TRABAJO CONCRETO ARMADO I - 2015 - 00.xlsx

100
CONCRETO ARMADO 1 CALCULO DE LOSA ALIGERADA EN UNA DIRECCIÓN UNIVERSIDAD CESAR VALLEJO ING. EDWIN RODRIGUEZ PLASENCIA ### ### . 4.5 VIGAS SECUNDARIAS VISTA EN PLANTA 4.5 Datos: f´c = ### fy = 4,200.00 S/C = ### 5 cm 15 cm Espesor de la losa: 10 cm . 10 cm . 30 cm . 10 cm . 10 cm . 30 cm . 40 cm . l/18 -> m aterial de pésim a calidad, m ano de obra no calificada y quipos y herram ientas convencionales.

Transcript of TRABAJO CONCRETO ARMADO I - 2015 - 00.xlsx

Page 1: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE LOSA ALIGERADA EN UNA DIRECCIÓN UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

---------------- 4.50 m ----------------- ---------------- 4.50 m -----------------. 4.5 VIGAS SECUNDARIAS

VISTA EN PLANTA 4.5Datos:

f´c = 210 kg/cm2fy = 4,200.00 1/4 0.32

S/C = 200 kg/cm2 3/8 0.71 1/2 1.27 5/8 1.98

5 cm 3/4 2.85

15 cm1 5.07

1 1/4 7.921 3/8 9.581 1/2 11.40

Espesor de la losa:

Ø (pulg) A (cm2)

10 cm. 10 cm.30 cm. 10 cm. 10 cm.30 cm.

5 cm.

15 cm.

40 cm.

l/18 -> material de pésima calidad, mano de obra no calificada y quipos y herramientas convencionales.

Page 2: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE LOSA ALIGERADA EN UNA DIRECCIÓN UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

t = Luz / 25t = 0.18 m ≈ 0.20 cm = 20 cm

455.2 kg/m

h (m)

0.17 2800.20 3000.25 350 ---------------- 4.50 m ----------------- ---------------- 4.50 m -----------------0.30 420

CÁLCULO Y DISEÑO DE LOSA ALIGERADA

METRADO DE CARGA

METRADO DE CARGA MUERTA (D)

Peso propio: 300

Acabado + cielo raso: 120 MOMENTOS ULTIMOS Tabiquería Movil: 150 1 2 3 4

Total: 570 0.40 m coefici. Mu a a a a

D = 228 kg/m 1/24 384.08 0.664 0.391 0.605 0.356 0.604 0.355 0.604 0.355 1/14 658.41 1.138 2.679 1.112 2.617 1.110 2.612 1.110 2.611

METRADO DE CARGA VIVA (L) 1/9 1024.20 1.771 1.042 1.644 0.967 1.641 0.965 1.640 0.965Sobre carga S/C: ### 0.40 m 1/9 1024.20 1.771 1.042 1.644 0.967 1.641 0.965 1.640 0.965

L = 80 kg/m 1/14 658.41 1.138 2.679 1.112 2.617 1.110 2.612 1.110 2.611 1/24 384.08 0.664 0.391 0.605 0.356 0.604 0.355 0.604 0.355

CARGA ULTIMA (Wu) 0.604 1/24 0.375 3/8''0.567 1.110 1/14 0.500 1/2''

Wu = 1.4(D) + 1.7(L) 1.640 1/9 0.625 5/8''

Peso propio (kg/m2)

kg/m2

kg/m2

kg/m2

kg/m2 x As As As As

kg/m2 x

RESU

LTAD

OS

FIN

ALES

As min = cm2

l/18 -> material de pésima calidad, mano de obra no calificada y quipos y herramientas convencionales.

l/25 -> material de buena calidad, mano de obra calificada y equipos y herramientas adecuados.

M =- WuL

24

2

M =- WuL

9

2M =

- WuL24

2

M =+ WuL

14

2M =

+ WuL14

2

APOYO

VIGA

APOYO

VIGA

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CONCRETO ARMADO 1 CALCULO DE LOSA ALIGERADA EN UNA DIRECCIÓN UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

2.303 1.640 1/9 0.625 5/8''Wu = 455.2 kg/m 1.110 1/14 0.500 1/2''

0.604 1/24 0.375 3/8''

3/8'' 5/8'' 5/8'' 3/8'' 1/2'' 1/2''

RESU

LTAD

OS

FIN

ALES

As máx = cm2

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CONCRETO ARMADO 1 CALCULO DE VIGAS PRINCIPALES Y SECUNDARIAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

Datos:Alt. = 3.00 m Peralte:

f´c = 210.00h =

fy = 4,200.00 4.01

De las expresiones (1) y (2) :

4.504.50

VIGAS PRINCIPALES 4.50

VIG

AS S

ECU

ND

ARIA

S

4.50

4.50

Y ---------------- 8.00 m ----------------- --------------- 8.00 m ---------------- 4.508 8

8.00 8.00

kg/cm2 Ln

kg/cm2

A

B

C

1 2 3

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CONCRETO ARMADO 1 CALCULO DE VIGAS PRINCIPALES Y SECUNDARIAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

X VISTA EN PLANTA

Datos:S/C = 200.00

Espesor de la losa:

t = Luz / 25.00t = 0.20 0.20 cm = 20.00

Wu = 0.11h (m)

0.17 280.00 Peralte:

0.20 300.00 h = h = 0.25 350.00 4.01 11.880.30 420.00

CÁLCULO Y DISEÑO DE LOSA ALIGERADAh = 67.37 cm tomamos a "h" igual a: 70 cm

METRADO DE CARGASComo el reglamento E-020 establece la base minima de una viga debe ser 25 cm

CARGA MUERTA (D) entonces:37.89

Peso propio: 300 VIGA PRINCIPAL = 35 X 70

Acabado + cielo raso: 120.00 Inercia 1,000,416.67 ###Tabiquería movil: 150.00

Total: 570.00 VIGA SECUNDARIA = 30 X 40

D = 0.06 Inercia 160,000.00

CARGA VIVA (L)

Peso propio (kg/m2)

Ln Ln

kg/m2 cm2

kg/m2 cm4

kg/m2

kg/m2 cm2

kg/cm2 cm4

l/18 -> material de pésima calidad, mano de obra no calificada y quipos y herramientas convencionales.

l/25 -> material de buena calidad, mano de obra calificada y equipos y herramientas adecuados.

1 2 3

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CONCRETO ARMADO 1 CALCULO DE VIGAS PRINCIPALES Y SECUNDARIAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

Sobre carga S/C: 200.00L = 0.02

PÓRTICO EJE X - A-A

METRADO DE CARGA PARA LA VIGA A - A EJE 1 -2

ELEMENTOS PESO PROPIO N° DIMENSION PESO PARCIAL P. Aligerado 300 1.00 2.2500 m 675.00 Kg/m

Tabiqueria Movil 150 1.00 2.2500 m 337.50 Kg/m

Muros de Soga 1800 1.00 1.2000 2,160.00 Kg/m120 1.00 2.2500 m 270.00 Kg/m

Peso de vigas 2400 1.00 0.2450 588.00 Kg/m

S/C 200 1.00 2.2500 m 450.00 Kg/mValor de P = 4,480.50 Kg/m

Pu = 1.4*CM + 1.7*CV 6,407.70 Kg/m 6.4077

METRADO DE CARGA PARA LA VIGA A - A EJE 2 - 3

ELEMENTOS PESO PROPIO N° DIMENSION PESO PARCIAL P. Aligerado 300 1.00 2.2500 m 675.00 Kg/m

Tabiqueria Movil 150 1.00 2.2500 m 337.50 Kg/m

Muros de Soga 1800 1.00 1.2000 2,160.00 Kg/m120 1.00 2.2500 m 270.00 Kg/m

Peso de vigas 2400 1.00 0.2450 588.00 Kg/m

S/C 200 1.00 2.2500 m 450.00 Kg/mValor de P = 4,480.50 Kg/m

Pu = 1.4*CM + 1.7*CV 6,407.70 Kg/m 6.4077

kg/m2

kg/m2

kg/m2

kg/m3 m2

Acabado + Cielo raso kg/m2

kg/m3 m2

kg/m2

kg/m2

kg/m2

kg/m3 m2

Acabado + Cielo raso kg/m2

kg/m3 m2

kg/m2

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CONCRETO ARMADO 1 CALCULO DE VIGAS PRINCIPALES Y SECUNDARIAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

MOMENTOS EN CADA NIVEL EJE X - A-A

VIGA DEL TERCER NIVEL

-40571.78 40571.7821379.645 -21380

20734.98 20734.98MOMENTOS ULTIMOS

1 2 3 4 1/4 0.32 Mu a a a a 3/8 0.71 21380 10.562 0.621 9.556 0.562 9.551 0.562 9.551 0.562 1/2 1.27 20735 10.244 0.603 9.266 0.545 9.262 0.545 9.262 0.545 5/8 1.98 40572 20.043 1.179 18.220 1.072 18.203 1.071 18.203 1.071 3/4 2.85 40572 20.043 1.179 18.220 1.072 18.203 1.071 18.203 1.071

1 5.07 20735 10.244 0.603 9.266 0.545 9.262 0.545 9.262 0.5451 1/4 7.92 21380 10.562 0.621 9.556 0.562 9.551 0.562 9.551 0.5621 3/8 9.58 9.551 = 4 Ø 5/8'' 1 Ø 1/2''

1 1/2 11.40 8.167 9.262 = 4 Ø 5/8'' 1 Ø 1/2''

18.203 = 4 Ø 5/8'' 3 Ø 3/4'' 1 Ø 1/2''

18.203 = 4 Ø 5/8'' 3 Ø 3/4'' 1 Ø 1/2''

9.262 = 4 Ø 5/8'' 1 Ø 1/2''

9.551 = 4 Ø 5/8'' 1 Ø 1/2''

1 Ø 1/2'' 1 Ø 1/2''2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8''

Ø (pulg) A (cm2)

As As As As

RESU

LTAD

OS

FIN

ALES

As min = cm2

Page 8: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE VIGAS PRINCIPALES Y SECUNDARIAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

1 Ø 1/2'' 1 Ø 1/2'' 3 Ø 3/4'' 3 Ø 3/4'' 1 Ø 1/2'' 1 Ø 1/2''

2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8''

MOMENTOS EN CADA NIVEL EJE X - A-A

VIGA DEL SEGUNDO NIVEL

-36779.40 36779.4028964.393 -28964.39

18464.17 18464.17MOMENTOS ULTIMOS

1 2 3 4 1/4 0.32 Mu a a a a 3/8 0.71 28964 14.309 0.842 12.970 0.763 12.961 0.762 12.961 0.762 1/2 1.27 18464 9.122 0.537 8.247 0.485 8.243 0.485 8.243 0.485 5/8 1.98 36779 18.170 1.069 16.501 0.971 16.487 0.970 16.487 0.970 3/4 2.85 36779 18.170 1.069 16.501 0.971 16.487 0.970 16.487 0.970

1 5.07 18464 9.122 0.537 8.247 0.485 8.243 0.485 8.243 0.4851 1/4 7.92 28964 14.309 0.842 12.970 0.763 12.961 0.762 12.961 0.7621 3/8 9.58 12.961 = 4 Ø 5/8'' 4 Ø 1/2''

1 1/2 11.40 8.167 8.243 = 4 Ø 5/8'' 1 Ø 1/2''

16.487 = 4 Ø 5/8'' 3 Ø 3/4''

16.487 = 4 Ø 5/8'' 3 Ø 3/4''

8.243 = 4 Ø 5/8'' 1 Ø 1/2''

12.961 = 4 Ø 5/8'' 4 Ø 1/2''

Ø (pulg) A (cm2)

As As As As

RESU

LTAD

OS

FIN

ALES

As min = cm2

Page 9: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE VIGAS PRINCIPALES Y SECUNDARIAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8''

4 Ø 1/2'' 1 Ø 1/2'' 3 Ø 3/4'' 3 Ø 3/4'' 1 Ø 1/2'' 4 Ø 1/2''

2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8''

MOMENTOS EN CADA NIVEL EJE X - A-A y C - C

VIGA DEL PRIMER NIVEL

-38220.06 38220.0626083.08 -26083.08

19289.63 19289.63MOMENTOS ULTIMOS

1 2 3 4 1/4 0.32 Mu a a a a 3/8 0.71 26083 12.886 0.758 11.671 0.687 11.664 0.686 11.664 0.686 1/2 1.27 19290 9.530 0.561 8.617 0.507 8.613 0.507 8.613 0.507 5/8 1.98 38220 18.882 1.111 17.154 1.009 17.139 1.008 17.139 1.008 3/4 2.85 38220 18.882 1.111 17.154 1.009 17.139 1.008 17.139 1.008

1 5.07 19290 9.530 0.561 8.617 0.507 8.613 0.507 8.613 0.5071 1/4 7.92 26083 12.886 0.758 11.671 0.687 11.664 0.686 11.664 0.6861 3/8 9.58 11.664 = 4 Ø 5/8'' 3 Ø 1/2''

1 1/2 11.40 8.167 8.613 = 4 Ø 5/8'' 1 Ø 1/2''

17.139 = 4 Ø 5/8'' 3 Ø 3/4''

17.139 = 4 Ø 5/8'' 3 Ø 3/4''

8.613 = 4 Ø 5/8'' 1 Ø 1/2''

11.664 = 4 Ø 5/8'' 3 Ø 1/2''

Ø (pulg) A (cm2)

As As As As

RESU

LTAD

OS

FIN

ALES

As min = cm2

Page 10: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE VIGAS PRINCIPALES Y SECUNDARIAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8''

3 Ø 1/2'' 1 Ø 1/2'' 3 Ø 3/4'' 3 Ø 3/4'' 1 Ø 1/2'' 3 Ø 1/2''

2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8'' 2 Ø 5/8''

MOMENTOS EN CADA NIVEL EJE X - B - B

METRADO DE CARGA PARA LA VIGA A - A EJE 1 -2

ELEMENTOS PESO PROPIO N° DIMENSION PESO PARCIAL P. Aligerado 300 1.00 4.5000 m 1,350.00 Kg/m

Tabiqueria Movil 150 1.00 4.5000 m 675.00 Kg/m

Muros de Soga 1800 1.00 1.2000 2,160.00 Kg/m120 1.00 4.5000 m 540.00 Kg/m

Peso de vigas 2400 1.00 0.2450 588.00 Kg/m

S/C 200 1.00 4.5000 m 900.00 Kg/mValor de P = 6,213.00 Kg/m

Pu = 1.4*CM + 1.7*CV 8,968.20 Kg/m ###

METRADO DE CARGA PARA LA VIGA A - A EJE 2 - 3

ELEMENTOS PESO PROPIO N° DIMENSION PESO PARCIAL P. Aligerado 300 1.00 4.5000 m 1,350.00 Kg/m

Tabiqueria Movil 150 1.00 4.5000 m 675.00 Kg/m

Muros de Soga 1800 1.00 1.2000 2,160.00 Kg/m120 1.00 4.5000 m 540.00 Kg/m

kg/m2

kg/m2

kg/m3 m2

Acabado + Cielo raso kg/m2

kg/m3 m2

kg/m2

kg/m2

kg/m2

kg/m3 m2

Acabado + Cielo raso kg/m2

Page 11: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE VIGAS PRINCIPALES Y SECUNDARIAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

Peso de vigas 2400 1.00 0.2450 588.00 Kg/m

S/C 200 1.00 4.5000 m 900.00 Kg/mValor de P = 6,213.00 Kg/m

Pu = 1.4*CM + 1.7*CV 8,968.20 Kg/m ###

MOMENTOS EN CADA NIVEL EJE X - B - B

VIGA DEL TERCER NIVEL

-56784.15 56784.1529922.9 -29923

29020.62 29020.62MOMENTOS ULTIMOS

1 2 3 4 1/4 0.32 Mu a a a a 3/8 0.71 29923 14.783 0.870 13.402 0.788 13.393 0.788 13.393 0.788 1/2 1.27 29021 14.337 0.843 12.995 0.764 12.987 0.764 12.987 0.764 5/8 1.98 56784 28.053 1.650 25.603 1.506 25.571 1.504 25.571 1.504 3/4 2.85 56784 28.053 1.650 25.603 1.506 25.571 1.504 25.571 1.504

1 5.07 29021 14.337 0.843 12.995 0.764 12.987 0.764 12.987 0.7641 1/4 7.92 29923 14.783 0.870 13.402 0.788 13.393 0.788 13.393 0.7881 3/8 9.58 13.393 = 4 Ø 3/4'' 1 Ø 1/2''

1 1/2 11.40 8.167 12.987 = 4 Ø 3/4'' 1 Ø 1/2''

25.571 = 4 Ø 3/4'' 2 Ø 1" 1 Ø 1/2''

25.571 = 4 Ø 3/4'' 3 Ø 3/4'' 1 Ø 1/2''

kg/m3 m2

kg/m2

Ø (pulg) A (cm2)

As As As AsRE

SULT

ADO

S FI

NAL

ES

As min = cm2

Page 12: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE VIGAS PRINCIPALES Y SECUNDARIAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

12.987 = 4 Ø 3/4'' 4 Ø 1/2''

13.393 = 4 Ø 3/4'' 4 Ø 1/2''

1 Ø 1/2'' 1 Ø 1/2''2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4''

1 Ø 1/2'' 1 Ø 1/2'' 2 Ø 1" 3 Ø 3/4'' 4 Ø 1/2'' 4 Ø 1/2''

2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4''

MOMENTOS EN CADA NIVEL EJE X - B - B

VIGA DEL SEGUNDO NIVEL

-51476.36 51476.3640538.487 -40538.49

25842.40 25842.40MOMENTOS ULTIMOS

1 2 3 4 1/4 0.32 Mu a a a a 3/8 0.71 40538 20.027 1.178 18.205 1.071 18.188 1.070 18.188 1.070 1/2 1.27 25842 12.767 0.751 11.563 0.680 11.556 0.680 11.556 0.680 5/8 1.98 51476 25.431 1.496 23.179 1.363 23.153 1.362 23.153 1.362 3/4 2.85 51476 25.431 1.496 23.179 1.363 23.153 1.362 23.153 1.362

1 5.07 25842 12.767 0.751 11.563 0.680 11.556 0.680 11.556 0.6801 1/4 7.92 40538 20.027 1.178 18.205 1.071 18.188 1.070 18.188 1.0701 3/8 9.58 18.188 = 4 Ø 3/4'' 2 Ø 3/4''

1 1/2 11.40 8.167 11.556 = 4 Ø 3/4''

23.153 = 4 Ø 3/4'' 1 Ø 1" 2 Ø 3/4''

RESU

LTAD

OS

FIN

ALES

Ø (pulg) A (cm2)

As As As As

RESU

LTAD

OS

FIN

ALES

As min = cm2

Page 13: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE VIGAS PRINCIPALES Y SECUNDARIAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

23.153 = 4 Ø 3/4'' 1 Ø 1" 2 Ø 3/4''

11.556 = 4 Ø 3/4''

18.188 = 4 Ø 3/4'' 2 Ø 3/4''

2 Ø 3/4'' 2 Ø 3/4''2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4''

2 Ø 3/4'' 0 Ø 0 '' 1 Ø 1" 1 Ø 1" 0 Ø 0 '' 2 Ø 3/4''

2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4''

MOMENTOS EN CADA NIVEL EJE X - B - B

VIGA DEL PRIMER NIVEL

-53492.69 53492.6936505.811 -36505.81

26997.72 26997.72MOMENTOS ULTIMOS

1 2 3 4 1/4 0.32 Mu a a a a 3/8 0.71 36506 18.035 1.061 16.377 0.963 16.364 0.963 16.364 0.963 1/2 1.27 26998 13.338 0.785 12.083 0.711 12.076 0.710 12.076 0.710 5/8 1.98 53493 26.427 1.555 24.099 1.418 24.071 1.416 24.070 1.416 3/4 2.85 53493 26.427 1.555 24.099 1.418 24.071 1.416 24.070 1.416

1 5.07 26998 13.338 0.785 12.083 0.711 12.076 0.710 12.076 0.7101 1/4 7.92 36506 18.035 1.061 16.377 0.963 16.364 0.963 16.364 0.9631 3/8 9.58 16.364 = 4 Ø 3/4'' 1 Ø 1"

1 1/2 11.40 8.167 12.076 = 4 Ø 3/4''

RESU

LTAD

OS

FIN

ALES

Ø (pulg) A (cm2)

As As As As

RESU

LTAD

OS

FIN

ALES

As min = cm2

Page 14: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE VIGAS PRINCIPALES Y SECUNDARIAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

24.070 = 4 Ø 3/4'' 2 Ø 1" 1 Ø 1/2''

24.070 = 4 Ø 3/4'' 2 Ø 1" 1 Ø 1/2''

12.076 = 4 Ø 3/4''

16.364 = 4 Ø 3/4'' 2 Ø 1/2''

1 Ø 1/2'' 1 Ø 1/2''2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4''

1 Ø 1" 0 Ø 0 '' 2 Ø 1" 2 Ø 1" 0 Ø 0 '' 2 Ø 1/2''

2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4'' 2 Ø 3/4''

PÓRTICO EJE Y - 1 - 1, 2- 2 y 3 - 3

METRADO DE CARGA PARA LA VIGA A - A EJE 1 -2

ELEMENTOS PESO PROPIO N° DIMENSION PESO PARCIAL Muros de Soga 1800 1.00 0.6750 1,215.00 Kg/m

Peso de vigas 2400 1.00 0.1200 288.00 Kg/m

S/C 200 1.00 0.3000 m 60.00 Kg/mValor de P = 1,563.00 Kg/m

Pu = 1.4*CM + 1.7*CV 2,206.20 Kg/m 2.2062

METRADO DE CARGA PARA LA VIGA A - A EJE 2 - 3

ELEMENTOS PESO PROPIO N° DIMENSION PESO PARCIAL Muros de Soga 1800 1.00 0.6750 1,215.00 Kg/m

RESU

LTAD

OS

FIN

ALES

kg/m3 m2

kg/m3 m2

kg/m2

kg/m3 m2

Page 15: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE VIGAS PRINCIPALES Y SECUNDARIAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

Peso de vigas 2400 1.00 0.1200 288.00 Kg/m

S/C 200 1.00 0.3000 m 60.00 Kg/mValor de P = 1,563.00 Kg/m

Pu = 1.4*CM + 1.7*CV 2,206.20 Kg/m 2.2062

MOMENTOS EN CADA NIVEL EJE Y - 1-1, 2-2 y 3-3

VIGA DEL TERCER NIVEL

-4009.31 4009.313150.3 -3150.3

2012.91 2012.91MOMENTOS ULTIMOS

1 2 3 4 1/4 0.32 Mu a a a a 3/8 0.71 3150 2.724 0.160 2.457 0.145 2.456 0.144 2.456 0.144 1/2 1.27 2013 1.740 0.102 1.569 0.092 1.568 0.092 1.568 0.092 5/8 1.98 4009 3.466 0.204 3.129 0.184 3.128 0.184 3.128 0.184 3/4 2.85 4009 3.466 0.204 3.129 0.184 3.128 0.184 3.128 0.184

1 5.07 2013 1.740 0.102 1.569 0.092 1.568 0.092 1.568 0.0921 1/4 7.92 3150 2.724 0.160 2.457 0.145 2.456 0.144 2.456 0.144

kg/m3 m2

kg/m2

Ø (pulg) A (cm2)

As As As As

Page 16: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE VIGAS PRINCIPALES Y SECUNDARIAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

1 3/8 9.58 4.000 = 4 Ø 1/2''

1 1/2 11.40 4.000 4.000 = 4 Ø 1/2''

4.000 = 4 Ø 1/2''

4.000 = 4 Ø 1/2''

4.000 = 4 Ø 1/2''

4.000 = 4 Ø 1/2''

0 Ø 0 '' 0 Ø 0 ''2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2''

0 Ø 0 '' 0 Ø 0 '' 0 Ø 0 '' 0 Ø 0 '' 0 Ø 0 '' 0 Ø 0 ''

2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2''

MOMENTOS EN CADA NIVEL EJE Y - 1-1, 2-2 y 3-3

VIGA DEL SEGUNDO NIVEL

-3795.45 3795.453577.9841 -3577.98

1898.26 1898.26MOMENTOS ULTIMOS

1 2 3 4 1/4 0.32 Mu a a a a 3/8 0.71 3578 3.093 0.182 2.791 0.164 2.791 0.164 2.791 0.164 1/2 1.27 1898 1.641 0.097 1.479 0.087 1.479 0.087 1.479 0.087 5/8 1.98 3795 3.281 0.193 2.962 0.174 2.961 0.174 2.961 0.174 3/4 2.85 3795 3.281 0.193 2.962 0.174 2.961 0.174 2.961 0.174

1 5.07 1898 1.641 0.097 1.479 0.087 1.479 0.087 1.479 0.087

RESU

LTAD

OS

FIN

ALES

As min = cm2

Ø (pulg) A (cm2)

As As As As

Page 17: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE VIGAS PRINCIPALES Y SECUNDARIAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

1 1/4 7.92 3578 3.093 0.182 2.791 0.164 2.791 0.164 2.791 0.1641 3/8 9.58 4.000 = 4 Ø 1/2''

1 1/2 11.40 4.000 4.000 = 4 Ø 1/2''

4.000 = 4 Ø 1/2''

4.000 = 4 Ø 1/2''

4.000 = 4 Ø 1/2''

4.000 = 4 Ø 1/2''

2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2''

0 Ø 0 '' 0 Ø 0 '' 0 Ø 0 '' 0 Ø 0 '' 0 Ø 0 '' 0 Ø 0 ''

2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2''

MOMENTOS EN CADA NIVEL EJE Y - 1-1, 2-2 y 3-3

VIGA DEL PRIMER NIVEL

-3879.43 3879.433410.021 -3410.02

1942.18 1942.18MOMENTOS ULTIMOS

1 2 3 4 1/4 0.32 Mu a a a a 3/8 0.71 3410 2.948 0.173 2.660 0.156 2.659 0.156 2.659 0.156 1/2 1.27 1942 1.679 0.099 1.513 0.089 1.513 0.089 1.513 0.089 5/8 1.98 3879 3.354 0.197 3.027 0.178 3.026 0.178 3.026 0.178 3/4 2.85 3879 3.354 0.197 3.027 0.178 3.026 0.178 3.026 0.178

RESU

LTAD

OS

FIN

ALES

As min = cm2

Ø (pulg) A (cm2)

As As As As

Page 18: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE VIGAS PRINCIPALES Y SECUNDARIAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

1 5.07 1942 1.679 0.099 1.513 0.089 1.513 0.089 1.513 0.0891 1/4 7.92 3410 2.948 0.173 2.660 0.156 2.659 0.156 2.659 0.1561 3/8 9.58 4.000 = 4 Ø 1/2''

1 1/2 11.40 4.000 4.000 = 4 Ø 1/2''

4.000 = 4 Ø 1/2''

4.000 = 4 Ø 1/2''

4.000 = 4 Ø 1/2''

4.000 = 4 Ø 1/2''

2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2''

0 Ø 0 '' 0 Ø 0 '' 0 Ø 0 '' 0 Ø 0 '' 0 Ø 0 '' 0 Ø 0 ''

2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2'' 2 Ø 1/2''

RESU

LTAD

OS

FIN

ALES

As min = cm2

Page 19: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE COLUMNAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

Datos:f´c = 210

fy = 4200Pisos = 3 Pisos

4.50 m

4.50 m

Y ---------------- 8.00 m ----------------- ---------------- 8.00 m -----------------

X VISTA EN PLANTA TÍPICAC-1 Columna CentralC-2 Columna Extrema de un pórtico principal interiorC-3 Columna Extrema de un pórtico secundario interiorC-4 Columna en esquina METRADO DE CARGA C - 4

ELEMENTOS PESO PROPIO N° DIMENSION PESO PARCIAL P. Aligerado 300 3 6.2500 5,625.00 Kg

Tabiqueria Movil 150 3 6.2500 2,812.50 Kg

Muros de Soga 1800 3 2.8125 15,187.50 Kg120 3 6.2500 2,250.00 Kg

Peso de vigas 2400 3 1.2500 9,000.00 Kg

Peso de Columnas 60 3 6.2500 1,125.00 Kg

S/C 200 3 6.2500 3,750.00 KgValor de P = 39,750.00 Kg

kg/cm2

kg/cm2

kg/m2 m2

kg/m2 m2

kg/m3 m2

Acabado + Cielo raso kg/m2 m2

kg/m3 m3

kg/m2 m2

kg/m2 m2

C-4 C-3

C-1C-2

A

B

C

1 2 3

Page 20: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE COLUMNAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

Pu = 1.4*CM + 1.7*CV 56,775.00 Kg

DIMENSION DE LA C - 4

Área de columna = 1.2xP (servicio)/0.35 f´c

648.98 cm2

Asumimos una columna de : 30 x 30

25.48 cm Inercia 67,500.00

METRADO DE CARGA C - 2

ELEMENTOS PESO PROPIO N° DIMENSION PESO PARCIAL P. Aligerado 300 3 18.0000 16,200.00 Kg

Tabiqueria Movil 150 3 18.0000 8,100.00 Kg

Muros de Soga 1800 3 3.8250 20,655.00 Kg120 3 18.0000 6,480.00 Kg

Peso de vigas 2400 3 1.5200 10,944.00 Kg

Peso de Columnas 60 3 18.0000 3,240.00 Kg

S/C 200 3 18.0000 10,800.00 KgValor de P = 76,419.00 Kg

Pu = 1.4*CM + 1.7*CV 110,226.60 Kg

DIMENSION DE LA C - 2

Área de columna = 1.2xP (servicio)/0.35 f´c

1247.66 cm2

Asumimos una columna de : 40 x 40

35.32 cm Inercia 213,333.33

AC =cm2

L C = cm4

kg/m2 m2

kg/m2 m2

kg/m3 m2

Acabado + Cielo raso kg/m2 m2

kg/m3 m3

kg/m2 m2

kg/m2 m2

AC =cm2

L C = cm4

Page 21: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE COLUMNAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

METRADO DE CARGA C - 3

ELEMENTOS PESO PROPIO N° DIMENSION PESO PARCIAL P. Aligerado 300 3 18.0000 16,200.00 Kg

Tabiqueria Movil 150 3 18.0000 8,100.00 Kg

Muros de Soga 1800 3 4.6125 24,907.50 Kg120 3 18.0000 6,480.00 Kg

Peso de vigas 2400 3 2.2300 16,056.00 Kg

Peso de Columnas 60 3 18.0000 3,240.00 Kg

S/C 200 3 18.0000 10,800.00 KgValor de P = 85,783.50 Kg

Pu = 1.4*CM + 1.7*CV 123,336.90 Kg

DIMENSION DE LA C - 3Área de columna = 1.2xP (servicio)/0.35 f´c

1400.55 cm2

Asumimos una columna de : 40 x 40

37.42 cm Inercia 213,333.33

METRADO DE CARGA C - 1ELEMENTOS PESO PROPIO N° DIMENSION PESO PARCIAL

P. Aligerado 300 3 36.0000 32,400.00 Kg

Tabiqueria Movil 150 3 36.0000 16,200.00 Kg

Muros de Soga 1800 3 5.6250 30,375.00 Kg120 3 36.0000 12,960.00 Kg

Peso de vigas 2400 3 2.5000 18,000.00 Kg

kg/m2 m2

kg/m2 m2

kg/m3 m2

Acabado + Cielo raso kg/m2 m2

kg/m3 m3

kg/m2 m2

kg/m2 m2

AC =cm2

L C = cm4

kg/m2 m2

kg/m2 m2

kg/m3 m2

Acabado + Cielo raso kg/m2 m2

kg/m3 m3

Page 22: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE COLUMNAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

Peso de Columnas 60 3 36.0000 6,480.00 Kg

S/C 200 3 36.0000 21,600.00 KgValor de P = 138,015.00 Kg

Pu = 1.4*CM + 1.7*CV 199,701.00 Kg

DIMENSION DE LA C - 1Área de columna = 1.2xP (servicio)/0.35 f´c

2253.31 cm2

Asumimos una columna de : 50 x 50

47.47 cm Inercia 520,833.33520833.3

ARMADURA DE LA COLUMNA C - 1DATOS:C- 1 50 x 50 Pu

= 0 Tn-m 199.70 Tn

= 0 Tn-m

As = 25

4 Ø 1"

kg/m2 m2

kg/m2 m2

AC =cm2

L C = cm4

Por ser simetrica la estructura en sus dos sentidos ambos momentos se anulan quedando cero, pero la cuantía mínima para una columna debe ser 1%

cm2

Page 23: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE COLUMNAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

4 Ø 1/2''

ARMADURA DE LA COLUMNA C - 2DATOS:C- 2 50 x 50 Pu

= 0 Tn-m 110.23 Tn

= 29.9229 Tn-m

0.32301 0.17537 Del Abaco As = 37.5una cuantía de : 1.50%

6 Ø 1"

4 Ø 5/8''

Kn = Rn = cm2

Page 24: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE COLUMNAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

ARMADURA DE LA COLUMNA C - 3DATOS:C - 3 50 x 50 Pu

= 3.15028 Tn-m 123.34 Tn

= 21.3796 Tn-m

0.36143 0.1253 Del Abaco As = 25una cuantía de : 1.00%

4 Ø 1"

4 Ø 1/2''

Por ser el Momento de un

rango bajo para la columna

se obtiene una cuantía

mínima de 1%

Kn = Rn = cm2

Page 25: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE COLUMNAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

ARMADURA DE LA COLUMNA C - 4DATOS:C - 4 50 x 50 Pu

= 3.1502868.13 Tn

= 21.3796

0.19965 0.1253 Del Abaco As = 25una cuantía de : 1.00%

4 Ø 1"

4 Ø 1/2''

Por ser el Momento de un

rango bajo para la columna

se obtiene una cuantía

mínima de 1%

Kn = Rn = cm2

Page 26: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE COLUMNAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

Page 27: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

ANALISIS MATRICIAL EN EJE X, A-A, C-C

E = 2,173,706,511.93

6407.70 kg/m 6407.70 kg/m

3.00 m e6407.70 kg/m 6407.70 kg/m

3.00 m d

6407.70 kg/m 6407.70 kg/m

3.00 m c

---------------- 8.00 m ----------------- ---------------- 8.00 m -----------------

Kg/m2

Page 28: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

a b

Page 29: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00

0.00 (4/d + 4/c + 4/a) 2/a 0.00 2/d 0.00 0.00 0.00 0.00 0.00

0.00 2/a ( 4/a + 4/b + 4/c + 4/d) 2/b 0.00 2/d 0.00 0.00 0.00 0.00

K =

0.00 0.00 2/b (4/b + 4/c + 4/d) 0.00 0.00 2/d 0.00 0.00 0.00

2/d 0.00 0.00 (4/d + 4/e + 4/a) 2/a 0.00 2/e 0.00 0.00

0.00 2/d 0.00 2/a (4/a + 4/b + 4/d + 4/e) 2/b 0.00 2/e 0.00

0.00 0.00 2/d 0.00 2/b (4/b + 4/d + 4/e) 0.00 0.00 2/e

0.00 0.00 0.00 0.00 2/e 0.00 0.00 (4/a + 4/e) 2/a 0.00

0.00 0.00 0.00 0.00 0.00 2/e 0.00 2/a (4/a + 4/b + 4/e) 2/b

0.00 0.00 0.00 0.00 0.00 0.00 2/e 0.00 2/b (4/b + 4/e)

a = 8.00 mEI 21,746,122.23 E (VIGAS) 2173706511.93 Tn/m2 INERCIA 0.01 m4 0.35 0.7

b = 8.00 m

c = 3.00 m EI 11,321,388.08 E (COLUM) 2173706511.93 Tn/m2 INERCIA COLUMNA 0.01 m4 0.5 0.5d = 3.00 m EI 11,321,388.08 E (COLUM) 2173706511.93 Tn/m2 INERCIA COLUMNA 0.01 m4 0.5 0.5e = 3.00 m EI 11,321,388.08 E (COLUM) 2173706511.93 Tn/m2 INERCIA COLUMNA 0.01 m4 0.5 0.5

30190368.22 -15095184.11 0 0.00 0.00 0.00 -7547592.06 -7547592.06 -7547592.06 0 0.00 0

-15095184.11 30190368.22 -15095184 7547592.06 7547592.06 7547592.06 0.00 0.00 0.00 -7547592 -7547592.06 -7547592

0.00 -15095184.11 15095184 0.00 0.00 0.00 7547592.06 7547592.06 7547592.06 7547592 7547592.06 7547592

0.00 7547592.06 0 41063429.34 5436530.56 0.00 7547592.06 0.00 0.00 0 0.00 0

0.00 7547592.06 0 5436530.56 51936490.45 5436530.56 0.00 7547592.06 0.00 0 0.00 0

K =

0.00 7547592.06 0 0.00 5436530.56 41063429.34 0.00 0.00 7547592.06 0 0.00 0

-7547592.06 0.00 7547592 7547592.06 0.00 0.00 41063429.34 5436530.56 0.00 7547592 0.00 0

-7547592.06 0.00 7547592 0.00 7547592.06 0.00 5436530.56 51936490.45 5436530.56 0 7547592.06 0

-7547592.06 0.00 7547592 0.00 0.00 7547592.06 0.00 5436530.56 41063429.34 0 0.00 75475920.00 -7547592.06 7547592 0.00 0.00 0.00 7547592.06 0.00 0.00 25968245 5436530.56 0

(36/d3 + 36/c3) 36/d3 (6/c2 - 6/d2) (6/c2 - 6/d2) (6/c2 - 6/d2) 6/d2 6/d2 6/d2

36/d3 (36/d3 + 36/e3) 36/e3 6/d2 6/d2 6/d2 (6/d2 - 6/e2) (6/d2 - 6/e2) (6/d2 - 6/e2) 6/e2 6/e2 6/e2

36/e3 36/e3 6/e2 6/e2 6/e2 6/e2 6/e2 6/e2

(6/c2 - 6/d2) 6/d2

(6/c2 - 6/d2) 6/d2

(6/c2 - 6/d2) 6/d2

6/d2 (6/d2 - 6/e2) 6/e2

6/d2 (6/d2 - 6/e2) 6/e2

6/d2 (6/d2 - 6/e2) 6/e2

6/e2 6/e2

6/e2 6/e2

6/e2 6/e2

Page 30: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

0.00 -7547592.06 7547592 0.00 0.00 0.00 0.00 7547592.06 0.00 5436531 36841306.34 54365310.00 -7547592.06 7547592 0.00 0.00 0.00 0.00 0.00 7547592.06 0 5436530.56 25968245

Page 31: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

P =

0.00 0.000000

0.00 0.000000

0.00 0.000000

-34174.40 -0.000744

0.00 0.000000

34174.40=

0.000744

-34174.40 -0.000479

0.00 0.000000

34174.40 0.000479

-34174.40 -0.00118

0.00 0.000000

34174.40 0.001177

Δ1

Δ2

Δ3

θ1

θ2

θ3

θ4

θ5

θ6

θ7

θ8

θ9

Page 32: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

M 1 0 7547592.1 0.0 0.0 7547592 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

M 2 0 7547592.1 0.0 0.0 15095184 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

M 3 34174 0.0 0.0 0.0 10873061 5436530.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0

M 4 -34174 0.0 0.0 0.0 5436531 10873061.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0

M 5 0 7547592.1 0.0 0.0 0 15095184.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0

M 6 0 7547592.1 0.0 0.0 0 7547592.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0

M 7 34174 0.0 0.0 0.0 0 10873061.1 5436530.6 0.0 0.0 0.0 0.0 0.0 0.0

M 8 -34174 0.0 0.0 0.0 0 5436530.6 10873061.1 0.0 0.0 0.0 0.0 0.0 0.0

M 9 0 7547592.1 0.0 0.0 0 0.0 15095184.1 0.0 0.0 0.0 0.0 0.0 0.0

M 10 0 7547592.1 0.0 0.0 0 0.0 7547592.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0000

M 11 0 -7547592.1 7547592.1 0.0 15095184 0.0 0.0 7547592.1 0.0 0.0 0.0 0.0 0.0 0.0000

M 12 0 -7547592.1 7547592.1 0.0 7547592 0.0 0.0 15095184.1 0.0 0.0 0.0 0.0 0.0 0.0000

M 13 34174 0.0 0.0 0.0 0 0.0 0.0 10873061.1 5436530.6 0.0 0.0 0.0 0.0 -0.0007

M 14 -34174 0.0 0.0 0.0 0 0.0 0.0 5436530.6 10873061.1 0.0 0.0 0.0 0.0 0.0000

M 15 = 0 + -7547592.1 7547592.1 0.0 0 7547592.1 0.0 0.0 15095184.1 0.0 0.0 0.0 0.0X

0.0007

M 16 0 -7547592.1 7547592.1 0.0 0 15095184.1 0.0 0.0 7547592.1 0.0 0.0 0.0 0.0 -0.0005

M 17 34174 0.0 0.0 0.0 0 0.0 0.0 0.0 10873061.1 5436530.6 0.0 0.0 0.0 0.0000

M 18 -34174 0.0 0.0 0.0 0 0.0 0.0 0.0 5436530.6 10873061.1 0.0 0.0 0.0 0.0005

M 19 0 -7547592.1 7547592.1 0.0 0 0.0 7547592.1 0.0 0.0 15095184.1 0.0 0.0 0.0 -0.0012

M 20 0 -7547592.1 7547592.1 0.0 0 0.0 15095184.1 0.0 0.0 7547592.1 0.0 0.0 0.0 0.0000

M 21 0 0.0 -7547592.1 7547592.1 0 0.0 0.0 15095184.1 0.0 0.0 7547592.1 0.0 0.0 0.0012

M 22 0 0.0 -7547592.1 7547592.1 0 0.0 0.0 7547592.1 0.0 0.0 15095184.1 0.0 0.0

M 23 34174 0.0 0.0 0.0 0 0.0 0.0 0.0 0.0 0.0 10873061.1 5436530.6 0.0

M 24 -34174 0.0 0.0 0.0 0 0.0 0.0 0.0 0.0 0.0 5436530.6 10873061.1 0.0

M 25 0 0.0 -7547592.1 7547592.1 0 0.0 0.0 0.0 7547592.1 0.0 0.0 15095184.1 0.0

M 26 0 0.0 -7547592.1 7547592.1 0 0.0 0.0 0.0 15095184.1 0.0 0.0 7547592.1 0.0

M 27 34174 0.0 0.0 0.0 0 0.0 0.0 0.0 0.0 0.0 0.0 10873061.1 5436530.6

M 28 -34174 0.0 0.0 0.0 0 0.0 0.0 0.0 0.0 0.0 0.0 5436530.6 10873061.1

M 29 0 0.0 -7547592.1 7547592.1 0 0.0 0.0 0.0 0.0 7547592.1 0.0 0.0 15095184.1

M 30 0 0.0 -7547592.1 7547592.1 0 0.0 0.0 0.0 0.0 15095184.1 0.0 0.0 7547592.1

Page 33: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

-40571.8 40571.777

M 1 -5617 21379.645 -21380M 2 -11233M 3 26083 -21379.645 0.000 21380M 4 -38220M 5 0 20734.98 20734.98M 6 0M 7 38220M 8 -26083M 9 11233 -36779 36779.4

M 10 5617 28964.393 -28964M 11 -14850 -16114.653 0.000 16114.653M 12 -12850 -12849.739 12849.739M 13 28964 18464.17 0.000 18464.17M 14 -36779M 15 = 0

4.3744 M 16 0M 17 36779 -38220.1 38220.1

3.6256 M 18 -28964 26083.080M 19 12850 26083.080 0.000 -26083.1M 20 14850 14849.8

427.59 M 21 -16115 -11233.263 11233M 22 -21380 -14849.817M 23 21380 19289.63 0.000 19289.63M 24 -40572M 25 0M 26 0M 27 40572M 28 -21380 0.000M 29 21380M 30 16115 -5616.632 5616.632

Page 34: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

23231.78 28030

12498.10

24653.92 -28029.82 26608 -23232

12498

9233.19

-26607.68 27148

24113.68 9233 -24654

5616.63 -27147.92 -24114

5617

Page 35: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

ANALISIS MATRICIAL EN EJE X , B-B

E = 2,173,706,511.93

8968.20 kg/m 8968.20 kg/m

3.00 m e8968.20 kg/m 8968.20 kg/m

3.00 m d

8968.20 kg/m 8968.20 kg/m

3.00 m c

---------------- 8.00 m ----------------- ---------------- 8.00 m -----------------

Kg/m2

Page 36: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

a b

Page 37: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00

0.00 (4/d + 4/c + 4/a) 2/a 0.00 2/d 0.00 0.00 0.00 0.00 0.00

0.00 2/a ( 4/a + 4/b + 4/c + 4/d) 2/b 0.00 2/d 0.00 0.00 0.00 0.00

K =

0.00 0.00 2/b (4/b + 4/c + 4/d) 0.00 0.00 2/d 0.00 0.00 0.00

2/d 0.00 0.00 (4/d + 4/e + 4/a) 2/a 0.00 2/e 0.00 0.00

0.00 2/d 0.00 2/a (4/a + 4/b + 4/d + 4/e) 2/b 0.00 2/e 0.00

0.00 0.00 2/d 0.00 2/b (4/b + 4/d + 4/e) 0.00 0.00 2/e

0.00 0.00 0.00 0.00 2/e 0.00 0.00 (4/a + 4/e) 2/a 0.00

0.00 0.00 0.00 0.00 0.00 2/e 0.00 2/a (4/a + 4/b + 4/e) 2/b

0.00 0.00 0.00 0.00 0.00 0.00 2/e 0.00 2/b (4/b + 4/e)

a = 8.00 mEI 21,746,122.23 E (VIGAS) 2173706511.93 Tn/m2 INERCIA 0.01 m4 0.35 0.7

b = 8.00 m

c = 3.00 m EI 11,321,388.08 E (COLUM) 2173706511.93 Tn/m2 INERCIA COLUMNA 0.01 m4 0.5 0.5d = 3.00 m EI 11,321,388.08 E (COLUM) 2173706511.93 Tn/m2 INERCIA COLUMNA 0.01 m4 0.5 0.5e = 3.00 m EI 11,321,388.08 E (COLUM) 2173706511.93 Tn/m2 INERCIA COLUMNA 0.01 m4 0.5 0.5

30190368.22 -15095184.11 0 0.00 0.00 0.00 -7547592.06 -7547592.06 -7547592.06 0 0.00 0

-15095184.11 30190368.22 -15095184 7547592.06 7547592.06 7547592.06 0.00 0.00 0.00 -7547592 -7547592.06 -7547592

0.00 -15095184.11 15095184 0.00 0.00 0.00 7547592.06 7547592.06 7547592.06 7547592 7547592.06 7547592

0.00 7547592.06 0 41063429.34 5436530.56 0.00 7547592.06 0.00 0.00 0 0.00 0

0.00 7547592.06 0 5436530.56 51936490.45 5436530.56 0.00 7547592.06 0.00 0 0.00 0

K =

0.00 7547592.06 0 0.00 5436530.56 41063429.34 0.00 0.00 7547592.06 0 0.00 0

-7547592.06 0.00 7547592 7547592.06 0.00 0.00 41063429.34 5436530.56 0.00 7547592 0.00 0

-7547592.06 0.00 7547592 0.00 7547592.06 0.00 5436530.56 51936490.45 5436530.56 0 7547592.06 0

-7547592.06 0.00 7547592 0.00 0.00 7547592.06 0.00 5436530.56 41063429.34 0 0.00 75475920.00 -7547592.06 7547592 0.00 0.00 0.00 7547592.06 0.00 0.00 25968245 5436530.56 0

(36/d3 + 36/c3) 36/d3 (6/c2 - 6/d2) (6/c2 - 6/d2) (6/c2 - 6/d2) 6/d2 6/d2 6/d2

36/d3 (36/d3 + 36/e3) 36/e3 6/d2 6/d2 6/d2 (6/d2 - 6/e2) (6/d2 - 6/e2) (6/d2 - 6/e2) 6/e2 6/e2 6/e2

36/e3 36/e3 6/e2 6/e2 6/e2 6/e2 6/e2 6/e2

(6/c2 - 6/d2) 6/d2

(6/c2 - 6/d2) 6/d2

(6/c2 - 6/d2) 6/d2

6/d2 (6/d2 - 6/e2) 6/e2

6/d2 (6/d2 - 6/e2) 6/e2

6/d2 (6/d2 - 6/e2) 6/e2

6/e2 6/e2

6/e2 6/e2

6/e2 6/e2

Page 38: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

0.00 -7547592.06 7547592 0.00 0.00 0.00 0.00 7547592.06 0.00 5436531 36841306.34 54365310.00 -7547592.06 7547592 0.00 0.00 0.00 0.00 0.00 7547592.06 0 5436530.56 25968245

Page 39: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

P =

0.00 0.000000

0.00 0.000000

0.00 0.000000

-47830.40 -0.001042

0.00 0.000000

47830.40=

0.001042

-47830.40 -0.000671

0.00 0.000000

47830.40 0.000671

-47830.40 -0.00165

0.00 0.000000

47830.40 0.001647

Δ1

Δ2

Δ3

θ1

θ2

θ3

θ4

θ5

θ6

θ7

θ8

θ9

Page 40: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

M 1 0 7547592.1 0.0 0.0 7547592 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

M 2 0 7547592.1 0.0 0.0 15095184 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

M 3 47830 0.0 0.0 0.0 10873061 5436530.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0

M 4 -47830 0.0 0.0 0.0 5436531 10873061.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0

M 5 0 7547592.1 0.0 0.0 0 15095184.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0

M 6 0 7547592.1 0.0 0.0 0 7547592.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0

M 7 47830 0.0 0.0 0.0 0 10873061.1 5436530.6 0.0 0.0 0.0 0.0 0.0 0.0

M 8 -47830 0.0 0.0 0.0 0 5436530.6 10873061.1 0.0 0.0 0.0 0.0 0.0 0.0

M 9 0 7547592.1 0.0 0.0 0 0.0 15095184.1 0.0 0.0 0.0 0.0 0.0 0.0

M 10 0 7547592.1 0.0 0.0 0 0.0 7547592.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0000

M 11 0 -7547592.1 7547592.1 0.0 15095184 0.0 0.0 7547592.1 0.0 0.0 0.0 0.0 0.0 0.0000

M 12 0 -7547592.1 7547592.1 0.0 7547592 0.0 0.0 15095184.1 0.0 0.0 0.0 0.0 0.0 0.0000

M 13 47830 0.0 0.0 0.0 0 0.0 0.0 10873061.1 5436530.6 0.0 0.0 0.0 0.0 -0.0010

M 14 -47830 0.0 0.0 0.0 0 0.0 0.0 5436530.6 10873061.1 0.0 0.0 0.0 0.0 0.0000

M 15 = 0 + -7547592.1 7547592.1 0.0 0 7547592.1 0.0 0.0 15095184.1 0.0 0.0 0.0 0.0X

0.0010

M 16 0 -7547592.1 7547592.1 0.0 0 15095184.1 0.0 0.0 7547592.1 0.0 0.0 0.0 0.0 -0.0007

M 17 47830 0.0 0.0 0.0 0 0.0 0.0 0.0 10873061.1 5436530.6 0.0 0.0 0.0 0.0000

M 18 -47830 0.0 0.0 0.0 0 0.0 0.0 0.0 5436530.6 10873061.1 0.0 0.0 0.0 0.0007

M 19 0 -7547592.1 7547592.1 0.0 0 0.0 7547592.1 0.0 0.0 15095184.1 0.0 0.0 0.0 -0.0016

M 20 0 -7547592.1 7547592.1 0.0 0 0.0 15095184.1 0.0 0.0 7547592.1 0.0 0.0 0.0 0.0000

M 21 0 0.0 -7547592.1 7547592.1 0 0.0 0.0 15095184.1 0.0 0.0 7547592.1 0.0 0.0 0.0016

M 22 0 0.0 -7547592.1 7547592.1 0 0.0 0.0 7547592.1 0.0 0.0 15095184.1 0.0 0.0

M 23 47830 0.0 0.0 0.0 0 0.0 0.0 0.0 0.0 0.0 10873061.1 5436530.6 0.0

M 24 -47830 0.0 0.0 0.0 0 0.0 0.0 0.0 0.0 0.0 5436530.6 10873061.1 0.0

M 25 0 0.0 -7547592.1 7547592.1 0 0.0 0.0 0.0 7547592.1 0.0 0.0 15095184.1 0.0

M 26 0 0.0 -7547592.1 7547592.1 0 0.0 0.0 0.0 15095184.1 0.0 0.0 7547592.1 0.0

M 27 47830 0.0 0.0 0.0 0 0.0 0.0 0.0 0.0 0.0 0.0 10873061.1 5436530.6

M 28 -47830 0.0 0.0 0.0 0 0.0 0.0 0.0 0.0 0.0 0.0 5436530.6 10873061.1

M 29 0 0.0 -7547592.1 7547592.1 0 0.0 0.0 0.0 0.0 7547592.1 0.0 0.0 15095184.1

M 30 0 0.0 -7547592.1 7547592.1 0 0.0 0.0 0.0 0.0 15095184.1 0.0 0.0 7547592.1

Page 41: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

-56784.2 56784.152

M 1 -7861 29922.895 -29922.9M 2 -15722M 3 36506 -29922.895 0.000 29923M 4 -53493M 5 0 29020.62 29021M 6 0M 7 53493M 8 -36506M 9 15722 -51476.4 51476.356

M 10 7861 40538.487 -40538.5M 11 -20784 -22554.026 0.000 22554.026M 12 -17984 -17984.461 17984.461M 13 40538 25842.40 0.000 25842.40M 14 -51476M 15 = 0

4.3744 M 16 0M 17 51476 -53492.7 53492.695

3.6256 M 18 -40538 36505.811M 19 17984 36505.811 0.000 -36505.811M 20 20784 20783.765

598.46 M 21 -22554 -15722.046 15722.05M 22 -29923 -20783.765M 23 29923 26997.72 0.000 26997.72M 24 -56784M 25 0M 26 0M 27 56784M 28 -29923 0.000M 29 29923M 30 22554 -7861.023 7861.023

Page 42: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

Page 43: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

32515.14 39230

17492.31

34505.57 -39230.46 37240 -32515.14

17492.3

12922.74

-37240.03 37996.16

33749.44 12922.7 -34506

7861.02 -37996.16 -33749

7861.02

Page 44: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

ANALISIS MATRICIAL EN EJE Y 1-1, 2-2 y 3-3

M 1

E = 2,173,706,511.93 M 2

M 3

2206.20 kg/m 2206.20 kg/m M 4

M 5

M 6

M 7

M 8

M 9

3.00 m e M 10

2206.20 kg/m 2206.20 kg/m M 11

M 12

M 13

M 14

M 15

M 16

3.00 m d M 17

M 18

2206.20 kg/m 2206.20 kg/m M 19

M 20

M 21

M 22

M 23

M 24

3.00 m c M 25

M 26

M 27

M 28

M 29

---------------- 4.50 m ----------------- ---------------- 4.50 m ----------------- M 30

Kg/m2

Page 45: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

a b

Page 46: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

MATRIZ DE RIGIDEZ DE LA ESTRUCTURA

0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00

0.00 (4/d + 4/c + 4/a) 2/a 0.00 2/d 0.00 0.00 0.00 0.00 0.00

0.00 2/a ( 4/a + 4/b + 4/c + 4/d) 2/b 0.00 2/d 0.00 0.00 0.00 0.00

K =

0.00 0.00 2/b (4/b + 4/c + 4/d) 0.00 0.00 2/d 0.00 0.00 0.00

2/d 0.00 0.00 (4/d + 4/e + 4/a) 2/a 0.00 2/e 0.00 0.00

0.00 2/d 0.00 2/a (4/a + 4/b + 4/d + 4/e) 2/b 0.00 2/e 0.00

0.00 0.00 2/d 0.00 2/b (4/b + 4/d + 4/e) 0.00 0.00 2/e

0.00 0.00 0.00 0.00 2/e 0.00 0.00 (4/a + 4/e) 2/a 0.00

0.00 0.00 0.00 0.00 0.00 2/e 0.00 2/a (4/a + 4/b + 4/e) 2/b

0.00 0.00 0.00 0.00 0.00 0.00 2/e 0.00 2/b (4/b + 4/e)

2.336527

a = 4.50 mEI 3,477,930.42 E (VIGAS) 2173706511.93 Tn/m2 INERCIA 0.00 m4 0.3 0.4

b = 4.50 m 2.163473c = 3.00 m EI 11,321,388.08 E (COLUM) 2173706511.93 Tn/m2 INERCIA COLUMNA 0.01 m4 0.5 0.5d = 3.00 m EI 11,321,388.08 E (COLUM) 2173706511.93 Tn/m2 INERCIA COLUMNA 0.01 m4 0.5 0.5e = 3.00 m EI 11,321,388.08 E (COLUM) 2173706511.93 Tn/m2 INERCIA COLUMNA 0.01 m4 0.5 0.5 63.00551

30190368.22 -15095184.11 0.00 0.00 0.00 0.00 -7547592.06 -7547592.06 -7547592.06 0 0.00 0

-15095184.11 30190368.22 ### 7547592.06 7547592.06 7547592.06 0.00 0.00 0.00 -7547592 -7547592.06 -7547592

0.00 -15095184.11 ### 0.00 0.00 0.00 7547592.06 7547592.06 7547592.06 7547592 7547592.06 7547592

0.00 7547592.06 0.00 33281861.93 1545746.85 0.00 7547592.06 0.00 0.00 0 0.00 0

0.00 7547592.06 0.00 1545746.85 36373355.63 1545746.85 0.00 7547592.06 0.00 0 0.00 0

K =

0.00 7547592.06 0.00 0.00 1545746.85 33281861.93 0.00 0.00 7547592.06 0 0.00 0

-7547592.06 0.00 ### 7547592.06 0.00 0.00 33281861.93 1545746.85 0.00 7547592 0.00 0

-7547592.06 0.00 ### 0.00 7547592.06 0.00 1545746.85 36373355.63 1545746.85 0 7547592.06 0

-7547592.06 0.00 ### 0.00 0.00 7547592.06 0.00 1545746.85 33281861.93 0 0.00 75475920.00 -7547592.06 ### 0.00 0.00 0.00 7547592.06 0.00 0.00 18186678 1545746.85 0

(36/d3 + 36/c3) 36/d3 (6/c2 - 6/d2) (6/c2 - 6/d2) (6/c2 - 6/d2) 6/d2 6/d2 6/d2

36/d3 (36/d3 + 36/e3) 36/e3 6/d2 6/d2 6/d2 (6/d2 - 6/e2) (6/d2 - 6/e2) (6/d2 - 6/e2) 6/e2 6/e2 6/e2

36/e3 36/e3 6/e2 6/e2 6/e2 6/e2 6/e2 6/e2

(6/c2 - 6/d2) 6/d2

(6/c2 - 6/d2) 6/d2

(6/c2 - 6/d2) 6/d2

6/d2 (6/d2 - 6/e2) 6/e2

6/d2 (6/d2 - 6/e2) 6/e2

6/d2 (6/d2 - 6/e2) 6/e2

6/e2 6/e2

6/e2 6/e2

6/e2 6/e2

Page 47: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

0.00 -7547592.06 ### 0.00 0.00 0.00 0.00 7547592.06 0.00 1545747 21278171.52 15457470.00 -7547592.06 ### 0.00 0.00 0.00 0.00 0.00 7547592.06 0 1545746.85 18186678

Page 48: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

P =

0.00 0.000000

0.00 0.000000

0.00 0.000000

-3722.96 -0.000101

0.00 0.000000

3722.96=

0.000101

-3722.96 -0.000047

0.00 0.000000

3722.96 0.000047

-3722.96 -0.00019

0.00 0.000000

3722.96 0.000185

Δ1

Δ2

Δ3

θ1

θ2

θ3

θ4

θ5

θ6

θ7

θ8

θ9

Page 49: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

0 7547592.1 0.0 0.0 7547592 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 7547592.1 0.0 0.0 15095184 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

3723 0.0 0.0 0.0 3091494 1545746.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0

-3723 0.0 0.0 0.0 1545747 3091493.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 7547592.1 0.0 0.0 0 15095184.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 7547592.1 0.0 0.0 0 7547592.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0

3723 0.0 0.0 0.0 0 3091493.7 1545746.9 0.0 0.0 0.0 0.0 0.0 0.0

-3723 0.0 0.0 0.0 0 1545746.9 3091493.7 0.0 0.0 0.0 0.0 0.0 0.0

0 7547592.1 0.0 0.0 0 0.0 15095184.1 0.0 0.0 0.0 0.0 0.0 0.0

0 7547592.1 0.0 0.0 0 0.0 7547592.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0000

0 -7547592.1 7547592.1 0.0 15095184 0.0 0.0 7547592.1 0.0 0.0 0.0 0.0 0.0 0.0000

0 -7547592.1 7547592.1 0.0 7547592 0.0 0.0 15095184.1 0.0 0.0 0.0 0.0 0.0 0.0000

3723 0.0 0.0 0.0 0 0.0 0.0 3091493.7 1545746.9 0.0 0.0 0.0 0.0 -0.0001

-3723 0.0 0.0 0.0 0 0.0 0.0 1545746.9 3091493.7 0.0 0.0 0.0 0.0 0.0000

= 0 + -7547592.1 7547592.1 0.0 0 7547592.1 0.0 0.0 15095184.1 0.0 0.0 0.0 0.0X

0.0001

0 -7547592.1 7547592.1 0.0 0 15095184.1 0.0 0.0 7547592.1 0.0 0.0 0.0 0.0 0.0000

3723 0.0 0.0 0.0 0 0.0 0.0 0.0 3091493.7 1545746.9 0.0 0.0 0.0 0.0000

-3723 0.0 0.0 0.0 0 0.0 0.0 0.0 1545746.9 3091493.7 0.0 0.0 0.0 0.0000

0 -7547592.1 7547592.1 0.0 0 0.0 7547592.1 0.0 0.0 15095184.1 0.0 0.0 0.0 -0.0002

0 -7547592.1 7547592.1 0.0 0 0.0 15095184.1 0.0 0.0 7547592.1 0.0 0.0 0.0 0.0000

0 0.0 -7547592.1 7547592.1 0 0.0 0.0 15095184.1 0.0 0.0 7547592.1 0.0 0.0 0.0002

0 0.0 -7547592.1 7547592.1 0 0.0 0.0 7547592.1 0.0 0.0 15095184.1 0.0 0.0

3723 0.0 0.0 0.0 0 0.0 0.0 0.0 0.0 0.0 3091493.7 1545746.9 0.0

-3723 0.0 0.0 0.0 0 0.0 0.0 0.0 0.0 0.0 1545746.9 3091493.7 0.0

0 0.0 -7547592.1 7547592.1 0 0.0 0.0 0.0 7547592.1 0.0 0.0 15095184.1 0.0

0 0.0 -7547592.1 7547592.1 0 0.0 0.0 0.0 15095184.1 0.0 0.0 7547592.1 0.0

3723 0.0 0.0 0.0 0 0.0 0.0 0.0 0.0 0.0 0.0 3091493.7 1545746.9

-3723 0.0 0.0 0.0 0 0.0 0.0 0.0 0.0 0.0 0.0 1545746.9 3091493.7

0 0.0 -7547592.1 7547592.1 0 0.0 0.0 0.0 0.0 7547592.1 0.0 0.0 15095184.1

0 0.0 -7547592.1 7547592.1 0 0.0 0.0 0.0 0.0 15095184.1 0.0 0.0 7547592.1

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CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

-4009.306 4009.306

M 1 -764.017 3150.275 -3150.28M 2 -1528.035M 3 3410.021 -3150.275 0.000 3150.3M 4 -3879.433M 5 0.000 2012.91 2012.91M 6 0.000M 7 3879.433M 8 -3410.021M 9 1528.035 -3795.452 3795.452

M 10 764.017 3577.984 -3577.98M 11 -1881.986 -2106.064 0.000 2106.064M 12 -1471.920 -1471.920 1471.920M 13 3577.984 1898.26 0.000 1898.26M 14 -3795.452M 15 = 0.000M 16 0.000M 17 3795.452 -3879.433 3879.433M 18 -3577.984 3410.021M 19 1471.920 3410.021 0.000 -3410.021M 20 1881.986 1881.986M 21 -2106.064 -1528.035 1528.03M 22 -3150.275 -1881.986M 23 3150.275 1942.18 0.000 1942.18M 24 -4009.306M 25 0.000M 26 0.000M 27 4009.306M 28 -3150.275 0.000M 29 3150.275M 30 2106.064 -764.017 764.017

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CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

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CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

4773.05 5154.85

1752.11

4915.62 -5154.85 5012.28 -4773.05

1752.11

1117.97

-5012.28 5068.26

4859.64 1117.97 -4915.62

764.02 -5068.26 -4859.64

764.02

Page 53: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE ZAPATAS CENTRICAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

Datos:f´c = 210

fy = 4200Pisos = 3 Pisos

2.0 kg/cm2

4.50 m

4.50 m

Y ---------------- 8.00 m ----------------- ---------------- 8.00 m -----------------

XZ-1 Zapata Central VISTA EN PLANTA TÍPICAZ-2 Zapata Extrema de un pórtico principal interiorZ-3 Zapata Extrema de un pórtico secundario interiorZ-4 Zapata en esquina METRADO DE CARGA Z - 4

ELEMENTOS PESO PROPIO N° DIMENSION PESO PARCIAL P. Aligerado 300 3 6.2500 5,625.00 Kg

Tabiqueria Movil 150 3 6.2500 2,812.50 Kg

Muros de Soga 1800 3 2.8125 15,187.50 Kg120 3 6.2500 2,250.00 Kg

Peso de vigas 2400 3 1.2500 9,000.00 Kg

Peso de Columnas 60 3 6.2500 1,125.00 Kg

S/C 200 3 6.2500 3,750.00 KgValor de P = 39,750.00 Kg

kg/cm2

kg/cm2

σterreno

kg/m2 m2

kg/m2 m2

kg/m3 m2

Acabado + Cielo raso kg/m2 m2

kg/m3 m3

kg/m2 m2

kg/m2 m2

Z-4 Z-3

Z-1Z-2

Page 54: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE ZAPATAS CENTRICAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

Pu = 1.4*CM + 1.7*CV 56,775.00 Kg

DIMENSION DE LA ZAPATA - 4

21862.50 cm2

Zapata de : 1.48 ###

147.86 cm Asumimos: 1.50 x 1.5

METRADO DE CARGA Z - 2

ELEMENTOS PESO PROPIO N° DIMENSION PESO PARCIAL P. Aligerado 300 3 18.0000 16,200.00 Kg

Tabiqueria Movil 150 3 18.0000 8,100.00 Kg

Muros de Soga 1800 3 3.8250 20,655.00 Kg120 3 18.0000 6,480.00 Kg

Peso de vigas 2400 3 1.5200 10,944.00 Kg

Peso de Columnas 60 3 18.0000 3,240.00 Kg

S/C 200 3 18.0000 10,800.00 KgValor de P = 76,419.00 Kg

Pu = 1.4*CM + 1.7*CV 110,226.60 Kg

DIMENSION DE LA ZAPATA - 2

42030.45 cm2

Zapata de : 2.05 2.05

Área de zapata = 1.1P u/σterreno

AC =m2

L C = m2

kg/m2 m2

kg/m2 m2

kg/m3 m2

Acabado + Cielo raso kg/m2 m2

kg/m3 m3

kg/m2 m2

kg/m2 m2

Área de zapata = 1.1P u/σterreno

AC =m2

Page 55: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE ZAPATAS CENTRICAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

205.01 cm Asumimos: 2.10 x 2.1

METRADO DE CARGA Z- 3

ELEMENTOS PESO PROPIO N° DIMENSION PESO PARCIAL P. Aligerado 300 3 18.0000 16,200.00 Kg

Tabiqueria Movil 150 3 18.0000 8,100.00 Kg

Muros de Soga 1800 3 4.6125 24,907.50 Kg120 3 18.0000 6,480.00 Kg

Peso de vigas 2400 3 2.2300 16,056.00 Kg

Peso de Columnas 60 3 18.0000 3,240.00 Kg

S/C 200 3 18.0000 10,800.00 KgValor de P = 85,783.50 Kg

Pu = 1.4*CM + 1.7*CV 123,336.90 Kg

DIMENSION DE LA ZAPATA - 3

47180.93 cm2

Zapata de : 2.17 ###

217.21 cm Asumimos: 2.20 x 2.2

METRADO DE CARGA Z - 1ELEMENTOS PESO PROPIO N° DIMENSION PESO PARCIAL

P. Aligerado 300 3 36.0000 32,400.00 Kg

L C = m2

kg/m2 m2

kg/m2 m2

kg/m3 m2

Acabado + Cielo raso kg/m2 m2

kg/m3 m3

kg/m2 m2

kg/m2 m2

Área de zapata = 1.1P u/σterreno

AC =m2

L C = m2

kg/m2 m2

Page 56: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE ZAPATAS CENTRICAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

Tabiqueria Movil 150 3 36.0000 16,200.00 Kg

Muros de Soga 1800 3 5.6250 30,375.00 Kg120 3 36.0000 12,960.00 Kg

Peso de vigas 2400 3 2.5000 18,000.00 Kg

Peso de Columnas 60 3 36.0000 6,480.00 Kg

S/C 200 3 36.0000 21,600.00 KgValor de P = 138,015.00 Kg

Pu = 1.4*CM + 1.7*CV 199,701.00 Kg

DIMENSION DE LA ZAPATA - 1

75908.25 cm2

Zapata de : 2.76 ###

275.51 cm Asumimos: 2.80 x 2.8

2.10 m2.80 m

kg/m2 m2

kg/m3 m2

Acabado + Cielo raso kg/m2 m2

kg/m3 m3

kg/m2 m2

kg/m2 m2

Área de zapata = 1.1P u/σterreno

AC =m2

L C = m2

Page 57: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE ZAPATAS CENTRICAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

2.10 m

2.80 m

2.20 m 1.50 m

1.50 m

2.20 mDISEÑOR POR CORTE Z - 1: DISEÑOR POR CORTE Z - 2: DISEÑOR POR CORTE Z - 3: DISEÑOR POR CORTE Z - 4:

2.547 2.499 2.548 2.523m = 1.150 m = 0.800 m = 0.850 m = 0.5d = 0.336 d = 0.231 d = 0.249 d = ###

DISEÑOR POR FLEXIÓN Z - 1: DISEÑOR POR FLEXIÓN Z - 2: DISEÑOR POR FLEXIÓN Z - 3: DISEÑOR POR FLEXIÓN Z - 4:M = 4.716 M = 1.680 M = 2.025 M = 0.473

j = 0.902 j = 0.902 j = 0.902 j = 0.902k = 0.293 k = 0.293 k = 0.293 k = 0.293n = 9.201 n = 9.201 n = 9.201 n = 9.201fc = 94.500 fc = 94.500 fc = 94.50 fc = 94.5

ωn = ωn = ωn = ωn =

Page 58: TRABAJO CONCRETO ARMADO  I - 2015 - 00.xlsx

CONCRETO ARMADO 1 CALCULO DE ZAPATAS CENTRICAS UNIVERSIDAD CESAR VALLEJO

ING. EDWIN RODRIGUEZ PLASENCIA

fs = 2100.0 fs = 2100.000 fs = 2100.00 fs = 2100d = 0.246 d = 0.147 d = 0.16 d = 0.078

DISEÑOR POR PUNZONAMIENTO Z - 1: DISEÑOR POR PUNZONAMIENTO Z - 2: DISEÑOR POR PUNZONAMIENTO Z - 3: DISEÑOR POR PUNZONAMIENTO Z - 4:d = 0.3911 d = 0.266 d = 0.289 d = 0.172

h = 45.69 cm h = 33.18 cm h = 35.48 cm h = 23.74 cm

Mu a a a aZ - 1 47.2 35.446 2.09 32.77 1.93 32.71 1.92 32.71 1.92 12 Ø 3/4'' @ 20 cmZ - 2 16.80 18.561 1.09 17.05 1.00 17.03 1.00 17.03 1.00 8 Ø 5/8'' @ 20 cmZ - 3 20.25 20.599 1.21 18.94 1.11 18.90 1.11 18.90 1.11 10 Ø 5/8'' @ 20 cmZ - 4 4.73 8.109 0.48 7.40 0.44 7.39 0.43 7.39 0.43 6 Ø 1/2'' @ 20 cm

As As As As