAs = 2.303 cm² a =2.17 cm REPETIR As = 4.052 cm² a =3.81 cmAs = 2.302 cm² a =2.17 cm OK As = 4.056 cm² a =3.82 cmAs = 2.302 cm² As = 4.057 cm²

Usar 2 Φ 1/2 ### Usar 1 Φ 1/2 + 1 Φ 3/4

Mmax (-) 3.746 Tn-m

b = 25.00 cmd = 29.10 cmФ = 0.9

Asumir: a = 0.10.d a =2.91 cm

REPETIR As = 3.585 cm² a =3.37 cm REPETIRREPETIR As = 3.616 cm² a =3.40 cm REPETIRREPETIR As = 3.618 cm² a =3.40 cm OK

OK As = 3.618 cm²

As =5.940 cm² Usar 3 Φ 1/2 ###


Mmax (-) 3.403 Tn-m

b = 25.00 cmd = 29.10 cmФ = 0.9

Asumir: a = 0.10.d a =2.91 cm

REPETIR As = 3.257 cm² a =3.07 cm REPETIRREPETIR As = 3.266 cm² a =3.07 cm OKREPETIR As = 3.266 cm²

OK

As =5.850 cm² Usar 1 Φ 1/2 + 1 Φ 5/8 ###


Mmax (-) 2.965 Tn-m

b = 25.00 cmd = 29.10 cmФ = 0.9

Asumir: a = 0.10.d a =2.91 cm

REPETIR As = 2.838 cm² a =2.67 cm REPETIRREPETIR As = 2.826 cm² a =2.66 cm REPETIR

OK As = 2.825 cm² a =2.66 cm OKAs = 2.825 cm²

As =4.140 cm² Usar 4 Φ 3/8 ###

PROYECTO VIVIENDA MULTIFAMILIAR - 3 PSIOS COMBINACIONES RECOMENDADAS

1/2 - 3/8" Area 1/2 - 5/8"DISEÑO DE VIGAS SECUNDARIAS 2 Φ 3/8 1.420 cm² 1 Φ 1/2 + 1 Φ 5/8

1 Φ 1/2 + 1 Φ 3/8 2.000 cm² 2 Φ 5/8VIGAS PRINCIPALES EJE A-A 3 Φ 3/8 2.130 cm² 2 Φ 1/2 + 1 Φ 5/8

PISOS VIGASMº Max. Negativos 2 Φ 1/2 2.580 cm² 1 Φ 1/2 + 2 Φ 5/8

Izquierda Derecha 1 Φ 1/2 + 2 Φ 3/8 2.710 cm² 3 Φ 1/2 + 1 Φ 5/8Volado 0.610 Tn-m 0.000 Tn-m 4 Φ 3/8 2.840 cm² 3 Φ 5/8

1.119 Tn-m 1.031 Tn-m 0.640 Tn-m 2 Φ 1/2 + 1 Φ 3/8 3.290 cm² 2 Φ 1/2 + 2 Φ 5/8Viga 3 - 4 0.955 Tn-m 1.059 Tn-m 0.480 Tn-m 3 Φ 1/2 3.870 cm² 1 Φ 1/2 + 3 Φ 5/8Viga 4 - 5 0.642 Tn-m 0.813 Tn-m 0.310 Tn-m 2 Φ 1/2 + 2 Φ 3/8 4.000 cm² 4 Φ 5/8

1.021 Tn-m 0.840 Tn-m 0.410 Tn-m 3 Φ 1/2 + 1 Φ 3/8 4.580 cm² 1/2 - 3/4"Viga 6 - 7 0.874 Tn-m 1.553 Tn-m 0.950 Tn-m 4 Φ 1/2 5.160 cm² 1 Φ 1/2 + 1 Φ 3/4

Volado 0.610 Tn-m 0.000 Tn-m 5/8 - 1" Area 2 Φ 1/2 + 1 Φ 3/41.102 Tn-m 1.103 Tn-m 0.610 Tn-m 1 Φ 1 + 1 Φ 5/8 7.080 cm² 2 Φ 3/4

Viga 3 - 4 0.655 Tn-m 1.120 Tn-m 0.560 Tn-m 2 Φ 1 10.200 cm² 1 Φ 1/2 + 2 Φ 3/4Volado 0.982 Tn-m 0.000 Tn-m 0.000 Tn-m 2 Φ 1+ 1 Φ 5/8 12.180 cm² 3 Φ 3/4

0.871 Tn-m 1.101 Tn-m 0.350 Tn-m 2 Φ 1+ 2 Φ 5/8 14.160 cm² 2 Φ 1/2 + 2 Φ 3/4Viga 6 - 7 0.923 Tn-m 1.528 Tn-m 0.930 Tn-m 3 Φ 1 15.300 cm² 4 Φ 3/4

Volado 0.186 Tn-m 0.000 Tn-m 3/4 - 1" Area

0.265 Tn-m 0.389 Tn-m 0.200 Tn-m 1 Φ 3/4 + 1 Φ 1 7.950 cm²Viga 3 - 4 0.204 Tn-m 0.316 Tn-m 0.200 Tn-m 1 Φ 1 + 2 Φ 3/4 10.800 cm²

Volado 0.300 Tn-m 0.000 Tn-m 2 Φ 1 + 1 Φ 3/4 13.050 cm²0.400 Tn-m 0.487 Tn-m 0.300 Tn-m 2 Φ 1+ 2 Φ 3/4 15.900 cm²

Viga 6 - 7 0.245 Tn-m 0.559 Tn-m 0.270 Tn-m


b = 25.00 cm Peralte Efectivo de la seccion:h = 30.00 cm Ф Asumo : 3/4" 1.91 cmf'c = 210 Kg/cm² Ф Estribos : 3/8" 0.95 cmfy = 4200 Kg/cm² d: h - Recub - Фestrib - Фasumo/2β = 0.85 d: 24.10 cm

Recub = 4.00 cm



As min = 1.455 cm² 2 Φ 3/8 1.420 cm²1 Φ 1/2 + 1 Φ 3/8 2.000 cm²


Pb = (0.723.f'c/fy)*(6300/(6300+fy))Pb = 0.0217

Pmax = 0.75.Pb 0.0163As max = 9.799 cm² 2 Φ 1 10.200 cm²



Volado 0.000 Tn-m

0.640 Tn-m 0 = colocar acero minimoViga 3 - 4 0.480 Tn-m

Mº Max. Posiitivo

PRIMER PISO

Viga 2 - 3

Viga 5 - 6

SEGUNDO PISO

Viga 2 - 3

Viga 5 - 6

TERCER PISO

NOTA: Las celdas que estan de fondo blanco son combinaciones que no se pueden tomar porque son menores

que el acerro minimo o mayores que el acero maximo, tambien cuando estan sobrepasando en ancho b = 0.25 m

Viga 2 - 3

Viga 5 - 6

PRIMER PISO

PRIMER PISO

Viga 2 - 3

Viga 4 - 5 0.310 Tn-m

0.410 Tn-mViga 6 - 7 0.950 Tn-m

Volado 0.000 Tn-m0.610 Tn-m

Viga 3 - 4 0.560 Tn-mVolado 0.000 Tn-m

0.350 Tn-mViga 6 - 7 0.930 Tn-m



0.300 Tn-mViga 6 - 7 0.270 Tn-m


Mmax (+) 0.640 Tn-m Mmax (+) 0.480 Tn-m Mmax (-)


Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cm Asumir:As = 0.740 cm² a =0.70 cm REPETIR As = 0.555 cm² a =0.52 cm REPETIR As =As = 0.713 cm² a =0.67 cm REPETIR As = 0.533 cm² a =0.50 cm REPETIR As =As = 0.713 cm² a =0.67 cm OK As = 0.533 cm² a =0.50 cm OK As =

As = 0.713 cm² As = 0.533 cm²

Usar 1 Φ 1/2 + 1 Φ 3/8 ### Usar 1 Φ 1/2 + 1 Φ 3/8 ### Usar



Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cm Asumir:As = 0.358 cm² a =0.34 cm REPETIR As = 0.474 cm² a =0.45 cm REPETIR As =As = 0.343 cm² a =0.32 cm REPETIR As = 0.454 cm² a =0.43 cm REPETIR As =As = 0.343 cm² a =0.32 cm OK As = 0.454 cm² a =0.43 cm OK As =As = 0.343 cm² As = 0.454 cm² As =


Mmax (+) 0.950 Tn-m Mmax (-)

b = 25.00 cm b =d = 24.10 cm d =Ф = 0.9 Ф =


Usar 1 Φ 1/2 + 1 Φ 3/8 ### Usar



b = 25.00 cm b = 25.00 cm b =

PRIMER PISO

PRIMER PISO

Viga 5 - 6

SEGUNDO PISO

SEGUNDO PISO

Viga 2 - 3

Viga 5 - 6

TERCER PISO

TERCER PISO

Viga 2 - 3

Viga 5 - 6

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

d = 24.10 cm d = 24.10 cm d =Ф = 0.9 Ф = 0.9 Ф =

Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cm Asumir:As = 0.705 cm² a =0.66 cm REPETIR As = 0.405 cm² a =0.38 cm REPETIR As =As = 0.679 cm² a =0.64 cm REPETIR As = 0.387 cm² a =0.36 cm REPETIR As =As = 0.679 cm² a =0.64 cm OK As = 0.387 cm² a =0.36 cm OK As =As = 0.679 cm² As = 0.387 cm² As =


Mmax (+) 0.930 Tn-m Mmax (-)

b = 25.00 cm b =d = 24.10 cm d =Ф = 0.9 Ф =


Usar 1 Φ 1/2 + 1 Φ 3/8 ### Usar

Mmax (-)

TERCER PISO TERCER PISO b =Mmax (+) 0.200 Tn-m Mmax (+) 0.200 Tn-m d =

b = 25.00 cm b = 25.00 cm Ф =d = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9 Asumir:

As =Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cm As =

As = 0.231 cm² a =0.22 cm REPETIR As = 0.231 cm² a =0.22 cm REPETIR As =As = 0.221 cm² a =0.21 cm OK As = 0.221 cm² a =0.21 cm OK As =

As = 0.221 cm² As = 0.221 cm² Usar

Usar 1 Φ 1/2 + 1 Φ 3/8 ### Usar 1 Φ 1/2 + 1 Φ 3/8 ###Mmax (+) 0.300 Tn-m Mmax (+) 0.270 Tn-m TERCER PISO

b = 25.00 cm b = 25.00 cm Mmax (+)

d = 24.10 cm d = 24.10 cm b =Ф = 0.9 Ф = 0.9 d =

Ф =Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cm

As = 0.347 cm² a =0.33 cm REPETIR As = 0.312 cm² a =0.29 cm REPETIR Asumir:As = 0.332 cm² a =0.31 cm REPETIR As = 0.298 cm² a =0.28 cm REPETIR As =As = 0.332 cm² a =0.31 cm OK As = 0.298 cm² a =0.28 cm OK As =As = 0.332 cm² As = 0.298 cm² As =

Usar 1 Φ 1/2 + 1 Φ 3/8 ### Usar 1 Φ 1/2 + 1 Φ 3/8 ###Usar

Mmax (+)

b =d =Ф =

Asumir:As =As =As =As =

Usar

Mmax (+)

b =d =Ф =


Usar

Mmax (+)

b =d =Ф =


Usar


1/2 - 5/8" Area ACEROS COMERCIALES

1 Φ 1/2 + 1 Φ 5/8 3.270 cm² BARRA DIAMETRO Peso Area

2 Φ 5/8 3.960 cm² numero pulg cm Kg/m cm2

2 Φ 1/2 + 1 Φ 5/8 4.560 cm² 3 3/8 0.95 0.559 0.71

1 Φ 1/2 + 2 Φ 5/8 5.250 cm² 4 1/2 1.27 0.993 1.29

3 Φ 1/2 + 1 Φ 5/8 5.850 cm² 5 5/8 1.59 1.552 1.98

3 Φ 5/8 5.940 cm² 6 3/4 1.91 2.235 2.85

2 Φ 1/2 + 2 Φ 5/8 6.540 cm² 7 7/8 2.22 3.042 3.88

1 Φ 1/2 + 3 Φ 5/8 7.230 cm² 8 1 2.54 3.973 5.1

4 Φ 5/8 7.920 cm² 9 1 1/8 2.86 5.028 6.45

1/2 - 3/4" Area 10 1 1/4 3.18 6.207 8.19

1 Φ 1/2 + 1 Φ 3/4 4.140 cm² 11 1 3/8 3.49 7.511 9.58

2 Φ 1/2 + 1 Φ 3/4 5.430 cm² 12 1 1/2 3.81 8.938 11.4

2 Φ 3/4 5.700 cm²

1 Φ 1/2 + 2 Φ 3/4 6.990 cm²

3 Φ 3/4 8.550 cm²

2 Φ 1/2 + 2 Φ 3/4 8.280 cm²11.400 cm²

B. ACEROS NEGATIVOS Izquierda Derecha FORMULASVolado 0.610 Tn-m 0.000 Tn-m

1.119 Tn-m 1.031 Tn-mViga 3 - 4 0.955 Tn-m 1.059 Tn-m 0 = colocar acero minimo



Viga 2 - 3

Viga 4 - 5 0.642 Tn-m 0.813 Tn-m

1.021 Tn-m 0.840 Tn-mViga 6 - 7 0.874 Tn-m 1.553 Tn-m

Volado 0.610 Tn-m 0.000 Tn-m1.102 Tn-m 1.103 Tn-m

Viga 3 - 4 0.655 Tn-m 1.120 Tn-mVolado 0.982 Tn-m 0.000 Tn-m



Viga 3 - 4 0.204 Tn-m 0.316 Tn-mVolado 0.300 Tn-m 0.000 Tn-m



0.610 Tn-m Mmax (-) 1.119 Tn-m Mmax (-) 1.031 Tn-m


0.9 Ф = 0.9 Ф = 0.9

a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cm0.705 cm² a =0.66 cm REPETIR As = 1.293 cm² a =1.22 cm REPETIR As = 1.192 cm² a =1.12 cm0.712 cm² a =0.67 cm OK As = 1.260 cm² a =1.19 cm REPETIR As = 1.159 cm² a =1.09 cm0.713 cm² As = 1.259 cm² a =1.19 cm OK As = 1.159 cm² a =1.09 cm

As = 1.259 cm² As = 1.159 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/81.059 Tn-m Mmax (-) 0.642 Tn-m Mmax (-) 0.813 Tn-m


0.9 Ф = 0.9 Ф = 0.9

a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cm1.224 cm² a =1.15 cm REPETIR As = 0.742 cm² a =0.70 cm REPETIR As = 0.939 cm² a =0.88 cm1.191 cm² a =1.12 cm REPETIR As = 0.715 cm² a =0.67 cm REPETIR As = 0.909 cm² a =0.86 cm1.191 cm² a =1.12 cm OK As = 0.714 cm² a =0.67 cm OK As = 0.908 cm² a =0.85 cm1.191 cm² As = 0.714 cm² As = 0.908 cm²



0.9 Ф = 0.9 Ф = 0.9


1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8


0.610 Tn-m Mmax (-) 1.102 Tn-m Mmax (-) 1.103 Tn-m

25.00 cm b = 25.00 cm b = 25.00 cm

Viga 5 - 6

Viga 2 - 3

Viga 5 - 6

Viga 2 - 3

Viga 5 - 6

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

24.10 cm d = 24.10 cm d = 24.10 cm0.9 Ф = 0.9 Ф = 0.9




0.9 Ф = 0.9 Ф = 0.9


1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/80.923 Tn-m Mmax (-) 1.528 Tn-m

25.00 cm b = 25.00 cm24.10 cm d = 24.10 cm

0.9 Ф = 0.9


1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²


0.186 Tn-m Mmax (+) 0.265 Tn-m Mmax (+) 0.389 Tn-m


0.9 Ф = 0.9 Ф = 0.9

a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cm0.215 cm² a =0.20 cm REPETIR As = 0.306 cm² a =0.29 cm REPETIR As = 0.450 cm² a =0.42 cm0.205 cm² a =0.19 cm OK As = 0.293 cm² a =0.28 cm REPETIR As = 0.431 cm² a =0.41 cm0.205 cm² As = 0.293 cm² a =0.28 cm OK As = 0.431 cm² a =0.41 cm

As = 0.293 cm² As = 0.431 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/80.204 Tn-m Mmax (+) 0.316 Tn-m Mmax (+) 0.300 Tn-m


0.9 Ф = 0.9 Ф = 0.9


1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/80.400 Tn-m Mmax (+) 0.487 Tn-m Mmax (+) 0.245 Tn-m


0.9 Ф = 0.9 Ф = 0.9


1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/80.559 Tn-m

25.00 cm24.10 cm

0.9a = 0.10.d a =2.41 cm0.646 cm² a =0.61 cm REPETIR0.621 cm² a =0.58 cm REPETIR0.621 cm² a =0.58 cm OK0.621 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²

VIGAS PRINCIPALES EJE B-B

PISOS VIGASMº Max. Negativos

Izquierda Derecha


0.933 Tn-m 0.859 Tn-mViga 3 - 4 0.617 Tn-m 0.793 Tn-mViga 4 - 5 0.764 Tn-m 0.682 Tn-m





Viga 6 - 7 0.306 Tn-m 0.579 Tn-m




Viga 6 - 7 0.229 Tn-m 0.507 Tn-m



Recub = 4.00 cm



As min = 1.455 cm² 2 Φ 3/81 Φ 1/2 + 1 Φ 3/8


Pb = (0.723.f'c/fy)*(6300/(6300+fy))Pb = 0.0217

Pmax = 0.75.Pb 0.0163As max = 9.799 cm² 2 Φ 1


A. ACEROS POSITIVOS FORMULASVolado 0.000 Tn-m


PRIMER PISO

Viga 2 - 3

Viga 5 - 6

SEGUNDO PISO

Viga 2 - 3

Viga 5 - 6

TERCER PISO

Viga 2 - 3

Viga 5 - 6

PRIMER PISO

Viga 2 - 3

Viga 4 - 5 0.300 Tn-m

0.500 Tn-mViga 6 - 7 0.240 Tn-m



0.500 Tn-mViga 6 - 7 0.220 Tn-m



0.280 Tn-mViga 6 - 7 0.300 Tn-m


Mmax (-) 0.955 Tn-m Mmax (+) 0.560 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9


REPETIR As = 1.104 cm² a =1.04 cm REPETIR As = 0.647 cm² a =0.61 cm REPETIRREPETIR As = 1.072 cm² a =1.01 cm REPETIR As = 0.623 cm² a =0.59 cm REPETIR

OK As = 1.071 cm² a =1.01 cm OK As = 0.622 cm² a =0.59 cm OKAs = 1.071 cm² As = 0.622 cm²

As =2.000 cm² Usar 2.000 cm² ### Usar 1 Φ 1/2 + 1 Φ 3/8 ###Mmax (-) 1.021 Tn-m Mmax (+) 0.300 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9




As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 ### Usar 1 Φ 1/2 + 1 Φ 3/8 ###Mmax (+) 0.240 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9

Asumir: a = 0.10.d a =2.41 cm



As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 ###


Mmax (-) 0.655 Tn-m Mmax (+) 0.520 Tn-m

b = 25.00 cm b = 25.00 cm

PRIMER PISO

Viga 5 - 6

SEGUNDO PISO

Viga 2 - 3

Viga 5 - 6

TERCER PISO

Viga 2 - 3

Viga 5 - 6

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

d = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9




As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 ### Usar 1 Φ 1/2 + 1 Φ 3/8 ###Mmax (-) 1.101 Tn-m Mmax (+) 0.300 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9




As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 ### Usar 1 Φ 1/2 + 1 Φ 3/8 ###Mmax (+) 0.220 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9

Asumir: a = 0.10.d a =2.41 cmAs = 0.254 cm² a =0.24 cm REPETIRAs = 0.243 cm² a =0.23 cm REPETIRAs = 0.243 cm² a =0.23 cm OKAs = 0.243 cm²

Usar 1 Φ 1/2 + 1 Φ 3/8 ###


Mmax (+) 0.190 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9

Asumir: a = 0.10.d a =2.41 cm

REPETIR As = 0.220 cm² a =0.21 cm REPETIRREPETIR As = 0.210 cm² a =0.20 cm OK

OK As = 0.209 cm²

As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 ###Mmax (+) 0.040 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9

Asumir: a = 0.10.d a =2.41 cm

REPETIR As = 0.046 cm² a =0.04 cm REPETIRREPETIR As = 0.044 cm² a =0.04 cm OK

OK As = 0.044 cm²

As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 ###

REPETIRREPETIR

OK

As =2.000 cm²

VIGAS PRINCIPALES EJE B-B

Mº Max. Posiitivo

0.000 Tn-m


0.000 Tn-m


0.000 Tn-m






1.420 cm²2.000 cm²


10.200 cm²


FORMULAS B. ACEROS NEGATIVOS Izquierda

Volado 0.515 Tn-m

0 = colocar acero minimo 0.933 Tn-mViga 3 - 4 0.617 Tn-mPRIMER

PISO

Viga 2 - 3

Viga 4 - 5 0.764 Tn-m

0.809 Tn-mViga 6 - 7 0.239 Tn-m



0.793 Tn-mViga 6 - 7 0.306 Tn-m



0.540 Tn-mViga 6 - 7 0.229 Tn-m


Mmax (+) 0.290 Tn-m Mmax (-) 0.515 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.500 Tn-m Mmax (-) 0.793 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (-) 0.902 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9

Asumir: a = 0.10.d a =2.41 cmAs = 1.042 cm² a =0.98 cmAs = 1.010 cm² a =0.95 cmAs = 1.010 cm² a =0.95 cmAs = 1.010 cm²

Usar 3 Φ 3/8


Mmax (+) 0.300 Tn-m Mmax (-) 0.493 Tn-m

b = 25.00 cm b = 25.00 cm

PRIMER PISO

Viga 5 - 6

SEGUNDO PISO

Viga 2 - 3

Viga 5 - 6

TERCER PISO

Viga 2 - 3

Viga 5 - 6

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

d = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9



b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9



b = 25.00 cmd = 24.10 cmФ = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8


Mmax (+) 0.160 Tn-m Mmax (+) 0.186 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9

Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cmAs = 0.185 cm² a =0.17 cm REPETIR As = 0.215 cm² a =0.20 cmAs = 0.176 cm² a =0.17 cm OK As = 0.205 cm² a =0.19 cmAs = 0.176 cm² As = 0.205 cm²

Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.280 Tn-m Mmax (+) 0.253 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.540 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.507 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8

Derecha FORMULAS0.000 Tn-m

0.859 Tn-m0.793 Tn-m 0 = colocar acero minimo

0.682 Tn-m

0.902 Tn-m0.617 Tn-m0.000 Tn-m0.876 Tn-m0.715 Tn-m0.000 Tn-m0.920 Tn-m0.579 Tn-m0.000 Tn-m0.327 Tn-m0.327 Tn-m0.000 Tn-m0.400 Tn-m0.507 Tn-m

PRIMER PISO PRIMER PISO SEGUNDO PISO

Mmax (-) 0.933 Tn-m Mmax (-) 0.859 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9




As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²Mmax (-) 0.764 Tn-m Mmax (-) 0.682 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9





b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9






Mmax (-) 0.858 Tn-m Mmax (-) 0.876 Tn-m

b = 25.00 cm b = 25.00 cm

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d = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9





b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9




As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²Mmax (-) 0.579 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9

Asumir: a = 0.10.d a =2.41 cm



As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²


Mmax (+) 0.340 Tn-m Mmax (+) 0.327 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9


REPETIR As = 0.392 cm² a =0.37 cm REPETIR As = 0.377 cm² a =0.36 cm REPETIROK As = 0.376 cm² a =0.35 cm REPETIR As = 0.361 cm² a =0.34 cm REPETIR

As = 0.376 cm² a =0.35 cm OK As = 0.361 cm² a =0.34 cm OKAs = 0.376 cm² As = 0.361 cm²

As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²Mmax (+) 0.327 Tn-m Mmax (+) 0.275 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9




As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²Mmax (+) 0.400 Tn-m Mmax (+) 0.229 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9





REPETIRREPETIR

OK

As =2.000 cm²

VIGAS PRINCIPALES EJE C-C

PISOS VIGASMº Max. Negativos

Izquierda Derecha


0.846 Tn-m 0.876 Tn-mViga 3 - 4 0.208 Tn-m 0.524 Tn-mViga 4 - 5 0.279 Tn-m 0.225 Tn-m





Viga 6 - 7 0.323 Tn-m 0.490 Tn-m




Viga 6 - 7 0.218 Tn-m 0.523 Tn-m



Recub = 4.00 cm



As min = 1.455 cm² 2 Φ 3/81 Φ 1/2 + 1 Φ 3/8


Pb = (0.723.f'c/fy)*(6300/(6300+fy))Pb = 0.0217

Pmax = 0.75.Pb 0.0163As max = 9.799 cm² 2 Φ 1


A. ACEROS POSITIVOS FORMULASVolado 0.000 Tn-m


PRIMER PISO

Viga 2 - 3

Viga 5 - 6

SEGUNDO PISO

Viga 2 - 3

Viga 5 - 6

TERCER PISO

Viga 2 - 3

Viga 5 - 6

PRIMER PISO

Viga 2 - 3

Viga 4 - 5 0.060 Tn-m

0.270 Tn-mViga 6 - 7 0.270 Tn-m



0.270 Tn-mViga 6 - 7 0.250 Tn-m



0.280 Tn-mViga 6 - 7 0.300 Tn-m


Mmax (-) 0.617 Tn-m Mmax (+) 0.590 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9

Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cmAs = 0.713 cm² a =0.67 cm REPETIR As = 0.682 cm² a =0.64 cm REPETIRAs = 0.687 cm² a =0.65 cm REPETIR As = 0.657 cm² a =0.62 cm REPETIRAs = 0.686 cm² a =0.65 cm OK As = 0.656 cm² a =0.62 cm OKAs = 0.686 cm² As = 0.656 cm²

Usar 2.000 cm² As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 ###Mmax (-) 0.809 Tn-m Mmax (+) 0.060 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9

Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cmAs = 0.935 cm² a =0.88 cm REPETIR As = 0.069 cm² a =0.07 cm REPETIRAs = 0.905 cm² a =0.85 cm REPETIR As = 0.066 cm² a =0.06 cm OKAs = 0.904 cm² a =0.85 cm OK As = 0.066 cm²

As = 0.904 cm²

Usar 3 Φ 3/8 As =2.130 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 ###Mmax (+) 0.270 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8 ###


Mmax (-) 0.621 Tn-m Mmax (+) 0.560 Tn-m

b = 25.00 cm b = 25.00 cm

PRIMER PISO

Viga 5 - 6

SEGUNDO PISO

Viga 2 - 3

Viga 5 - 6

TERCER PISO

Viga 2 - 3

Viga 5 - 6

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d = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9

Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cmAs = 0.718 cm² a =0.68 cm REPETIR As = 0.647 cm² a =0.61 cm REPETIRAs = 0.691 cm² a =0.65 cm REPETIR As = 0.623 cm² a =0.59 cm REPETIRAs = 0.691 cm² a =0.65 cm OK As = 0.622 cm² a =0.59 cm OKAs = 0.691 cm² As = 0.622 cm²

Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 ###Mmax (-) 0.920 Tn-m Mmax (+) 0.060 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9

Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cmAs = 1.063 cm² a =1.00 cm REPETIR As = 0.069 cm² a =0.07 cm REPETIRAs = 1.032 cm² a =0.97 cm REPETIR As = 0.066 cm² a =0.06 cm OKAs = 1.031 cm² a =0.97 cm OK As = 0.066 cm²

As = 1.031 cm²

Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 ###Mmax (+) 0.250 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8 ###

TERCER PISO

Mmax (+) 0.190 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9

Asumir: a = 0.10.d a =2.41 cmAs = 0.220 cm² a =0.21 cm REPETIRAs = 0.210 cm² a =0.20 cm OKAs = 0.209 cm² a =0.20 cm OKAs = 0.209 cm²

Usar 1 Φ 1/2 + 1 Φ 3/8 ###Mmax (+) 0.030 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9

Asumir: a = 0.10.d a =2.41 cmAs = 0.035 cm² a =0.03 cm REPETIRAs = 0.033 cm² a =0.03 cm OKAs = 0.033 cm²

Usar 1 Φ 1/2 + 1 Φ 3/8 ###

VIGAS PRINCIPALES EJE C-C

0.000 Tn-m


0.000 Tn-m


0.000 Tn-m






1.420 cm²2.000 cm²


10.200 cm²


FORMULAS B. ACEROS NEGATIVOS Izquierda

Volado 0.515 Tn-m

0 = colocar acero minimo 0.846 Tn-mViga 3 - 4 0.208 Tn-m

Mº Max. Posiitivo

PRIMER PISO

Viga 2 - 3

Viga 4 - 5 0.279 Tn-m

0.500 Tn-mViga 6 - 7 0.265 Tn-m



0.468 Tn-mViga 6 - 7 0.323 Tn-m



0.504 Tn-mViga 6 - 7 0.218 Tn-m


Mmax (+) 0.090 Tn-m Mmax (-) 0.515 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9

Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cmAs = 0.104 cm² a =0.10 cm REPETIR As = 0.595 cm² a =0.56 cmAs = 0.099 cm² a =0.09 cm OK As = 0.572 cm² a =0.54 cmAs = 0.099 cm² As = 0.572 cm² a =0.54 cm

As = 0.572 cm²


b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9



b = 25.00 cmd = 24.10 cmФ = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8


Mmax (+) 0.100 Tn-m Mmax (-) 0.493 Tn-m

b = 25.00 cm b = 25.00 cm

PRIMER PISO

Viga 5 - 6

SEGUNDO PISO

Viga 2 - 3

Viga 5 - 6

TERCER PISO

Viga 2 - 3

Viga 5 - 6

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d = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9

Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cmAs = 0.116 cm² a =0.11 cm REPETIR As = 0.570 cm² a =0.54 cmAs = 0.110 cm² a =0.10 cm OK As = 0.547 cm² a =0.52 cmAs = 0.110 cm² a =0.10 cm OK As = 0.547 cm² a =0.52 cmAs = 0.110 cm² As = 0.547 cm²


b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9



b = 25.00 cmd = 24.10 cmФ = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8


Mmax (+) 0.100 Tn-m Mmax (+) 0.186 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9

Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d a =2.41 cmAs = 0.116 cm² a =0.11 cm REPETIR As = 0.215 cm² a =0.20 cmAs = 0.110 cm² a =0.10 cm OK As = 0.205 cm² a =0.19 cmAs = 0.110 cm² a =0.10 cm OK As = 0.205 cm²

As = 0.110 cm²

Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.280 Tn-m Mmax (+) 0.296 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.504 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.523 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8

Derecha FORMULAS0.000 Tn-m

0.876 Tn-m0.524 Tn-m 0 = colocar acero minimo

0.225 Tn-m

0.452 Tn-m0.517 Tn-m0.000 Tn-m0.890 Tn-m0.405 Tn-m0.000 Tn-m0.483 Tn-m0.490 Tn-m0.000 Tn-m0.317 Tn-m0.284 Tn-m0.000 Tn-m0.430 Tn-m0.523 Tn-m


Mmax (-) 0.846 Tn-m Mmax (-) 0.876 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9




OK As = 0.947 cm² a =0.89 cm OK As = 0.981 cm² a =0.92 cmAs = 0.947 cm² As = 0.981 cm²

As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (-) 0.279 Tn-m Mmax (-) 0.225 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9






b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9





As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8


Mmax (-) 0.768 Tn-m Mmax (-) 0.890 Tn-m

b = 25.00 cm b = 25.00 cm

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d = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9






b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9





As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (-) 0.490 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9

Asumir: a = 0.10.d a =2.41 cm



As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²


Mmax (+) 0.351 Tn-m Mmax (+) 0.317 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9



OK As = 0.389 cm² a =0.37 cm REPETIR As = 0.351 cm² a =0.33 cmAs = 0.388 cm² a =0.37 cm OK As = 0.350 cm² a =0.33 cmAs = 0.388 cm² As = 0.350 cm²

As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.284 Tn-m Mmax (+) 0.281 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9





As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.430 Tn-m Mmax (+) 0.218 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9






REPETIRREPETIR

OK

As =2.000 cm²

VIGAS PRINCIPALES EJE D-D

PISOS VIGAS

Volado

Viga 3 - 4Viga 4 - 5

Viga 6 - 7

Volado

Viga 3 - 4Volado

Viga 6 - 7

Volado

Viga 3 - 4Volado

Viga 6 - 7


b = 25.00 cmh = 30.00 cmf'c = 210 Kg/cm²fy = 4200 Kg/cm²β = 0.85

Recub = 4.00 cm



As min = 1.455 cm²


Pb = (0.723.f'c/fy)*(6300/(6300+fy))Pb = 0.0217

Pmax = 0.75.PbAs max = 9.799 cm²


A. ACEROS POSITIVOS

Volado

Viga 3 - 4

PRIMER PISO

Viga 2 - 3

Viga 5 - 6

SEGUNDO PISO

Viga 2 - 3

Viga 5 - 6

TERCER PISO

Viga 2 - 3

Viga 5 - 6

PRIMER PISO

Viga 2 - 3

Viga 4 - 5

Viga 6 - 7Volado

Viga 3 - 4Volado

Viga 6 - 7Volado

Viga 3 - 4Volado

Viga 6 - 7


Mmax (-) 0.208 Tn-m Mmax (+) 0.640 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9

Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.d

REPETIR As = 0.240 cm² a =0.23 cm REPETIR As = 0.740 cm²


OK As = 0.229 cm² a =0.22 cm OK As = 0.713 cm²As = 0.229 cm² As = 0.713 cm²

As =2.000 cm² Usar 2.000 cm² As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (-) 0.500 Tn-m Mmax (+) 0.000 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9




OK As = 0.555 cm² a =0.52 cm OK As = 0.000 cm²

As = 0.555 cm²

As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.880 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9

Asumir: a = 0.10.d

REPETIR As = 1.017 cm²


OK As = 0.985 cm²As = 0.985 cm²

As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8


Mmax (-) 0.234 Tn-m Mmax (+) 0.620 Tn-m

b = 25.00 cm b = 25.00 cm

PRIMER PISO

Viga 5 - 6

SEGUNDO PISO

Viga 2 - 3

Viga 5 - 6

TERCER PISO

Viga 2 - 3

Viga 5 - 6

d = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9





As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (-) 0.483 Tn-m Mmax (+) 0.990 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9






TERCER PISO

Mmax (+) 0.210 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9


TERCER PISO Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.320 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9

Asumir: a = 0.10.d



OK As = 0.354 cm²As = 0.354 cm²

As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8

REPETIRREPETIR

OK

As =2.000 cm²

REPETIRREPETIR

OK

As =2.000 cm²

VIGAS PRINCIPALES EJE D-D

Mº Max. NegativosIzquierda Derecha

0.610 Tn-m 0.000 Tn-m 0.000 Tn-m

1.148 Tn-m 1.020 Tn-m 0.640 Tn-m0.777 Tn-m 1.115 Tn-m 0.540 Tn-m0.673 Tn-m 0.468 Tn-m 0.000 Tn-m1.674 Tn-m 1.412 Tn-m 0.910 Tn-m0.900 Tn-m 1.675 Tn-m 0.880 Tn-m

0.610 Tn-m 0.000 Tn-m 0.000 Tn-m


0.186 Tn-m 0.000 Tn-m 0.000 Tn-m




Ф Asumo : 3/4" 1.91 cm

Ф Estribos : 3/8" 0.95 cmd: h - Recub - Фestrib - Фasumo/2d: 24.10 cm


2 Φ 3/8 1.420 cm²1 Φ 1/2 + 1 Φ 3/8 2.000 cm²


(0.723.f'c/fy)*(6300/(6300+fy))

0.0163

2 Φ 1 10.200 cm²



0.000 Tn-m Volado

0.640 Tn-m 0 = colocar acero minimo0.540 Tn-m Viga 3 - 4

Mº Max. Posiitivo

PRIMER PISO

Viga 2 - 3

0.000 Tn-m Viga 4 - 5

0.910 Tn-m0.880 Tn-m Viga 6 - 70.000 Tn-m Volado0.620 Tn-m0.580 Tn-m Viga 3 - 40.000 Tn-m Volado0.990 Tn-m0.830 Tn-m Viga 6 - 70.000 Tn-m Volado0.210 Tn-m0.180 Tn-m Viga 3 - 40.000 Tn-m Volado0.320 Tn-m0.260 Tn-m Viga 6 - 7


Mmax (+) 0.540 Tn-m Mmax (-) 0.610 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9

a =2.41 cm Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.da =0.70 cm REPETIR As = 0.624 cm² a =0.59 cm REPETIR As = 0.705 cm²a =0.67 cm REPETIR As = 0.600 cm² a =0.56 cm REPETIR As = 0.679 cm²a =0.67 cm OK As = 0.600 cm² a =0.56 cm OK As = 0.679 cm²

As = 0.600 cm² As = 0.679 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.910 Tn-m Mmax (-) 1.115 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9

a =2.41 cm Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.da =0.00 cm REPETIR As = 1.052 cm² a =0.99 cm REPETIR As = 1.288 cm²a =0.00 cm OK As = 1.020 cm² a =0.96 cm REPETIR As = 1.256 cm²

As = 1.019 cm² a =0.96 cm OK As = 1.255 cm²As = 1.019 cm² As = 1.255 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (-) 1.412 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9

a =2.41 cm Asumir: a = 0.10.da =0.96 cm REPETIR As = 1.632 cm²a =0.93 cm REPETIR As = 1.602 cm²a =0.93 cm OK As = 1.601 cm²

As = 1.601 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8


Mmax (+) 0.580 Tn-m Mmax (-) 0.610 Tn-m

b = 25.00 cm b = 25.00 cm

PRIMER PISO

Viga 5 - 6

SEGUNDO PISO

Viga 2 - 3

Viga 5 - 6

TERCER PISO

Viga 2 - 3

Viga 5 - 6

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MuAs

bcf

fyAsa

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.

d = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9


As = 0.645 cm² As = 0.679 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.830 Tn-m Mmax (-) 1.124 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9


As = 0.928 cm² As = 1.265 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (-) 1.025 Tn-m

TERCER PISO TERCER PISO b = 25.00 cmMmax (+) 0.180 Tn-m d = 24.10 cm

b = 25.00 cm Ф = 0.9d = 24.10 cmФ = 0.9 Asumir: a = 0.10.d

As = 1.184 cm²a =2.41 cm Asumir: a = 0.10.d a =2.41 cm As = 1.152 cm²a =0.23 cm REPETIR As = 0.208 cm² a =0.20 cm REPETIR As = 1.151 cm²a =0.22 cm REPETIR As = 0.198 cm² a =0.19 cm OK As = 1.151 cm²

a =0.22 cm OK As = 0.198 cm² Usar 1 Φ 1/2 + 1 Φ 3/8

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² TERCER PISO

Mmax (+) 0.260 Tn-m Mmax (+) 0.186 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9


As = 0.287 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.257 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.407 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.407 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9


Usar 1 Φ 1/2 + 1 Φ 3/8

Izquierda Derecha FORMULAS0.610 Tn-m 0.000 Tn-m

1.148 Tn-m 1.020 Tn-m0.777 Tn-m 1.115 Tn-m 0 = colocar acero minimo

0.673 Tn-m 0.468 Tn-m

1.674 Tn-m 1.412 Tn-m0.900 Tn-m 1.675 Tn-m0.610 Tn-m 0.000 Tn-m1.131 Tn-m 1.073 Tn-m0.673 Tn-m 1.124 Tn-m0.000 Tn-m 0.164 Tn-m1.193 Tn-m 1.726 Tn-m1.025 Tn-m 1.628 Tn-m0.186 Tn-m 0.000 Tn-m0.281 Tn-m 0.362 Tn-m0.257 Tn-m 0.290 Tn-m0.000 Tn-m 0.097 Tn-m0.407 Tn-m 0.458 Tn-m0.362 Tn-m 0.407 Tn-m


Mmax (-) 1.148 Tn-m Mmax (-) 1.020 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9


As = 1.293 cm² As = 1.145 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (-) 0.673 Tn-m Mmax (-) 0.468 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9


As = 0.750 cm² As = 0.519 cm²


b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9


As = 1.008 cm² As = 1.910 cm²



Mmax (-) 1.131 Tn-m Mmax (-) 1.073 Tn-m

b = 25.00 cm b = 25.00 cm

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d = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9


As = 1.273 cm² As = 1.207 cm²


b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9

a =2.41 cm Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.da =1.22 cm REPETIR As = 0.189 cm² a =0.18 cm REPETIR As = 1.379 cm²a =1.19 cm REPETIR As = 0.181 cm² a =0.17 cm OK As = 1.346 cm²a =1.19 cm OK As = 0.181 cm² As = 1.346 cm²

As = 1.346 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 2 Φ 1/2Mmax (-) 1.628 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9

a =2.41 cm Asumir: a = 0.10.d a =2.41 cma =1.11 cm REPETIR As = 1.881 cm² a =1.77 cm REPETIRa =1.08 cm REPETIR As = 1.856 cm² a =1.75 cm REPETIRa =1.08 cm OK As = 1.855 cm² a =1.75 cm OK

As = 1.855 cm²



Mmax (+) 0.281 Tn-m Mmax (+) 0.362 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9

a =2.41 cm Asumir: a = 0.10.d a =2.41 cm Asumir: a = 0.10.da =0.20 cm REPETIR As = 0.325 cm² a =0.31 cm REPETIR As = 0.418 cm²a =0.19 cm OK As = 0.311 cm² a =0.29 cm REPETIR As = 0.400 cm²

As = 0.311 cm² a =0.29 cm OK As = 0.400 cm²As = 0.311 cm² As = 0.400 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.290 Tn-m Mmax (+) 0.097 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9


As = 0.321 cm² As = 0.106 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8Mmax (+) 0.458 Tn-m Mmax (+) 0.362 Tn-m

b = 25.00 cm b = 25.00 cmd = 24.10 cm d = 24.10 cmФ = 0.9 Ф = 0.9


As = 0.508 cm² As = 0.401 cm²


a =2.41 cma =0.44 cm REPETIRa =0.42 cm REPETIRa =0.42 cm OK

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²


Mmax (-) 0.777 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9


As = 0.867 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 2.000 cm² As =2.000 cm²Mmax (-) 1.674 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9


As = 1.909 cm²



1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²


Mmax (-) 0.673 Tn-m

b = 25.00 cm

d = 24.10 cmФ = 0.9


As = 0.750 cm²

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²Mmax (-) 1.726 Tn-m

b = 25.00 cmd = 24.10 cmФ = 0.9


As = 1.971 cm²

2 Φ 1/2 As =2.580 cm² Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²

TERCER PISO


1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²

a =2.41 cma =0.11 cm REPETIRa =0.10 cm OKa =0.10 cm OK

1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²


1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm²


PROYECTO VIVIENDA MULTIFAMILIAR - 3 PSIOS 1/2 - 3/8"

1 Φ 3/8ESPECIFICACIONES TÉCNICAS: PROYECTO DEPARTAMENTOS 3 NIVELES 1 Φ 1/2

CARACTERISTICAS DE MATERIALES PESO POR METRO CUADRADO

P. E. Muro de Albañileria 1800 Kg/cm² Vivienda (S/C) 200 Kg/m² 1 Φ 1/2 + 1 Φ 3/8Resist.a la compresion : f 210 Kg/cm² Aligerado (0.20cm) 300 Kg/m²P. Esp. Del Cº: Γc 2400 Kg/cm² E. de P. Muerto: 0.075 m 2 Φ 1/2Fluencia del acero 4200 Kg/cm² Ancho tabiqueria: 0.150 m 1 Φ 1/2 + 2 Φ 3/8P. Esp. Del Cº: Γc 2000 Kg/m³ P. Tab.Eq. 2º piso: 319 Kg/m² 4 Φ 3/8Altura Entrepiso 2.60 m P. Tab.Eq. 3º piso: 324 Kg/m² 2 Φ 1/2 + 1 Φ 3/8

Azotea: S/C 100 Kg/m² 3 Φ 1/2

DISEÑO DE LOSA ALIGERADA

1. METRADO DE CARGAS

P. Losa Alig. (h=20 cm) 300 Kg/m²Peso Muerto 150 Kg/m²P. Tabiqueria Equivalent 324 Kg/m²Carga Muerta (Cm) 774 Kg/m²Wu Cm = 1.4 Cm 1083 Kg/m²

Sobrecarga (S/C) 200 Kg/m²Carga Viva (Cv) 200 Kg/m²Wu Cv = 1.7 Cv 340 Kg/m²

Carga Ultima (Wu) 1423 Kg/m²

CARGA PUNTUAL EN VOLADOS O OEspesor de muro 0.150 m

Altura de Muro 2.600 m O O

Ancho 1.000 m 0.10 mPm = 702.00 Kg

1.00 m

PARA 1.00 m DE ANCHO DE LOSA

1.00 m = 2.5 viguetas

Wu Cm 1083 Kg/mWu Cv 340 Kg/mCarga Ultima (Wu) 1423 Kg/m

2. MOMENTOS DE FLEXION

EMVOLVENTE ALIGERADO A

APOYO Mº NEGATIVO TRAMO Mº POSITIVO

2 1.610 2 - 3 1.1403 1.820 3 - 4 0.8104 1.590 4 - 5 1.0405 0.000

EMVOLVENTE ALIGERADO B


6 2.050 6 - 7 1.9907 0.000

EMVOLVENTE ALIGERADO C

2 Φ 3/8

3 Φ 3/8


menores que el acerro minimo o mayores que el acero maximo.


2 1.610 2 - 3 1.1003 1.920 3 - 4 0.9804 1.149 4 - 5 0.3605 1.960 5 - 6 1.5306 3.040 6 - 7 1.8807 0.000

EMVOLVENTE ALIGERADO D


3 0.000 3 - 4 0.7804 1.095 4 - 5 0.0505 1.240 5 - 6 0.9706 1.978 6 - 7 1.2107 0.000

EMVOLVENTE ALIGERADO E


2 1.460 2 - 3 0.7903 1.520 3 - 4 0.6804 1.050

EMVOLVENTE ALIGERADO F


5 0.000 5 - 6 1.9706 2.870 6 - 7 1.4307 0.000

EMVOLVENTE ALIGERADO G


B 0.000 B - C 0.900C 0.000

3. DIMENSION Y PROPIEDADES DE LA VIGUETA 4. ACERO MINIMO POR VIGUETA

b = 25.00 cm As min = Pmin.b.dh = 20.00 cm Pmin = 0.00242f'c = 210 Kg/cm² As min = 1.028 cm²fy = 4200 Kg/cm² As min / Vigueta = 0.411 cm²

Recub = 2.50 cm 1 Φ 3/8 As =0.710 cm²Peralte Efectivo de la seccion:

Ф Asumo : 3/8" 0.95 cmd: h - Recub - Фasumo/2d: 17.03 cm

6. REFUERZO POSITIVO Y NEGATIVOS DE ALIGERADOS

ACEROS NEGATIVOS ACEROS POSITIVOS

bw = 2500.00 cm bw = 100.00 cmf'c = 210 Kg/cm² f'c = 210 Kg/cm²fy = 4200 Kg/cm² fy = 4200 Kg/cm²Ф = 0.90 Ф = 0.90d = 17.03 cm d = 17.03 cm

ALIGERADO TIPO A


Mmax (-) 1.610 Tn-m Mmax (+) 1.140 Tn-m

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Asumir: a = 0.10.d a =1.70 cm Asumir: a = 0.10.d a =1.70 cmAs = 2.633 cm² a =0.02 cm REPETIR As = 1.865 cm² a =0.02 cmAs = 2.504 cm² a =0.02 cm OK As = 1.772 cm² a =0.02 cmAs = 2.504 cm² As vigueta = 1.001 cm² As = 1.772 cm² As vigueta =

Usar 1 Φ 1/2 As =1.290 cm² Usar 1 Φ 3/8Mmax (-) 1.820 Tn-m Mmax (+) 0.810 Tn-m




Usar 1 Φ 1/2 As =1.290 cm² Usar 1 Φ 3/8Mmax (-) 0.000 Tn-m

Asumir: a = 0.10.d a =1.70 cmAs = 0.000 cm² a =0.00 cm REPETIRAs = 0.000 cm² a =0.00 cm OKAs = 0.000 cm² As vigueta = 0.000 cm²

Usar 1 Φ 3/8 As =0.710 cm²

ALIGERADO TIPO B


Mmax (-) 2.050 Tn-m Mmax (+) 1.990 Tn-m




Usar 1 Φ 3/8 As =0.710 cm²

ALIGERADO TIPO C


Mmax (-) 1.610 Tn-m Mmax (+) 1.100 Tn-m

Asumir: a = 0.10.d a =1.70 cm Asumir: a = 0.10.d a =1.70 cmAs = 2.633 cm² a =0.02 cm REPETIR As = 1.799 cm² a =0.02 cmAs = 2.504 cm² a =0.02 cm OK As = 1.710 cm² a =0.02 cm

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As = 2.504 cm² As vigueta = 1.001 cm² As = 1.710 cm² As vigueta =









Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2

ALIGERADO TIPO D


Mmax (-) 0.000 Tn-m Mmax (+) 0.780 Tn-m








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Usar 1 Φ 1/2 As =1.290 cm² Usar 1 Φ 1/2

ALIGERADO TIPO E


Mmax (-) 1.460 Tn-m Mmax (+) 0.790 Tn-m






Usar 1 Φ 3/8 As =0.710 cm²

ALIGERADO TIPO F


Mmax (-) 2.870 Tn-m Mmax (+) 1.970 Tn-m


Usar 1 Φ 1/2 + 1 Φ 3/8 As =2.000 cm² Usar 1 Φ 1/2Mmax (-) 0.000 Tn-m Mmax (+) 1.430 Tn-m


Usar 1 Φ 3/8 As =0.710 cm² Usar 1 Φ 1/2

ALIGERADO TIPO G


Mmax (-) 0.000 Tn-m Mmax (+) 0.900 Tn-m


Usar 1 Φ 3/8 As =0.710 cm² Usar 1 Φ 3/8

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COMBINACIONES RECOMENDADAS ACEROS COMERCIALES

Area BARRA DIAMETRO Peso Area

0.710 cm² numero pulg cm Kg/m cm2

1.290 cm² 3 3/8 0.95 0.559 0.711.420 cm² 4 1/2 1.27 0.993 1.292.000 cm² 5 5/8 1.59 1.552 1.982.130 cm² 6 3/4 1.91 2.235 2.852.580 cm² 7 7/8 2.22 3.042 3.882.710 cm² 8 1 2.54 3.973 5.12.840 cm² 9 1 1/8 2.86 5.028 6.453.290 cm² 10 1 1/4 3.18 6.207 8.193.870 cm² 11 1 3/8 3.49 7.511 9.58

12 1 1/2 3.81 8.938 11.4

DETALLE DE ALIGERADO (h = 0.20 m)

0.05 m

0.20 mO O O O

0.15 mO O O O

0.30 m 0.10 m 0.30 m 0.10 m 0.30 m

1.00 m

2.5 VIGUETAS


menores que el acerro minimo o mayores que el acero maximo.

5. ACERO MAXIMO POR VIGUETA

As max = Pmax.b.dρ maxina = 0.75 ρb = 0.01627Cuantia Balanceada (ρb) 0.022 cm²As max = 6.924 cm²As max / Vigueta = 2.770 cm²

2 Φ 1/2 As =2.580 cm²

As a

REPETIR As VIGUETA #REF!

OK USAR 1 ф 1/2" + 1 ф 3/8"

0.709 cm²

As =0.710 cm²

REPETIROK

0.504 cm²

As =0.710 cm²

REPETIROK

0.647 cm²

As =0.710 cm²

REPETIROK

1.238 cm²

As =1.290 cm²

REPETIROK

0.684 cm²

As =0.710 cm²

REPETIROK

0.609 cm²

As =0.710 cm²

REPETIROK

0.224 cm²

As =0.710 cm²

REPETIROK

0.952 cm²

As =1.290 cm²

REPETIROK

1.169 cm²

As =1.290 cm²

REPETIROK

0.485 cm²

As =0.710 cm²

REPETIROK

0.031 cm²

As =0.710 cm²

REPETIROK

0.603 cm²

As =0.710 cm²

REPETIROK

0.752 cm²

As =1.290 cm²

REPETIROK

0.491 cm²

As =0.710 cm²

REPETIROK

0.423 cm²

As =0.710 cm²

REPETIROK

1.226 cm²

As =1.290 cm²

REPETIROK

0.889 cm²

As =1.290 cm²

REPETIROK

0.560 cm²

As =0.710 cm²

As VIGUETA #REF!

USAR 1 ф 3/8"


LOSA ALIGERADA - ALTERNANCIA DE CARGAS VIGUETA D

TOTALMENTE CARGADA

CARACTERISTICAS b = 0.25 m INERCIA 0.000167 m4h = 0.20 m

2.900 m 2.450 m 3.730 m 3.370 m

A. MOMENTOS DE EMPOTRAMIENTOM34 = -1.00 Tn-m

M43 = 1.00 Tn-m

M45 = -0.71 Tn-m Wu Cm = 1.4 Cm 1083 Kg/m

M54 = 0.71 Tn-m Wu Cv = 1.7 Cv 340 Kg/m

M56 = -1.65 Tn-m Wu = 1423 Kg/m

M65 = 1.65 Tn-m

M67 = -1.35 Tn-m

M76 = 1.35 Tn-m

B. FACTORES DE DISTRIBUCIONNUDO 3 K34 = 0.000043 FD34 = 1.0000

ΣK = 0.000043 1.0000NUDO 4 K43 = 0.000043 F43 = 0.3879

K45 = 0.000068 F45 = 0.6121ΣK = 0.000111 1.0000

NUDO 5 K54 = 0.000068 F54 = 0.6036K56 = 0.000045 F56 = 0.3964ΣK = 0.000113 1.0000

NUDO 6 K65 = 0.000045 F65 = 0.5464K67 = 0.000037 F67 = 0.4536ΣK = 0.000082 1.0000

NUDO 7 K76 = 0.000049 F76 = 1.0000ΣK = 0.000049 1.0000

C. DISTRIBUCION DE MOMENTOS

1.0000 0.3879 0.6121 0.6036 0.3964-0.9975 0.9975 -0.7120 0.7120 -1.65030.9975 0.4988 0.2832 0.5663 0.3720

3 4 5

-0.4140 -0.6535 -0.3267 0.05040.0834 0.1668 0.1096

-0.0323 -0.0511 -0.0255 -0.01500.0122 0.0244 0.0161

-0.0047 -0.0075 -0.0037 -0.00220.0018 0.0036 0.0024

-0.0007 -0.0011 -0.0005 -0.00030.0003 0.0005 0.0003

-0.0001 -0.0002 -0.0001 0.00000.0000 1.0444 -1.0444 1.1170 -1.1171

CARGA VIVA 1

2.900 m 2.450 m 3.730 m 3.370 m

A. MOMENTOS DE EMPOTRAMIENTOM34 = -1.00 Tn-m

M43 = 1.00 Tn-m

M45 = -0.54 Tn-m Wu Cm = 1.4 Cm 1083 Kg/m

M54 = 0.54 Tn-m Wu Cv = 1.7 Cv 340 Kg/m

M56 = -1.65 Tn-m Wu = 1423 Kg/m

M65 = 1.65 Tn-m

M67 = -1.03 Tn-m

M76 = 1.03 Tn-m


1.0000 0.3879 0.6121 0.6036 0.3964-0.9975 0.9975 -0.5419 0.5419 -1.65030.9975 0.4988 0.3345 0.6690 0.4394

-0.4999 -0.7890 -0.3945 -0.09070.1464 0.2928 0.1923

-0.0568 -0.0896 -0.0448 -0.02630.0215 0.0429 0.0282

-0.0083 -0.0131 -0.0066 -0.00380.0031 0.0063 0.0041

-0.0012 -0.0019 -0.0010 -0.00060.0005 0.0009 0.0006

-0.0002 -0.0003 -0.0001 -0.00010.0000 0.9299 -0.9299 1.1069 -1.1071

CARGA VIVA 2

3 4 5

2.900 m 2.450 m 3.730 m 3.370 m

A. MO MENTOS DE EMPOTRAMIENTOM34 = -0.76 Tn-m

M43 = 0.76 Tn-m

M45 = -0.71 Tn-m Wu Cm = 1.4 Cm 1083 Kg/m

M54 = 0.71 Tn-m Wu Cv = 1.7 Cv 340 Kg/m

M56 = -1.26 Tn-m Wu = 1423 Kg/m

M65 = 1.26 Tn-m

M67 = -1.35 Tn-m

M76 = 1.35 Tn-m


1.0000 0.3879 0.6121 0.6036 0.3964-0.7593 0.7593 -0.7120 0.7120 -1.25610.7593 0.3796 0.1642 0.3284 0.2157

-0.2293 -0.3618 -0.1809 0.17940.0005 0.0009 0.0006

-0.0002 -0.0003 -0.0001 -0.00010.0001 0.0001 0.0001

0.0000 0.0000 0.0000 0.00000.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.00000.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.00000.0000 0.9094 -0.9094 0.8604 -0.8604

CARGA VIVA 3

2.900 m 2.450 m 3.730 m 3.370 m


M43 = 1.00 Tn-m

M45 = -0.71 Tn-m Wu Cm = 1.4 Cm 1083 Kg/m

M54 = 0.71 Tn-m Wu Cv = 1.7 Cv 340 Kg/m

M56 = -1.26 Tn-m Wu = 1423 Kg/m

M65 = 1.26 Tn-m

M67 = -1.03 Tn-m

M76 = 1.03 Tn-m


1.0000 0.3879 0.6121 0.6036 0.3964

3 4 5

3 4 5

-0.9975 0.9975 -0.7120 0.7120 -1.25610.9975 0.4988 0.1642 0.3284 0.2157

-0.3679 -0.5806 -0.2903 0.04760.0733 0.1465 0.0962

-0.0284 -0.0448 -0.0224 -0.01310.0107 0.0215 0.0141

-0.0042 -0.0066 -0.0033 -0.00190.0016 0.0031 0.0021

-0.0006 -0.0010 -0.0005 -0.00030.0002 0.0005 0.0003

-0.0001 -0.0001 -0.0001 0.00000.0000 1.0951 -1.0951 0.8954 -0.8955

CARGA VIVA 4

2.900 m 2.450 m 3.730 m 3.370 m


M43 = 0.76 Tn-m

M45 = -0.71 Tn-m Wu Cm = 1.4 Cm 1083 Kg/m

M54 = 0.71 Tn-m Wu Cv = 1.7 Cv 340 Kg/m

M56 = -1.65 Tn-m Wu = 1423 Kg/m

M65 = 1.65 Tn-m

M67 = -1.03 Tn-m

M76 = 1.03 Tn-m


1.0000 0.3879 0.6121 0.6036 0.3964-0.7593 0.7593 -0.7120 0.7120 -1.65030.7593 0.3796 0.2832 0.5663 0.3720

-0.2754 -0.4347 -0.2173 -0.08150.0902 0.1804 0.1185

-0.0350 -0.0552 -0.0276 -0.01620.0132 0.0264 0.0174

-0.0051 -0.0081 -0.0040 -0.00240.0019 0.0039 0.0025

-0.0008 -0.0012 -0.0006 -0.00030.0003 0.0006 0.0004

-0.0001 -0.0002 -0.0001 -0.00010.0000 0.8225 -0.8225 1.2399 -1.2400

CARGA VIVA 5

3 4 5

2.900 m 2.450 m 3.730 m 3.370 m


M43 = 0.76 Tn-m

M45 = -0.54 Tn-m Wu Cm = 1.4 Cm 1083 Kg/m

M54 = 0.54 Tn-m Wu Cv = 1.7 Cv 340 Kg/m

M56 = -1.65 Tn-m Wu = 1423 Kg/m

M65 = 1.65 Tn-m

M67 = -1.35 Tn-m

M76 = 1.35 Tn-m


1.0000 0.3879 0.6121 0.6036 0.3964-0.7593 0.7593 -0.5419 0.5419 -1.65030.7593 0.3796 0.3345 0.6690 0.4394

-0.3613 -0.5702 -0.2851 0.04120.0736 0.1472 0.0967

-0.0286 -0.0451 -0.0225 -0.01320.0108 0.0216 0.0142

-0.0042 -0.0066 -0.0033 -0.00190.0016 0.0032 0.0021

-0.0006 -0.0010 -0.0005 -0.00030.0002 0.0005 0.0003

-0.0001 -0.0001 -0.0001 0.00000.0000 0.7442 -0.7442 1.0718 -1.0719

CARGA VIVA 6

2.900 m 2.450 m 3.730 m 3.370 m


M43 = 1.00 Tn-m

M45 = -0.71 Tn-m Wu Cm = 1.4 Cm 1083 Kg/m

M54 = 0.71 Tn-m Wu Cv = 1.7 Cv 340 Kg/m

M56 = -1.65 Tn-m Wu = 1423 Kg/m

M65 = 1.65 Tn-m

M67 = -1.03 Tn-m

M76 = 1.03 Tn-m


1.0000 0.3879 0.6121 0.6036 0.3964

3 4 5

3 4 5

-0.9975 0.9975 -0.7120 0.7120 -1.65030.9975 0.4988 0.2832 0.5663 0.3720

-0.4140 -0.6535 -0.3267 -0.08150.1232 0.2464 0.1618

-0.0478 -0.0754 -0.0377 -0.02210.0181 0.0361 0.0237

-0.0070 -0.0110 -0.0055 -0.00320.0026 0.0053 0.0035

-0.0010 -0.0016 -0.0008 -0.00050.0004 0.0008 0.0005

-0.0002 -0.0002 -0.0001 -0.00010.0000 1.0263 -1.0263 1.1960 -1.1961

CARGA VIVA 7

2.900 m 2.450 m 3.730 m 3.370 m


M43 = 0.76 Tn-m

M45 = -0.71 Tn-m Wu Cm = 1.4 Cm 1083 Kg/m

M54 = 0.71 Tn-m Wu Cv = 1.7 Cv 340 Kg/m

M56 = -1.65 Tn-m Wu = 1423 Kg/m

M65 = 1.65 Tn-m

M67 = -1.35 Tn-m

M76 = 1.35 Tn-m


1.0000 0.3879 0.6121 0.6036 0.3964-0.7593 0.7593 -0.7120 0.7120 -1.65030.7593 0.3796 0.2832 0.5663 0.3720

-0.2754 -0.4347 -0.2173 0.05040.0504 0.1008 0.0662

-0.0195 -0.0308 -0.0154 -0.00900.0074 0.0148 0.0097

-0.0029 -0.0045 -0.0023 -0.00130.0011 0.0022 0.0014

-0.0004 -0.0007 -0.0003 -0.00020.0002 0.0003 0.0002

-0.0001 -0.0001 0.0000 0.00000.0000 0.8406 -0.8406 1.1609 -1.1610

EMVOLVENTE

0.0000 1.0951 -1.0951 1.2399 -1.2400

APOYO 3 APOYO 4 APOYO 5

3 4 5

EMVOLVENTE ALIGERADO DAPOYO Mº NEGATIVO TRAMO Mº POSITIVO

3 0.0000 3 - 4 0.784 -1.0951 4 - 5 0.055 -1.2400 5 - 6 0.976 -1.9780 6 - 7 1.217 0.0000

0.5464 0.4536 1.00001.6503 -1.3471 1.34710.1860 -0.6735 -1.3471

6 7

0.1007 0.08360.0548-0.0299 -0.02480.0080-0.0044 -0.00360.0012-0.0006 -0.00050.0002-0.0001 -0.00011.9661 -1.9661 0.0000

0.5464 0.4536 1.00001.6503 -1.0253 1.02530.2197 -0.5127 -1.0253-0.1814 -0.15060.0962-0.0526 -0.04360.0141-0.0077 -0.00640.0021-0.0011 -0.00090.0003-0.0002 -0.00011.7396 -1.7396 0.0000

6 7

0.5464 0.4536 1.00001.2561 -1.3471 1.34710.1078 -0.6735 -1.34710.3588 0.29790.0003-0.0002 -0.00010.00000.0000 0.00000.00000.0000 0.00000.00000.0000 0.00001.7229 -1.7229 0.0000

0.5464 0.4536 1.0000

6 7

6 7

1.2561 -1.0253 1.02530.1078 -0.5127 -1.02530.0951 0.07890.0481-0.0263 -0.02180.0071-0.0039 -0.00320.0010-0.0006 -0.00050.0002-0.0001 -0.00011.4846 -1.4846 0.0000

0.5464 0.4536 1.00001.6503 -1.0253 1.02530.1860 -0.5127 -1.0253-0.1630 -0.13530.0592-0.0324 -0.02690.0087-0.0047 -0.00390.0013-0.0007 -0.00060.0002-0.0001 -0.00011.7047 -1.7047 0.0000

6 7

0.5464 0.4536 1.00001.6503 -1.3471 1.34710.2197 -0.6735 -1.34710.0823 0.06830.0484-0.0264 -0.02190.0071-0.0039 -0.00320.0010-0.0006 -0.00050.0002-0.0001 -0.00011.9780 -1.9780 0.0000

0.5464 0.4536 1.0000

6 7

6 7

1.6503 -1.0253 1.02530.1860 -0.5127 -1.0253-0.1630 -0.13530.0809-0.0442 -0.03670.0119-0.0065 -0.00540.0017-0.0009 -0.00080.0003-0.0001 -0.00011.7163 -1.7163 0.0000

0.5464 0.4536 1.00001.6503 -1.3471 1.34710.1860 -0.6735 -1.34710.1007 0.08360.0331-0.0181 -0.01500.0048-0.0026 -0.00220.0007-0.0004 -0.00030.0001-0.0001 0.00001.9546 -1.9546 0.0000

EMVOLVENTE

1.9780 -1.9780 0.0000

APOYO 6 APOYO 7

6 7


VERIFICACION POR CORTE - ALIGERADOS

Carga Ultima (Wu) 1423 Kg/mPm = 702.00 KgResist.a la compresion : f'c 210 Kg/cm²

Fluencia del acero 4200 Kg/cm²

Ancho de columna (t) : 0.25 cm

Base de vigueta: bw 25.00 cm

Peralte Efectivo de la seccion: 17.03 cm2779 Kg/cm²

ALIGERADO A

0.930 m 3.150 m 2.900 m 2.450 marriba (-) abajo (+)

APOYO As/ vigueta Ast a Mr Vi Vi'

Volado -702.00 Kg2 1 Φ 1/2 1.290 cm² 3.225 cm² 3.04 cm 1890.42 Kg-m -2025.74 Kg 2241.81 Kg3 1 Φ 1/2 1.290 cm² 3.225 cm² 3.04 cm 1890.42 Kg-m -2241.81 Kg 2063.89 Kg4 1 Φ 1/2 1.290 cm² 3.225 cm² 3.04 cm 1890.42 Kg-m -2063.89 Kg 2071.87 Kg5 1 Φ 3/8 0.710 cm² 1.775 cm² 1.67 cm 1086.25 Kg-m -1415.40 Kg

Vmax 2241.81 Kg

Vud 1821.56 Kg

DISEÑO DE LOSA CORRECTO

ALIGERADO B

1.310 m 3.370 marriba (-) abajo (+)


Volado -702.00 Kg6 1 Φ 1/2 1.290 cm² 3.225 cm² 3.04 cm 1890.42 Kg-m -2566.62 Kg 2637.01 Kg7 1 Φ 3/8 0.710 cm² 1.775 cm² 1.67 cm 1086.25 Kg-m -2159.75 Kg

Vmax 2637.01 Kg

Vud 2216.76 KgDISEÑO DE LOSA CORRECTO

ALIGERADO C

Cortante tomado por el cº: ΦVc

)2/.(.. adAsfyMr wbcf

fyAsa

.'.85.0

.

l

MMlwV jiui

)(

2

.

cVVn

dbfVc wc ..53.0 '

0.930 m 3.150 m 2.890 m 2.450 m 3.730 m 3.370 marriba (-) abajo (+)


Volado -702.00 Kg2 1 Φ 1/2 1.290 cm² 3.225 cm² 3.04 cm 1890.42 Kg-m -2025.74 Kg 2241.81 Kg3 1 Φ 1/2 1.290 cm² 3.225 cm² 3.04 cm 1890.42 Kg-m -2241.81 Kg 2056.77 Kg4 1 Φ 1/2 1.290 cm² 3.225 cm² 3.04 cm 1890.42 Kg-m -2056.77 Kg 1743.63 Kg5 1 Φ 1/2 1.290 cm² 3.225 cm² 3.04 cm 1890.42 Kg-m -1743.63 Kg 2654.59 Kg6 1/2 1.290 cm² 3.225 cm² 3.04 cm 1890.42 Kg-m -2654.59 Kg 2637.01 Kg7 1 Φ 3/8 0.710 cm² 1.775 cm² 1.67 cm 1086.25 Kg-m -2159.75 Kg

Vmax 2654.59 Kg


ALIGERADO D



3 1 Φ 3/8 0.710 cm² 1.775 cm² 1.67 cm 1086.25 Kg-m 2063.89 Kg4 1 Φ 3/8 0.710 cm² 1.775 cm² 1.67 cm 1086.25 Kg-m -2063.89 Kg 1415.40 Kg5 1 Φ 1/2 1.290 cm² 3.225 cm² 3.04 cm 1890.42 Kg-m -2071.87 Kg 2654.59 Kg6 1 Φ 1/2 1.290 cm² 3.225 cm² 3.04 cm 1890.42 Kg-m -2654.59 Kg 2637.01 Kg7 1 Φ 3/8 0.710 cm² 1.775 cm² 1.67 cm 1086.25 Kg-m -2159.75 Kg

Vmax 2654.59 Kg


ALIGERADO E



Volado -702.00 Kg2 1 Φ 1/2 1.290 cm² 3.225 cm² 3.04 cm 1890.42 Kg-m -2025.74 Kg 2241.81 Kg3 1 Φ 1/2 1.290 cm² 3.225 cm² 3.04 cm 1890.42 Kg-m -2241.81 Kg 2341.19 Kg4 1 Φ 3/8 0.710 cm² 1.775 cm² 1.67 cm 1086.25 Kg-m -1786.59 Kg 2025.74 Kg

Volado 702.00 KgVmax 2341.19 Kg


ALIGERADO F

3.730 m 3.370 marriba (-) abajo (+)


5 1 Φ 3/8 0.710 cm² 1.775 cm² 1.67 cm 1086.25 Kg-m 2438.99 Kg6 1/2 1.290 cm² 3.225 cm² 3.04 cm 1890.42 Kg-m -2870.19 Kg 2637.01 Kg7 1 Φ 3/8 0.710 cm² 1.775 cm² 1.67 cm 1086.25 Kg-m -2159.75 Kg

Vmax 2870.19 Kg


ALIGERADO G

3.730 marriba (-) abajo (+)


B 1 Φ 3/8 0.710 cm² 1.775 cm² 1.67 cm 1086.25 Kg-m 2654.59 KgC 1 Φ 3/8 0.710 cm² 1.775 cm² 1.67 cm 1086.25 Kg-m -2654.59 Kg

Vmax 2654.59 Kg



DISEÑO DE REFUERZO TRANSVERSAL

VIGAS PRINCIPALES: PRIMER PISO

DATOS:

f'c = 210 Kg/cm²

fy = 4200 Kg/cm²

Ǿ flex. 0.9

Ǿ corte 0.85

b: 25.00 cm

h: 35.00 cm

d: 29.10 cm

t : 25.00 cm

VIGA PRINCIPAL: VP-101

3.290 cm² Wu = 3.73 T/m 5.850 cm² Wu = 3.73 T/m

4.25 m 2.25 m

1. DIAGRAMA DE MOMENTOS REALES

MOMENTOS RESISTENTES:Usando las formulas de flexion simple:

APOYO A APOYO B APOYO C

As = 3.290 cm² As = 5.850 cm² As =a = 3.096 cm a = 5.506 cm a =Mr A = 3.426 Tn-m/m Mr B = 6.091 Tn-m/m Mr C =

DIAGRAMA DE MO MENTOS RESISTENTES

Mr A = 3.426 Tn-m Mr B = 6.091 Tn-m Mr C =

4.25 m 2.25 m

APOYO "A" APOYO "B" APOYO "C"

wbcf

fyAsa

.'.85.0

. )2/.(.. adAsfyMr

2. DIAGRAMA DE FUERZA CORTANTE

arriba (-) abajo (+)APOYO Mr Vi Vi'

APOYO A 3.426 Tn-m 7.304 TnAPOYO B 6.091 Tn-m -8.558 Tn 4.786 TnAPOYO C 4.769 Tn-m -3.611 Tn 8.105 TnAPOYO D 4.030 Tn-m -7.757 Tn

-8.558 Tn -3.611 Tn

4.25 m 2.25 m

7.304 Tn 4.786 Tn 8.105 Tn

3. DISEÑO DEL REFUERZO TRANSVERSAL

TRAMO A-B TRAMO B-C

CALCULO DEL CORTANTE A UNA DISTANCIA "d" CALCULO DEL CORTANTE A UNA DISTANCIA "d"

Vud = 5.751 Tn Vud = 3.234 Tn

CORTE TOMADO POR EL CONCRETO CORTE TOMADO POR EL CONCRETO

Vc = 5.587 Tn Vc = 5.587 Tn

CORTE TOMADO POR EL ACERO CORTE TOMADO POR EL ACERO

Vs = 0.165 Tn Vs = -2.353 Tn

MAXIMO CORTANTE TOMADO POR EL REFUERZO MAXIMO CORTANTE TOMADO POR EL REFUERZO

V's = 22.135 Tn mayor que: 0.165 Tn V's = 22.135 Tn mayor que: -2.353 Tn

Si se puede diseñar refuerzo para que tome el corte Si se puede diseñar refuerzo para que tome el corte

ESPACIAMIENTO MAXIMO ESPACIAMIENTO MAXIMO


Espaciamiento debe ser: d/2 14.55 cm Espaciamiento debe ser: d/2 14.55 cm12.50 cm 12.50 cm

4. DETERMINACION DEL ESPACIAMIENTO DE LOS ESTRIBOS4. DETERMINACION DEL ESPACIAMIENTO DE LOS ESTRIBOS

Z = 2.000 m Z = 1.500 m

Los espaciamientos se realizan generalmente a: Los espaciamientos se realizan generalmente a:0.75 cm 0.75 cm10.00 cm 10.00 cm

S 12.50 cm S 12.50 cm

VnVud

s

dfyAsVS

min

i

jiiui l

MrMrlwV

)(

2

.

)( VcVsVud

dbcfsV ..'1.2'

dbcfVc ´53.0

dbcfsV ..'1.1'

dbcfsV ..'1.2'

dbcfsV ..'1.1' dbcfsV ..'1.1'

15.00 cm 15.00 cm

17.50 cm As min = 1.420 cm² 17.50 cm

@ 5.0 cm Por norma @ 5.0 cm Por norma

@ 10.0 cm @ 10.0 cmVs = 17.352 Tn Vs = 17.352 TnCubre Tranquilament 7.304 Tn Cubre Tranquilament 4.786 Tn

5. DETERMINACION DE LAS LONGITUDES CUBIERTAS 5. DETERMINACION DE LAS LONGITUDES CUBIERTAS

TRAMO DE ESTRIBOS A @ 0.125 m TRAMO DE ESTRIBOS A @ 0.125 m

1.530 m 1.751 mNº de estribos 13 estribos 13 @ 0,125 Nº de estribos : 15 estribos 15 @ 0,125Longitud Estr 1.625 m Longitud Estribad 1.875 m

SEGUIMOS COLOCANDO ESTRIBOS TODA LA VIGA ESTA ESTRIBADA

TRAMO DE ESTRIBOS A @ 0.100 m

3.127 m

Execde distancia que queda por estribar

0.325 mNº de estribos 4 estribos 4 @ 0,1Longitud Estr 0.40 m

6. DISTRIBUCION DE ESTRIBOS 6. DISTRIBUCION DE ESTRIBOS

3/8 1@0,05, 4@0,1, 13@0,125∎ 3/8 1@0,05, 15@0,125∎


3.870 cm² Wu = 4.99 T/m 8.280 cm² Wu = 4.48 T/m

4.25 m 2.25 m






s

dfyAsVS

min

wbcf

fyAsa

.'.85.0

. )2/.(.. adAsfyMr



4.25 m 2.25 m



APOYO A 4.030 Tn-m 9.533 Tn

APOYO B 8.622 Tn-m -11.693 Tn 5.044 Tn

APOYO C 8.622 Tn-m -5.044 Tn 11.377 Tn

APOYO D 5.373 Tn-m -9.849 Tn

-11.693 Tn -5.044 Tn

4.25 m 2.25 m

9.533 Tn 5.044 Tn 11.377 Tn


TRAMO A-B TRAMO B-C


Vud = 7.455 Tn Vud = 3.179 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = 1.869 Tn Vs = -2.408 Tn





VnVud

i

jiiui l

MrMrlwV

)(

2

.

)( VcVsVud

dbcfsV ..'1.2'

dbcfVc ´53.0

dbcfsV ..'1.2'


Espaciamiento debe ser: d/2 14.55 cm Espaciamiento debe ser: d/2 14.55 cm

12.50 cm 12.50 cm


Z = 2.000 m Z = 1.500 m

Los espaciamientos se realizan generalmente a: Los espaciamientos se realizan generalmente a:

0.75 cm 0.75 cm

10.00 cm 10.00 cm

S 12.50 cm S 12.50 cm

15.00 cm 15.00 cm

17.50 cm As min = 1.420 cm² 17.50 cm


@ 10.0 cm @ 10.0 cm

Vs = 17.352 Tn Vs = 17.352 Tn

Cubre Tranquilament 9.533 Tn Cubre Tranquilament 5.044 Tn



1.172 m 1.661 m

Nº de estribos 10 estribos 10 @ 0,125 Nº de estribos : 14 estribos 14 @ 0,125

Longitud Estr 1.250 m Longitud Estribad 1.750 m



2.391 m


0.700 m

Nº de estribos 7 estribos 7 @ 0,1

Longitud Estr 0.70 m


3/8 1@0,05, 7@0,1, 10@0,125∎ 3/8 1@0,05, 14@0,125∎

º VIGA PRINCIPAL: VP-103

4.560 cm² Wu = 3.99 T/m 6.540 cm² Wu = 3.99 T/m


s

dfyAsVS

min

dbcfsV ..'1.1' dbcfsV ..'1.1' dbcfsV ..'1.1'

4.25 m 2.25 m


MOMENTOS RESISTENTES:

Usando las formulas de flexion simple:


As = 4.560 cm² As = 6.540 cm² As =

a = 4.292 cm a = 6.155 cm a =

Mr A = 4.748 Tn-m/m Mr B = 6.810 Tn-m/m Mr C =



4.25 m 2.25 m


arriba (-) abajo (+)

APOYO Mr Vi Vi'


APOYO B 6.810 Tn-m -8.958 Tn 4.486 Tn

APOYO C 6.810 Tn-m -4.486 Tn 8.958 Tn

APOYO D 4.748 Tn-m -7.988 Tn

-8.958 Tn -4.486 Tn

4.25 m 2.25 m

7.988 Tn 4.486 Tn 8.958 Tn

VnVud

wbcf

fyAsa

.'.85.0

. )2/.(.. adAsfyMr

i

jiiui l

MrMrlwV

)(

2

.

)( VcVsVud dbcfVc ´53.0


TRAMO A-B TRAMO B-C


Vud = 6.329 Tn Vud = 2.827 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = 0.743 Tn Vs = -2.759 Tn








Z = 2.500 m Z = 1.500 m


S 12.50 cm S 12.50 cm

15.00 cm 15.00 cm

17.50 cm As min = 1.420 cm² 17.50 cm






VnVud

s

dfyAsVS

min

)( VcVsVud

dbcfsV ..'1.2'

dbcfVc ´53.0

dbcfsV ..'1.1'

dbcfsV ..'1.2'




3.681 m




3/8 1@0,05, 7@0,1, 14@0,125∎ 3/8 1@0,05, 15@0,125∎


6.990 cm² Wu = 5.74 T/m 9.840 cm² Wu = 5.20 T/m

4.25 m 2.25 m







4.25 m 2.25 m





wbcf

fyAsa

.'.85.0

. )2/.(.. adAsfyMr

i

jiiui l

MrMrlwV

)(

2

.

-12.886 Tn -5.855 Tn

4.25 m 2.25 m

11.489 Tn 5.855 Tn 12.458 Tn


TRAMO A-B TRAMO B-C


Vud = 9.104 Tn Vud = 3.690 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = 3.517 Tn Vs = -1.896 Tn








Z = 2.500 m Z = 1.500 m


S 12.50 cm S 12.50 cm

15.00 cm 15.00 cm

17.50 cm As min = 1.420 cm² 17.50 cm


@ 10.0 cm @ 10.0 cmVs = 17.352 Tn Vs = 17.352 Tn

VnVud

s

dfyAsVS

min

)( VcVsVud

dbcfsV ..'1.2'

dbcfVc ´53.0

dbcfsV ..'1.1'

dbcfsV ..'1.2'


Cubre Tranquilament 11.489 Tn Cubre Tranquilament 5.855 Tn






2.526 m




3/8 1@0,05, 12@0,1, 10@0,125∎ 3/8 1@0,05, 12@0,125∎


6.990 cm² Wu = 5.36 T/m 9.840 cm² Wu = 6.03 T/m

4.25 m 2.25 m







4.25 m 2.25 m


wbcf

fyAsa

.'.85.0

. )2/.(.. adAsfyMr




-12.083 Tn -6.787 Tn

4.25 m 2.25 m

10.686 Tn 6.787 Tn 11.430 Tn


TRAMO A-B TRAMO B-C


Vud = 8.458 Tn Vud = 4.278 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = 2.871 Tn Vs = -1.309 Tn








Z = 2.000 m Z = 1.500 m


VnVud

i

jiiui l

MrMrlwV

)(

2

.

)( VcVsVud

dbcfsV ..'1.2'

dbcfVc ´53.0

dbcfsV ..'1.1'

dbcfsV ..'1.2'


0.75 cm 0.75 cm10.00 cm 10.00 cm

S 12.50 cm S 12.50 cm

15.00 cm 15.00 cm

17.50 cm As min = 1.420 cm² 17.50 cm






SEGUIMOS COLOCANDO ESTRIBOS SEGUIMOS COLOCANDO ESTRIBOS


2.123 m 2.585 m

Execde distancia que queda por estribar Execde distancia que queda por estribar



3/8 1@0,05, 9@0,1, 9@0,125∎ 3/8 1@0,05, 2@0,1, 10@0,125∎


3.870 cm² Wu = 3.74 T/m 6.540 cm² Wu = 3.74 T/m

4.25 m 2.25 m






s

dfyAsVS

min

wbcf

fyAsa

.'.85.0

. )2/.(.. adAsfyMr



4.25 m 2.25 m




-8.595 Tn -4.204 Tn

4.25 m 2.25 m

7.287 Tn 4.204 Tn 8.595 Tn


TRAMO A-B TRAMO B-C


Vud = 5.733 Tn Vud = 2.650 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = 0.146 Tn Vs = -2.937 Tn






VnVud

i

jiiui l

MrMrlwV

)(

2

.

)( VcVsVud

dbcfsV ..'1.2'

dbcfVc ´53.0

dbcfsV ..'1.1'

dbcfsV ..'1.2'




Z = 2.000 m Z = 1.500 m


S 12.50 cm S 12.50 cm

15.00 cm 15.00 cm

17.50 cm As min = 1.420 cm² 17.50 cm








3.137 m




3/8 1@0,05, 4@0,1, 13@0,125∎ 3/8 1@0,05, 16@0,125∎

s

dfyAsVS

min

VIGAS PRINCIPALES: SEGUNDO PISO

DATOS:

f'c = 210 Kg/cm²

fy = 4200 Kg/cm²

Ǿ flex. 0.9

Ǿ corte 0.85

b: 25.00 cm

h: 35.00 cm

d: 29.10 cm

t : 25.00 cm

4.580 cm² Wu = 3.73 T/m 3.870 cm² 3.290 cm² Wu = 3.75 T/m

4.25 m 4.25 m



APOYO C APOYO D APOYO A

4.580 cm² As = 3.870 cm² As = 3.290 cm²4.311 cm a = 3.642 cm a = 3.096 cm

4.769 Tn-m/m Mr D = 4.030 Tn-m/m Mr A = 3.426 Tn-m/m


4.769 Tn-m Mr D = 4.030 Tn-m Mr A = 3.426 Tn-m

4.25 m 4.25 m

APOYO "C" APOYO "D" APOYO "A"


arriba (-)APOYO Mr Vi

APOYO A 3.426 Tn-mAPOYO B 6.091 Tn-m -8.591 TnAPOYO C 4.769 Tn-m -3.628 TnAPOYO D 4.748 Tn-m -7.958 Tn

-7.757 Tn

4.25 m 4.25 m

7.336 Tn


TRAMO C-D TRAMO A-B


Vud = 6.552 Tn Vud = 5.777 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = 0.966 Tn Vs = 0.191 Tn


V's = 22.135 Tn mayor que: 0.966 Tn V's = 22.135 Tn mayor que:




Espaciamiento debe ser: d/2 14.55 cm Espaciamiento debe ser: d/212.50 cm

4. DETERMINACION DEL ESPACIAMIENTO DE LOS ESTRI 4. DETERMINACION DEL ESPACIAMIENTO DE LOS ESTRIBOS

Z = 2.500 m Z = 2.000 m


S 12.50 cm S 12.50 cm

dbcfVc ´53.0

dbcfsV ..'1.2'

dbcfsV ..'1.1'

VnVud

s

dfyAsVS

min

dbcfsV ..'1.2'

dbcfsV ..'1.1'

15.00 cm 15.00 cm

17.50 cm As min = 17.50 cm As min =


@ 10.0 cm @ 10.0 cmVs = 17.352 Tn Vs = 17.352 TnCubre Tranqu 8.105 Tn Cubre Tranquilame 7.336 Tn



1.723 m 1.523 mNº de estribos : 14 estribos 14 @ 0,125 Nº de estribos : 13 estribos 13 @ 0,125Longitud Estribad 1.750 m Longitud Estribada 1.625 m



3.602 m 3.106 m




3/8 1@0,05, 7@0,1, 14@0,125∎ 3/8 1@0,05, 4@0,1, 13@0,125∎

8.280 cm² Wu = 4.99 T/m 5.160 cm² 6.540 cm² Wu = 5.01 T/m

4.25 m 4.25 m







s

dfyAsVS

min



4.25 m 4.25 m



APOYO A 6.810 Tn-m

APOYO B 8.622 Tn-m -11.079 Tn

APOYO C 8.622 Tn-m -5.065 Tn

APOYO D 4.748 Tn-m -9.741 Tn

-9.849 Tn

4.25 m 4.25 m

10.226 Tn


TRAMO C-D TRAMO A-B


Vud = 9.300 Tn Vud = 8.674 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = 3.713 Tn Vs = 3.087 Tn





dbcfVc ´53.0

dbcfsV ..'1.2'

VnVud

dbcfsV ..'1.2'


Espaciamiento debe ser: d/2 14.55 cm Espaciamiento debe ser: d/2

12.50 cm


Z = 2.500 m Z = 2.500 m


0.75 cm 0.75 cm

10.00 cm 10.00 cm

S 12.50 cm S 12.50 cm

15.00 cm 15.00 cm



@ 10.0 cm @ 10.0 cm

Vs = 17.352 Tn Vs = 17.352 Tn

Cubre Tranqu 11.377 Tn Cubre Tranquilame 10.226 Tn



1.228 m 1.366 m

Nº de estribos : 10 estribos 10 @ 0,125 Nº de estribos : 11 estribos 11 @ 0,125

Longitud Estribad 1.250 m Longitud Estribada 1.375 m



2.563 m 2.867 m


1.200 m 1.075 m


Longitud Estribad 1.20 m Longitud Estribada 1.10 m


3/8 1@0,05, 12@0,1, 10@0,125∎ 3/8 1@0,05, 11@0,1, 11@0,125∎

º

6.540 cm² Wu = 3.99 T/m 4.560 cm² 4.560 cm² Wu = 4.00 T/m


dbcfsV ..'1.1'

s

dfyAsVS

min

dbcfsV ..'1.1'

4.25 m 4.25 m





6.540 cm² As = 4.560 cm² As = 4.560 cm²

6.155 cm a = 4.292 cm a = 4.292 cm




4.25 m 4.25 m


arriba (-)

APOYO Mr Vi

APOYO A 4.748 Tn-m

APOYO B 6.810 Tn-m -8.993 Tn

APOYO C 6.810 Tn-m -4.504 Tn

APOYO D 4.748 Tn-m -8.023 Tn

-7.988 Tn

4.25 m 4.25 m

8.023 Tn

dbcfVc ´53.0 VnVud


TRAMO C-D TRAMO A-B


Vud = 7.300 Tn Vud = 6.470 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = 1.713 Tn Vs = 0.884 Tn








Z = 2.500 m Z = 2.500 m


S 12.50 cm S 12.50 cm

15.00 cm 15.00 cm







dbcfVc ´53.0

dbcfsV ..'1.2'

dbcfsV ..'1.1'

VnVud

s

dfyAsVS

min

dbcfsV ..'1.2'

dbcfsV ..'1.1'



3.218 m 3.657 m




3/8 1@0,05, 9@0,1, 13@0,125∎ 3/8 1@0,05, 7@0,1, 14@0,125∎

º

9.840 cm² Wu = 5.53 T/m 6.990 cm² 6.990 cm² Wu = 5.76 T/m

4.25 m 4.25 m








4.25 m 4.25 m





-11.061 Tn

4.25 m 4.25 m

11.531 Tn


TRAMO C-D TRAMO A-B


Vud = 10.156 Tn Vud = 9.979 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = 4.569 Tn Vs = 4.392 Tn








Z = 2.500 m Z = 2.500 m


S 12.50 cm S 12.50 cm

15.00 cm 15.00 cm



@ 10.0 cm @ 10.0 cmVs = 17.352 Tn Vs = 17.352 Tn

dbcfVc ´53.0

dbcfsV ..'1.2'

dbcfsV ..'1.1'

VnVud

s

dfyAsVS

min

dbcfsV ..'1.2'

dbcfsV ..'1.1'

Cubre Tranqu 12.458 Tn Cubre Tranquilame 11.531 Tn






2.357 m 2.512 m




3/8 1@0,05, 14@0,1, 9@0,125∎ 3/8 1@0,05, 12@0,1, 10@0,125∎

9.840 cm² Wu = 5.05 T/m 6.990 cm² 6.990 cm² Wu = 5.38 T/m

4.25 m 4.25 m








4.25 m 4.25 m





-10.033 Tn

4.25 m 4.25 m

10.731 Tn


TRAMO C-D TRAMO A-B


Vud = 9.329 Tn Vud = 9.178 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = 3.743 Tn Vs = 3.592 Tn








Z = 2.500 m Z = 2.000 m


dbcfVc ´53.0

dbcfsV ..'1.2'

dbcfsV ..'1.1'

VnVud

dbcfsV ..'1.2'

dbcfsV ..'1.1'

0.75 cm 0.75 cm10.00 cm 10.00 cm

S 12.50 cm S 12.50 cm

15.00 cm 15.00 cm









2.545 m 2.109 m




3/8 1@0,05, 12@0,1, 10@0,125∎ 3/8 1@0,05, 9@0,1, 9@0,125∎

6.540 cm² Wu = 3.74 T/m 3.870 cm² 4.560 cm² Wu = 3.75 T/m

4.25 m 4.25 m







s

dfyAsVS

min



4.25 m 4.25 m




-7.287 Tn

4.25 m 4.25 m

7.649 Tn


TRAMO C-D TRAMO A-B


Vud = 7.041 Tn Vud = 6.096 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = 1.454 Tn Vs = 0.510 Tn






dbcfVc ´53.0

dbcfsV ..'1.2'

dbcfsV ..'1.1'

VnVud

dbcfsV ..'1.2'

dbcfsV ..'1.1'



Z = 2.500 m Z = 2.500 m


S 12.50 cm S 12.50 cm

15.00 cm 15.00 cm









3.422 m 3.797 m




3/8 1@0,05, 9@0,1, 13@0,125∎ 3/8 1@0,05, 6@0,1, 15@0,125∎

s

dfyAsVS

min

VIGAS PRINCIPALES: SEGUNDO PISO


5.850 cm² Wu = 3.75 T/m 4.580 cm² Wu = 3.75 T/m

4.25 m 2.25 m 4.25 m

APOYO B APOYO C APOYO D

As = 5.850 cm² As = 4.580 cm² As =a = 5.506 cm a = 4.311 cm a =Mr B = 6.091 Tn-m/m Mr C = 4.769 Tn-m/m Mr D =

Mr B = 6.091 Tn-m Mr C = 4.769 Tn-m Mr D =

4.25 m 2.25 m 4.25 m

APOYO "B" APOYO "C"

wbcf

fyAsa

.'.85.0

. )2/.(.. adAsfyMr

abajo (+)Vi'

7.336 Tn4.804 Tn7.968 Tn

-8.591 Tn -3.628 Tn -7.958 Tn

2.25 m 4.25 m

4.804 Tn 7.968 Tn

TRAMO B-C TRAMO C-D

CALCULO DEL CORTANTE A UNA DISTANCIA "d" CALCULO DEL CORTANTE A UNA DISTANCIA "d" CALCULO DEL CORTANTE A UNA DISTANCIA "d"

Vud = 3.245 Tn Vud = 6.409 Tn

CORTE TOMADO POR EL CONCRETO CORTE TOMADO POR EL CONCRETO CORTE TOMADO POR EL CONCRETO

Vc = 5.587 Tn Vc = 5.587 Tn

CORTE TOMADO POR EL ACERO CORTE TOMADO POR EL ACERO CORTE TOMADO POR EL ACERO

Vs = -2.342 Tn Vs = 0.823 Tn

MAXIMO CORTANTE TOMADO POR EL REFUERZO MAXIMO CORTANTE TOMADO POR EL REFUERZO MAXIMO CORTANTE TOMADO POR EL REFUERZO

0.191 Tn V's = 22.135 Tn mayor que: -2.342 Tn V's = 22.135 Tn mayor que:

Si se puede diseñar refuerzo para que tome el corte Si se puede diseñar refuerzo para que tome el corte Si se puede diseñar refuerzo para que tome el corte

ESPACIAMIENTO MAXIMO ESPACIAMIENTO MAXIMO ESPACIAMIENTO MAXIMO


14.55 cm Espaciamiento debe ser: d/2 14.55 cm Espaciamiento debe ser: d/212.50 cm 12.50 cm

4. DETERMINACION DEL ESPACIAMIENTO DE LOS ESTRIBOS 4. DETERMINACION DEL ESPACIAMIENTO DE LOS ESTRIB4. DETERMINACION DEL ESPACIAMIENTO DE LOS ESTRIBOS

Z = 1.500 m Z = 2.500 m


S 12.50 cm S 12.50 cms

dfyAsVS

min

i

jiiui l

MrMrlwV

)(

2

.




15.00 cm 15.00 cm

1.420 cm² 17.50 cm 17.50 cm As min =


@ 10.0 cm @ 10.0 cmVs = 17.352 Tn Vs = 17.352 TnCubre Tranquil 4.804 Tn Cubre Tranqu 7.968 Tn

5. DETERMINACION DE LAS LONGITUDES CUBIERTAS 5. DETERMINACION DE LAS LONGITUDES CUBIERTAS 5. DETERMINACION DE LAS LONGITUDES CUBIERTAS


1.744 m 1.753 mNº de estribos : 14 estribos 14 @ 0,125 Nº de estribos : 15 estribos 15 @ 0,125Longitud Estribad 1.750 m Longitud Estribada : 1.875 m

SEGUIMOS COLOCANDO ESTRIBOS TODA LA VIGA ESTA ESTRIBADA SEGUIMOS COLOCANDO ESTRIBOS


3.569 m


0.575 mNº de estribos : 6 estribos 6 @ 0,1Longitud Estribada : 0.60 m

6. DISTRIBUCION DE ESTRIBOS 6. DISTRIBUCION DE ESTRIBOS 6. DISTRIBUCION DE ESTRIBOS

3/8 1@0,05, 4@0,1, 13@0,125∎ 3/8 1@0,05, 14@0,125∎ 3/8 1@0,05, 6@0,1, 15@0,125∎


8.280 cm² Wu = 4.50 T/m 8.280 cm² Wu = 5.01 T/m

4.25 m 2.25 m 4.25 m



APOYO "B" APOYO "C"

s

dfyAsVS

min

wbcf

fyAsa

.'.85.0

. )2/.(.. adAsfyMr


4.25 m 2.25 m 4.25 m

abajo (+)Vi'

10.226 Tn

5.065 Tn

11.564 Tn

-11.079 Tn -5.065 Tn -9.741 Tn

2.25 m 4.25 m

5.065 Tn 11.564 Tn

TRAMO B-C TRAMO C-D


Vud = 3.512 Tn Vud = 10.011 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = -2.074 Tn Vs = 4.425 Tn





i

jiiui l

MrMrlwV

)(

2

.




14.55 cm Espaciamiento debe ser: d/2 14.55 cm Espaciamiento debe ser: d/2

12.50 cm 12.50 cm


Z = 1.500 m Z = 2.500 m


0.75 cm 0.75 cm

10.00 cm 10.00 cm

S 12.50 cm S 12.50 cm

15.00 cm 15.00 cm

1.420 cm² 17.50 cm 17.50 cm As min =


@ 10.0 cm @ 10.0 cm

Vs = 17.352 Tn Vs = 17.352 Tn

Cubre Tranquil 5.065 Tn Cubre Tranqu 11.564 Tn



1.655 m 1.208 m


Longitud Estribad 1.750 m Longitud Estribada : 1.250 m



2.501 m


1.200 m

Nº de estribos : 12 estribos 12 @ 0,1

Longitud Estribada : 1.20 m


3/8 1@0,05, 11@0,1, 11@0,125∎ 3/8 1@0,05, 14@0,125∎ 3/8 1@0,05, 12@0,1, 10@0,125∎


6.540 cm² Wu = 4.00 T/m 6.540 cm² Wu = 4.00 T/m

APOYO "B" APOYO "C"

s

dfyAsVS

min


4.25 m 2.25 m 4.25 m


As = 6.540 cm² As = 6.540 cm² As =

a = 6.155 cm a = 6.155 cm a =

Mr B = 6.810 Tn-m/m Mr C = 6.810 Tn-m/m Mr D =


4.25 m 2.25 m 4.25 m

abajo (+)

Vi'

8.023 Tn

4.504 Tn

8.993 Tn

-8.993 Tn -4.504 Tn -8.023 Tn

2.25 m 4.25 m

4.504 Tn 8.993 Tn

wbcf

fyAsa

.'.85.0

. )2/.(.. adAsfyMr

i

jiiui l

MrMrlwV

)(

2

.


TRAMO B-C TRAMO C-D


Vud = 2.952 Tn Vud = 7.440 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = -2.635 Tn Vs = 1.854 Tn








Z = 1.500 m Z = 2.500 m


S 12.50 cm S 12.50 cm

15.00 cm 15.00 cm

1.420 cm² 17.50 cm 17.50 cm As min =






s

dfyAsVS

min






3.199 m




3/8 1@0,05, 7@0,1, 14@0,125∎ 3/8 1@0,05, 15@0,125∎ 3/8 1@0,05, 9@0,1, 13@0,125∎


9.840 cm² Wu = 5.15 T/m 9.840 cm² Wu = 5.55 T/m

4.25 m 2.25 m 4.25 m




4.25 m 2.25 m 4.25 m

abajo (+)Vi'

11.531 Tn5.794 Tn

12.500 Tn

APOYO "B" APOYO "C"

wbcf

fyAsa

.'.85.0

. )2/.(.. adAsfyMr

i

jiiui l

MrMrlwV

)(

2

.

-12.928 Tn -5.794 Tn -11.103 Tn

2.25 m 4.25 m

5.794 Tn 12.500 Tn

TRAMO B-C TRAMO C-D


Vud = 4.242 Tn Vud = 10.947 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = -1.344 Tn Vs = 5.361 Tn








Z = 1.500 m Z = 2.500 m


S 12.50 cm S 12.50 cm

15.00 cm 15.00 cm

1.420 cm² 17.50 cm 17.50 cm As min =


@ 10.0 cm @ 10.0 cmVs = 17.352 Tn Vs = 17.352 Tn

s

dfyAsVS

min




Cubre Tranquil 5.794 Tn Cubre Tranqu 12.500 Tn






2.346 m




3/8 1@0,05, 12@0,1, 10@0,125∎ 3/8 1@0,05, 12@0,125∎ 3/8 1@0,05, 14@0,1, 9@0,125∎


9.840 cm² Wu = 6.05 T/m 8.280 cm² Wu = 5.07 T/m

4.25 m 2.25 m 4.25 m




4.25 m 2.25 m 4.25 m

APOYO "B" APOYO "C"

wbcf

fyAsa

.'.85.0

. )2/.(.. adAsfyMr

abajo (+)Vi'

10.731 Tn7.533 Tn

11.092 Tn

-12.127 Tn -6.089 Tn -10.460 Tn

2.25 m 4.25 m

7.533 Tn 11.092 Tn

TRAMO B-C TRAMO C-D


Vud = 5.980 Tn Vud = 9.540 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = 0.394 Tn Vs = 3.953 Tn


3.592 Tn V's = 22.135 Tn mayor que: 0.394 Tn V's = 22.135 Tn mayor que:



3.592 Tn V's = 11.595 Tn mayor que: 0.394 Tn V's = 11.595 Tn mayor que:



Z = 1.500 m Z = 2.500 m


i

jiiui l

MrMrlwV

)(

2

.




0.75 cm 0.75 cm10.00 cm 10.00 cm

S 12.50 cm S 12.50 cm

15.00 cm 15.00 cm

1.420 cm² 17.50 cm 17.50 cm As min =






SEGUIMOS COLOCANDO ESTRIBOS SEGUIMOS COLOCANDO ESTRIBOS SEGUIMOS COLOCANDO ESTRIBOS


2.330 m 2.536 m

Execde distancia que queda por estribar Execde distancia que queda por estribar Execde distancia que queda por estribar



3/8 1@0,05, 9@0,1, 9@0,125∎ 3/8 1@0,05, 4@0,1, 9@0,125∎ 3/8 1@0,05, 11@0,1, 11@0,125∎


5.850 cm² Wu = 3.75 T/m 5.850 cm² Wu = 3.75 T/m

4.25 m 2.25 m 4.25 m



APOYO "B" APOYO "C"

s

dfyAsVS

min

wbcf

fyAsa

.'.85.0

. )2/.(.. adAsfyMr


4.25 m 2.25 m 4.25 m

abajo (+)Vi'

7.649 Tn4.217 Tn8.281 Tn

-8.281 Tn -4.217 Tn -7.649 Tn

2.25 m 4.25 m

4.217 Tn 8.281 Tn

TRAMO B-C TRAMO C-D


Vud = 2.664 Tn Vud = 6.728 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = -2.922 Tn Vs = 1.142 Tn






i

jiiui l

MrMrlwV

)(

2

.






Z = 1.500 m Z = 2.500 m


S 12.50 cm S 12.50 cm

15.00 cm 15.00 cm

1.420 cm² 17.50 cm 17.50 cm As min =








3.489 m




3/8 1@0,05, 6@0,1, 15@0,125∎ 3/8 1@0,05, 16@0,125∎ 3/8 1@0,05, 7@0,1, 14@0,125∎

s

dfyAsVS

min

VIGAS PRINCIPALES: TERCER PISO

DATOS:

f'c = 210 Kg/cm²

fy = 4200 Kg/cm²

Ǿ flex. 0.9

Ǿ corte 0.85

b: 25.00 cm

h: 35.00 cm

d: 29.10 cm

t : 25.00 cm

4.560 cm² 2.580 cm² Wu = 2.19 T/m 3.870 cm²

4.25 m 4.25 m



APOYO D APOYO A APOYO B


4.748 Tn-m/m Mr A = 2.686 Tn-m/m Mr B = 4.030 Tn-m/m


4.748 Tn-m Mr A = 2.686 Tn-m Mr B = 4.030 Tn-m

4.25 m 2.25 m

APOYO "D" APOYO "A" APOYO "B"

wbcf

fyAsa

.'.85.0

.




-4.968 Tn

4.25 m

4.336 Tn 2.463 Tn


TRAMO A-B


Vud = 3.425 Tn


Vc = 5.587 Tn


Vs = -2.161 Tn


0.823 Tn V's = 22.135 Tn mayor que: -2.161 Tn V's =




14.55 cm Espaciamiento debe ser: d/2 14.55 cm Espaciamiento debe ser:12.50 cm 12.50 cm

4. DETERMINACION DEL ESPACIAMIENTO DE LOS ESTRIBOS 4. DETERMINACION DEL ESPACIAMIENTO DE LOS ESTRIBOS 4. DETERMINACION DEL ESPACIAMIENTO DE LOS ESTRIBOS

Z = 2.000 m Z =

Los espaciamientos se realizan generalmente a: Los espaciamientos se realizan generalmente a:0.75 cm10.00 cm

S 12.50 cm S

dbcfsV ..'1.2'

dbcfsV ..'1.1'

VnVud

s

dfyAsVS

min

i

jiiui l

MrMrlwV

)(

2

.

)( VcVsVud

dbcfsV ..'1.2'

dbcfsV ..'1.1'

15.00 cm

17.50 cm As min = 1.420 cm²

@ 5.0 cm Por norma @ 5.0 cm

@ 10.0 cm @ 10.0 cmVs = 17.352 TnCubre Tranquilame 4.336 Tn


TRAMO DE ESTRIBOS A @ 0.125 m TRAMO DE ESTRIBOS A

2.577 mNº de estribos : 21 estribos 21 @ 0,125 Nº de estribos :Longitud Estribada 2.625 m Longitud Estribada

SEGUIMOS COLOCANDO ESTRIBOS TODA LA VIGA ESTA ESTRIBADA TODA LA VIGA ESTA ESTRIBADA



3/8 1@0,05, 6@0,1, 15@0,125∎ 3/8 1@0,05, @, 21@0,125∎ 3/8 1@0,05, 28@0,125∎


4.560 cm² 2.580 cm² Wu = 2.61 T/m 4.560 cm²

4.25 m 4.25 m







s

dfyAsVS

min

wbcf

fyAsa

.'.85.0

.



4.25 m 2.25 m




APOYO B 4.748 Tn-m -6.038 Tn 2.940 Tn

APOYO C 4.748 Tn-m -2.940 Tn 6.038 Tn

APOYO D 2.686 Tn-m -5.068 Tn

-6.038 Tn

4.25 m

5.068 Tn 2.940 Tn


TRAMO A-B


Vud = 3.515 Tn


Vc = 5.587 Tn


Vs = -2.071 Tn





dbcfsV ..'1.2'

VnVud

i

jiiui l

MrMrlwV

)(

2

.

)( VcVsVud

dbcfsV ..'1.2'


14.55 cm Espaciamiento debe ser: d/2 14.55 cm Espaciamiento debe ser:

12.50 cm 12.50 cm


Z = 2.000 m Z =


0.75 cm

10.00 cm

S 12.50 cm S

15.00 cm

17.50 cm As min = 1.420 cm²


@ 10.0 cm @ 10.0 cm

Vs = 17.352 Tn

Cubre Tranquilame 5.068 Tn



2.205 m

Nº de estribos : 18 estribos 18 @ 0,125 Nº de estribos :

Longitud Estribada 2.250 m Longitud Estribada




3/8 1@0,05, 12@0,1, 10@0,125∎ 3/8 1@0,05, @, 18@0,125∎ 3/8 1@0,05, 23@0,125∎


4.560 cm² 2.580 cm² Wu = 2.33 T/m 3.870 cm²


dbcfsV ..'1.1'

s

dfyAsVS

min

dbcfsV ..'1.1'

4.25 m 4.25 m





4.560 cm² As = 2.580 cm² As = 3.870 cm²

4.292 cm a = 2.428 cm a = 3.642 cm




4.25 m 2.25 m


arriba (-) abajo (+)

APOYO Mr Vi Vi'


APOYO B 4.030 Tn-m -5.274 Tn 2.625 Tn

APOYO C 4.030 Tn-m -2.625 Tn 5.274 Tn

APOYO D 2.686 Tn-m -4.642 Tn

-5.274 Tn

4.25 m

4.642 Tn 2.625 Tn

VnVud

wbcf

fyAsa

.'.85.0

.

i

jiiui l

MrMrlwV

)(

2

.

)( VcVsVud


TRAMO A-B


Vud = 3.089 Tn


Vc = 5.587 Tn


Vs = -2.497 Tn








Z = 2.000 m Z =


S 12.50 cm S

15.00 cm

17.50 cm As min = 1.420 cm²






dbcfsV ..'1.2'

dbcfsV ..'1.1'

VnVud

s

dfyAsVS

min

)( VcVsVud

dbcfsV ..'1.2'

dbcfsV ..'1.1'




3/8 1@0,05, 9@0,1, 13@0,125∎ 3/8 1@0,05, @, 20@0,125∎ 3/8 1@0,05, 26@0,125∎


6.990 cm² 3.290 cm² Wu = 2.77 T/m 4.560 cm²

4.25 m 4.25 m








4.25 m 2.25 m





wbcf

fyAsa

.'.85.0

.

i

jiiui l

MrMrlwV

)(

2

.

-6.187 Tn

4.25 m

5.564 Tn 3.111 Tn


TRAMO A-B


Vud = 4.012 Tn


Vc = 5.587 Tn


Vs = -1.574 Tn








Z = 2.500 m Z =


S 12.50 cm S

15.00 cm

17.50 cm As min = 1.420 cm²


@ 10.0 cm @ 10.0 cmVs = 17.352 Tn

dbcfsV ..'1.2'

dbcfsV ..'1.1'

VnVud

s

dfyAsVS

min

)( VcVsVud

dbcfsV ..'1.2'

dbcfsV ..'1.1'

Cubre Tranquilame 5.564 Tn







3/8 1@0,05, 14@0,1, 9@0,125∎ 3/8 1@0,05, @, 21@0,125∎ 3/8 1@0,05, 22@0,125∎


6.990 cm² 4.560 cm² Wu = 2.93 T/m 4.560 cm²

4.25 m 4.25 m








4.25 m 2.25 m


wbcf

fyAsa

.'.85.0

.




-6.233 Tn

4.25 m

6.233 Tn 3.300 Tn


TRAMO A-B


Vud = 4.680 Tn


Vc = 5.587 Tn


Vs = -0.906 Tn








Z = 2.500 m Z =


dbcfsV ..'1.2'

dbcfsV ..'1.1'

VnVud

i

jiiui l

MrMrlwV

)(

2

.

)( VcVsVud

dbcfsV ..'1.2'

dbcfsV ..'1.1'

0.75 cm10.00 cm

S 12.50 cm S

15.00 cm

17.50 cm As min = 1.420 cm²






SEGUIMOS COLOCANDO ESTRIBOS SEGUIMOS COLOCANDO ESTRIBOS TODA LA VIGA ESTA ESTRIBADA


4.710 m


0.200 mNº de estribos : 2 estribos 2 @ 0,1Longitud Estribada 0.20 m


3/8 1@0,05, 11@0,1, 11@0,125∎ 3/8 1@0,05, 2@0,1, 18@0,125∎ 3/8 1@0,05, @, 21@0,125∎


4.560 cm² 2.580 cm² Wu = 2.62 T/m 4.560 cm²

4.25 m 4.25 m







s

dfyAsVS

min

wbcf

fyAsa

.'.85.0

.



4.25 m 2.25 m




-6.052 Tn

4.25 m

5.082 Tn 2.947 Tn


TRAMO A-B


Vud = 3.530 Tn


Vc = 5.587 Tn


Vs = -2.057 Tn






dbcfsV ..'1.2'

dbcfsV ..'1.1'

VnVud

i

jiiui l

MrMrlwV

)(

2

.

)( VcVsVud

dbcfsV ..'1.2'

dbcfsV ..'1.1'



Z = 2.000 m Z =


S 12.50 cm S

15.00 cm

17.50 cm As min = 1.420 cm²









3/8 1@0,05, 7@0,1, 14@0,125∎ 3/8 1@0,05, @, 18@0,125∎ 3/8 1@0,05, 23@0,125∎

s

dfyAsVS

min


Wu = 2.19 T/m 3.870 cm² Wu = 2.19 T/m 2.580 cm²

2.25 m 4.25 m

APOYO C APOYO D

As = 3.870 cm² As = 2.580 cm²a = 3.642 cm a = 2.428 cmMr C = 4.030 Tn-m/m Mr D = 2.686 Tn-m/m

Mr C = 4.030 Tn-m Mr D = 2.686 Tn-m

2.25 m 4.25 m

APOYO "B" APOYO "C" APOYO "D"

)2/.(.. adAsfyMr

-2.463 Tn -4.336 Tn

2.25 m 4.25 m

4.968 Tn

TRAMO B-C TRAMO C-D


Vud = 1.552 Tn Vud = 4.057 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = -4.034 Tn Vs = -1.529 Tn


22.135 Tn mayor que: -4.034 Tn V's = 22.135 Tn mayor que: -1.529 Tn





4. DETERMINACION DEL ESPACIAMIENTO DE LOS ESTRIBOS 4. DETERMINACION DEL ESPACIAMIENTO DE LOS ESTRIBOS

1.500 m Z = 2.500 m

Los espaciamientos se realizan generalmente a: Los espaciamientos se realizan generalmente a:0.75 cm 0.75 cm10.00 cm 10.00 cm12.50 cm S 12.50 cm

i

jiiui l

MrMrlwV

)(

2

.




15.00 cm 15.00 cm

17.50 cm 17.50 cm As min =

Por norma @ 5.0 cm Por norma

@ 10.0 cmVs = 17.352 Tn Vs = 17.352 TnCubre Tranquilame 2.463 Tn Cubre Tranquilame 4.968 Tn



3.403 m 2.811 m28 estribos 28 @ 0,125 Nº de estribos : 23 estribos 23 @ 0,125

3.500 m Longitud Estribada 2.875 m

TODA LA VIGA ESTA ESTRIBADA TODA LA VIGA ESTA ESTRIBADA


3/8 1@0,05, 28@0,125∎ 3/8 1@0,05, @, 23@0,125∎


Wu = 2.61 T/m 4.560 cm² Wu = 2.61 T/m 2.580 cm²

2.25 m 4.25 m

APOYO C APOYO D



)2/.(.. adAsfyMr

Mr C = 4.748 Tn-m Mr D = 2.686 Tn-m

2.25 m 4.25 m

-2.940 Tn -5.068 Tn

2.25 m 4.25 m

6.038 Tn

TRAMO B-C TRAMO C-D


Vud = 1.387 Tn Vud = 4.485 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = -4.199 Tn Vs = -1.101 Tn





i

jiiui l

MrMrlwV

)(

2

.




Espaciamiento debe ser: d/2 14.55 cm Espaciamiento debe ser: d/2 14.55 cm

12.50 cm 12.50 cm


1.500 m Z = 2.500 m


0.75 cm 0.75 cm

10.00 cm 10.00 cm

12.50 cm S 12.50 cm

15.00 cm 15.00 cm

17.50 cm 17.50 cm As min =


@ 10.0 cm

Vs = 17.352 Tn Vs = 17.352 Tn

Cubre Tranquilame 2.940 Tn Cubre Tranquilame 6.038 Tn



2.851 m 2.313 m

23 estribos 23 @ 0,125 Nº de estribos : 19 estribos 19 @ 0,125


TODA LA VIGA ESTA ESTRIBADA SEGUIMOS COLOCANDO ESTRIBOS


3/8 1@0,05, 23@0,125∎ 3/8 1@0,05, @, 19@0,125∎


Wu = 2.33 T/m 3.870 cm² Wu = 2.33 T/m 2.580 cm²



2.25 m 4.25 m

APOYO C APOYO D

As = 3.870 cm² As = 2.580 cm²

a = 3.642 cm a = 2.428 cm

Mr C = 4.030 Tn-m/m Mr D = 2.686 Tn-m/m

Mr C = 4.030 Tn-m Mr D = 2.686 Tn-m

2.25 m 4.25 m

-2.625 Tn -4.642 Tn

2.25 m 4.25 m

5.274 Tn

)2/.(.. adAsfyMr

i

jiiui l

MrMrlwV

)(

2

.


TRAMO B-C TRAMO C-D


Vud = 1.072 Tn Vud = 3.721 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = -4.514 Tn Vs = -1.865 Tn








1.500 m Z = 2.500 m


15.00 cm 15.00 cm

17.50 cm 17.50 cm As min =










TODA LA VIGA ESTA ESTRIBADA TODA LA VIGA ESTA ESTRIBADA


3/8 1@0,05, 26@0,125∎ 3/8 1@0,05, @, 22@0,125∎


Wu = 2.77 T/m 4.560 cm² Wu = 2.77 T/m 2.580 cm²

2.25 m 4.25 m

APOYO C APOYO D


Mr C = 4.748 Tn-m Mr D = 2.686 Tn-m

2.25 m 4.25 m


)2/.(.. adAsfyMr

i

jiiui l

MrMrlwV

)(

2

.

-3.111 Tn -5.391 Tn

2.25 m 4.25 m

6.361 Tn

TRAMO B-C TRAMO C-D


Vud = 1.558 Tn Vud = 4.808 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = -4.028 Tn Vs = -0.778 Tn








1.500 m Z = 2.500 m


15.00 cm 15.00 cm

17.50 cm 17.50 cm As min =


@ 10.0 cmVs = 17.352 Tn Vs = 17.352 Tn




Cubre Tranquilame 3.111 Tn Cubre Tranquilame 6.361 Tn







3/8 1@0,05, 22@0,125∎ 3/8 1@0,05, @, 18@0,125∎


Wu = 2.93 T/m 4.560 cm² Wu = 2.93 T/m 2.710 cm²

2.25 m 4.25 m

APOYO C APOYO D


Mr C = 4.748 Tn-m Mr D = 2.822 Tn-m

2.25 m 4.25 m


)2/.(.. adAsfyMr

-3.300 Tn -5.779 Tn

2.25 m 4.25 m

6.686 Tn

TRAMO B-C TRAMO C-D


Vud = 1.747 Tn Vud = 5.133 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = -3.839 Tn Vs = -0.453 Tn








1.500 m Z = 2.500 m


i

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MrMrlwV

)(

2

.




0.75 cm 0.75 cm10.00 cm 10.00 cm12.50 cm S 12.50 cm

15.00 cm 15.00 cm

17.50 cm 17.50 cm As min =









4.363 m




3/8 1@0,05, @, 21@0,125∎ 3/8 1@0,05, 4@0,1, 17@0,125∎


Wu = 2.62 T/m 4.560 cm² Wu = 2.62 T/m 2.580 cm²

2.25 m 4.25 m

APOYO C APOYO D



)2/.(.. adAsfyMr

Mr C = 4.748 Tn-m Mr D = 2.686 Tn-m

2.25 m 4.25 m

-2.947 Tn -5.082 Tn

2.25 m 4.25 m

6.052 Tn

TRAMO B-C TRAMO C-D


Vud = 1.395 Tn Vud = 4.500 Tn


Vc = 5.587 Tn Vc = 5.587 Tn


Vs = -4.192 Tn Vs = -1.087 Tn






i

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MrMrlwV

)(

2

.






1.500 m Z = 2.500 m


15.00 cm 15.00 cm

17.50 cm 17.50 cm As min =









4.793 m




3/8 1@0,05, 23@0,125∎ 3/8 1@0,05, 1@0,1, 19@0,125∎

APOYO "D"

TABLAS - PREDIMENSIONADO TABLAS - DISEÑO


1/2 - 3/8" Area

2 Φ 3/8 1.420 cm²

1 Φ 1/2 + 1 Φ 3/8 2.000 cm²

3 Φ 3/8 2.130 cm²

2 Φ 1/2 2.580 cm²

1 Φ 1/2 + 2 Φ 3/8 2.710 cm²

4 Φ 3/8 2.840 cm²

2 Φ 1/2 + 1 Φ 3/8 3.290 cm²

3 Φ 1/2 3.870 cm²

2 Φ 1/2 + 2 Φ 3/8 4.000 cm²

3 Φ 1/2 + 1 Φ 3/8 4.580 cm²

4 Φ 1/2 5.160 cm²

5/8 - 1" Area

1 Φ 1 + 1 Φ 5/8 7.080 cm²

2 Φ 1 10.200 cm²

2 Φ 1+ 1 Φ 5/8 12.180 cm²

2 Φ 1+ 2 Φ 5/8 14.160 cm²

3 Φ 1 15.300 cm²

3/4 - 1" Area

1 Φ 3/4 + 1 Φ 1 7.950 cm²

1 Φ 1 + 2 Φ 3/4 10.800 cm²

2 Φ 1 + 1 Φ 3/4 13.050 cm²

2 Φ 1+ 2 Φ 3/4 15.900 cm²

TABLAS - DISEÑO


1/2 - 5/8" Area ACEROS COMERCIALES

1 Φ 1/2 + 1 Φ 5/8 3.270 cm² BARRA DIAMETRO Peso Area

2 Φ 5/8 3.960 cm² numero pulg cm Kg/m cm2

2 Φ 1/2 + 1 Φ 5/8 4.560 cm² 3 3/8 0.95 0.559 0.71

1 Φ 1/2 + 2 Φ 5/8 5.250 cm² 4 1/2 1.27 0.993 1.29

3 Φ 1/2 + 1 Φ 5/8 5.850 cm² 5 5/8 1.59 1.552 1.98

3 Φ 5/8 5.940 cm² 6 3/4 1.91 2.235 2.85

2 Φ 1/2 + 2 Φ 5/8 6.540 cm² 7 7/8 2.22 3.042 3.88

1 Φ 1/2 + 3 Φ 5/8 7.230 cm² 8 1 2.54 3.973 5.1

4 Φ 5/8 7.920 cm² 9 1 1/8 2.86 5.028 6.45

1/2 - 3/4" Area 10 1 1/4 3.18 6.207 8.19

1 Φ 1/2 + 1 Φ 3/4 4.140 cm² 11 1 3/8 3.49 7.511 9.58

2 Φ 1/2 + 1 Φ 3/4 5.430 cm² 12 1 1/2 3.81 8.938 11.4

2 Φ 3/4 5.700 cm²

1 Φ 1/2 + 2 Φ 3/4 6.990 cm²

3 Φ 3/4 8.550 cm²

2 Φ 1/2 + 2 Φ 3/4 8.280 cm²

4 Φ 3/4 11.400 cm²



Excel - Concreto Armado i - Joshe Luis

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