Ejercicios

PREDIMENSIONADO DE VIGAS 1. APOYO EMPOTRADO h= L/12

2. APOYO ARTICULADO Y EMPOTRADO h= L/10

3. SIMPLEMENTE APOYADO y APOYO ARTICULADO

h= L/8

DESIGNACION DE VIGA Vx1 Vx2 Vx3 Vx4 Vx5 Vx6 Vx8 Vx9 Vx10 Vx11 Vx12 Vx13 Vx14 Vx15

LUZ (metros) COEF. 2.55 10 3.20 10 3.35 12 3.70 12 3.35 12 3.70 12 1.65 12 2.35 10 4.55 10 1.00 10 1.00 12 1.00 10 3.35 12 4.5 12

H de VIGA 0.26 0.32 0.28 0.31 0.28 0.31 0.14 0.24 0.46 0.10 0.08 0.10 0.28 0.38

H de VIGA redondeada 0.30 0.35 0.30 0.35 0.30 0.35 0.15 0.25 0.50 0.10 0.10 0.10 0.30 0.40

ADOPTO MINIMO: 0.20

ADOPTO MINIMO: 0.20 ADOPTO MINIMO: 0.20 ADOPTO MINIMO: 0.20

1. Q LOZA

Bovedilla (e: 0.05m) Mortero de Asiento (e: 0.05 m) Membrana asfaltica (e: despreciable)

Mortero de Hº Liviano c/ telgopor (e: 0.08m) Loza de vigueta (e: 0.22m)

Cielorraso c/metal desplegado (e: 0.03m)

Capa

Espesor (m) Peso unitario (kg/m2)

Subtotal (kg/m2)

Bovedilla Mortero Asiento

0.05 0.05

2100

45 105

Mortero Hº Liviano c/ telgopor

0.08

600

48

Cielorraso Loza

0.03 0.22

50 -

1.5 301

PESO PROPIO SOBRE CARGA DE USO

199.5

Kg/m2

200

Kg/m2

2. Qt mayorado (Qd x 1.2) + (Ql x 1.6) Qt= Qt=

Qt=

199.5 239.4

x

1.2

+

320

559.4 Kg/m2

+

200

x

0.5594 t/m2

2. Q ENTREPISO Piso ceramico (e: 0.01m)

Mortero de Asiento (e: 0.05 m)

Cielorraso c/metal desplegado (e: 0.03m)

Loza de vigueta (e: 0.22m)

Cielorraso c/metal desplegado (e: 0.03m)

Capa

Espesor (m) Peso unitario (kg/m2)

Piso ceramico Mortero Asiento Cielorraso Loza

0.05 0.05 0.03 0.22

Subtotal (kg/m2)

20 2100 50 -

1.00 105 1.5 301

PESO PROPIO SOBRE CARGA DE USO

107.5

Kg/m2

200

Kg/m2

2. Qt mayorado (Qd x 1.2) + (Ql x 1.6) Qt= Qt=

107.5 129

Qt=

x

1.2

+

320

449 Kg/m2

+

200

x

0.449 t/m2

3. PESO PROPIO DE VIGAS POR METRO DESIGNACION DE LARGO (m) VIGA Vx1 Vx2 Vx3 Vx4 Vx5 Vx6 Vx8 Vx9 Vx10 Vx11 Vx12 Vx13 Vx14 Vx15

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

4. Qf Pp VIGA + Pp LOZA

ANCHO (m)

ALTO (m)

PESO UNITARIO Hº (kg/m2)

SUBTOTAL (kg/m)

SUBTOTAL (t/m)

0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.15 0.15 0.15 0.15 0.15 0.15

0.30 0.35 0.30 0.35 0.30 0.35 0.20 0.25 0.50 0.20 0.20 0.20 0.30 0.40

2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400

144 168 144 168 144 168 96 120 180 72 72 72 108 144

0.144 0.168 0.144 0.168 0.144 0.168 0.096 0.120 0.180 0.072 0.072 0.072 0.108 0.144

AREA DESIGNACION DE INFLUENCIA VIGA (m2) Vx1 Vx2 Vx3 Vx4 Vx5 Vx6 Vx8 Vx9 Vx10 Vx11 Vx12 Vx13 Vx14 Vx15

4.78 2.85 5.05 5.10 1.85 1.85 1.55 1.73 2.65 2.90 2.90 2.90 2.90 2.90

Qt (t/m) 0.449 0.449 0.449 0.449 0.449 0.449 0.559 0.559 0.559 0.559 0.559 0.559 0.559 0.559

SUBTOTAL PESO PROPIO LOZA VIGA (t/m) (tn/m) 2.146 1.280 2.267 2.290 0.831 0.831 0.867 0.965 1.482 1.622 1.622 1.622 1.622 1.622

0.173 0.202 0.173 0.202 0.173 0.202 0.115 0.144 0.216 0.086 0.086 0.086 0.130 0.173

Qf (t/m) 2.319 1.481 2.440 2.492 1.003 1.032 0.982 1.109 1.698 1.709 1.709 1.709 1.752 1.795

t/m t/m t/m t/m t/m t/m t/m t/m t/m t/m t/m t/m t/m t/m

0.05m)

Asiento (e: 0.05 m)

asfaltica (e: despreciable)

Hº Liviano c/ telgopor (e: 0.08m)

eta (e: 0.22m)

1.6

eramico (e: 0.01m)

ro de Asiento (e: 0.05 m)

de vigueta (e: 0.22m)

1.6

MAYORADO (1,2) 0.173 0.202 0.173 0.202 0.173 0.202 0.115 0.144 0.216 0.086 0.086 0.086 0.130 0.173

t/m t/m t/m t/m t/m t/m t/m t/m t/m t/m t/m t/m t/m t/m

ENTREPISO

CUBIERTA

1. MOMENTO VIGA Y APOYOS DESIGNACION DE VIGA

ALTURA (m)

APOYO / TRAMOS

Vx1 Vx2

0.30 0.35

Vx3

0.30

Vx4

0.35

Vx5

0.30

Vx6

0.35

Vx8

0.20

Vx9

0.25

Vx10

0.50

Vx11 Vx12 Vx13

0.20 0.20 0.20

Vx14

0.30

Vx15

0.40

TRAMO 3-7 TRAMO10-16 TRAMO 21-24 APOYO 24 APOYO 24 TRAMO 24-30 TRAMO 30 TRAMO 45-49 APOYO 49 APOYO 49 APOYO 53 TRAMO 49-53 TRAMO 53 APOYO 32 TRAMO 32-40 TRAMO 32 TRAMO 62-65 APOYO 54 TRAMO 54 TRAMO 54-59 TRAMO 11-17 TRAMO 29-41 TRAMO 12-18 APOYO 23 TRAMO 22-23 APOYO 23 TRAMO 23-42

MOMENTO MOMENTO NOMINAL (tm) MN: Mu/0.9 1.041 0.957 1.142 2.304 2.304 1.152 0.151 0.459 0.966 0.966 0.966 0.483 0.047 0.143 0.048 0.143 0.265 3.373 0.262 1.918 0.147 0.086 0.076 3.072 0.847 3.072 1.536

MOMENTO NOMINAL (MNm) MN: Mn/100

1.157 1.063 1.269 2.560 2.560 1.280 0.168 0.510 1.073 1.073 1.073 0.537 0.052 0.159 0.053 0.159 0.294 3.748 0.291 2.131 0.163 0.096 0.084 3.413 0.941 3.413 1.707

VIGA (Vx1)-TRAMO 3-7 2.CALCULO kd *Adopto Hormigon H20 y Acero ADN 420 A) Calculo d

b= 20

cm

d= h (cm) - recubr. (4cm)

0.20 m

0.012 0.011 0.013 0.026 0.026 0.013 0.002 0.005 0.011 0.011 0.011 0.005 0.001 0.002 0.001 0.002 0.003 0.037 0.003 0.021 0.002 0.001 0.001 0.034 0.009 0.034 0.017

d=

30

-

d=

26 cm

4

0.26 m

A) Calculo kd kd=

d MNm b (m)

kd=

0.26 0.012 0.20

kd=

0.26 0.058

kd=

0.26 0.24048562

kd=

kd= Adopto

1.081 *Buscar en tabla

kz= 0.9

1.218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

MNm kz x d x Fy

x 10000

As= 0.9

0.012 0.26

x

As=

0.012 98.28

x 10000

As=

0.000117691

x 10000

As=

x

420

1.18 cm2

C) Calculo Cuantia minima (P min.) P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

1.716 cm2 As NO VERIFICA!

1.716

1.18 VERIFICA!

* Adopto As min. 1

1.716 cm2

D) Calculo Cuantia maxima (P max.) P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

6.708 cm2 As VERIFICA!

6.708

1.18 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.26 2

x 0.469 2

M* =

0.20

x

0.0676 0.220

M* =

0.01352 0.220

M* = 0.061

MNm = 0.012

VSA

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm

x 10000

26

26

1. MOMENTO VIGA Y APOYOS DESIGNACION DE ALTURA (m) VIGA Vx1 Vx2

0.30 0.35

Vx3

0.30

Vx4

0.35

Vx5

0.30

Vx6

0.35

Vx8

0.20

Vx9

0.25

Vx10

0.50

Vx11 Vx12 Vx13

0.20 0.20 0.20

Vx14

0.30

Vx15

0.40

APOYO / TRAMOS

MOMENTO MOMENTO NOMINAL (tm) MN: Mu/0.9

TRAMO 3-7 TRAMO10-16 TRAMO 21-24 APOYO 24 APOYO 24 TRAMO 24-30 TRAMO 30 TRAMO 45-49 APOYO 49 APOYO 49 APOYO 53 TRAMO 49-53 TRAMO 53 APOYO 32 TRAMO 32-40 TRAMO 32 TRAMO 62-65 APOYO 54 TRAMO 54 TRAMO 54-59 TRAMO 11-17 TRAMO 29-41 TRAMO 12-18 APOYO 23 TRAMO 22-23 APOYO 23 TRAMO 23-42

1.041 0.957 1.142 2.304 2.304 1.152 0.151 0.459 0.966 0.966 0.966 0.483 0.047 0.143 0.048 0.143 0.265 3.373 0.262 1.918 0.147 0.086 0.076 3.072 0.847 3.072 1.536

MOMENTO NOMINAL (MNm) MN: Mn/100

1.157 1.063 1.269 2.560 2.560 1.280 0.168 0.510 1.073 1.073 1.073 0.537 0.052 0.159 0.053 0.159 0.294 3.748 0.291 2.131 0.163 0.096 0.084 3.413 0.941 3.413 1.707

VIGA (Vx2)-TRAMO 10-16 2.CALCULO kd *Adopto Hormigon H20 y Acero ADN 420 A) Calculo d

b= 20

cm

d= h (cm) - recubr. (4cm)

0.20 m

0.012 0.011 0.013 0.026 0.026 0.013 0.002 0.005 0.011 0.011 0.011 0.005 0.001 0.002 0.001 0.002 0.003 0.037 0.003 0.021 0.002 0.001 0.001 0.034 0.009 0.034 0.017

d=

35

-

d=

31 cm

4

0.31 m

A) Calculo kd kd=

d MNm b (m)

kd=

0.31 0.011 0.20

kd=

0.31 0.053

kd=

0.31 0.230578981

kd=

1.344 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

MNm kz x d x Fy

x 10000

As= 0.9

0.011 0.31

x

As=

0.011 117.18

x 10000

As=

0.000090744

x 10000

As=

x

420

0.91 cm2

C) Calculo Cuantia minima (P min.) P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

2.046 cm2 As NO VERIFICA!

2.046

0.91 VERIFICA!

* Adopto As min. 1

2.046 cm2

D) Calculo Cuantia maxima (P max.) P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

7.998 cm2 As VERIFICA!

7.998

0.91 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.31 2

x 0.469 2

M* =

0.20

x

0.0961 0.220

M* =

0.01922 0.220

M* = 0.087

MNm = 0.011

VSA

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm

x 10000

31

31

1. MOMENTO VIGA Y APOYOS DESIGNACION DE ALTURA (m) VIGA Vx1 Vx2

0.30 0.35

Vx3

0.30

Vx4

0.35

Vx5

0.30

Vx6

0.35

Vx8

0.20

Vx9

0.25

Vx10

0.50

Vx11 Vx12 Vx13

0.20 0.20 0.20

Vx14

0.30

Vx15

0.40

APOYO / TRAMOS

MOMENTO MOMENTO NOMINAL (tm) MN: Mu/0.9

TRAMO 3-7 TRAMO10-16 TRAMO 21-24 APOYO 24 APOYO 24 TRAMO 24-30 TRAMO 30 TRAMO 45-49 APOYO 49 APOYO 49 APOYO 53 TRAMO 49-53 TRAMO 53 APOYO 32 TRAMO 32-40 TRAMO 32 TRAMO 62-65 APOYO 54 TRAMO 54 TRAMO 54-59 TRAMO 11-17 TRAMO 29-41 TRAMO 12-18 APOYO 23 TRAMO 22-23 APOYO 23 TRAMO 23-42

1.041 0.957 1.142 2.304 2.304 1.152 0.151 0.459 0.966 0.966 0.966 0.483 0.047 0.143 0.048 0.143 0.265 3.373 0.262 1.918 0.147 0.086 0.076 3.072 0.847 3.072 1.536

MOMENTO NOMINAL (MNm) MN: Mn/100

1.157 1.063 1.269 2.560 2.560 1.280 0.168 0.510 1.073 1.073 1.073 0.537 0.052 0.159 0.053 0.159 0.294 3.748 0.291 2.131 0.163 0.096 0.084 3.413 0.941 3.413 1.707

VIGA (Vx3)-TRAMO 21-24 2.CALCULO kd *Adopto Hormigon H20 y Acero ADN 420 A) Calculo d

b= 20

cm

0.20 m

d= h (cm) - recubr. (4cm) d=

30

-

4

0.012 0.011 0.013 0.026 0.026 0.013 0.002 0.005 0.011 0.011 0.011 0.005 0.001 0.002 0.001 0.002 0.003 0.037 0.003 0.021 0.002 0.001 0.001 0.034 0.009 0.034 0.017

d=

26 cm

0.26 m

A) Calculo kd kd=

d MNm b (m)

kd=

0.26 0.013 0.20

kd=

0.26 0.063

kd=

0.26 0.251881806

kd=

1.032 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

MNm kz x d x Fy

As=

As=

As=

x 10000

0.9 0.013 98.28 0.00012911

As=

0.013 0.26

x

x

420

x 10000

x 10000

1.29 cm2

C) Calculo Cuantia minima (P min.) P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

1.716 cm2 As NO VERIFICA!

1.716

1.29 VERIFICA!

* Adopto As min. 1.

1.716 cm2

D) Calculo Cuantia maxima (P max.) P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

6.708 cm2 As VERIFICA!

6.708

1.29 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.26 2

x 0.469 2

M* =

0.20

x

0.0676 0.220

M* =

0.01352 0.220

M* = 0.061

MNm = 0.013

VSA

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm

VIGA (Vx3)-APOYO 24

A) Calculo kd kd=

d MNm b (m)

kd=

0.26 0.026 0.20

kd=

0.26 0.128

kd=

0.26 0.3577708764

kd=

0.727 *Buscar en tabla

kz= 0.9

kd= Adopto 0,749

B) Calculo Armadura (As) ( Inferior- TRAMO) As= MNm kz x d x Fy

x 10000

As=

As=

As=

x 10000

0.9 0.026 98.28

x

0.26

x

420

x 10000

0.0002604803

As=

0.026

x 10000

2.60 cm2

C) Calculo Cuantia minima (P min.) 26

P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

1.716 cm2 As NO VERIFICA!

1.716

2.60 VERIFICA!

D) Calculo Cuantia maxima (P max.) 26

P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

6.708 cm2 As VERIFICA!

6.708

2.60 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.26 2

x 0.469 2

M* =

0.20

x

0.0676 0.220

M* =

0.01352 0.220

M* = 0.061

MNm = 0.026

VSA

x 10000

26

26

1. MOMENTO VIGA Y APOYOS DESIGNACION DE VIGA

ALTURA (m)

APOYO / TRAMOS

Vx1 Vx2

0.30 0.35

Vx3

0.30

Vx4

0.35

Vx5

0.30

Vx6

0.35

Vx8

0.20

Vx9

0.25

Vx10

0.50

Vx11 Vx12 Vx13

0.20 0.20 0.20

Vx14

0.30

Vx15

0.40

TRAMO 3-7 TRAMO10-16 TRAMO 21-24 APOYO 24 APOYO 24 TRAMO 24-30 TRAMO 30 TRAMO 45-49 APOYO 49 APOYO 49 APOYO 53 TRAMO 49-53 TRAMO 53 APOYO 32 TRAMO 32-40 TRAMO 32 TRAMO 62-65 APOYO 54 TRAMO 54 TRAMO 54-59 TRAMO 11-17 TRAMO 29-41 TRAMO 12-18 APOYO 23 TRAMO 22-23 APOYO 23 TRAMO 23-42

MOMENTO MOMENTO NOMINAL (tm) MN: Mu/0.9 1.041 0.957 1.142 2.304 2.304 1.152 0.151 0.459 0.966 0.966 0.966 0.483 0.047 0.143 0.048 0.143 0.265 3.373 0.262 1.918 0.147 0.086 0.076 3.072 0.847 3.072 1.536

MOMENTO NOMINAL (MNm) MN: Mn/100

1.157 1.063 1.269 2.560 2.560 1.280 0.168 0.510 1.073 1.073 1.073 0.537 0.052 0.159 0.053 0.159 0.294 3.748 0.291 2.131 0.163 0.096 0.084 3.413 0.941 3.413 1.707

VIGA (Vx4)-TRAMO 24-30 2.CALCULO kd *Adopto Hormigon H20 y Acero ADN 420 A) Calculo d

b= 20

cm

d= h (cm) - recubr. (4cm)

0.20 m

0.012 0.011 0.013 0.026 0.026 0.013 0.002 0.005 0.011 0.011 0.011 0.005 0.001 0.002 0.001 0.002 0.003 0.037 0.003 0.021 0.002 0.001 0.001 0.034 0.009 0.034 0.017

d=

35

-

d=

31 cm

4

0.31 m

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.31 0.013 0.20

kd=

0.31 0.064

kd=

0.31 0.252982213

kd=

1.225 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

MNm kz x d x Fy

As=

x 10000

0.9

0.013 0.31

x

As=

0.013 117.18

x 10000

As=

0.000109234

x 10000

As=

x

420

1.09 cm2

C) Calculo Cuantia minima (P min.) P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

2.046 cm2 As NO VERIFICA!

2.046

1.09 VERIFICA!

* Adopto As min. 1

2.046 cm2

D) Calculo Cuantia maxima (P max.) P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

7.998 cm2 As VERIFICA!

7.998

1.09 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.31 2

x 0.469 2

M* =

0.20

x

0.0961 0.220

M* =

0.01922 0.220

M* = 0.087

MNm = 0.026

VSA

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm

VIGA (Vx4)-APOYO 24

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.31 0.026 0.20

kd=

0.31 0.128

kd=

0.31 0.3577708764

kd=

0.866 *Buscar en tabla

kz= 0.9

kd= Adopto 0,749

B) Calculo Armadura (As) ( Inferior- TRAMO) As= MNm kz x d x Fy

x 10000

x 10000

As=

As=

As=

0.9 0.026 117.18 0.0002184673

As=

0.026

x

0.31

x

420

x 10000

x 10000

2.18 cm2

C) Calculo Cuantia minima (P min.) 31

P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

2.046 cm2 As NO VERIFICA!

2.046

2.18 VERIFICA!

D) Calculo Cuantia maxima (P max.) 31

P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

7.998 cm2 As VERIFICA!

7.998

2.18 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.31 2

x 0.469 2

M* =

0.20

x

0.0961 0.220

M* =

0.01922 0.220

M* = 0.087

MNm = 0.026

VSA

VIGA (Vx4)-TRAMO 30

* Uso M* de ambos tramos A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.31 0.013 0.20

kd=

0.31 0.064

kd=

0.31 0.2529822128

kd=

1.225 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As= MNm kz x d x Fy

x 10000

As=

As=

x 10000

0.9 0.013 117.18

As= 0.0001092337

As=

0.013 0.31

x

x

x 10000

x 10000

1.09 cm2

C) Calculo Cuantia minima (P min.) 31

P min. x b (cm) x d (cm) =

0.0033

x

20

As min. =

2.046 cm2

As min.

As

2.046

* Adopto As m

1.09

2.046 cm2

D) Calculo Cuantia maxima (P max.) 31

P min. x b (cm) x d (cm) =

0.0129

x

As max. =

7.998 cm2

As max.

As

7.998

20

1.09

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.31 2

x 0.469 2

M* =

0.20

x

0.0961 0.220

M* =

0.01922 0.220

M* = 0.087

MNm = 0.002

VSA

x 10000

420

x

31

NO VERIFICA! VERIFICA!

x

VERIFICA! NO VERIFICA!

31

1. MOMENTO VIGA Y APOYOS DESIGNACION ALTURA (m) DE VIGA Vx1 Vx2

0.30 0.35

Vx3

0.30

Vx4

0.35

Vx5

0.30

Vx6

0.35

Vx8

0.20

Vx9

0.25

Vx10

0.50

Vx11 Vx12 Vx13

0.20 0.20 0.20

Vx14

0.30

Vx15

0.40

APOYO / TRAMOS

MOMENTO MOMENTO NOMINAL (tm) MN: Mu/0.9

TRAMO 3-7 TRAMO10-16 TRAMO 21-24 APOYO 24 APOYO 24 TRAMO 24-30 TRAMO 30 TRAMO 45-49 APOYO 49 APOYO 49 APOYO 53 TRAMO 49-53 TRAMO 53 APOYO 32 TRAMO 32-40 TRAMO 32 TRAMO 62-65 APOYO 54 TRAMO 54 TRAMO 54-59 TRAMO 11-17 TRAMO 29-41 TRAMO 12-18 APOYO 23 TRAMO 22-23 APOYO 23 TRAMO 23-42

1.041 0.957 1.142 2.304 2.304 1.152 0.151 0.459 0.966 0.966 0.966 0.483 0.047 0.143 0.048 0.143 0.265 3.373 0.262 1.918 0.147 0.086 0.076 3.072 0.847 3.072 1.536

MOMENTO NOMINAL (MNm) MN: Mn/100

1.157 1.063 1.269 2.560 2.560 1.280 0.168 0.510 1.073 1.073 1.073 0.537 0.052 0.159 0.053 0.159 0.294 3.748 0.291 2.131 0.163 0.096 0.084 3.413 0.941 3.413 1.707

VIGA (Vx5)-TRAMO 45-49 2.CALCULO kd *Adopto Hormigon H20 y Acero ADN 420 A) Calculo d

b= 20

cm

0.20 m

d= h (cm) - recubr. (4cm) d=

30

-

4

0.012 0.011 0.013 0.026 0.026 0.013 0.002 0.005 0.011 0.011 0.011 0.005 0.001 0.002 0.001 0.002 0.003 0.037 0.003 0.021 0.002 0.001 0.001 0.034 0.009 0.034 0.017

d=

26 cm

0.26 m

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.26 0.005 0.20

kd=

0.26 0.026

kd=

0.26 0.159687194

kd=

1.628 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

MNm kz x d x Fy

As=

As=

As=

x 10000

0.9 0.005 98.28 0.00005189

As=

0.005 0.26

x

x

420

x 10000

x 10000

0.52 cm2

C) Calculo Cuantia minima (P min.) P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

1.716 cm2 As NO VERIFICA!

1.716

0.52 VERIFICA!

* Adopto As min.

1.716 cm2

D) Calculo Cuantia maxima (P max.) P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

6.708 cm2 As VERIFICA!

6.708

0.52 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.26 2

x 0.469 2

M* =

0.20

x

0.0676 0.220

M* =

0.01352 0.220

M* = 0.061

MNm = 0.005

VSA

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm

VIGA (Vx5)-APOYO 49

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.26 0.011 0.20

kd=

0.26 0.054

kd=

0.26 0.2316606714

kd=

1.122 *Buscar en tabla

kz= 0.9

kd= Adopto 0,749

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

x 10000

MNm kz x d x Fy

As=

As=

As=

x 10000

0.9 0.011 98.28

x

0.26

x

x 10000

0.0001092118

As=

0.011

x 10000

1.09 cm2

C) Calculo Cuantia minima (P min.) 26

P min. x b (cm) x d (cm) =

0.0033

x

20

As min. = As min.

1.716 cm2 As

1.716

* Adopto As min.

1.09

1.716 cm2

D) Calculo Cuantia maxima (P max.) 26

P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

6.708 cm2 As

6.708

1.09

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.26 2

x 0.469 2

M* =

0.20

x

0.0676 0.220

M* =

0.01352 0.220

M* = 0.061

MNm = 0.011

VSA

420

x

x 10000

26

NO VERIFICA! VERIFICA!

x

VERIFICA! NO VERIFICA!

26

1. MOMENTO VIGA Y APOYOS DESIGNACION DE ALTURA (m) VIGA Vx1 Vx2

0.30 0.35

Vx3

0.30

Vx4

0.35

Vx5

0.30

Vx6

0.35

Vx8

0.20

Vx9

0.25

Vx10

0.50

Vx11 Vx12 Vx13

0.20 0.20 0.20

Vx14

0.30

Vx15

0.40

APOYO / TRAMOS

MOMENTO MOMENTO NOMINAL (tm) MN: Mu/0.9

TRAMO 3-7 TRAMO10-16 TRAMO 21-24 APOYO 24 APOYO 24 TRAMO 24-30 TRAMO 30 TRAMO 45-49 APOYO 49 APOYO 49 APOYO 53 TRAMO 49-53 TRAMO 53 APOYO 32 TRAMO 32-40 TRAMO 32 TRAMO 62-65 APOYO 54 TRAMO 54 TRAMO 54-59 TRAMO 11-17 TRAMO 29-41 TRAMO 12-18 APOYO 23 TRAMO 22-23 APOYO 23 TRAMO 23-42

1.041 0.957 1.142 2.304 2.304 1.152 0.151 0.459 0.966 0.966 0.966 0.483 0.047 0.143 0.048 0.143 0.265 3.373 0.262 1.918 0.147 0.086 0.076 3.072 0.847 3.072 1.536

MOMENTO NOMINAL (MNm) MN: Mn/100

1.157 1.063 1.269 2.560 2.560 1.280 0.168 0.510 1.073 1.073 1.073 0.537 0.052 0.159 0.053 0.159 0.294 3.748 0.291 2.131 0.163 0.096 0.084 3.413 0.941 3.413 1.707

VIGA (Vx6)-TRAMO 49-53 2.CALCULO kd *Adopto Hormigon H20 y Acero ADN 420 A) Calculo d

b= 20

cm

d= h (cm) - recubr. (4cm)

0.20 m

0.012 0.011 0.013 0.026 0.026 0.013 0.002 0.005 0.011 0.011 0.011 0.005 0.001 0.002 0.001 0.002 0.003 0.037 0.003 0.021 0.002 0.001 0.001 0.034 0.009 0.034 0.017

d=

35

-

d=

31 cm

4

0.31 m

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.31 0.005 0.20

kd=

0.31 0.027

kd=

0.31 0.163808832

kd=

1.892 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

MNm kz x d x Fy

As=

x 10000

0.9

0.005 0.31

x

As=

0.005 117.18

x 10000

As=

0.000045798

x 10000

As=

x

420

0.46 cm2

C) Calculo Cuantia minima (P min.) P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

2.046 cm2 As NO VERIFICA!

2.046

0.46 VERIFICA!

* Adopto As min. 1.

2.046 cm2

D) Calculo Cuantia maxima (P max.) P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

7.998 cm2 As VERIFICA!

7.998

0.46 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.31 2

x 0.469 2

M* =

0.20

x

0.0961 0.220

M* =

0.01922 0.220

M* = 0.087

MNm = 0.011

VSA

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm

VIGA (Vx6)-APOYO 49

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.31 0.011 0.20

kd=

0.31 0.054

kd=

0.31 0.2316606714

kd=

1.338 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

x 10000

MNm kz x d x Fy

x 10000

As=

0.9

0.011

x

As=

0.011 117.18

x 10000

As=

0.000091597

x 10000

As=

0.31

x

0.92 cm2

C) Calculo Cuantia minima (P min.) 31

P min. x b (cm) x d (cm) =

0.0033

x

20

As min. = As min.

2.046 cm2 As

2.046

* Adopto As min. 1

0.92

2.046 cm2

D) Calculo Cuantia maxima (P max.) 31

P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

7.998 cm2 As

7.998

0.92

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.31 2

x 0.469 2

M* =

0.20

x

0.0961 0.220

M* =

0.01922 0.220

M* = 0.087

MNm = 0.011

VSA

VIGA (Vx6)-APOYO 53

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.31 0.011 0.20

kd=

0.31 0.054

kd=

0.31 0.2316606714

kd=

1.338 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

420

x 10000

MNm kz x d x Fy

As=

As=

As=

x 10000

0.9 0.011 117.18 0.000091597

As=

0.011 0.31

x

x 10000

x 10000

0.92 cm2

C) Calculo Cuantia minima (P min.) x

31

P min. x b (cm) x d (cm) =

0.0033

x

As min. =

2.046 cm2

As min.

As

NO VERIFICA!

2.046

0.92

VERIFICA! * Adopto As min. 1.

2.046 cm2

D) Calculo Cuantia maxima (P max.) x

31

P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

7.998 cm2 As

VERIFICA!

7.998

0.92

NO VERIFICA! E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

x

0.31 0.469 2

M* =

0.20

x

0.0961 0.220

M* =

0.01922 0.220

M* = 0.087

MNm =

VSA

VIGA (Vx6)-TRAMO 53

* Uso M* de ambos tramos A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.31 0.005 0.20

kd=

0.31 0.027

kd=

0.31 0.16380883

kd=

1.892 *Buscar en tabla

kd= Adopto 1,218

kz=

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

0.011

x

420

x 10000

MNm kz x d x Fy

As=

x 10000

0.9

0.005

x

As=

0.005 117.18

x

As=

4.5798E-05

x

As=

0.46 cm2

C) Calculo Cuantia minima (P min.) 20

x

31

P min. x b (cm) x d (cm) =

0.0033

As min. = As min.

2.046 As

NO VERIFICA!

2.046

0.46

VERIFICA! * Adopto As min. 1

2.046 cm2

D) Calculo Cuantia maxima (P max.) 20

x

31

P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

7.998 As

VERIFICA!

7.998

0.46

NO VERIFICA! E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 2

M* =

0.20

x 0.469

M* =

0.20

x 0.220

M* =

0.011

0.01922 0.220

M* = 0.087

VSA

MO 53

*Buscar en tabla

0.9

or- TRAMO)

0.005 0.31

x

420

x 10000

10000

10000

x

20

x

31

cm2

NO VERIFICA! VERIFICA!

x

20

x

cm2

VERIFICA! NO VERIFICA!

EMENTE ARMADA

0.31 2 2

0.0961

MNm = 0.005

31

1. MOMENTO VIGA Y APOYOS DESIGNACION DE VIGA

ALTURA (m)

APOYO / TRAMOS

Vx1 Vx2

0.30 0.35

Vx3

0.30

Vx4

0.35

Vx5

0.30

Vx6

0.35

Vx8

0.20

Vx9

0.25

Vx10

0.50

Vx11 Vx12 Vx13

0.20 0.20 0.20

Vx14

0.30

Vx15

0.40

TRAMO 3-7 TRAMO10-16 TRAMO 21-24 APOYO 24 APOYO 24 TRAMO 24-30 TRAMO 30 TRAMO 45-49 APOYO 49 APOYO 49 APOYO 53 TRAMO 49-53 TRAMO 53 APOYO 32 TRAMO 32-40 TRAMO 32 TRAMO 62-65 APOYO 54 TRAMO 54 TRAMO 54-59 TRAMO 11-17 TRAMO 29-41 TRAMO 12-18 APOYO 23 TRAMO 22-23 APOYO 23 TRAMO 23-42

MOMENTO MOMENTO NOMINAL (tm) MN: Mu/0.9 1.041 0.957 1.142 2.304 2.304 1.152 0.151 0.459 0.966 0.966 0.966 0.483 0.047 0.143 0.048 0.143 0.265 3.373 0.262 1.918 0.147 0.086 0.076 3.072 0.847 3.072 1.536

MOMENTO NOMINAL (MNm) MN: Mn/100

1.157 1.063 1.269 2.560 2.560 1.280 0.168 0.510 1.073 1.073 1.073 0.537 0.052 0.159 0.053 0.159 0.294 3.748 0.291 2.131 0.163 0.096 0.084 3.413 0.941 3.413 1.707

VIGA (Vx8)-TRAMO 32-40 2.CALCULO kd *Adopto Hormigon H20 y Acero ADN 420 A) Calculo d

b= 20

cm

d= h (cm) - recubr. (4cm)

0.20 m

0.012 0.011 0.013 0.026 0.026 0.013 0.002 0.005 0.011 0.011 0.011 0.005 0.001 0.002 0.001 0.002 0.003 0.037 0.003 0.021 0.002 0.001 0.001 0.034 0.009 0.034 0.017

d=

20

-

d=

16 cm

4

0.16 m

* Uso M* de ambos tramos A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.16 0.002 0.20

kd=

0.16 0.008

kd=

0.16 0.089131613

kd=

1.795 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

MNm kz x d x Fy

As=

x 10000

0.9

0.002 0.16

x

As=

0.002 60.48

x 10000

As=

0.000026271

x 10000

As=

x

420

0.26 cm2

C) Calculo Cuantia minima (P min.) P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

1.056 cm2 As NO VERIFICA!

1.056

0.26 VERIFICA!

* Adopto As min.

1.056 cm2

D) Calculo Cuantia maxima (P max.) P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

4.128 cm2 As VERIFICA!

4.128

0.26 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.16 2

x 0.469 2

M* =

0.20

x

0.0256 0.220

M* =

0.00512 0.220

M* = 0.023

MNm = 0.001

VSA

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm

VIGA (Vx6)-APOYO 32

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.16 0.002 0.20

kd=

0.16 0.008

kd=

0.16 0.089131613

kd=

1.795 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

x 10000

MNm kz x d x Fy

As=

x 10000

0.9

0.002

x

As=

0.002 60.48

x 10000

As=

2.627131099E-05

x 10000

As=

0.16

x

0.26 cm2

C) Calculo Cuantia minima (P min.) 16

P min. x b (cm) x d (cm) =

0.0033

x

20

As min. = As min.

1.056 cm2 As

1.056

* Adopto As min. 1

0.26

1.056 cm2

D) Calculo Cuantia maxima (P max.) 16

P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

4.128 cm2 As

4.128

0.26

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.16 2

x 0.469 2

M* =

0.20

x

0.0256 0.220

M* =

0.00512 0.220

M* = 0.023

MNm = 0.002

VSA

VIGA (Vx8)-TRAMO 32

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.16 0.002 0.20

kd=

0.16 0.008

kd=

0.16 0.089131613

kd=

1.795 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

420

x 10000

MNm kz x d x Fy

As=

x 10000

0.9

0.002 0.16

x

As=

0.002 60.48

x 10000

As=

2.6271311E-05

x 10000

As=

0.26 cm2

C) Calculo Cuantia minima (P min.) x

16

P min. x b (cm) x d (cm) =

0.0033

x

As min. =

1.056 cm2

As min.

As

NO VERIFICA!

1.056

0.26

VERIFICA! * Adopto As min. 1

1.056 cm2

D) Calculo Cuantia maxima (P max.) x

16

P min. x b (cm) x d (cm) =

0.0129

x

As max. =

4.128 cm2

As max.

As

VERIFICA!

4.128

0.26

NO VERIFICA! E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

x

0.16 0.469 2

M* =

0.20

x

0.0256 0.220

M* =

0.00512 0.220

M* = 0.023

MNm =

VSA

0.002

x

20

420

x

x 10000

16

NO VERIFICA! VERIFICA!

20

x

VERIFICA! NO VERIFICA!

2

0.002

16

1. MOMENTO VIGA Y APOYOS DESIGNACION DE ALTURA (m) VIGA Vx1 Vx2

0.30 0.35

Vx3

0.30

Vx4

0.35

Vx5

0.30

Vx6

0.35

Vx8

0.20

Vx9

0.25

Vx10

0.50

Vx11 Vx12 Vx13

0.20 0.20 0.20

Vx14

0.30

Vx15

0.40

APOYO / TRAMOS

MOMENTO MOMENTO NOMINAL (tm) MN: Mu/0.9

TRAMO 3-7 TRAMO10-16 TRAMO 21-24 APOYO 24 APOYO 24 TRAMO 24-30 TRAMO 30 TRAMO 45-49 APOYO 49 APOYO 49 APOYO 53 TRAMO 49-53 TRAMO 53 APOYO 32 TRAMO 32-40 TRAMO 32 TRAMO 62-65 APOYO 54 TRAMO 54 TRAMO 54-59 TRAMO 11-17 TRAMO 29-41 TRAMO 12-18 APOYO 23 TRAMO 22-23 APOYO 23 TRAMO 23-42

1.041 0.957 1.142 2.304 2.304 1.152 0.151 0.459 0.966 0.966 0.966 0.483 0.047 0.143 0.048 0.143 0.265 3.373 0.262 1.918 0.147 0.086 0.076 3.072 0.847 3.072 1.536

MOMENTO NOMINAL (MNm) MN: Mn/100

1.157 1.063 1.269 2.560 2.560 1.280 0.168 0.510 1.073 1.073 1.073 0.537 0.052 0.159 0.053 0.159 0.294 3.748 0.291 2.131 0.163 0.096 0.084 3.413 0.941 3.413 1.707

VIGA (Vx9)-TRAMO 62-65 2.CALCULO kd *Adopto Hormigon H20 y Acero ADN 420 A) Calculo d

b= 20

cm

d= h (cm) - recubr. (4cm)

0.20 m

0.012 0.011 0.013 0.026 0.026 0.013 0.002 0.005 0.011 0.011 0.011 0.005 0.001 0.002 0.001 0.002 0.003 0.037 0.003 0.021 0.002 0.001 0.001 0.034 0.009 0.034 0.017

d=

25

-

d=

21 cm

4

0.21 m

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.21 0.003 0.20

kd=

0.21 0.015

kd=

0.21 0.121335165

kd=

1.731 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

MNm kz x d x Fy

As=

As=

As=

x 10000

0.9 0.003 79.38 0.00003709

As=

0.003 0.21

x

x

420

x 10000

x 10000

0.37 cm2

C) Calculo Cuantia minima (P min.) P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

1.386 cm2 As NO VERIFICA!

1.386

0.37 VERIFICA!

* Adopto As min. 1

1.386 cm2

D) Calculo Cuantia maxima (P max.) P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

5.418 cm2 As VERIFICA!

5.418

0.37 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.21 2

x 0.469 2

M* =

0.20

x

0.0441 0.220

M* =

0.00882 0.220

M* = 0.040

MNm = 0.003

VSA

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm

x 10000

21

21

1. MOMENTO VIGA Y APOYOS DESIGNACION DE VIGA

ALTURA (m)

APOYO / TRAMOS

Vx1 Vx2

0.30 0.35

Vx3

0.30

Vx4

0.35

Vx5

0.30

Vx6

0.35

Vx8

0.20

Vx9

0.25

Vx10

0.50

Vx11 Vx12 Vx13

0.20 0.20 0.20

Vx14

0.30

Vx15

0.40

TRAMO 3-7 TRAMO10-16 TRAMO 21-24 APOYO 24 APOYO 24 TRAMO 24-30 TRAMO 30 TRAMO 45-49 APOYO 49 APOYO 49 APOYO 53 TRAMO 49-53 TRAMO 53 APOYO 32 TRAMO 32-40 TRAMO 32 TRAMO 62-65 APOYO 54 TRAMO 54 TRAMO 54-59 TRAMO 11-17 TRAMO 29-41 TRAMO 12-18 APOYO 23 TRAMO 22-23 APOYO 23 TRAMO 23-42

MOMENTO MOMENTO NOMINAL (tm) MN: Mu/0.9 1.041 0.957 1.142 2.304 2.304 1.152 0.151 0.459 0.966 0.966 0.966 0.483 0.047 0.143 0.048 0.143 0.265 3.373 0.262 1.918 0.147 0.086 0.076 3.072 0.847 3.072 1.536

MOMENTO NOMINAL (MNm) MN: Mn/100

1.157 1.063 1.269 2.560 2.560 1.280 0.168 0.510 1.073 1.073 1.073 0.537 0.052 0.159 0.053 0.159 0.294 3.748 0.291 2.131 0.163 0.096 0.084 3.413 0.941 3.413 1.707

VIGA (Vx10)-TRAMO 54-59 2.CALCULO kd *Adopto Hormigon H20 y Acero ADN 420 A) Calculo d

b= 20

cm

d= h (cm) - recubr. (4cm)

0.20 m

0.012 0.011 0.013 0.026 0.026 0.013 0.002 0.005 0.011 0.011 0.011 0.005 0.001 0.002 0.001 0.002 0.003 0.037 0.003 0.021 0.002 0.001 0.001 0.034 0.009 0.034 0.017

d=

50

-

d=

46 cm

4

0.46 m

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.46 0.021 0.20

kd=

0.46 0.107

kd=

0.46 0.326428485

kd=

1.409 *Buscar en tabla

kz= 0.9

kd= Adopto 0,890

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

MNm kz x d x Fy

As=

x 10000

0.9

0.021 0.46

x

As=

0.021 173.88

x 10000

As=

0.000122562

x 10000

As=

x

420

1.23 cm2

C) Calculo Cuantia minima (P min.) P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

3.036 cm2 As NO VERIFICA!

3.036

1.23 VERIFICA!

* Adopto As min. 3.036 cm2 D) Calculo Cuantia maxima (P max.) P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

11.868 cm2 As VERIFICA!

11.868

1.23 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.46 2

x 0.469 2

M* =

0.20

x

0.2116 0.220

M* =

0.04232 0.220

M* = 0.192 VSA

MNm = 0.021

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm

VIGA (Vx10)-APOYO 54

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.46 0.037 0.20

kd=

0.46 0.187

kd=

0.46 0.4328843828

kd=

1.063 *Buscar en tabla

kz= 0.9

kd= Adopto 0,615

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

x 10000

MNm kz x d x Fy

x 10000

As=

As=

As=

0.9 0.037 173.88 0.0002155382

As=

0.037

x

0.46

x

x 10000

x 10000

2.16 cm2

C) Calculo Cuantia minima (P min.) 46

P min. x b (cm) x d (cm) =

0.0033

x

20

As min. =

3.036 cm2

As min.

As

3.036

2.16

* Adopto As min. 1 3.036 cm2 D) Calculo Cuantia maxima (P max.) 46

P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

11.868 cm2 As

11.868

2.16

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.46 2

x 0.469 2

M* =

0.20

x

0.2116 0.220

M* =

0.04232 0.220

M* = 0.192 VSA

MNm = 0.037

VIGA (Vx10)-TRAMO 54

* Uso M* de ambos tramos A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.46 0.021 0.20

kd=

0.46 0.107

kd=

0.46 0.32642848

kd=

1.409 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

420

x 10000

MNm kz x d x Fy

As=

x 10000

0.9

0.021 0.46

x

As=

0.021 173.88

x 10000

As=

0.00012256

x 10000

As=

1.23 cm2

C) Calculo Cuantia minima (P min.) x

46

P min. x b (cm) x d (cm) =

0.0033

x

As min. = As min.

3.036 cm2 As

NO VERIFICA!

3.036

1.23

VERIFICA! * Adopto As min. 3.036 cm2 D) Calculo Cuantia maxima (P max.) x

46

P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

11.868 cm2 As

VERIFICA!

11.868

1.23

NO VERIFICA! E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

x

0.46 0.469 2

M* =

0.20

x

0.2116 0.220

M* =

0.04232 0.220

M* = 0.192 VSA

MNm =

0.021

x

20

420

x

x 10000

46

NO VERIFICA! VERIFICA!

20

x

VERIFICA! NO VERIFICA!

2

0.021

46

1. MOMENTO VIGA Y APOYOS DESIGNACION ALTURA (m) DE VIGA Vx1 Vx2

0.30 0.35

Vx3

0.30

Vx4

0.35

Vx5

0.30

Vx6

0.35

Vx8

0.20

Vx9

0.25

Vx10

0.50

Vx11 Vx12 Vx13

0.20 0.20 0.20

Vx14

0.30

Vx15

0.40

APOYO / TRAMOS TRAMO 3-7 TRAMO10-16 TRAMO 21-24 APOYO 24 APOYO 24 TRAMO 24-30 TRAMO 30 TRAMO 45-49 APOYO 49 APOYO 49 APOYO 53 TRAMO 49-53 TRAMO 53 APOYO 32 TRAMO 32-40 TRAMO 32 TRAMO 62-65 APOYO 54 TRAMO 54 TRAMO 54-59 TRAMO 11-17 TRAMO 29-41 TRAMO 12-18 APOYO 23 TRAMO 22-23 APOYO 23 TRAMO 23-42

MOMENTO MOMENTO NOMINAL (tm) MN: Mu/0.9 1.041 0.957 1.142 2.304 2.304 1.152 0.151 0.459 0.966 0.966 0.966 0.483 0.047 0.143 0.048 0.143 0.265 3.373 0.262 1.918 0.147 0.086 0.076 3.072 0.847 3.072 1.536

MOMENTO NOMINAL (MNm) MN: Mn/100

1.157 1.063 1.269 2.560 2.560 1.280 0.168 0.510 1.073 1.073 1.073 0.537 0.052 0.159 0.053 0.159 0.294 3.748 0.291 2.131 0.163 0.096 0.084 3.413 0.941 3.413 1.707

VIGA (Vx11)-TRAMO 11-17 2.CALCULO kd *Adopto Hormigon H20 y Acero ADN 420 A) Calculo d

b= 20

cm

d= h (cm) - recubr. (4cm)

0.20 m

0.012 0.011 0.013 0.026 0.026 0.013 0.002 0.005 0.011 0.011 0.011 0.005 0.001 0.002 0.001 0.002 0.003 0.037 0.003 0.021 0.002 0.001 0.001 0.034 0.009 0.034 0.017

d=

20

-

d=

16 cm

4

0.16 m

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.16 0.002 0.20

kd=

0.16 0.008

kd=

0.16 0.090369611

kd=

1.771 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

MNm kz x d x Fy

As=

x 10000

0.9

0.002 0.16

x

As=

0.002 60.48

x 10000

As=

0.000027006

x 10000

As=

x

420

0.27 cm2

C) Calculo Cuantia minima (P min.) P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

1.056 cm2 As NO VERIFICA!

1.056

0.27 VERIFICA!

* Adopto As min.

1.056 cm2

D) Calculo Cuantia maxima (P max.) P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

4.128 cm2 As VERIFICA!

4.128

0.27 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.16 2

x 0.469 2

M* =

0.20

x

0.0256 0.220

M* =

0.00512 0.220

M* = 0.023

MNm = 0.002

VSA

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm

x 10000

16

16

1. MOMENTO VIGA Y APOYOS DESIGNACION ALTURA (m) DE VIGA Vx1 Vx2

0.30 0.35

Vx3

0.30

Vx4

0.35

Vx5

0.30

Vx6

0.35

Vx8

0.20

Vx9

0.25

Vx10

0.50

Vx11 Vx12 Vx13

0.20 0.20 0.20

Vx14

0.30

Vx15

0.40

APOYO / TRAMOS TRAMO 3-7 TRAMO10-16 TRAMO 21-24 APOYO 24 APOYO 24 TRAMO 24-30 TRAMO 30 TRAMO 45-49 APOYO 49 APOYO 49 APOYO 53 TRAMO 49-53 TRAMO 53 APOYO 32 TRAMO 32-40 TRAMO 32 TRAMO 62-65 APOYO 54 TRAMO 54 TRAMO 54-59 TRAMO 11-17 TRAMO 29-41 TRAMO 12-18 APOYO 23 TRAMO 22-23 APOYO 23 TRAMO 23-42

MOMENTO MOMENTO NOMINAL (tm) MN: Mu/0.9 1.041 0.957 1.142 2.304 2.304 1.152 0.151 0.459 0.966 0.966 0.966 0.483 0.047 0.143 0.048 0.143 0.265 3.373 0.262 1.918 0.147 0.086 0.076 3.072 0.847 3.072 1.536

MOMENTO NOMINAL (MNm) MN: Mn/100

1.157 1.063 1.269 2.560 2.560 1.280 0.168 0.510 1.073 1.073 1.073 0.537 0.052 0.159 0.053 0.159 0.294 3.748 0.291 2.131 0.163 0.096 0.084 3.413 0.941 3.413 1.707

VIGA (Vx12)-TRAMO 29-41 2.CALCULO kd *Adopto Hormigon H20 y Acero ADN 420 A) Calculo d

b= 20

cm

d= h (cm) - recubr. (4cm)

0.20 m

0.012 0.011 0.013 0.026 0.026 0.013 0.002 0.005 0.011 0.011 0.011 0.005 0.001 0.002 0.001 0.002 0.003 0.037 0.003 0.021 0.002 0.001 0.001 0.034 0.009 0.034 0.017

d=

20

-

d=

16 cm

4

0.16 m

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.16 0.001 0.20

kd=

0.16 0.005

kd=

0.16 0.069121471

kd=

2.315 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

MNm kz x d x Fy

As=

x 10000

0.9

0.001 0.16

x

As=

0.001 60.48

x 10000

As=

1.57995E-05

x 10000

As=

x

420

0.16 cm2

C) Calculo Cuantia minima (P min.) P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

1.056 cm2 As NO VERIFICA!

1.056

0.16 VERIFICA!

* Adopto As min.

1.056 cm2

D) Calculo Cuantia maxima (P max.) P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

4.128 cm2 As VERIFICA!

4.128

0.16 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.16 2

x 0.469 2

M* =

0.20

x

0.0256 0.220

M* =

0.00512 0.220

M* = 0.023

MNm = 0.001

VSA

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm

x 10000

16

16

1. MOMENTO VIGA Y APOYOS DESIGNACION DE VIGA

ALTURA (m)

APOYO / TRAMOS

Vx1 Vx2

0.30 0.35

Vx3

0.30

Vx4

0.35

Vx5

0.30

Vx6

0.35

Vx8

0.20

Vx9

0.25

Vx10

0.50

Vx11 Vx12 Vx13

0.20 0.20 0.20

Vx14

0.30

Vx15

0.40

TRAMO 3-7 TRAMO10-16 TRAMO 21-24 APOYO 24 APOYO 24 TRAMO 24-30 TRAMO 30 TRAMO 45-49 APOYO 49 APOYO 49 APOYO 53 TRAMO 49-53 TRAMO 53 APOYO 32 TRAMO 32-40 TRAMO 32 TRAMO 62-65 APOYO 54 TRAMO 54 TRAMO 54-59 TRAMO 11-17 TRAMO 29-41 TRAMO 12-18 APOYO 23 TRAMO 22-23 APOYO 23 TRAMO 23-42

MOMENTO MOMENTO NOMINAL (tm) MN: Mu/0.9 1.041 0.957 1.142 2.304 2.304 1.152 0.151 0.459 0.966 0.966 0.966 0.483 0.047 0.143 0.048 0.143 0.265 3.373 0.262 1.918 0.147 0.086 0.076 3.072 0.847 3.072 1.536

MOMENTO NOMINAL (MNm) MN: Mn/100

1.157 1.063 1.269 2.560 2.560 1.280 0.168 0.510 1.073 1.073 1.073 0.537 0.052 0.159 0.053 0.159 0.294 3.748 0.291 2.131 0.163 0.096 0.084 3.413 0.941 3.413 1.707

VIGA (Vx13)-TRAMO 12-18 2.CALCULO kd *Adopto Hormigon H20 y Acero ADN 420 A) Calculo d

b= 20

cm

d= h (cm) - recubr. (4cm)

0.20 m

0.012 0.011 0.013 0.026 0.026 0.013 0.002 0.005 0.011 0.011 0.011 0.005 0.001 0.002 0.001 0.002 0.003 0.037 0.003 0.021 0.002 0.001 0.001 0.034 0.009 0.034 0.017

d=

20

-

d=

16 cm

4

0.16 m

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.16 0.001 0.20

kd=

0.16 0.004

kd=

0.16 0.064978629

kd=

2.462 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

MNm kz x d x Fy

As=

x 10000

0.9

0.001 0.16

x

As=

0.001 60.48

x 10000

As=

1.39624E-05

x 10000

As=

x

420

0.14 cm2

C) Calculo Cuantia minima (P min.) P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

1.056 cm2 As NO VERIFICA!

1.056

0.14 VERIFICA!

* Adopto As min. 1

1.056 cm2

D) Calculo Cuantia maxima (P max.) P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

4.128 cm2 As VERIFICA!

4.128

0.14 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.16 2

x 0.469 2

M* =

0.20

x

0.0256 0.220

M* =

0.00512 0.220

M* = 0.023

MNm = 0.001

VSA

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm

x 10000

16

16

1. MOMENTO VIGA Y APOYOS DESIGNACION ALTURA (m) DE VIGA Vx1 Vx2

0.30 0.35

Vx3

0.30

Vx4

0.35

Vx5

0.30

Vx6

0.35

Vx8

0.20

Vx9

0.25

Vx10

0.50

Vx11 Vx12 Vx13

0.20 0.20 0.20

Vx14

0.30

Vx15

0.40

APOYO / TRAMOS TRAMO 3-7 TRAMO10-16 TRAMO 21-24 APOYO 24 APOYO 24 TRAMO 24-30 TRAMO 30 TRAMO 45-49 APOYO 49 APOYO 49 APOYO 53 TRAMO 49-53 TRAMO 53 APOYO 32 TRAMO 32-40 TRAMO 32 TRAMO 62-65 APOYO 54 TRAMO 54 TRAMO 54-59 TRAMO 11-17 TRAMO 29-41 TRAMO 12-18 APOYO 23 TRAMO 22-23 APOYO 23 TRAMO 23-42

MOMENTO MOMENTO NOMINAL (tm) MN: Mu/0.9 1.041 0.957 1.142 2.304 2.304 1.152 0.151 0.459 0.966 0.966 0.966 0.483 0.047 0.143 0.048 0.143 0.265 3.373 0.262 1.918 0.147 0.086 0.076 3.072 0.847 3.072 1.536

MOMENTO NOMINAL (MNm) MN: Mn/100

1.157 1.063 1.269 2.560 2.560 1.280 0.168 0.510 1.073 1.073 1.073 0.537 0.052 0.159 0.053 0.159 0.294 3.748 0.291 2.131 0.163 0.096 0.084 3.413 0.941 3.413 1.707

VIGA (Vx14)-TRAMO 22-23 2.CALCULO kd *Adopto Hormigon H20 y Acero ADN 420 A) Calculo d

b= 20

cm

d= h (cm) - recubr. (4cm)

0.20 m

0.012 0.011 0.013 0.026 0.026 0.013 0.002 0.005 0.011 0.011 0.011 0.005 0.001 0.002 0.001 0.002 0.003 0.037 0.003 0.021 0.002 0.001 0.001 0.034 0.009 0.034 0.017

d=

30

-

d=

26 cm

4

0.26 m

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.26 0.009 0.20

kd=

0.26 0.047

kd=

0.26 0.216922925

kd=

1.199 *Buscar en tabla

kz= 0.9

kd= Adopto 1,218

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

MNm kz x d x Fy

As=

x 10000

0.9

0.009 0.26

x

As=

0.009 98.28

x 10000

As=

9.57582E-05

x 10000

As=

x

420

0.96 cm2

C) Calculo Cuantia minima (P min.) P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

1.716 cm2 As NO VERIFICA!

1.716

0.96 VERIFICA!

* Adopto As min.

1.716 cm2

D) Calculo Cuantia maxima (P max.) P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

6.708 cm2 As VERIFICA!

6.708

0.96 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.26 2

x 0.469 2

M* =

0.20

x

0.0676 0.220

M* =

0.01352 0.220

M* = 0.061

MNm = 0.009

VSA

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm

VIGA (Vx14)-APOYO 23

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.26 0.034 0.20

kd=

0.26 0.171

kd=

0.26 0.4131182236

kd=

0.629 *Buscar en tabla

kz= 0.9

kd= Adopto 0,668

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

x 10000

MNm kz x d x Fy

As=

As=

As=

x 10000

0.9 0.034 98.28

0.26

x

x 10000

0.000347307

As=

0.034

x

x 10000

3.47 cm2

C) Calculo Cuantia minima (P min.) 26

P min. x b (cm) x d (cm) =

0.0033

x

20

As min. = As min.

1.716 cm2 As

1.716

3.47

D) Calculo Cuantia maxima (P max.) 26

P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

6.708 cm2 As

6.708

3.47

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.26 2

x 0.469 2

M* =

0.20

x

0.0676 0.220

M* =

0.01352 0.220

M* = 0.061

MNm = 0.034

VSA

420

x

x 10000

26

NO VERIFICA! VERIFICA!

x

VERIFICA! NO VERIFICA!

26

1. MOMENTO VIGA Y APOYOS DESIGNACION ALTURA (m) DE VIGA Vx1 Vx2

0.30 0.35

Vx3

0.30

Vx4

0.35

Vx5

0.30

Vx6

0.35

Vx8

0.20

Vx9

0.25

Vx10

0.50

Vx11 Vx12 Vx13

0.20 0.20 0.20

Vx14

0.30

Vx15

0.40

APOYO / TRAMOS TRAMO 3-7 TRAMO10-16 TRAMO 21-24 APOYO 24 APOYO 24 TRAMO 24-30 TRAMO 30 TRAMO 45-49 APOYO 49 APOYO 49 APOYO 53 TRAMO 49-53 TRAMO 53 APOYO 32 TRAMO 32-40 TRAMO 32 TRAMO 62-65 APOYO 54 TRAMO 54 TRAMO 54-59 TRAMO 11-17 TRAMO 29-41 TRAMO 12-18 APOYO 23 TRAMO 22-23 APOYO 23 TRAMO 23-42

MOMENTO MOMENTO NOMINAL (tm) MN: Mu/0.9 1.041 0.957 1.142 2.304 2.304 1.152 0.151 0.459 0.966 0.966 0.966 0.483 0.047 0.143 0.048 0.143 0.265 3.373 0.262 1.918 0.147 0.086 0.076 3.072 0.847 3.072 1.536

MOMENTO NOMINAL (MNm) MN: Mn/100

1.157 1.063 1.269 2.560 2.560 1.280 0.168 0.510 1.073 1.073 1.073 0.537 0.052 0.159 0.053 0.159 0.294 3.748 0.291 2.131 0.163 0.096 0.084 3.413 0.941 3.413 1.707

VIGA (Vx15)-TRAMO 23-42 2.CALCULO kd *Adopto Hormigon H20 y Acero ADN 420 A) Calculo d

b= 20

cm

d= h (cm) - recubr. (4cm)

0.20 m

0.012 0.011 0.013 0.026 0.026 0.013 0.002 0.005 0.011 0.011 0.011 0.005 0.001 0.002 0.001 0.002 0.003 0.037 0.003 0.021 0.002 0.001 0.001 0.034 0.009 0.034 0.017

d=

40

-

d=

36 cm

4

0.36 m

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.36 0.017 0.20

kd=

0.36 0.085

kd=

0.36 0.292118697

kd=

kd= Adopto 1,

1.232 *Buscar en tabla

kz= 0.9

0.890

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

MNm kz x d x Fy

As=

x 10000

0.9

0.017 0.36

x

As=

0.017 136.08

x 10000

As=

0.000125416

x 10000

As=

x

420

1.25 cm2

C) Calculo Cuantia minima (P min.) P min. x b (cm) x d (cm) =

0.0033

x

20

x

As min. = As min.

2.376 cm2 As NO VERIFICA!

2.376

1.25 VERIFICA!

* Adopto As min.

2.376 cm2

D) Calculo Cuantia maxima (P max.) P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

x

9.288 cm2 As VERIFICA!

9.288

1.25 NO VERIFICA!

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.36 2

x 0.469 2

M* =

0.20

x

0.1296 0.220

M* =

0.02592 0.220

M* = 0.118 VSA

MNm = 0.017

MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm MNm

VIGA (Vx15)-APOYO 23

A) Calculo kd kd=

d (m) MNm b (m)

kd=

0.36 0.034 0.20

kd=

0.36 0.171

kd=

0.36 0.4131182236

kd=

0.871 *Buscar en tabla

kz= 0.9

kd= Adopto 0,668

B) Calculo Armadura (As) ( Inferior- TRAMO) As=

x 10000

MNm kz x d x Fy

x 10000

As=

As=

As=

0.9 0.034 136.08 0.0002508328

As=

0.034

x

0.36

x

x 10000

x 10000

2.51 cm2

C) Calculo Cuantia minima (P min.) 36

P min. x b (cm) x d (cm) =

0.0033

x

20

As min. = As min.

2.376 cm2 As

2.376

2.51

D) Calculo Cuantia maxima (P max.) 36

P min. x b (cm) x d (cm) =

0.0129

As max. = As max.

x

20

9.288 cm2 As

9.288

2.38

E) Verificar VIGA DOBLE O SIMPLEMENTE ARMADA 1. CALCULO MOMENTO CRITICO M*:

*Adopto Horm. H20 - Kd= 0.469

M* = b (m) x d2 (m) Kd2 M* =

0.20

0.36 2

x 0.469 2

M* =

0.20

x

0.1296 0.220

M* =

0.02592 0.220

M* = 0.118 VSA

MNm = 0.034

420

x

x 10000

36

NO VERIFICA! VERIFICA!

x

VERIFICA! NO VERIFICA!

36

1. ESFUERZO CORTE APOYOS DESIGNACION ALTURA (m) DE VIGA Vx1

0.30

Vx2

0.35

Vx3

0.30

Vx4

0.35

Vx5

0.30

Vx6

Vx8

0.35

0.20

APOYO

ESFUERZO CORTE (Tn)

APOYO 3 APOYO 7 APOYO 10

3.89 2.65 1.86

Tn Tn Tn

APOYO 16 APOYO 21

2.80 4.09

Tn Tn

APOYO 24

4.09

Tn

APOYO 24

4.13

Tn

APOYO 30 APOYO 45

4.13 1.64

Tn Tn

APOYO 49

1.64

Tn

APOYO 49

1.71

Tn

APOYO 53

1.71

Tn

APOYO 53´

0.31

Tn

APOYO 32 APOYO 32´

0.52 0.52

Tn Tn

APOYO 40 APOYO 62

0.52 1.10

Tn Tn

APOYO 65

0.77

Tn

Vx9

0.25

APOYO 54

4.28

Tn

Vx10

0.50

APOYO 54´ APOYO 59

0.95 2.65

Tn Tn

Vx11

0.20

APOYO 11 APOYO 17

0.71 1.16

Tn Tn

Vx12

0.20

APOYO 29

0.93

Tn

APOYO 41

0.93

Tn

Vx13

0.20

APOYO 12 APOYO 18

1.00 0.89

Tn Tn

Vx14

0.30

APOYO 27 APOYO 23

3.00 3.00

Tn Tn

Vx15

0.40

APOYO 23

4.10

Tn

APOYO 42

4.10

Tn

2. CALCULO d´ d= h (m) - recubr. (0,04m)

Vx1-Vx3-Vx5-Vx14 d=

0.30

-

d´= 0.26 cm

Vx2-Vx4-Vx6 d=

0.35

-

d´= 0.31 cm

Vx8-Vx11-Vx12-Vx13 d=

0.20

-

d´= 0.16 cm

Vx9 d=

0.25

-

d´= 0.21 cm

Vx10 d=

0.50

d´= 0.46 cm

-

Vx15 d=

0.40

d´= 0.36 cm

1.CORTE REDUCIDO (Vu) DESIGNACION DE VIGA

APOYO

CORTE REDUCIDO (Vu)

CORTE NOMINAL (Vn) Vn=Vu/0,75

VNm (VN/100)

Vx1

APOYO 3 APOYO 7

3.06 1.82

4.07 2.42

0.0407 0.0242

Tn Tn

APOYO 10 APOYO 16 APOYO 21 APOYO 24 APOYO 24 APOYO 30

1.03 1.85 3.21 3.21 3.13 3.13

1.37 2.47 4.28 4.28 4.17 4.17

0.0137 0.0247 0.0428 0.0428 0.0417 0.0417

Tn Tn Tn Tn Tn Tn

APOYO 45

1.28

1.71

0.0171

Tn

APOYO 49

1.28

1.71

0.0171

Tn

APOYO 49

1.29

1.72

0.0172

Tn

APOYO 53

1.29

1.72

0.0172

Tn

APOYO 53´

-0.11

-0.15

-0.0015

Tn

APOYO 32

0.26

0.35

0.0035

Tn

APOYO 32´

0.26

0.35

0.0035

Tn

APOYO 40

0.26

0.35

0.0035

Tn

APOYO 62

0.76

1.01

0.0101

Tn

APOYO 65

0.43

0.57

0.0057

Tn

APOYO 54 APOYO 54´ APOYO 59 APOYO 11 APOYO 17 APOYO 29

3.33 0.00 1.70 0.27 0.72 0.49

4.44 0.00 2.27 0.35 0.95 0.65

0.0444 0.0000 0.0227 0.0035 0.0095 0.0065

Tn Tn Tn Tn Tn Tn

Vx2 Vx3 Vx4 Vx5

Vx6

Vx8

Vx9

Vx10 Vx11 Vx12

-

Vx12 Vx13 Vx14 Vx15

APOYO 41 APOYO 12

0.49 0.56

0.65 0.74

0.0065 0.0074

Tn Tn

APOYO 18 APOYO 27

0.45 2.37

0.59 3.16

0.0059 0.0316

Tn Tn

APOYO 23 APOYO 23 APOYO 42

2.37 3.27 3.27

3.16 4.37 4.37

0.0316 0.0437 0.0437

Tn Tn Tn

4. CALCULO DE LA CONTRCION DEL HORMIGON Vc=

1 6

f´c x b x d

VIGA 20 x 20 (Vx8-Vx11-Vx12-Vx13) Vc=

1 6

20

Vc=

1 6

0.64

Vc=

1 6

x

0.80

x

0.80

Vc= 0.166666667

Vc=

x

0.20

x

0.16

0.20

x

0.21

0.133 MNm

VIGA 20 x 25 (Vx9) Vc=

1 6

20

Vc=

1 6

0.84

Vc=

1 6

x

x

0.92

Vc= 0.166666667

Vc=

x

0.92

0.153 MNm

VIGA 20 x 30 (Vx1-Vx3-Vx5-Vx14) Vc=

1 6

20

Vc=

1 6

1.04

Vc=

1 6

x

1.02

x

1.02

Vc= 0.166666667

Vc=

x

0.20

x

0.26

0.170 MNm

4. DISEÑO CON ESTRIBO s max=

Vs= VNm - Vc

DESIGNACION DE VIGA

APOYO

VNm

Vs= VNm - Vc

Vx1

APOYO 3 APOYO 7 APOYO 10 APOYO 16 APOYO 21

0.0407 0.0242 0.0137 0.0247 0.0428

-0.13 -0.15 -0.17 -0.16 -0.13

Tn Tn Tn Tn Tn

APOYO 24 APOYO 24

0.0428 0.0417

-0.13 -0.14

Tn Tn

APOYO 30 APOYO 45 APOYO 49 APOYO 49 APOYO 53

0.0417 0.0171 0.0171 0.0172 0.0172

-0.14 -0.15 -0.15 -0.17 -0.17

Tn Tn Tn Tn Tn

APOYO 53´ APOYO 32

-0.0015 0.0035

0.19 -0.13

Tn Tn

Vx2 Vx3 Vx4 Vx5 Vx6

Vx8

VIGA 20 x 20 (Vx8-Vx11-V s max=

s max=

VIGA 20 x 25 (Vx9) s max=

s max=

Vx8

APOYO 32´ APOYO 40 APOYO 62 APOYO 65 APOYO 54

0.0035 0.0035 0.0101 0.0057 0.0444

-0.13 -0.13 -0.14 -0.15 -0.18

Tn Tn Tn Tn Tn

Vx10

APOYO 54´ APOYO 59

0.0000 0.0227

-0.23 -0.20

Tn Tn

Vx11

APOYO 11 APOYO 17 APOYO 29 APOYO 41 APOYO 12

0.0035 0.0095 0.0065 0.0065 0.0074

-0.13 -0.12 -0.13 -0.13 -0.13

Tn Tn Tn Tn Tn

APOYO 18 APOYO 27 APOYO 23 APOYO 23 APOYO 42

0.0059 0.0316 0.0316 0.0437 0.0437

-0.13 -0.14 -0.14 -0.16 -0.16

Tn Tn Tn Tn Tn

Vx9

Vx12 Vx13 Vx14 Vx15

VIGA 20 x 30 (Vx1-Vx3-Vx s max=

s max=

VIGA 20 x 35 (Vx2-Vx4-Vx s max=

s max=

5. CALCULO DE ABSORCION DE ESFUERZO POR ESTRIBOS VIGA 20 x 20 (Vx8-Vx11-Vx12-Vx13) *Se usa estribos daim.6- 2Ramas de dimetro 6 c/ 10 cm ( 2x 0,28 cm2) *Se usa acero ADN 420

Vs =

As

x

fy

x

d

0.28

x

420

s

Vs =

2

x 10000

Vs =

0.56

0.10

x

67.2

10000

Vs = Vs = S=

0.0001

0.10 x

672

x

fy

0.038 MN

As

x

Vs

x

d

0.16

S=

2

x

0.28

x

420

10000

S=

0.56

x

10000

S= S=

0.0001

0.1000 MN

0.038 67.2 0.0376

x

x

1785.71428571

0.10 cm

0.16

2. CALCULO d

ecubr. (0,04m)

d=

C 2

Vx5-Vx14

C= 0.20 x 0,20

+

d´

+

0.26

d=

0.10

+

0.26

+

0.31

d=

0.10

+

0.31

+

0.16

d=

0.10

+

0.16

+

0.21

d=

0.10

+

0.21

+

0.46

d=

0.10

+

0.46

Vx1-Vx3-Vx5-Vx14

0.04

d=

0.20 2

Vx2-Vx4-Vx6 0.04

d=

0.20 2

-Vx12-Vx13

Vx8-Vx11-Vx12-Vx13

0.04

d=

0.20 2

Vx9 0.04

d=

0.20 2

Vx10 0.04

d=

0.20 2

Vx15 0.04

d=

0.20 2

+

d=

0.36

0.10

+

0.36

3. VERIFICACION DE LA SECCION *Verifico con el Vu mayor de acuerdo a la seccion V=

VNm bxd

H20=

3.727 Mpa

VERIFICA

VIGA 20 x 20

VIGA 20 x 35

V=

0.0074 0.20

V=

x

V= 0.16

0.0074

0.0417 0.20

V=

0.31

0.0417

0.032

0.062

V= 0.232 Mpa

V= 0.673 Mpa

VIGA 20 x 25

VIGA 20 x 40

V= 0.20 V=

x

0.0101 x 0.0101

V= 0.21

0.20 V=

0.0437 x 0.0437

0.36

0.042

0.072

V= 0.240 Mpa

V= 0.606 Mpa

VIGA 20 x 30

VIGA 20 x 50

V= 0.20 V=

0.0428 x

V= 0.26

0.20

0.0428 0.052

V=

V= 0.823 Mpa

Vc=

1 6

20

Vc=

1 6

1.24

Vc=

1 6

x

1.11

x

1.11

Vc=

0.186

x

0.20

x

0.31

0.20

x

0.36

MNm

VIGA 20 x 40 (Vx15) Vc=

1 6

20

Vc=

1 6

1.44

Vc=

1 6

x

0.0444 0.092

V= 0.482 Mpa

VIGA 20 x 35 (Vx2-Vx4-Vx6)

Vc= 0.16667

0.0444 x

x

1.20

0.46

Vc= 0.16667

Vc=

x

0.200

1.20

MNm

VIGA 20 x 50 (Vx10) Vc=

1 6

20

Vc=

1 6

1.84

Vc=

1 6

x

1.36

x

1.36

Vc= 0.16667

Vc=

0.226

x

0.20

x

0.46

MNm

d 2

20 x 20 (Vx8-Vx11-Vx12-Vx13)

s max=

0.16 2

0.08

VIGA 20 x 40 (Vx15)

= 0.10

20 x 25 (Vx9)

0.36 2

s max= 0.18

= 0.20

VIGA 20 x 50 (Vx10) s max=

0.21 2

0.105

= 0.10

0.46 2

s max= 0.23

= 0.25

20 x 30 (Vx1-Vx3-Vx5-Vx14) 0.26 2

= 0.15

0.13

20 x 35 (Vx2-Vx4-Vx6) 0.31 2

0.155

= 0.15

VIGA 20 x 25 (Vx9) *Se usa estribos daim.6- 2Ramas de dimetro 6 c/ 10 cm ( 2x 0,28 cm2) *Se usa acero ADN 420

Vs =

As

x

fy

x

d

0.28

x

420

s

Vs =

2

x 10000

Vs =

0.56

x

10000

Vs = Vs = S=

0.0001

0.10 88.2 0.10

x

882

x

fy

0.049 MN

As

x

Vs

x

d

0.21

S=

2

x

0.28

x

420

10000

S=

0.56

x

10000

S= S=

0.0001

0.1000 MN

0.049 88.2 0.0494

x

x

1785.71

0.10 cm

0.21

3. CALCULO DE CORTE REDUCIDO Vu=

CORTE

-

d (m)

x

x

Vx1- apoyo 3 d= 0.36

d= 0.41

d= 0.26

m

m

m

Vu=

3.89

-

0.36

Vu=

3.89

-

0.834847

Vu=

3.06

Tn

Vx1- apoyo 7 Vu=

2.65

-

0.36

Vu=

2.65

-

0.834847

Vu=

1.82

x

Tn

Vx2- apoyo 10

d= 0.31

m

Vu=

1.86

-

0.36

Vu=

1.86

-

0.834847

Vu=

1.03

x

Tn

Vx2- apoyo 16 d= 0.56

m

Vu=

2.80

-

0.41

Vu=

2.80

-

0.950798

x

Vu= d= 0.46

1.85

Tn

m

VIGA 20 x 20 = No requiere estribos. VIGA 20 x 25 = No requiere estribos. VIGA 20 x 30 = Se requiere estribos minimos. VIGA 20 x 35 = Se requiere estribos minimos. VIGA 20 x 40 = Se requiere estribos minimos. VIGA 20 x 50 = No requiere estribos.

VIGA 20 x 30 (Vx1-Vx3-Vx5-Vx14)

VIGA 20 x 35 (Vx2-Vx4

*Se usa estribos daim.6- 2Ramas de dimetro 6 c/ 15 cm ( 2x 0,28 cm2)

*Se usa estri

*Se usa acero ADN 420

Vs =

As

x

*Se u

fy

x

d

0.28

x

420

Vs =

s

Vs =

2

x 10000

Vs =

0.56

x

10000

Vs = Vs = S=

0.0001

0.26

Vs =

0.15

Vs =

109.2 0.15

x

Vs =

728

0.041 MN

As

x

Vs =

x

fy Vs

x

d

S=

S=

2

x

0.28

x

420

10000

S=

0.56

x

10000

S= S=

0.0001

x

0.26

S=

0.041

S=

109.2 0.0408

x

0.1500 MN

S=

2678.57143

0.15 cm

S=

Qf (t/m)

Vx3- apoyo 21 2.31902

Vu=

4.09

-

0.36

Vu=

4.09

-

0.87849

Vu=

3.21

x

2.44025

x

2.44025

x

2.44025

x

2.44025

Tn

Vx3- apoyo 24 2.31902

Vu=

4.09

-

0.36

Vu=

4.09

-

0.87849

Vu=

3.21

Tn

Vx4- apoyo 24 2.31902

Vu=

4.13

-

0.41

Vu=

4.13

-

1.0005025

Vu=

3.13

Tn

Vx4- apoyo 30 2.31902

Vu=

4.13

-

0.41

Vu=

4.13

-

1.0005025

Vu=

3.13

Tn

VIGA 20 x 35 (Vx2-Vx4-Vx6) *Se usa estribos daim.6- 2Ramas de dimetro 6 c/ 15 cm ( 2x 0,28 cm2) *Se usa acero ADN 420 As

x

fy

x

d

x

420

s 2

x

0.28

10000 0.56

x

10000 0.0001

0.15 130.2 0.15

x

868

x

fy

0.049 MN

As

x

Vs

x

d

0.31

2

x

0.28

x

10000 0.56

x

10000 0.0001

0.1500 MN

x 0.049

130.2 0.0486

x

420

2678.57143

0.15 cm

0.31

Vx5- apoyo 45 Vu=

1.64

-

0.36

Vu=

1.64

-

0.361242

Vu=

1.28

x

1.00345

x

1.00345

x

1.03225

x

1.03225

Tn

Vx5- apoyo 49 Vu=

1.64

-

0.36

Vu=

1.64

-

0.361242

Vu=

1.28

Tn

Vx6- apoyo 49 Vu=

1.71

-

0.41

Vu=

1.71

-

0.4232225

Vu=

1.29

Tn

Vx6- apoyo 53 Vu=

1.71

-

0.41

Vu=

1.71

-

0.4232225

Vu=

1.29

Tn

VIGA 20 x 40 (Vx15) *Se usa estribos daim.6- 2Ramas de dimetro 6 c/ 10 cm ( 2x 0,28 cm2) *Se usa acero ADN 420

Vs =

As

x

fy

x

d

0.28

x

420

s

Vs =

2

x 10000

Vs =

0.56

x

10000

Vs = Vs = S=

0.0001

0.20 151.2 0.20

x

756

x

fy

0.042 MN

As

x

Vs

x

d

S=

2

x

0.28

x

10000

S=

0.56

x

10000

S= S=

0.0001

0.2000 MN

x 0.042

151.2 0.0423

x

420

3571.42857

0.20 cm

Vx6- apoyo 53´

Vx9- apoyo 62

Vu=

0.31

-

0.41

Vu=

0.31

-

0.4232225

Vu=

-0.11

x

1.03225

Vu= Vu= Vu=

Tn

Vx8- apoyo 32´

Vx9- apoyo 65

Vu=

0.52

-

0.26

Vu=

0.52

-

0.2553902

Vu=

0.26

x

0.98227

Vu= Vu= Vu=

Tn

Vx8- apoyo 32

Vx10- apoyo 54´

Vu=

0.52

-

0.26

Vu=

0.52

-

0.2553902

Vu=

0.26

x

0.98227

Vu= Vu= Vu=

Tn

Vx8- apoyo 40

Vx10- apoyo 54

Vu=

0.52

-

0.26

Vu=

0.52

-

0.2553902

x

0.98227

Vu= Vu=

Vu=

0.26

Tn

Vu=

VIGA 20 x 50 (Vx10)

cm ( 2x 0,28 cm2)

*Se usa estribos daim.6- 2Ramas de dimetro 6 c/ 10 cm ( 2 *Se usa acero ADN 420

Vs =

As

x

fy

x

s 0.36

Vs =

2

0.20

x

0.28

x

10000

Vs =

0.56

x

10000

Vs = Vs = S=

0.0001

193.2 0.25

x

772.8

x

fy

0.043 MN

As

Vs

x

S=

0.36

2

0.042

x

0.28

x

10000

S=

0.56

x

10000

S= S=

0.0001

0.2500 MN

193.2 0.0433

x

4464.28571

0.25

Vx9- apoyo 62

Vx10- apoyo 59

1.10

-

0.31

1.10

-

0.34386586

0.76

x

1.1092447

Tn

Vx9- apoyo 65 -

0.31

0.77

-

0.34386586

x

1.1092447

Tn

Vx10- apoyo 54´

Vu=

2.65

Vu=

1.70

Vu=

0.71

Vu=

0.71

Vu=

0.27

Vx11- apoyo 17

0.95

-

0.56

0.95

-

0.9511096

0.00

2.65

Vx11- apoyo 11

0.77

0.43

Vu=

x

1.69841

Tn

Vx10- apoyo 54

Vu=

1.16

Vu=

1.16

Vu=

0.72

Vx12- apoyo 29

4.28

-

0.56

4.28

-

0.9511096

x

1.69841

Vu=

0.93

Vu=

0.93

3.33

Tn

Vu=

0.49

mas de dimetro 6 c/ 10 cm ( 2x 0,28 cm2)

d

420

x 0.25

d

0.46

420

x 0.043

cm

0.46

Vx12- apoyo 41 -

0.56

-

0.9511096

x

1.69841

Tn

Vu=

0.93

-

Vu=

0.93

-

Vu=

0.49

Tn

Vx13- apoyo 12 -

0.26

-

0.4442516

x

1.70866

Tn

Vu=

1.00

-

Vu=

1.00

-

Vu=

0.56

Tn

Vx13- apoyo 18 -

0.26

-

0.4442516

x

1.70866

Tn

Vu=

0.89

-

Vu=

0.89

-

Vu=

0.45

Tn

Vx14- apoyo 27 -

0.26

-

0.4442516

x

1.70866

Vu=

3.00

-

Vu=

3.00

-

Tn

Vu=

2.37

Tn

Vx14- apoyo 23 0.26

x

1.70866

0.4442516

Vu=

3.00

-

0.36

Vu=

3.00

-

0.6306696

Vu=

2.37

Tn

Vx15- apoyo 23 0.26

x

1.70866

0.4442516

Vu=

4.10

-

0.46

Vu=

4.10

-

0.8257276

Vu=

3.27

Tn

Vx15- apoyo 42 0.26

x

1.70866

0.4442516

0.36 0.6306696

x

1.75186

Vu=

4.10

-

0.46

Vu=

4.10

-

0.8257276

Vu=

3.27

Tn

x

1.75186

x

1.79506

x

1.79506

1. AREA DE INFLUENCIA SOBRE COLUMNA DESIGNACION DE VIGA

LUZ (m)

Vx1 Vx2

2.55 3.20

Vx3

3.35 3.40

Vx4

0.30 Vx5

3.35

Vx6

Qf s/ LOZA (Tn/m) COLUMNA PORCENTAJE LUZ de VIGA PESO(AREA (Tn) DE ( 60% -40% o CON (AREA DE INFLUENCIA 50% - 50%) INFLUENCIA INFLUENCIA LOZA ) LOZA x VIGA) 2.319 2.957 50 1.275 1.481 2.370 50 1.600 3.270 40 1.340 2.440 4.905 60 2.010 4.236 50 1.700 2.492 4.236 50 1.700 1.570 0.471 100 0.300 1.345 40 1.340 1.003 2.017 60 2.010 50 50

1.700 1.700

1.032

0.30

100 100

0.300 0.550

0.650

0.195

0.540

0.297

1.10

60 40

0.660 0.440

0.982

2.35

50 60

1.175 2.400

1.109

1.303

1.698

4.076

100 50

0.550 0.550

2.480

1.364

1.709

0.940

0.55 Vx8 Vx9

4.00

Vx10

1.755

3.40

0.55

Vx11

1.10

Vx12

1.10

50 50

0.550 0.550

1.709

Vx13

1.10 3.35

0.550 1.340

1.709

Vx14

50 40

Vx15

4.45

60 60

2.010 2.670

40

1.780

1.752 1.795

1.755

0.648 0.432

0.940 0.940 0.940 2.347 3.521 4.793 3.195

A) CONOCER VALOR Pn Pn =

Pu

Fi c/ estribo simple =

0.65

Fi zunchada=

0.70

Limite sup. Col. simple = Limite sup. Col. zunchada =

0.80 0.85

valor limite x Fi

CALCULO C1

CALCULO C5

Pn =

0.030 0.65

Pn =

Pn =

x

Pn = 0.80

0.030 0.52

Pn =

0.06 MNm

Pn =

CALCULO C2

CALCULO C6

Pn = 0.65 Pn =

Pn =

0.056 x

Pn = 0.80

0.056 0.52

Pn =

0.11 MNm

Pn =

CALCULO C3

CALCULO C7

Pn = 0.65 Pn =

Pn =

0.175 x

Pn = 0.80

0.175 0.52

Pn =

0.34 MNm

Pn =

CALCULO C4

CALCULO C8

Pn = 0.65 Pn =

Pn =

0.066 x

Pn = 0.80

0.066 0.52

Pn =

0.13 MNm

Pn =

B) CALCULAR Ag Ag =

Pn

P min. = P max. =

(0,85 x Fc´ ) + P min x ( Fy - 0,85 x Fc´)

Hormigon H20 =

Acero ADN 420 = CALCULO C3 - MAS SOLICITADA Ag = 0.85

x

20

Ag =

420

403

17

+

0.01

0.34 x

17

+

0.34 0.01

x

17

0.34 +

4.03

x

10000

Ag =

Ag =

Ag =

+

0.34 0.01

0.34 21.03

Ag = 0.015961

160 SECCION COLUMNA= ADOPTO SECCION MINIMA=

C) CALCULAR Ast Ast = P min x Ag Ast =

0.01

Ast =

x

400

4 cm2

ADOPTO 4 HIERROS DEL 12 POR NORMA CIRSOC 201-2005 ADOPTO =

D) CALCULAR SEPARACION ESTRIBOS S = 12 x db S= S=

12 mm

12

x 14.4

1.2 ADOPTO SEPARACION 15 cm

1.2

Qu DESIGNACION COLUMNA DE COLUMNA (Tn) C1 C2

2.957 3.270

Tn Tn Tn

C3

9.140

C4

4.706

C5

1.345

C6

3.772

Tn Tn Tn Tn Tn Tn

C7

1.950

C8

0.945

C9

0.432

C10

1.303

C11

5.440

C12

0.940

C13

0.940

C14

0.940

C15

0.940

C16

2.347

C17 C18

1.) PESO COLUMNA PB

C1= C2=

3.270

C2= VOLADIZO VOLADIZO

C3=

Tn Tn

+

C16

+

2.347

VOLADIZO

C3

C3=

17.455 Tn

C4=

C4

Tn Tn

0.056

5.617 Tn

9.140

Tn Tn Tn Tn

C2

VOLADIZO

Tn Tn Tn Tn

0.030

2.957 Tn

4.706

+

C17

+

8.314

0.175 +

C8

+

0.945

+

C13 0.940

Tn Tn

C4=

6.592 Tn

0.066

8.314

Tn Tn

C5=

1.345 Tn

0.013

3.195

Tn

C6=

3.772 Tn

0.038

C7=

C7 1.950

C7=

7.390 Tn

+

C11

+

5.440

0.074

CALCULO C9 0.013 0.65

Pn = x

0.80

0.013 0.52

0.65 Pn =

0.03 MNm

0.014

Pn =

x

0.80

0.014 0.52

0.03 MNm

CALCULO C10 0.038 0.65

Pn = x

0.80

0.038 0.52

0.65 Pn =

0.07 MNm

Pn =

0.013 x

0.80

0.013 0.52

0.03 MNm

CALCULO C11 0.074 0.65

Pn = x

0.80

0.074 0.52

0.65 Pn =

0.14 MNm

Pn =

0.054 x

0.80

0.054 0.52

0.10 MNm

CALCULO C12 0.019 0.65

Pn = x

0.019 0.52

Hormigon H20 =

0.65 Pn =

0.04 MNm

P min. = P max. =

0.80

0.01 0.08 20

Pn =

0.019 x

0.019 0.52

0.04 MNm

0.80

Acero ADN 420 =

420

0.34 x

420

-

17

-

0.85

x

20

cm2 12.6337539443 20 x 20 =

400 cm2

CIRSOC 201-2005 ADOPTO = DIAMETRO HASTA 16 ADOPTO ESTRIBOS DE 6 mm

cm

2.) PESO COLUMNA GALERIA

3.) PESO PA

MNm C8=

MNm

MNm

MNm

MNm

+

C13

0.945

+

0.940

C8=

1.885 Tn

C9=

C9 0.432

C14=

C14 0.940

0.019 MNm

C14=

5.646 Tn

+

C14

C15=

0.940 Tn

+

0.940

C16=

2.347 Tn

C9=

1.372 Tn

0.014 MNm

C17=

8.314 Tn

C10=

1.303 Tn

0.013 MNm

C18=

3.195 Tn

C11=

5.440 Tn

0.054 MNm

C12=

C12

+

C15

0.940

+

0.940

MNm MNm

C8

C12=

1.880 Tn

0.019 MNm

C13=

0.940 Tn

0.009 MNm

+ +

CALCULO C13

CALCULO C17

Pn =

0.009 0.65

Pn =

Pn = x

0.80

0.009 0.52

Pn =

Pn =

CALCULO C14 0.056 0.65

0.80

0.11 MNm

Pn =

Pn =

0.009 0.65

x

0.80

0.009 0.52

Pn =

0.02 MNm

CALCULO C16 Pn =

0.023 0.65

Pn =

0.16 MNm

0.65 Pn =

CALCULO C15

Pn =

0.80

0.083 0.52

Pn = x

0.056 0.52

Pn =

Pn =

x

CALCULO C18

Pn =

Pn =

0.65 Pn =

0.02 MNm

0.083

x

0.023 0.52

0.05 MNm

0.80

0.032 x

0.032 0.52

0.06 MNm

0.80

C18 4.706

0.056 MNm 0.009 MNm 0.023 MNm 0.083 MNm 0.032 MNm

1. FUNDACION TIPO = PUNTA = FRICCION = DIAMETRO FUSTE = DIAMETRO CAMPANA = RADIO CAMPANA = TIPO = SUELO LOESSICO (LOESS) =

POZO 50 T/m2 (Manto de poyo 2 T/m2 (Prof. Activa 0.80 m 1.60 m 0.80 m

12 mt ) 8 mt)

ZAPATA AISLADA 0.5 Kg/cm2

DESIGNACION DE COLUMNA

Qu COLUMNA (Tn)

C1 C2

2.957 5.617

C3 C4 C5 C6

17.455 6.592 1.345 3.772

C7

7.390

C8 C9 C10 C11 C12 C13 C14 C15

1.885 1.372 1.303 5.440 1.880 0.940 5.646 0.940

C16 C17 C18

2. FUNDACION = POZO

A. CALCULO Sup. FRICCION

PB

Sf = Sf =

Sf =

Pi x Diam. Fuste x M 3.14

30.16

B. CALCULO Sup. PUNTA

Sp =

Pi x (Diam. Campana)²

Sp =

3.14

2.347 8.314

Sp =

3.14

3.195

Sp =

2.01

2. FUNDACION = ZAPATA AISLADA A. CALCULO AREA A=

Qu T adm.

A = 17454.501

0.5

A=

34909

LADO (cm)

187

C. CALCULO CAPACIDAD DE TRABAJO DE FRICCION

Pi x Diam. Fuste x Manto de Apoyo x

0.80

x

CTf = 12

m2

CTf =

CTf =

Sf x Tf 30.16

x

2.00

60.32 tn

C. CALCULO CAPACIDAD DE TRABAJO A PUNTA

Pi x (Diam. Campana)² x

0.80

x

0.64

CTp = ²

CTp =

2.01

x

CTp = 100.53 tn

m2 ZAPATA AISLADA

17.455 tn

Sp x Tp

17454.501 kg

50.00

cm2 cm

O DE FRICCION