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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
CONCRETO ARMADO 1 CALCULO DE COLUMNAS UNIVERSIDAD CESAR VALLEJO
ING. EDWIN RODRIGUEZ PLASENCIA
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
CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO
ING. EDWIN RODRIGUEZ PLASENCIA
a b
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
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
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
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
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
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
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
CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO
ING. EDWIN RODRIGUEZ PLASENCIA
a b
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
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
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
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
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
CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO
ING. EDWIN RODRIGUEZ PLASENCIA
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
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
CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO
ING. EDWIN RODRIGUEZ PLASENCIA
a b
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
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
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
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
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
CONCRETO ARMADO 1 MOMENTO PARA VIGA Y COLUMNA UNIVERSIDAD CESAR VALLEJO
ING. EDWIN RODRIGUEZ PLASENCIA
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
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
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
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
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
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 =
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