UNIVERSIDAD DE HUANUCO E.A.P INGENIERIA CIVIL NOMBRE:
MEZA DOMINGUEZ, MIGUEL ANGEL
DOCENTE:
JERRY MARLON DAVILA MARTEL
GRUPO:
"B"
CURSO:
INGENIERIA DE CIMENTACIONES
PROYECTO:
"MEJORAMIENTO DE LOS SERVICIOS ACADÉMICOS DE EXPERIMENTACIÓN E INVESTIGACIÓN EN LAS CARRERAS DE ENFERMERÍA, OBSTETRICIA, PSICOLOGÍA Y ODONTOLOGÍA DE LA UNHEVAL – HUÁNUCO"
METRADO DE CARGAS - MODULO ENFERMERIA PRIMER NIVEL CARGA MUERTA N°
DESCRIPCIÓN
1
VIGAS
ϪPeso esp. (Kg/m³)
N° DE VECES
LARGO (m)
ANCHO (m)
ALTO (m)
1
7.19
0.3
0.7
2400
2
3.1
0.3
0.7
2400
3124.8
2
7.37
0.3
0.7
2400
7428.96
1
4.27
0.3
0.7
2400
2152.08
2
7.09
0.3
0.7
2400
7146.72
2
2.65
0.3
0.7
2400
2671.2
1
7.18
0.3
0.7
2400
3618.72
1
6.95
0.3
0.7
2400
3502.8
1
5.38
0.3
0.7
2400
2711.52
2
2.39
0.3
0.7
2400
2409.12
1
5.6
0.3
0.7
2400
2822.4
1
5.61
0.3
0.7
2400
2827.44
1
2.89
0.3
0.7
2400
1456.56
1
5.84
0.3
0.4
2400
1681.92
1
2.06
0.3
0.4
2400
593.28
1
5.78
0.3
0.4
2400
1664.64
1
5.98
0.3
0.4
2400
1722.24
1
2.05
0.3
0.4
2400
590.4
1
5.74
0.3
0.4
2400
1653.12
7
4.87
0.3
0.4
2400
9817.92
7
4.88
0.3
0.4
2400
9838.08
7
2.3
0.3
0.2
2400
2318.4
7
0.4
0.6
4
2400
16128
2400
8444.60
0.4
0.7
2400
32256
AREA (m²)
TOTAL (kg)
VIGAS LONGITUDINALES Eje G ÷ 19 y 25
Eje H ÷ 19 y 25
Eje I ÷ 19 y 25
Eje J ÷ 19 y 25
3623.76
VIGAS TRANSVERSALES Ejes 19 - 25 ÷ G y J
2
COLUMNAS C-1 C-2
7
C-3
12
4 4
0.1257
3
4
5
PLACAS Pl-1
1
4
0.64
2400
6144
Pl-2
1
4
0.6925
2400
6648
LOSA(e=0.20) EJE 19 y 20 ÷ G y H
1
39.6882
300
11906.46
EJE 19 y 20 ÷ H y I
1
33.5442
300
10063.26
EJE 19 y 20 ÷ I y J
1
14.4224
300
4326.72
EJE 20 y 21 ÷ G y H
1
15.8387
300
4751.61
EJE 20 y 21 ÷ H y I
1
13.2581
300
3977.43
EJE 20 y 21 ÷ I y J
1
5.5508
300
1665.24
EJE 21 y 22 ÷ G y H
1
39.1608
300
11748.24
EJE 21 y 22 ÷ H y I
1
33.4649
300
10039.47
EJE 21 y 22 ÷ I y J
1
14.3298
300
4298.94
EJE 22 y 23 ÷ G y H
1
40.1916
300
12057.48
EJE 22 y 23 ÷ H y I
1
34.286
300
10285.8
EJE 22 y 23 ÷ I y J
1
14.6641
300
4399.23
EJE 23 y 24 ÷ G y H
1
15.8308
300
4749.24
EJE 23 y 24 ÷ H y I
1
13.2586
300
3977.58
EJE 23 y 24 ÷ I y J
1
5.5555
300
1666.65
EJE 24 y 25 ÷ G y H
1
38.8902
300
11667.06
EJE 24 y 25 ÷ H y I
1
33.2364
300
9970.92
EJE 24 y 25 ÷ I y J
1
14.2383
300
4271.49
2723.625
MUROS MUROS LONGITUDINALES Eje I ÷ 19 y 25
1
5.38
0.15
2.25
1500
2
5.6
0.15
2.25
1500
5670
1
2.89
0.15
2.25
1500
1463.0625
3
4.87
0.24
3.6
1500
18934.56
3
4.88
0.24
3.6
1500
18973.44
4
3.68
0.15
3.15
1500
10432.8
4
2.62
0.15
3.15
1500
7427.7
4
1.05
0.15
3.15
1500
2976.75
P-1
2
1.5
0.01
2.1
1000
63
P-2
8
1.2
0.01
2.1
1000
201.6
V-1
1
2.89
0.006
0.75
2500
32.5125
V-2
2
5.6
0.006
0.75
2500
126
V-3
1
5.38
0.006
0.75
2500
60.525
MUROS TRANSVERSALES Ejes 19 - 25 ÷ G y J
6
7
PUERTAS
VENTANAS
TOTAL =
339905.0760529
SEGUNDO NIVEL CARGA MUERTA N°
1
DESCRIPCIÓN
ϪPeso esp. (Kg/m³)
N° DE VECES
LARGO (m)
ANCHO (m)
ALTO (m)
1
7.19
0.3
0.7
2400
2
3.1
0.3
0.7
2400
3124.8
2
7.37
0.3
0.7
2400
7428.96
1
4.27
0.3
0.7
2400
2152.08
2
7.09
0.3
0.7
2400
7146.72
2
2.65
0.3
0.7
2400
2671.2
1
7.18
0.3
0.7
2400
3618.72
1
6.95
0.3
0.7
2400
3502.8
1
5.38
0.3
0.7
2400
2711.52
2
2.39
0.3
0.7
2400
2409.12
1
5.6
0.3
0.7
2400
2822.4
1
5.61
0.3
0.7
2400
2827.44
1
2.89
0.3
0.7
2400
1456.56
1
5.84
0.3
0.4
2400
1681.92
1
2.06
0.3
0.4
2400
593.28
1
5.78
0.3
0.4
2400
1664.64
1
5.98
0.3
0.4
2400
1722.24
1
2.05
0.3
0.4
2400
590.4
1
5.74
0.3
0.4
2400
1653.12
7
4.87
0.3
0.4
2400
9817.92
7
4.88
0.3
0.4
2400
9838.08
7
2.3
0.3
0.2
2400
2318.4
C-1
7
0.4
0.6
3.85
2400
15523.2
C-2
7
2400
8127.93
C-3
12
2400
31046.4
AREA (m²)
TOTAL (kg)
VIGAS VIGAS LONGITUDINALES Eje G ÷ 19 y 25
Eje H ÷ 19 y 25
Eje I ÷ 19 y 25
Eje J ÷ 19 y 25
3623.76
VIGAS TRANSVERSALES Ejes 19 - 25 ÷ G y J
2
3
COLUMNAS 3.85 0.4
0.7
0.1257
3.85
PLACAS Pl-1
1
3.85
0.64
2400
5913.6
Pl-2
1
3.85
0.6925
2400
6398.7
4
5
LOSA(e=0.20) EJE 19 y 20 ÷ G y H
1
39.6882
300
11906.46
EJE 19 y 20 ÷ H y I
1
33.5442
300
10063.26
EJE 19 y 20 ÷ I y J
1
14.4224
300
4326.72
EJE 20 y 21 ÷ G y H
1
15.8387
300
4751.61
EJE 20 y 21 ÷ H y I
1
13.2581
300
3977.43
EJE 20 y 21 ÷ I y J
1
5.5508
300
1665.24
EJE 21 y 22 ÷ G y H
1
39.1608
300
11748.24
EJE 21 y 22 ÷ H y I
1
33.4649
300
10039.47
EJE 21 y 22 ÷ I y J
1
14.3298
300
4298.94
EJE 22 y 23 ÷ G y H
1
40.1916
300
12057.48
EJE 22 y 23 ÷ H y I
1
34.286
300
10285.8
EJE 22 y 23 ÷ I y J
1
14.6641
300
4399.23
EJE 23 y 24 ÷ G y H
1
15.8308
300
4749.24
EJE 23 y 24 ÷ H y I
1
13.2586
300
3977.58
EJE 23 y 24 ÷ I y J
1
5.5555
300
1666.65
EJE 24 y 25 ÷ G y H
1
38.8902
300
11667.06
EJE 24 y 25 ÷ H y I
1
33.2364
300
9970.92
EJE 24 y 25 ÷ I y J
1
14.2383
300
4271.49
2723.625
MUROS MUROS LONGITUDINALES Eje I ÷ 19 y 25
1
5.38
0.15
2.25
1500
2
5.6
0.15
2.25
1500
5670
1
2.89
0.15
2.25
1500
1463.0625
3
4.87
0.24
3.45
1500
18145.62
3
4.88
0.24
3.45
1500
18182.88
4
3.68
0.15
3.15
1500
10432.8
4
2.62
0.15
3.15
1500
7427.7
4
1.05
0.15
3.15
1500
2976.75
8
1.2
0.01
2.1
1000
201.6
V-1
1
2.89
0.006
0.75
2500
32.5125
V-2
2
5.6
0.006
0.75
2500
126
V-3
1
5.38
0.006
0.75
2500
60.525
MUROS TRANSVERSALES Ejes 19 - 25 ÷ G y J
6
PUERTAS P-2
7
VENTANAS
TOTAL =
335651.8035134
CARGA VIVA
AREA (m²)
ϪPeso esp. (Kg/m²)
AULA 5
75.593
250
18898.25
AULA 6
74.7472
250
18686.8
AULA 7
76.6256
250
19156.4
AULA 8
74.208
250
18552
PASADIZO
133.4092
400
53363.68
TOTAL =
128657.13
TOTAL (kg)
TERCER NIVEL CARGA MUERTA N°
1
DESCRIPCIÓN
ϪPeso esp. (Kg/m³)
N° DE VECES
LARGO (m)
ANCHO (m)
ALTO (m)
1
7.19
0.3
0.7
2400
2
3.1
0.3
0.7
2400
3124.8
2
7.37
0.3
0.7
2400
7428.96
1
4.27
0.3
0.7
2400
2152.08
2
7.09
0.3
0.7
2400
7146.72
2
2.65
0.3
0.7
2400
2671.2
1
7.18
0.3
0.7
2400
3618.72
1
6.95
0.3
0.7
2400
3502.8
1
5.38
0.3
0.7
2400
2711.52
2
2.39
0.3
0.7
2400
2409.12
1
5.6
0.3
0.7
2400
2822.4
1
5.61
0.3
0.7
2400
2827.44
1
2.89
0.3
0.7
2400
1456.56
1
5.84
0.3
0.4
2400
1681.92
1
2.06
0.3
0.4
2400
593.28
1
5.78
0.3
0.4
2400
1664.64
1
5.98
0.3
0.4
2400
1722.24
1
2.05
0.3
0.4
2400
590.4
1
5.74
0.3
0.4
2400
1653.12
7
4.87
0.3
0.4
2400
9817.92
7
4.88
0.3
0.4
2400
9838.08
7
2.3
0.3
0.2
2400
2318.4
C-1
7
0.4
0.6
3.85
2400
15523.2
C-2
7
2400
8127.93
C-3
12
2400
31046.4
AREA (m²)
TOTAL (kg)
VIGAS VIGAS LONGITUDINALES Eje G ÷ 19 y 25
Eje H ÷ 19 y 25
Eje I ÷ 19 y 25
Eje J ÷ 19 y 25
3623.76
VIGAS TRANSVERSALES Ejes 19 - 25 ÷ G y J
2
3
COLUMNAS 3.85 0.4
0.7
0.1257
3.85
PLACAS Pl-1
1
3.85
0.64
2400
5913.6
Pl-2
1
3.85
0.6925
2400
6398.7
4
5
LOSA(e=0.20) EJE 19 y 20 ÷ G y H
1
39.6882
300
11906.46
EJE 19 y 20 ÷ H y I
1
33.5442
300
10063.26
EJE 19 y 20 ÷ I y J
1
14.4224
300
4326.72
EJE 20 y 21 ÷ G y H
1
15.8387
300
4751.61
EJE 20 y 21 ÷ H y I
1
13.2581
300
3977.43
EJE 20 y 21 ÷ I y J
1
5.5508
300
1665.24
EJE 21 y 22 ÷ G y H
1
39.1608
300
11748.24
EJE 21 y 22 ÷ H y I
1
33.4649
300
10039.47
EJE 21 y 22 ÷ I y J
1
14.3298
300
4298.94
EJE 22 y 23 ÷ G y H
1
40.1916
300
12057.48
EJE 22 y 23 ÷ H y I
1
34.286
300
10285.8
EJE 22 y 23 ÷ I y J
1
14.6641
300
4399.23
EJE 23 y 24 ÷ G y H
1
15.8308
300
4749.24
EJE 23 y 24 ÷ H y I
1
13.2586
300
3977.58
EJE 23 y 24 ÷ I y J
1
5.5555
300
1666.65
EJE 24 y 25 ÷ G y H
1
38.8902
300
11667.06
EJE 24 y 25 ÷ H y I
1
33.2364
300
9970.92
EJE 24 y 25 ÷ I y J
1
14.2383
300
4271.49
2723.625
MUROS MUROS LONGITUDINALES Eje I ÷ 19 y 25
1
5.38
0.15
2.25
1500
2
5.6
0.15
2.25
1500
5670
1
2.89
0.15
2.25
1500
1463.0625
3
4.87
0.24
3.45
1500
18145.62
3
4.88
0.24
3.45
1500
18182.88
2
3.68
0.15
3.15
1500
5216.4
3
2.62
0.15
3.15
1500
5570.775
3
1.05
0.15
3.15
1500
2232.5625
1
4.88
0.15
3.15
1500
3458.7
2
4.07
0.15
3.15
1500
5769.225
1
3.32
0.15
3.15
1500
2353.05
1
5.84
0.15
3.15
1500
4139.1
P-2
5
1.2
0.01
2.1
1000
126
P-6
3
0.8
0.006
2.1
1000
30.24000
V-1
1
2.89
0.006
0.75
2500
32.5125
V-2
2
5.6
0.006
0.75
2500
126
V-3
1
5.38
0.006
0.75
2500
60.525
V-8
1
2.63
0.006
0.9
2500
35.505
MUROS TRANSVERSALES Ejes 19 - 25 ÷ G y J
6
7
PUERTAS
VENTANAS
TOTAL =
343544.5110134
CARGA VIVA
AREA (m²)
ϪPeso esp. (Kg/m²)
SALA DE COMPUTO
75.593
250
18898.25
LABORATORIO DE ENFERMERIA CLINICA
62.5826
300
18774.78
DEPOSITO (LABORATORIO DE ENFERMERIA CLINICA)
11.7906
300
3537.18
TOTAL (kg)
LABORATORIO DE NIÑO
40.2075
300
12062.25
DEPOSITO (LABORATORIO DEL NIÑO)
9.7898
300
2936.94
LABORATORIO DE NEONATOLOGIA
36.8851
300
11065.53
LABORATORIO DE MUJER
74.208
300
22262.4
DEPOSITO (LABORATORIO DE LA MUJER)
7.9176
300
2375.28
PASADIZO
116.7896
400
46715.84
TOTAL =
138628.45
CUARTO NIVEL CARGA MUERTA N°
DESCRIPCIÓN
1
VIGAS
ϪPeso esp. (Kg/m³)
N° DE VECES
LARGO (m)
ANCHO (m)
ALTO (m)
1
7.19
0.3
0.7
2400
2
3.1
0.3
0.7
2400
3124.8
2
7.37
0.3
0.7
2400
7428.96
1
4.27
0.3
0.7
2400
2152.08
1
7.09
0.3
0.7
2400
3573.36
1
2.65
0.3
0.7
2400
1335.6
1
5.38
0.3
0.7
2400
2711.52
2
2.39
0.3
0.7
2400
2409.12
1
5.6
0.3
0.7
2400
2822.4
1
5.61
0.3
0.7
2400
2827.44
1
2.89
0.3
0.7
2400
1456.56
1
5.84
0.3
0.4
2400
1681.92
1
2.06
0.3
0.4
2400
593.28
1
5.78
0.3
0.4
2400
1664.64
1
5.98
0.3
0.4
2400
1722.24
1
2.05
0.3
0.4
2400
590.4
1
5.74
0.3
0.4
2400
1653.12
4
4.87
0.3
0.4
2400
5610.24
4
4.88
0.3
0.4
2400
5621.76
3
10.35
0.3
0.8
2400
17884.8
7
2.3
0.3
0.2
2400
2318.4
C-1
4
0.4
0.6
4.15
C-2
7
C-3
12
AREA (m²)
TOTAL (kg)
VIGAS LONGITUDINALES Eje G ÷ 19 y 25
Eje H ÷ 19 y 25
Eje I ÷ 19 y 25
Eje J ÷ 19 y 25
3623.76
VIGAS TRANSVERSALES Ejes 19 - 25
2
3
4
÷GyJ
COLUMNAS 4.15 0.4
0.7
0.1257
4.15
2400
9561.6
2400
8761.27
2400
33465.6
PLACAS Pl-1
1
4.15
0.64
2400
6374.4
Pl-2
1
4.15
0.6925
2400
6897.3
LOSA(e=0.20) EJE 19 y 20 ÷ G y H
1
39.6882
300
11906.46
EJE 19 y 20 ÷ H y I
1
33.5442
300
10063.26
EJE 19 y 20 ÷ I y J
1
14.4224
300
4326.72
EJE 20 y 21 ÷ G y H
1
15.8387
300
4751.61
EJE 20 y 21 ÷ H y I
1
13.2581
300
3977.43
EJE 20 y 21 ÷ I y J
1
5.5508
300
1665.24
EJE 21 y 22 ÷ G y I
1
74.7472
300
22424.16
EJE 21 y 22 ÷ I y J
1
14.3298
300
4298.94
5
EJE 22 y 23 ÷ G y I
1
76.6256
300
22987.68
EJE 22 y 23 ÷ I y J
1
14.6641
300
4399.23
EJE 23 y 24 ÷ G y I
1
29.8616
300
8958.48
EJE 23 y 24 ÷ I y J
1
5.5555
300
1666.65
EJE 24 y 25 ÷ G y I
1
74.208
300
22262.4
EJE 24 y 25 ÷ I y J
1
14.2383
300
4271.49
480.9375
MUROS MUROS LONGITUDINALES Eje I ÷ 19 y 25
1
0.75
0.15
2.85
1500
1
0.64
0.15
0.95
1500
136.8
1
4.2
0.15
3.35
1500
3165.75
2
4.87
0.24
3.35
1500
11746.44
2
4.88
0.24
3.35
1500
11770.56
1
2.92
0.1
3.35
1500
1467.3
1
0.4
0.1
3.35
1500
201
1
4.87
0.15
3.35
1500
3670.7625
1
4.88
0.15
3.35
1500
3678.3
1
8.55
0.15
2.75
1500
5290.3125
1
1.4
0.15
2.75
1500
866.25
1
3.3
0.15
2.75
1500
2041.875
1
0.95
0.15
2.75
1500
587.8125
1
1.35
0.15
2.75
1500
835.3125
P-4
3
0.9
0.078125
2.1
1000
442.96875
P-7
2
1.8
0.01
3.35
1000
120.6
P-7-A
1
1.5
0.01
3.35
1000
50.25
P-7-B
1
1.2
0.01
2.1
1000
25.2
P-8
3
0.8
0.006
2.1
1000
30.24
P-8-A
1
0.8
0.078125
2.1
1000
131.25
V-9
1
1.09
0.008
3.35
2500
73.03
V-10
2
0.7
0.008
3.35
2500
93.8
V-11
4
0.64
0.008
3.35
2500
171.52
V-12
1
0.75
0.008
0.5
2500
7.5
V-13
1
0.64
0.006
0.95
2500
9.12
M-1
1
2.39
0.008
3.35
2500
160.13
M-2
1
3.38
0.008
3.35
2500
226.46
M-3
1
2.68
0.008
3.35
2500
179.56
M-4
1
3.2
0.008
3.35
2500
214.4
M-5
1
2
0.008
3.35
2500
134
M-6
1
3.3
0.008
3.35
2500
221.1
M-7
1
4.98
0.008
3.35
2500
333.66
MUROS TRANSVERSALES Ejes 19 - 25 ÷ G y J
6
7
8
PUERTAS
VENTANAS
MAMPARAS
TOTAL =
314390.5248423
CARGA VIVA
AREA (m²)
ϪPeso esp. (Kg/m²)
ADMINISTRACION DE ENFERMERIA
114.0416
250
28510.4
DEPOSITO
20.8378
250
5209.45
TOTAL (kg)
DEPOSITO
20.8378
250
5209.45
COCINETA
12.6256
250
3156.4
PROSCENIO
45.236
300
13570.8
SALA DE CONFERENCIAS
191.9415
300
57582.45
PASADIZO
84.4783
400
33791.32
AZOTEA
525.1993
100
52519.93
TOTAL =
194340.75
RESUMEN NIVELES
CARGA MUERTA
CARGA VIVA
339905.076052849
0
2DO NIVEL
335651.803513367
128657.13
464308.933513368
3ER NIVEL
343544.511013368
138628.45
482172.961013368
4TO NIVEL
314390.524842331
194340.75
508731.274842331
SUB TOTAL DE CARGAS
1333491.91542192
461626.33
1795118.24542192
1ER NIVEL
CARGA TOTAL DE LA INFRAESTRUCTURA MODULO ENFERMERIA
Ps 339905.076052849
1795118.25
KG
1795.12
TN
AREA 1 AREA 2 AREA 3 AREA 4 AREA 5 AREA 6 AREA 7 AREA 8 AREA 9 AREA 10 AREA 11 AREA 12 AREA 13 AREA 14 AREA 15 AREA 16 AREA 17 AREA 18 AREA 19 AREA 20 AREA 21 AREA 22 AREA 23 AREA 24 AREA 25 AREA 26 AREA 27 AREA 28
m2 5.1956 14.0477 21.1997 11.645 15.917 28.773 18.9913 6.8761 6.9408 19.3154 29.2357 16.1635 22.0929 39.9367 26.4979 9.9886 6.9154 19.377 29.2872 16.1756 11.8434 21.3192 13.8996 6.8543 5.1233 18.3451 27.894 14.8294
Total =
484.6804
CALCULO DE LA CARGA NETA Cn = Peso Total Area Total
Cn = 1795.12 484.6804 Cn = 3.7037
CALCULO DE CARGA EN CADA COLUMNA Columna =
Area x Cn
Tn 19.24 52.03 78.52 43.13 58.95 106.57 70.34 25.47 25.71 71.54 108.28 59.87 81.83 147.91 98.14 36.99 25.61 71.77 108.47 59.91 43.86 78.96 51.48 25.39 18.98 67.95 103.31 54.92
c-2 c-3 c-1 c-3 c-3 c-1 c-3 c-2 c-2 c-3 c-1 c-3 c-3 c-1 c-3 c-2 c-2 c-3 c-1 c-3 c-3 c-1 c-3 c-2 c-2 p-2 c-1 p-1 Total =
1795.12
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2 (Area Tributaria 1) En el Plano Columna Viga x Viga y Losa
y
1.55 m
Peso (Tn) 4.7816 3.4330 0.6624 6.2347
CARGAS PUNTUALES EN X 4.7816
14.5477
x y
CM=
x
Pasadizo
3.4330
1.49 m 1.69 m
15.1117 8.3130
3.38 m
3.38 m CV= Ps=
8.3130 CM+CV =
23.4247 CARGAS PUNTUALES EN Y
CM CV
Veces 1 4 4 4
EJE X Columna Losa Viga Pasadizo
Largo (m)
Veces 1 4 4 4
EJE Y Columna Losa Viga Pasadizo
Largo (m)
Alto (m) 15.85
2.98
Area (m²) 0.1257 5.1956 0.12 5.1956
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4
Peso (Tn) 4.7816 6.2347 3.4330 8.3130
C.g 0 1.49 1.69 1.49
Area (m²) 0.1257 5.1956 0.06 5.1956
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4
Peso (Tn) 4.7816 6.2347 0.6624 8.3130
C.g 0 0.575 0.775 0.575
4.7816
14.5477
0.6624
y 0.575 m
CM CV
My= ∑ Wx * X1
Ҽx= My P
Mx= ∑ Wy * Y1
1.15
Alto (m) 15.85
My= (4.78*0.0) + (6.23*1.49) + (3.43*1.69) +(8.31*1.49) My= 27.4777 Ҽx= 27.4777 23.4247 Ҽx= 1.1730
Mx= (4.78*0.0) + (6.23*0.58) + (0.66*0.78) +(8.31*.575) Mx= 8.8783
0.75 m 1.55 m
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y
1.1730 0.3790
Ҽy= Mx P
Ҽy= 8.8783 23.4247
X
Ҽy= 0.3790
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 2) y
En el Plano Columna Viga x Viga y Losa Muro x Muro y
3.99m
x
Peso 10.6512 5.7456 3.4733 16.8572 4.6524 12.1219
CARGAS PUNTUALES EN X
Sala Com. Adm. Enf. Pasadizo Aula
53.5017
CV=
10.6512 2.3232 2.3232 7.6032 4.6464
0.3240
x 0.67 m 1.425 m 1.775 m
1.35 m CM=
16.8960
3.55 m Ps=
CM
CV
CM
CV
Veces 1 4 4 3 1 2 1 1 4
EJE X Largo (m) Columna Losa Viga 2.85 Muro 2.85 Muro 0.64 Aula Sala de Computo Adm. Enf. Pasadizo
Alto (m) 15.85
Veces 1 4 4 4 4 4 2 1 1 4
EJE Y Largo (m) Columna Losa Losa Viga 1.15 Viga 2.44 Muro 2.44 Aula Sala de Computo Adm. Enf. Pasadizo
Alto (m) 15.85
Area (m²) 0.28 14.0477 0.21
2.25 2.25 9.2928 9.2928 9.2928 4.752 Area (m²) 0.28 9.2928 4.752 0.06 0.12
3.45 9.2928 9.2928 9.2928 4.752
CM+CV =
70.3977
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.225 0.225 0.25 0.25 0.25 0.4
Peso (Tn) 10.6512 16.8572 5.7456 4.3284 0.3240 4.6464 2.3232 2.3232 7.6032
C.g 0 1.425 1.775 1.775 0.67 1.425 1.425 1.425 1.425
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.36 0.25 0.25 0.25 0.4
Peso (Tn) 10.6512 11.1514 5.7024 0.6624 2.8109 12.1219 4.6464 2.3232 2.3232 7.6032
C.g 0 1.32 -0.675 -0.775 1.42 1.42 1.32 1.32 1.32 -0.675
33.7532 10.0740
3.55 m
CARGAS PUNTUALES EN Y 13.3056
0.6624
10.6512
20.4442 14.9328
y - 0.675 m
1.32 m
- 0.775 m
1.42 m 3.99m
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y
0.9403 My= ∑ Wx * X1
Mx= ∑ Wy * Y1 0.5497 My= 66.1969
Mx= 38.6962
X
Ҽx= My P
Ҽx= 66.1969 70.3977 Ҽx= 0.9403
Ҽy= Mx P
Ҽy= 38.6962 70.3977 Ҽy= 0.5497
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-1 (Area Tributaria 3) En el Plano Columna Viga x Viga y Losa Muro y
5.48 2.74
CM= 3.85
CV
CM
CV
EJE X Largo (m) Columna Losa Viga 3.35 Aula Sala de Computo Adm. Enf.
Alto (m) 15.85
Veces EJE Y Largo (m) Columna 1 Losa 4 Losa 4 Viga 2.44 4 Viga 2.44 4 Muro 2.44 4 Muro 2.44 4 2 Aula 1 Sala de Computo 1 Adm. Enf.
Alto (m) 15.85
My= ∑ Wx * X1 Ҽx= My P
Mx= ∑ Wy * Y1
Sala Com. Adm. Enf. Aula
5.2999 5.2999 10.5999
71.1884
CV=
21.1997
CM+CV =
Area (m²) 0.24 21.1997 0.21 21.1997 21.1997 21.1997
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.25 0.25 0.25
Peso (Tn) 9.1296 25.4396 6.7536 10.5999 5.2999 5.2999
Area (m²) 0.24 10.5985 10.5985 0.12 0.12
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.36 0.36 0.25 0.25 0.25
Peso (Tn) 9.1296 12.7182 12.7182 2.8109 2.8109 12.1219 12.1219 10.5999 5.2999 5.2999
3.45 3.45 21.1997 21.1997 21.1997
CARGAS PUNTUALES EN X 25.4396
46.6393
6.7536
x 1.725 m 1.925 m
92.3881
3.85
C.g 0 1.725 1.925 1.725 1.725 1.725
C.g
CARGAS PUNTUALES EN Y 14.9328 12.7182
14.9328 12.7182
y
0 1.37 -1.37 1.52 -1.52 1.52 -1.52
0 0 0
9.1296
- 1.37 m
1.37 m
- 1.52 m
1.52 m 5.48
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y
My= 93.4535 Ҽx= 93.4535 92.3881 Ҽx= 1.0115
Mx= 0.0000
Ҽx= 1.0115 Ҽy= 0.0000
CM
Veces 1 4 4 2 1 1
Ps=
Peso 9.1296 6.7536 5.6218 25.4396 24.2438
X
Ҽy= Ҽy= Mx P
Ҽy= 0.0000 92.3881 Ҽy= 0.0000
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 4) En el Plano Columna Viga x Viga y Losa Muro y
2.84
CM= 4.3
CM
CV
Ps=
Veces 1 4 4 2 1 1
EJE X Largo (m) Columna Losa Viga 3.6 Aula Sala de Computo Adm. Enf.
Alto (m) 15.85
Veces 1 4 4 4 2 1 1
EJE Y Largo (m) Columna Losa Viga 2.44 Muro 2.44 Aula Sala de Computo Adm. Enf.
Alto (m) 15.85
Peso 10.6512 7.2576 2.8109 13.9740 12.1219
Sala Com. Adm. Enf. Aula
2.9113 2.9113 5.8225
46.8156
CV=
11.6450
CM+CV =
CARGAS PUNTUALES EN X 10.6512
25.6190
x 1.8 m 2.15 m
58.4606
Area (m²) 0.28 11.645 0.21 11.645 11.645 11.645
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.25 0.25 0.25
Peso (Tn) 10.6512 13.9740 7.2576 5.8225 2.9113 2.9113
C.g 0 1.8 2.15 1.8 1.8 1.8
Area (m²) 0.28 11.645 0.12
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.36 0.25 0.25 0.25
Peso (Tn) 10.6512 13.9740 2.8109 12.1219 5.8225 2.9113 2.9113
C.g 0 -1.22 -1.42 -1.42 -1.22 -1.22 -1.22
7.2576
4.3
CARGAS PUNTUALES EN Y 14.9328 25.6190
10.6512
y
CM
CV
3.45 11.645 11.645 11.645
- 1.22 m - 1.42 m 2.84
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD My= ∑ Wx * X1 Ҽx= My P
My= 61.7180
Y
Ҽx= 61.7180 58.4606 Ҽx= 1.0557
X -0.8974 1.0557
Mx= ∑ Wy * Y1 Ҽy= Mx
Mx= -52.4598 Ҽy= -52.4598
P
58.4606 Ҽy= -0.8974
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 5) En el Plano Columna Viga x Viga y Losa Muro y
2.84
Peso 10.6512 10.3824 2.8109 19.1004 2.6366
CARGAS PUNTUALES EN X Sala Com. Adm. Enf. Aula Pasadizo
2.8045 2.8045 5.6090 6.4752
45.5814
CV=
17.6932
2.8045
7.2576
21.8751
10.6512
12.9504
3.1248
x CM= 3.95
CM
CV
CM
CV
Veces 1 4 4 4 4 2 1 1 3 Veces 1 4 4 3 2 1 1 3
1.9 5.85 EJE X Largo (m) Columna Losa Losa Viga 3.6 Viga 1.55 Aula Sala de Computo Adm. Enf. Pasadizo EJE Y Largo (m) Columna Losa Viga 2.44 Muro 1.24 Aula Sala de Computo Adm. Enf. Pasadizo
My= ∑ Wx * X1 Ҽx= My P
Ps= Alto (m) 15.85
Alto (m) 15.85
Area (m²) 0.28 11.218 5.396 0.21 0.21 11.218 11.218 11.218 5.396 Area (m²) 0.28 15.917 0.12
3.15 11.218 11.218 11.218 5.396
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.25 0.25 0.4 ϪP.e (Tn/m³) 2.4 0.3 2.4 0.225 0.25 0.25 0.25 0.4
CM+CV = Peso (Tn) 10.6512 13.4616 6.4752 7.2576 3.1248 5.6090 2.8045 2.8045 6.4752 Peso (Tn) 10.6512 19.1004 2.8109 2.6366 5.6090 2.8045 2.8045 6.4752
- 1.025 m - 1.975 m - 2.15 m
63.2746 C.g 0 -1.975 0.95 -2.15 1.125 -1.975 -1.975 -1.025 0.95 C.g 0 -1.22 -1.42 -2.02 -1.22 -1.22 -1.22 -1.22
5.85
CARGAS PUNTUALES EN Y 2.6366
2.8109 36.7936
10.6512
y - 1.22 m - 1.42 m - 2.02 m 2.84
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD
My= -45.8635 Ҽx= -45.8635 63.2746 Ҽx= -0.7248
0.95 m 1.125 m
Y
X -0.8567 -0.7248
Mx= ∑ Wy * Y1
Mx= -54.2055
Ҽy= Mx P
Ҽy= -54.2055 63.2746 Ҽy= -0.8567
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-1 (Area Tributaria 6) En el Plano Columna Viga x Viga y Losa Muro y
5.48 2.74 3.6
0.4
Peso 9.1296 9.8784 2.3424 34.5276 13.8348
CARGAS PUNTUALES EN X Sala Com. Adm. Enf. Aula Pasadizo
5.2060 5.2060 10.4120 13.1520
69.7128
CV=
33.9760
7.2576
CM
CV
CM
CV
Veces 1 4 4 4 4 2 1 1 4
EJE X Largo (m) Columna Losa Losa Viga 3.6 Viga 1.3 Aula Sala de Computo Adm. Enf. Pasadizo
Alto (m) 15.85
Veces 1 4 4 4 4 4 2 1 1 4
EJE Y Largo (m) Columna Losa Viga 2.44 Viga 2.44 Muro 2.44 Muro 2.44 Aula Sala de Computo Adm. Enf. Pasadizo
Alto (m) 15.85
CM+CV =
103.6888
Area (m²) 0.24 20.824 8.22 0.21 0.21 20.824 20.824 20.824 8.22
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.25 0.25 0.4
Peso (Tn) 9.1296 24.9888 9.8640 7.2576 2.6208 10.4120 5.2060 5.2060 13.1520
C.g 0 -1.9 0.75 -2 0.85 -1.9 -1.9 -1.9 0.75
Area (m²) 0.24 28.773 0.12 0.12
ϪP.e (Tn/m³) 2.4 0.3
Peso (Tn) 9.1296 34.5276 1.1712 1.1712 6.9174 6.9174 10.4120 5.2060 5.2060 13.1520
C.g 0 0 -1.52 1.52 -1.52 1.52 0 0 0 0
3.15 3.15 20.824 20.824 20.824 8.22
0.225 0.225 0.25 0.25 0.25 0.4
23.0160
- 1.90 m - 2.00 m
5.3 Ps=
9.1296
2.6208
x
1.3 CM=
45.8128
0.75 m 0.85 m
5.3
CARGAS PUNTUALES EN Y 8.0886
9.1296
8.0886
y 1.52 m - 1.52 m 5.48
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y
My= ∑ Wx * X1
Mx= ∑ Wy * Y1 X My= -82.0698
Ҽx= My P
Ҽx= -82.0698 103.6888 Ҽx= -0.7915
-0.7915
Mx= 0.0000 Ҽy= Mx P
Ҽy= 0.0000 103.6888 Ҽy= 0.0000
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 7) En el Plano Columna Viga x Viga y Losa Muro y
2.84
Peso 10.6512 10.3824 2.8109 0.0000 2.6366
CARGAS PUNTUALES EN X Sala Com. Adm. Enf. Aula Pasadizo
2.8045 2.8045 5.6090 6.4752
26.4810
CV=
17.6932
2.8045
7.2576
21.8751
10.6512
12.9504
3.1248
x CM= 3.95
CM
CV
CM
CV
Veces 1 4 4 4 4 2 1 1 3 Veces 1 4 4 3 2 1 1 3
1.9 5.85 EJE X Largo (m) Columna Losa Losa Viga 3.6 Viga 1.55 Aula Sala de Computo Adm. Enf. Pasadizo EJE Y Largo (m) Columna Losa Viga 2.44 Muro 1.24 Aula Sala de Computo Adm. Enf. Pasadizo
My= ∑ Wx * X1 Ҽx= My P
Ps= Alto (m) 15.85
Alto (m) 15.85
Area (m²) 0.28 11.218 5.396 0.21 0.21 11.218 11.218 11.218 5.396 Area (m²) 0.28 0 0.12
3.15 11.218 11.218 11.218 5.396
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.25 0.25 0.4 ϪP.e (Tn/m³) 2.4 0.3 2.4 0.225 0.25 0.25 0.25 0.4
CM+CV = Peso (Tn) 10.6512 13.4616 6.4752 7.2576 3.1248 5.6090 2.8045 2.8045 6.4752 Peso (Tn) 10.6512 0.0000 2.8109 2.6366 5.6090 2.8045 2.8045 6.4752
- 1.025 m - 1.975 m - 2.15 m
44.1742 C.g 0 1.975 0.95 -2.15 1.125 -1.975 1.975 -1.025 0.95 C.g 0 -1.22 -1.42 -2.02 -1.22 -1.22 -1.22 -1.22
0.95 m 1.125 m
5.85
CARGAS PUNTUALES EN Y 2.6366
2.8109 17.6932
10.6512
y - 1.22 m - 1.42 m - 2.02 m 2.84
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD
My= 40.5432
Y
Ҽx= 40.5432 44.1742 Ҽx= 0.9178
0.9178 -0.6996
X
Mx= ∑ Wy * Y1 Ҽy= Mx P
Mx= -30.9030 Ҽy= -30.9030 44.1742 Ҽy= -0.6996
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2 (Area Tributaria 8) En el Plano Columna Viga x Viga y Losa
1.55
Peso 4.7816 4.6541 0.6624 8.2513
CARGAS PUNTUALES EN X
Pasadizo
11.0018
18.3494
CV=
11.0018
3.4445
13.8446
4.7816
5.4250
1.2096
x CM= 3.19
1.25
Ps=
CM+CV =
- 1.595 m - 1.695 m
29.3512
0.625 m 0.725 m
4.44 4.44
CM
CV
Veces 1 4 4 4 4 4 4
EJE X Columna Losa Losa Viga Viga Pasadizo Pasadizo
Largo (m)
Alto (m) 15.85
2.99 1.05
Area (m²) 0.1257 4.9445 1.9375 0.12 0.12 4.9445 1.9375
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.4 0.4
Peso (Tn) 4.7816 5.9334 2.3250 3.4445 1.2096 7.9112 3.1000
C.g 0 -1.595 0.625 -1.695 0.725 -1.595 0.625
CARGAS PUNTUALES EN Y 4.7816
19.2531
0.6624
y 0.575 m 0.775 m
CM CV
Veces 1 4 4 4
EJE Y Columna Losa Viga Pasadizo
Largo (m)
My= ∑ Wx * X1 Ҽx= My P
Mx= ∑ Wy * Y1
1.15
Alto (m) 15.85
Area (m²) 0.1257 6.8761 0.06 6.8761
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4
My= -23.6529
Peso (Tn) 4.7816 8.2513 0.6624 11.0018
C.g 0 0.575 0.775 0.575
1.55
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD
Ҽx= -23.6529 29.3512 Ҽx= -0.8059
Y
Mx= 11.5839 -0.8059
Ҽy= Mx
Ҽy= 11.5839
P
29.3512 Ҽy= 0.3947
0.3947
X
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2 (Area Tributaria 9) En el Plano Columna Viga x Viga y Losa
1.55
Peso 4.7816 4.7462 0.6624 8.3290
CARGAS PUNTUALES EN X
Pasadizo
11.1053
18.5192
CV=
11.1053
1.2211
5.4684
4.7816
14.1484
3.5251
x CM= 1.26
3.26
Ps=
CM+CV =
- 0.63 m - 0.73 m
29.6245
1.63 m 1.73 m
4.52 4.52
CM
CV
Veces 1 4 4 4 4 4 4
EJE X Columna Losa Losa Viga Viga Pasadizo Pasadizo
Largo (m)
Alto (m) 15.85
1.06 3.06
Area (m²) 0.1257 1.9530 5.053 0.12 0.12 1.953 5.053
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.4 0.4
Peso (Tn) 4.7816 2.3436 6.0636 1.2211 3.5251 3.1248 8.0848
C.g 0 -0.63 1.63 -0.73 1.73 -0.63 1.63
CARGAS PUNTUALES EN Y 4.7816
19.4342
0.6624
y 0.575 m 0.775 m
CM CV
Veces 1 4 4 4
EJE Y Largo (m) W Columna W Losa W Viga 1.15 Pasadizo
My= ∑ Wx * X1 Ҽx= My P
Mx= ∑ Wy * Y1
Alto (m) 15.85
Area (m²) 0.1257 6.9408 0.06 6.9408
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4
My= 24.8238 Ҽx= 24.8238 29.6245 Ҽx= 0.8379
Peso (Tn) 4.7816 8.3290 0.6624 11.1053
C.g 0 0.575 0.775 0.575
1.55
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y
Mx= 11.6880 0.8379
Ҽy= Mx
Ҽy= 11.6880
P
29.6245 Ҽy= 0.3945
0.3945
X
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-1 (Area Tributaria 11) En el Plano Columna Viga x Viga y Losa Muro y
5.48 2.74 1.3
0.4
Peso 9.1296 9.9792 2.3424 35.0828 13.8348
Aula Lab.Enf. Adm. Enf. Deopsito Pasadizo
10.5490 6.3294 2.0550 5.2745 9.8640
CARGAS PUNTUALES EN X
70.3688
CV=
34.0719
2.6208
- 0.75 m - 0.85 m
5.35 Ps=
CM
CV
Veces 1 4 4 4 4 2 1 1 1 3
EJE X Columna Losa Losa Viga Viga Aula Lab.Enf. Adm. Enf. Deopsito Pasadizo
Largo (m)
Veces 1 4 4 4 4 4 2 1 1
EJE Y Columna Losa Viga Viga Muro Muro Aula Lab.Enf. Adm. Enf.
Largo (m)
Alto (m) 15.85
1.3 3.65
CM+CV =
104.4407
Area (m²) 0.24 8.22 21.098 0.21 0.21 21.098 21.098 8.22 21.098 8.22
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.3 0.25 0.25 0.4
Peso (Tn) 9.1296 9.8640 25.3176 2.6208 7.3584 10.5490 6.3294 2.0550 5.2745 9.8640
C.g 0 -0.75 1.925 -0.85 2.025 1.925 1.925 -0.75 1.925 -0.75
Area (m²) 0.24 29.2357 0.12 0.12
ϪP.e (Tn/m³) 2.4 0.3
Peso (Tn) 9.1296 35.0828 1.1712 1.1712 6.9174 6.9174 10.5490 6.3294 2.0550
C.g 0 0 -1.52 1.52 -1.52 1.52 0 0 0
9.1296
47.4705
7.3584
x
3.65 CM=
21.7830
1.925 m 2.025 m 5.35
CARGAS PUNTUALES EN Y 8.0886
9.1296
8.0886
y 1.52 m - 1.52 m 5.48
CM
CV
2.44 2.44 2.44 2.44
Alto (m) 15.85
3.15 3.15 21.098 21.098 8.22
0.225 0.225 0.25 0.3 0.25
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y
CV 1 3
Deopsito Pasadizo
21.098 8.22
0.25 0.4
5.2745 9.8640
0 0
X 0.8399
My= ∑ Wx * X1
Mx= ∑ Wy * Y1 My= 87.7165
Ҽx= My P
Ҽx= 87.7165 104.4407 Ҽx= 0.8399
Mx= 0.0000 Ҽy= Mx P
Ҽy= 0.0000 104.4407 Ҽy= 0.0000
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 12) En el Plano Columna Viga x Viga y Losa Muro y
2.84
1.9
4.03
CM=
5.93
CM
CV
CM
CV
Ps=
Veces 1 4 4 4 4 2 1 1 1 3
EJE X Columna Losa Losa Viga Viga Aula Lab. Enfer. Adm. Enf. Deposito Pasadizo
Largo (m)
Veces 1 4 4 1 3 2 1 1 1 3
EJE Y Columna Losa Viga Muro Muro Aula Lab. Enfer. Adm. Enf. Deposito Pasadizo
Largo (m)
Alto (m) 15.85
1.55 3.68
2.44 2.44 1.24
Alto (m) 15.85
Peso 10.6512 10.5437 2.8109 19.3962 4.3659
Lab. Enf. Adm. Enf. Deposito Pasadizo
5.7226 3.4336 1.3490 2.8613 6.4752
47.7679
CV=
19.8417
CM+CV =
CARGAS PUNTUALES EN X Aula
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.3 0.25 0.25 0.4
Peso (Tn) 10.6512 6.4752 13.7342 3.1248 7.4189 5.7226 3.4336 1.3490 2.8613 6.4752
C.g 0 -0.95 2.015 -1.125 2.19 2.015 2.015 -0.95 2.015 -0.95
Area (m²) 0.28 16.1635 0.12
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.225 0.225 0.25 0.3 0.25 0.25 0.4
Peso (Tn) 10.6512 19.3962 2.8109 1.7294 2.6366 5.7226 3.4336 1.3490 2.8613 6.4752
C.g 0 -1.22 -1.42 -1.42 -2.02 -1.22 -1.22 -1.22 -1.22 -1.22
11.4452 11.4452 5.396 11.4452 5.396
14.2994
10.6512
25.7517
7.4189
x - 0.95 m -1.125 m
67.6095
Area (m²) 0.28 5.396 11.4452 0.21 0.21 11.4452 11.4452 5.396 11.4452 5.396
3.15 3.15
3.1248
2.015 m 2.19 m 5.93
CARGAS PUNTUALES EN Y 2.6366
4.5402 39.2379
10.6512
y - 1.22 m - 1.42 m - 2.02 m 2.84
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y
X My= ∑ Wx * X1
Mx= ∑ Wy * Y1 My= 51.0372
-0.8822 Mx= -59.6431
0.7549
Ҽx= My P
Ҽx= 51.0372 67.6095 Ҽx= 0.7549
Ҽy= Mx P
Ҽy= -59.6431 67.6095 Ҽy= -0.8822
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 13) En el Plano Columna Viga x Viga y Losa Muro y
2.84
4.03
4.03
CM=
8.06
CM
CV
CM
CV
Ps=
Veces 1 4 4 4 4 2 1 1 1
EJE X Columna Losa Losa Viga Viga Aula Lab. Enfer. Lab. Niño Proscenio
Largo (m)
Veces 1 4 4 3 2 1 1 1
EJE Y Columna Losa Viga Muro Aula Lab. Enfer. Adm. Enf. Proscenio
Largo (m)
My= ∑ Wx * X1
Alto (m) 15.85
3.68 3.68
2.44 2.44
Alto (m) 15.85
Peso 10.6512 14.8378 2.8109 26.5115 8.3009
Aula Lab. Enfer. Lab. Niño Proscenio
11.0465 3.4336 3.4336 6.6279
63.1122
CV=
24.5414
CM+CV =
CARGAS PUNTUALES EN X
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.3 0.3 0.3
Peso (Tn) 10.6512 13.7342 13.7342 7.4189 7.4189 11.0465 3.4336 3.4336 6.6279
C.g 0 -2.015 2.015 -2.19 2.19 0 -2.015 2.015 0
Area (m²) 0.28 22.0929 0.12
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.36 0.25 0.3 0.3 0.3
Peso (Tn) 10.6512 26.5115 2.8109 8.3009 5.7226 3.4336 3.4336 3.4336
C.g 0 -1.22 -1.42 -1.42 -1.22 -1.22 -1.22 -1.22
11.4452 11.4452 11.4452 11.4452
Mx= ∑ Wy * Y1
17.1678
10.6512
17.1678
7.4189
x - 2.015 m -2.19 m
87.6536
Area (m²) 0.28 11.4452 11.4452 0.21 0.21 22.0929 11.4452 11.4452 22.0929
3.15
7.4189
2.015 m 2.19 m 8.06
CARGAS PUNTUALES EN Y 11.1118 42.5348
10.6512
y - 1.22 m - 1.42 m 2.84
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y
X
-0.7720
My= 0.0000 Ҽx= My P
Mx= -67.6711 Ҽx= 0.0000 87.6536 Ҽx= 0.0000
Ҽy= Mx P
Ҽy= -67.6711 87.6536 Ҽy= -0.7720
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-1 (Area Tributaria 14) En el Plano Columna Viga x Viga y Losa Muro y
5.48 2.74
3.65
3.65
CM=
7.3
CM
CV
CM
Ps=
Veces 1 4 4 3 3 2 1 1 1
EJE X Columna Losa Losa Viga Viga Aula Lab. Enfer. Lab. Niño Proscenio
Largo (m)
Veces 1 4 4 4 3 3
EJE Y Columna Losa Viga Viga Muro Muro
Largo (m)
Alto (m) 11.7
3.65 3.65
2.44 2.44 2.44 2.44
Alto (m) 11.7
3.15 3.15
Peso 6.7392 11.0376 5.6218 47.9240 16.6018
Aula Lab. Enfer. Lab. Niño Proscenio
19.9684 6.0006 6.0006 11.9810
87.9244
CV=
43.9506
CM+CV =
CARGAS PUNTUALES EN X 5.5188
30.0030
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.3 0.3 0.3
Peso (Tn) 6.7392 24.0024 24.0024 5.5188 5.5188 19.9684 6.0006 6.0006 11.9810
C.g 0 -1.825 1.825 -1.925 1.925 0 -1.825 1.825 0
Area (m²) 0.24 39.9367 0.12 0.12
ϪP.e (Tn/m³) 2.4 0.3 2.4 2.4 0.36 0.36
Peso (Tn) 6.7392 47.9240 2.8109 2.8109 8.3009 8.3009
C.g 0 0 -1.52 1.52 1.52 -1.52
30.0030
5.5188
x - 1.825 m - 1.925 m
131.8749
Area (m²) 0.24 20.0020 20.0020 0.21 0.21 39.9367 20.0020 20.0020 39.9367
6.7392
1.825 m 1.925 m 7.3
CARGAS PUNTUALES EN Y 11.1118
6.7392
11.1118
y 1.52 m
- 1.52 m 5.48
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD
2 1 1 1
CV
Aula Lab. Enfer. Adm. Enf. Proscenio
20.0020 20.0020 20.0020 20.0020
0.25 0.3 0.3 0.3
10.0010 6.0006 6.0006 6.0006
0 0 0 0
Y
X My= ∑ Wx * X1
Mx= ∑ Wy * Y1 My= 0.0000
Ҽx= My P
Mx= 0.0000 Ҽx= 0.0000 131.8749 Ҽx= 0.0000
Ҽy= Mx P
Ҽy= 0.0000 131.8749 Ҽy= 0.0000
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2 (Area Tributaria 16) En el Plano Columna Viga x Viga y Losa
1.55
Peso 4.7816 6.9350 0.6624 11.9863
CARGAS PUNTUALES EN X
Pasadizo
15.9818
24.3654
CV=
15.9818
3.4906
14.0182
4.7816
13.8446
x CM= 3.23
3.19
Ps=
CM+CV =
- 1.615 m - 1.715 m
40.3471
1.595 m 1.695 m
6.42 6.42
CM
CV
Veces 1 4 4 4 4 4 4
EJE X Columna Losa Losa Viga Viga Pasadizo Pasadizo
Largo (m)
Alto (m) 15.85
3.03 2.99
Area (m²) 0.1257 5.0065 4.9445 0.12 0.12 5.0065 4.9445
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.4 0.4
Peso (Tn) 4.7816 6.0078 5.9334 3.4906 3.4445 8.0104 7.9112
C.g 0 -1.615 1.595 -1.715 1.695 -1.615 1.595
CARGAS PUNTUALES EN Y 4.7816
27.9681
0.6624
y 0.575 m 0.775 m
Veces EJE Y Largo (m) 1 W Columna CM
Alto (m) 15.85
Area (m²) 0.1257
ϪP.e (Tn/m³) 2.4
Peso (Tn) 4.7816
C.g 0
1.55
3.4445
CM CV
4 4 4
W Losa W Viga Pasadizo
9.9886 0.06 9.9886
1.15
My= ∑ Wx * X1
0.3 2.4 0.4
11.9863 0.6624 15.9818
0.575 0.775 0.575
My= -0.7052
Ҽx= My P
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD
Ҽx= -0.7052 40.3471 Ҽx= -0.0175
Mx= ∑ Wy * Y1
Y
Mx= 16.5950 -0.0175
Ҽy= Mx P
Ҽy= 16.5950 40.3471 Ҽy= 0.4113
0.4113
X
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2 (Area Tributaria 17) En el Plano Columna Viga x Viga y Losa
1.55
Peso 4.7816 4.7002 0.6624 8.2985
CARGAS PUNTUALES EN X
Pasadizo
11.0646
18.4427
CV=
11.0646
3.4560
13.8880
4.7816
5.5552
x CM= 3.2
1.28
Ps=
CM+CV =
- 1.6 m - 1.7 m
29.5073
0.64 m 0.74 m
4.48 4.48
CM
CV
Veces 1 4 4 4 4 4
EJE X Columna Losa Losa Viga Viga Pasadizo
Largo (m)
3 1.08
Alto (m) 15.85
Area (m²) 0.1257 4.96 1.984 0.12 0.12 4.96
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.4
Peso (Tn) 4.7816 5.9520 2.3808 3.4560 1.2442 7.9360
C.g 0 -1.6 0.64 -1.7 0.74 -1.6
CARGAS PUNTUALES EN Y 4.7816
y
19.3631
0.6624
1.2442
CV
4
Pasadizo
1.984
0.4
3.1744
0.64
0.575 m 0.775 m
CM CV
Veces 1 4 4 4
EJE Y Columna Losa Viga Pasadizo
Largo (m)
My= ∑ Wx * X1 Ҽx= My P
Mx= ∑ Wy * Y1
1.15
Alto (m) 15.85
Area (m²) 0.1257 6.9154 0.06 6.9154
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4
My= -23.6200
Peso (Tn) 4.7816 8.2985 0.6624 11.0646
C.g 0 0.575 0.775 0.575
1.55
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD
Ҽx= -23.6200 29.5073 Ҽx= -0.8005
Y
Mx= 11.6472 -0.8005
Ҽy= Mx P
Ҽy= 11.6472 29.5073 Ҽy= 0.3947
0.3947
X
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 19) En el Plano Columna Viga x Viga y Losa Muro x Muro y
5.48 2.74 3.6
0.4
1.3
5.3
CM=
Peso 9.1296 7.4088 2.3424 35.1446 0.6581 10.3761
Aula Lab. Niño Pasadizo Deposito Sala Conf. Pasadizo
10.4120 6.2472 1.6440 1.2330 8.7862 6.5760
65.0597
CV=
34.8984
Ҽx= My P Ҽx= -77.1803 99.9580 Ҽx= -0.7721 CARGAS PUNTUALES EN X
5.4432 Ps=
CM
CV
CM
CV
Veces 1 4 4 3 3 1 2 1 1 1 1 2
EJE X Columna Losa Losa Viga Viga Muro Aula Lab. Niño Pasadizo Deposito Sala Conf. Pasadizo
Largo (m)
Veces 1 4 4 4 3 3 2 1 1 1 1 2
EJE Y Columna Losa Viga Viga Muro Muro Aula Lab. Niño Pasadizo Deposito Sala Conf. Pasadizo
Largo (m)
3.6 1.3 1.3
Alto (m) 15.85
Area (m²) 0.24 20.824 8.22 0.21 0.21
2.25 20.824 20.824 4.11 4.11 29.2872 8.22
2.44 2.44 2.44 2.44
Alto (m) 15.85
Area (m²) 0.24 29.2872 0.12 0.12
3.15 3.15 20.824 20.824 4.11 4.11 29.2872 8.22
CM+CV =
41.6480
8.7862 9.1296
19.3170
2.6237
99.9580
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.225 0.25 0.3 0.4 0.3 0.3 0.4
Peso (Tn) 9.1296 24.9888 9.8640 5.4432 1.9656 0.6581 10.4120 6.2472 1.6440 1.2330 8.7862 6.5760
C.g 0 -1.7 0.55 -2 0.85 0.85 -1.7 -1.7 0.55 0.55 -0.95 0.55
ϪP.e (Tn/m³) 2.4 0.3
Peso (Tn) 9.1296 35.1446 1.1712 1.1712 5.1881 5.1881 10.4120 6.2472 1.6440 1.2330 8.7862 6.5760
C.g 0 0 -1.52 1.52 -1.52 1.52 0 0 -1.37 1.37 0 0
0.225 0.225 0.25 0.3 0.4 0.3 0.3 0.4
Ҽy= Mx P Ҽy= -0.5631 99.9580 Ҽy= -0.0056
-0.95 m
x
- 1.70 m - 2.00 m
0.55 m 0.85 m
5.3 CARGAS PUNTUALES EN Y 1.6440 6.3593
1.2330 6.3593
9.1296
y -1.37 m - 1.52 m
1.37 m 1.52 m
5.48 UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y
-0.7721 -0.0056
X
My= ∑ Wx * X1
Mx= ∑ Wy * Y1
My= -77.1803
Mx= -0.5631
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 20) En el Plano Columna Viga x Viga y Losa Muro y
2.84
Peso 10.6512 10.5638 4.0992 19.4107 2.9201
Aula Deposito Lab. Niño Sala Conf. Pasadizo
5.7368 3.4421 1.6188 4.8527 4.3168
CARGAS PUNTUALES EN X
47.6450
CV=
19.9672
7.4390
22.9472 4.8527
10.6512
12.4108
3.1248
x 4.04
1.9
CM=
5.94
CM
CV
CM
CV
Ps=
Veces 1 4 4 4 4 2 1 1 1 2
EJE X Columna Losa Losa Viga Viga Aula Lab. Niño Deposito Sala Conf. Pasadizo
Largo (m)
Veces 1 4 3 1 2 1 2 1 1 1
EJE Y Columna Losa Viga Viga Muro Muro Aula Lab. Niño Deposito Sala Conf.
Largo (m)
Alto (m) 15.85
3.69 1.55
2.44 2.44 1.24 1.64
Alto (m) 15.85
CM+CV =
67.6122
Area (m²) 0.28 11.4736 5.3960 0.21 0.21 11.4736 11.4736 5.3960 16.1756 5.3960
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.3 0.3 0.3 0.4
Peso (Tn) 10.6512 13.7683 6.4752 7.4390 3.1248 5.7368 3.4421 1.6188 4.8527 4.3168
C.g 0 -2.02 0.95 -2.195 1.125 -2.02 -2.02 0.95 -1.07 0.95
Area (m²) 0.28 16.1756 0.12 0.24
ϪP.e (Tn/m³) 2.4 0.3 2.4 3.4 0.225 0.225 0.25 0.3 0.3 0.3
Peso (Tn) 10.6512 19.4107 2.1082 1.9910 1.7577 1.1624 5.7368 3.4421 1.6188 4.8527
C.g 0 -1.22 -1.42 -1.42 -2.02 -1.82 -1.22 -1.22 -1.22 -1.22
3.15 3.15 11.4736 11.4736 5.3960 16.1756
- 1.07 m - 2.02 m
0.95 m 1.125 m
- 2.195 m 5.94
CARGAS PUNTUALES EN Y
1.7577
1.1624 4.0992 39.3779
10.6512
y - 1.22 m - 1.42 m - 1.82 m - 2.02 m 2.84
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y
CV 2
Pasadizo
5.3960
My= ∑ Wx * X1
0.4
4.3168
-1.22
Mx= ∑ Wy * Y1
X -0.8804
My= -52.5687
Mx= -59.5279 -0.7775
Ҽx= My P
Ҽx= -52.5687 67.6122 Ҽx= -0.7775
Ҽy= Mx P
Ҽy= -59.5279 67.6122 Ҽy= -0.8804
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-3 (Area Tributaria 21) En el Plano Columna Viga x Viga y Losa Muro y
2.84
Peso 10.6512 Aula 7.4390 Lab. Mujer 2.8109 Sala Conf. 14.2121 Deposito 3.4871 Pasadizo
CARGAS PUNTUALES EN X 3.5358 2.1215 3.5530 1.6188 4.3168
3.1248
12.4108
10.6512
3.553 14.1432
4.3142
x 1.9
2.49
CM=
4.39
CM
CV
CM
Ps=
Veces 1 4 4 4 4 2 1 1 1 2
EJE X Largo (m) Columna Losa Losa Viga 1.55 Viga 2.14 Aula Lab. Mujer Sala Conf. Deposito Pasadizo
Alto (m) 15.85
Veces 1 4 4 1 2
EJE Y Columna Losa Viga Muro Muro
Alto (m) 15.85
Largo (m)
2.44 2.44 1.24
3.15 3.15
38.6003 CM+CV =
CV=
15.1459
- 0.95 m -1.125 m
53.7462
Area (m²) 0.28 5.396 7.0716 0.21 0.21 7.0716 7.0716 11.843 5.396 5.396
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.3 0.3 0.3 0.4
Peso (Tn) 10.6512 6.4752 8.4859 3.1248 4.3142 3.5358 2.1215 3.5530 1.6188 4.3168
C.g 0 -0.95 1.245 -1.125 1.42 1.245 1.245 0.295 -0.95 -0.95
Area (m²) 0.28 11.8434 0.12
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.225 0.225
Peso (Tn) 10.6512 14.2121 2.8109 1.7294 1.7577
C.g 0 -1.22 -1.42 -1.42 -2.02
0.295 m 1.245 m 1.42 m 4.39
CARGAS PUNTUALES EN Y 1.7577
4.5402 27.9264
10.6512
y - 1.22 m - 1.42 m - 2.02 m 2.84
2 1 1 1 2
CV
Aula Lab. Mujer Sala Conf. Deposito Pasadizo
7.0716 7.0716 5.396 7.0716 5.396
0.25 0.3 0.3 0.3 0.4
3.5358 2.1215 1.6188 2.1215 4.3168
-1.22 -1.22 -1.22 -1.22 -1.22
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y
X My= ∑ Wx * X1
Mx= ∑ Wy * Y1
-0.8199
My= 9.4770 Ҽx= My P
0.1763
Mx= -44.0679 Ҽx= 9.4770 53.7462 Ҽx= 0.1763
Ҽy= Mx P
Ҽy= -44.0679 53.7462 Ҽy= -0.8199
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-1 (Area Tributaria 22) En el Plano Columna Viga x Viga y Losa Muro y
5.48 2.74 1.32
0.4
Peso 9.1296 7.1366 2.3424 25.5830 13.8348
Aula Lab.Enf. Adm. Enf. Deopsito Pasadizo
6.6308 3.9785 2.0824 3.3154 9.9955
CARGAS PUNTUALES EN X
58.0265
CV=
26.0026
2.6611
CM=
- 0.76 m - 0.86 m
3.94 Ps=
CM
CV
Veces 1 4 4 4 4 2 1 1 1 3
EJE X Columna Losa Losa Viga Viga Aula Lab.Enf. Adm. Enf. Deopsito Pasadizo
Largo (m)
1.32 2.22
Alto (m) 15.85
Area (m²) 0.24 8.3296 13.2616 0.21 0.21 13.2616 13.2616 8.33 13.2616 8.33
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.25 0.3 0.25 0.25 0.4
CM+CV =
Peso (Tn) 9.1296 9.9955 15.9139 2.6611 4.4755 6.6308 3.9785 2.0824 3.3154 9.9955
9.1296
84.0291
C.g 0 -0.76 1.21 -0.86 1.31 1.21 1.21 -0.76 1.21 -0.76
29.8386
x
2.22
.
22.0734
1.21 m 1.31 m 3.94
CARGAS PUNTUALES EN Y 8.0886
9.1296
8.0886
y 1.52 m - 1.52 m 5.48
4.4755
CM
CV
Veces 1 4 4 4 4 4 2 1 1 1 3
EJE Y Columna Losa Viga Viga Muro Muro Aula Lab.Enf. Adm. Enf. Deopsito Pasadizo
Largo (m)
2.44 2.44 2.44 2.44
Alto (m) 15.85
Area (m²) 0.24 21.3192 0.12 0.12
3.15 3.15 13.2616 13.2616 8.3296 13.2616 8.3296
ϪP.e (Tn/m³) 2.4 0.3
0.225 0.225 0.25 0.3 0.25 0.25 0.4
Peso (Tn) 9.1296 25.5830 1.1712 1.1712 6.9174 6.9174 6.6308 3.9785 2.0824 3.3154 9.9955
C.g 0 0 -1.52 1.52 -1.52 1.52 0 0 0 0 0
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y
X 0.2726
My= ∑ Wx * X1
Mx= ∑ Wy * Y1 My= 22.9033
Ҽx= My P
Mx= 0.0000
Ҽx= 22.9033 84.0291 Ҽx= 0.2726
Ҽy= Mx P
Ҽy= 0.0000 84.0291 Ҽy= 0.0000
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2 (Area Tributaria 24) En el Plano Columna Viga x Viga y Losa
1.55
Peso 4.7816 4.6426 0.6624 8.2252
CARGAS PUNTUALES EN X
Pasadizo
10.9669
18.3117
CV=
10.9669
1.2557
5.5986
4.7816
13.6276
x CM= 1.29
3.14
Ps=
CM+CV =
- 0.645 m - 0.745 m
29.2786
1.57 m 1.67 m
4.43 4.43
CM
CV
Veces 1 4 4 4 4 4
EJE X Columna Losa Losa Viga Viga Pasadizo
Largo (m)
1.09 2.94
Alto (m) 15.85
Area (m²) 0.1257 1.9995 4.867 0.12 0.12 1.9995
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.4
Peso (Tn) 4.7816 2.3994 5.8404 1.2557 3.3869 3.1992
C.g 0 -0.645 1.57 -0.745 1.67 -0.645
CARGAS PUNTUALES EN Y 4.7816
y
19.1920
0.6624
3.3869
CV
4
Pasadizo
4.867
0.4
7.7872
1.57
0.575 m 0.775 m
CM CV
Veces 1 4 4 4
EJE Y Largo (m) W Columna W Losa W Viga 1.15 Pasadizo
Alto (m) 15.85
Area (m²) 0.1257 6.8543 0.06 6.8543
My= ∑ Wx * X1
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4
Peso (Tn) 4.7816 8.2252 0.6624 10.9669
C.g 0 0.575 0.775 0.575
1.55
My= 22.5048
Ҽx= My P
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD
Ҽx= 22.5048 29.2786 Ҽx= 0.7686
Mx= ∑ Wy * Y1
Y
Mx= 11.5488 0.7686
Ҽy= Mx P
Ҽy= 11.5488 29.2786 Ҽy= 0.3944
0.3944
X
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2 (Area Tributaria 25) y
1.55 m
En el Plano Columna Viga x Viga y Losa
Peso (Tn) 4.7816 3.3984 0.6624 6.1480
CARGAS PUNTUALES EN X 3.3984
14.3452
x y
CM=
x
Pasadizo
1.475 m 1.675 m
14.9904 8.1973
3.35 m
3.35 m CV= Ps=
8.1973 CM+CV =
23.1877 CARGAS PUNTUALES EN Y
4.7816
CM CV
Veces 1 4 4 4
EJE X Columna Losa Viga Pasadizo
Largo (m)
Veces 1 4 4 4
EJE Y Columna Losa Viga Pasadizo
Largo (m)
Alto (m) 15.85
2.95
Area (m²) 0.1257 5.1233 0.12 5.1233
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4
Peso (Tn) 4.7816 6.1480 3.3984 8.1973
C.g 0 1.475 1.675 1.475
Area (m²) 0.1257 5.1233 0.06 5.1233
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.4
Peso (Tn) 4.7816 6.1480 0.6624 8.1973
C.g 0 0.575 0.775 0.575
4.7816
14.3452
0.6624
y 0.575 m
CM CV
My= ∑ Wx * X1
Alto (m) 15.85
1.15
1.55 m
My= (4.78*0.0) + (6.23*1.49) + (3.43*1.69) +(8.31*1.49) My= 26.8515
Ҽx= My P
Mx= ∑ Wy * Y1
0.75 m
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD
Ҽx= 26.8515 23.1877 Ҽx= 1.1580
Y
Mx= (4.78*0.0) + (6.23*0.58) + (0.66*0.78) +(8.31*.575) Mx= 8.7619
1.1580 0.3779
Ҽy= Mx P
Ҽy= 8.7619 23.1877 Ҽy= 0.3779
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-1 (Area Tributaria 27)
5.48 2.74
En el Plano Columna Viga x Viga y Losa Muro y CM=
Peso 9.1296 5.0652 5.6218 Aula 33.4728 Lab. Mujer 24.2438 Sala Conf.
13.9470 6.9735 6.9735
77.5332
27.8940
CV=
CARGAS PUNTUALES EN X 33.4728
61.3668
x -2.35 m -2.55 m
5.0652
X
5.1
CV
CM
CV
EJE X Largo (m) Columna Losa Viga 3.35 Aula Lab. Mujer Sala Conf.
Alto (m) 15.85
Veces EJE Y Largo (m) Columna 1 Losa 4 Losa 4 Viga 2.44 4 Viga 2.44 4 Muro 2.44 4 Muro 2.44 4 2 Aula 1 Lab. Mujer 1 Sala Conf.
Alto (m) 15.85
My= ∑ Wx * X1 Ҽx= My P
Mx= ∑ Wy * Y1 Ҽy= Mx P
CM+CV =
Area (m²) 0.24 27.894 0.21 27.894 27.894 27.894
ϪP.e (Tn/m³) 2.4 0.3 2.4 0.25 0.25 0.25
Peso (Tn) 9.1296 33.4728 5.0652 13.9470 6.9735 6.9735
Area (m²) 0.24 13.9740 13.9740 0.12 0.12
ϪP.e (Tn/m³) 2.4 0.3 0.3 2.4 2.4 0.36 0.36 0.25 0.25 0.25
Peso (Tn) 9.1296 16.7688 16.7688 2.8109 2.8109 12.1219 12.1219 13.9470 6.9735 6.9735
3.45 3.45 27.894 27.894 27.894
105.4272
5.1
C.g 0 -2.35 -2.55 -2.35 -2.35 -2.35
C.g
CARGAS PUNTUALES EN Y 14.9328 16.7688
14.9328 16.7688
y
0 1.37 -1.37 1.52 -1.52 1.52 -1.52
0 0 0
9.1296
- 1.37 m
1.37 m
- 1.52 m
1.52 m 5.48
UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD Y
My= -157.1282 Ҽx= -157.1282 105.4272 Ҽx= -1.4904
Mx= 0.0000 Ҽy= 0.0000 105.4272 Ҽy= 0.0000
Ҽx= -1.4904 Ҽy= 0.0000
CM
Veces 1 4 3 2 1 1
Ps=
X
CÁLCULO DE MOMENTOS Y EXCENTRICIDADES COLUMNA TIPO C-2-1 CÁLCULO DE EXCENTRICIDADES COLUMNAS TIPO C-2-1 8132.7 Tn 1718.47 Tn CV
CÁLCULO DE CM 8132.7 1173.21 x 22.9075 CÁLCULO DE CV 1718.47 1173.2121 x 22.9075
CM
ÁREA TRIBUTARI A
22.9075
AREA TOTA 1173.2121
5.9500 3.8500
T S
m2 m2 m m
x
=
158.79
x
=
33.554
S'=S-2e1= T'=T-2e2=
0.88 4.03
CÁLCULO DE ÁREA REDUCIDA Y e2
C-2-1
S'
C-2-1
e 1
T= 5.95
X
P T'
S= 3.85 UBICACIÓN DEL PUNTO DE LA EXCENTRICIDAD T= 5.95 Y CÁLCULO DE LAS EXCENTRICIDADES EJE X 192.35
CÁLCULO DE LAS EXCENTRICIDADES EJE Y 192.35 0.96
2.98
2.98
Ray
1.925 RBy
∑▒ 〖� � =� 〗
∑▒ 〖� � =� 〗
Mizq. = Mder. =
Cálculo de las reacciones
RBy
96.17
RAy = 96.17 Cálculo de los momentos 286.12 286.12 Cálculo de las excentricidades
e1= 286.12 192.35
1.49
1.925
Ray
RBy
S' '
1.49
Cálculo de las reacciones
∑▒ 〖�� =� 〗
RBy
∑▒ 〖� � =� 〗
96.17
RAy = 96.17 Cálculo de los momentos
Mizq. = Mder. =
185.14 185.14 Cálculo de las excentricidades
e2= 185.14 192.35
0.96
X T'
* DISEÑO DE UNA ZAPATA AISLADA * Datos de la Zapata: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P
87.92 43.95 2.30 1.95 210.00 500.00 3.50 4200.00 131.87
* Datos de la Columna: F'c: t1 t2
280.00 60.00 40.00
GRAFICA
Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn
N.P.T + 0.30
N.T.N ± 0.00 0.15
hf: 2.00
Df:
Kg/cm2 cm cm
* Datos de la Terreno:
N.F.C-1.95 σ(ult):
NPT NTN NFC
0.15 0.00 -1.85
m m m
* Esfuezo neto del terreno:
* Dimenciones de la Zapata:
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =
7.2142
* Area de la Zapata: �_𝑍 = 𝑃/�_𝑛
3.50
Tn/m2
𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2
T= 4.3755
≈
T=
4.40
m
S= 4.1755
≈
S=
4.20
m
Az =
18.48
m2
* Nueva Area de la Zapata: * Debe Cumplir: �_𝑣1= �_𝑣2
�_𝑣1= (𝑇 − 𝑡_1)/2
1.85
�_𝑍 = 𝑃/�_𝑛 Az = 18.2800 m2
�_𝑣1= �_𝑣2
�_𝑣1= (𝑇 − 𝑡_1)/2 �_𝑣2= (𝑆 − 𝑡_1)/2
Lv1 =
1.9
m Cumple
Lv2 =
1.9
m
ok !!
* DISEÑO POR PUNZONAMIENTO: 0.60 +d
�_𝑛𝑢= 𝑃_𝑢/�_𝑧 𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣
m
Pu = 197.81006 Tn
S = 4.20
0.40
n
0.40 +d Wnu = 10.7040 Tn/m2
0.60
T = 4.40 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶
Ø = 0.85
* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =
197.81006 − 10.7040 197.81006 − 10.7040 197.81006 − 2.5690 195.2411 − 10.7040
x (0.60 + d ) ( 0.40 + d ) x (0.24 + 1.00 d + d² ) − 10.7040 d − 10.7040 d² d −10.7040 d² 1
2
0.27 x
4
0.60 0.40 =
* Usamos:
+
d²
+
( 307.2172d 261.1346 d d
−
+ +
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d =
1.06
ok !!
* bo = 2m + 2n
1.26 Vc = Vc = Vc =
x 2 (0.60 +d + 0.40 + d ) d 1.06 210 x 10 307.2172 ( 1.00 + 2 d ) d + 307.2172 d 614.4344 d² 2
* Reemplazando 1 y 2 195.2411 − 10.7040 d −10.7040 d² ≤ 195.2411 − 10.7040 d −10.7040 d² ≤
^
614.4344 d² ) * 0.85 522.2692 d²
532.9732
d²
+
271.8386
d
−
d= d=
ℎ_𝑧 = d + ∅/2 +r
195.2411 ≥ 0 0.4018 -0.9118
ℎ_𝑧 = d + ∅/2 +r
hz = 0.4018
+ (3/4")
hz = 0.48133 𝑑 = ℎ_𝑧 − ∅/2 −r d=
0.50
− (3/4")
d=
0.42
m
+
0.0254 2 ≈
0.07 hz =
−
0.0254 2
0.50
m
0.07
* VERIFICACION POR CORTANTE: �_𝑛 ≤ �_�
�_𝑛= �_𝑢𝑑/∅
�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑
Ø = 0.85
�_𝑢𝑑= �_𝑛𝑢 ∗𝑆 ∗(�_𝑣 −𝑑) Vud = 10.7040 * 4.20 Vud = 66.53611 Tn
Vc = Vc =
* ( 1.9
−
0.53 210 x 10 x 4.20 x 0.42 135.4828 Tn �_𝑛 ≤ �_�
0.42 )
78.277776
Vn = 66.53611 0.85 Vn = 78.277776 Tn
≤
135.4828
Cumple
ok !!
* DISEÑO POR FLEXION: �_𝑢= �_𝑛𝑢 ∗ 𝑆∗ 〖� _𝑣 〗 ^2/2 Mu = 10.7040
* 4.20 *
Mu = 81.1471 Tn - m
Ø = 0.9 ( 1.9 )² 2
𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2
a= a=
0.8103 0.0297
〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑
a=
0.0297
m
〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑
�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 81.1471
As = 0.9
*
4.2 *
As =
0.42 − 0.0297 2
52.9854
0.22 *
As min =
210 10.197 4200 10.197
* 4.20
* 0.42
As min = 0.004276 m2 As min = 42.76 cm2
cm2
�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛
52.9854 > 42.76
*VARILLAS LONGITUDINALES Diametro(ø) =
0.75
〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅
n°v =
Cumple
Pulg.
52.9854 2.8502
n°v = 18.5899
≈
n°v =
19
varillas
* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
4.20 − 0.75 * 0.0254 − 2* 0.07 − 19
s=
0.2245
m
1
s=
22.4497
≈
*VARILLAS TRANSVERSALES Diametro(ø) =
0.75
Pulg.
�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅
As(T) =
n°v =
52.9854 *
55.5086 2.8502
4.40 4.20 n°v = 19.4751
* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
−
* 0.0254 − 2*
As(T) =
≈
55.5086
n°v =
cm2
20
varillas
s=
22
cm
ok !!
𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
4.40 − 0.75 * 0.0254 − 2* 0.07 − 20
s=
0.2232
m
1
s=
22.3208
s=
≈
22
cm
* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA 𝑃_𝑛 < 𝑃_𝑛𝑏
�_1= 𝑡_(1 )∗ 𝑡_2
Ø = 0.7
A1 = A1 =
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =
0.85 * 280 571.2 Tn
0.60 0.24
*
𝑃_𝑛= 𝑃_𝑢/∅
0.40 m2
𝑃_𝑛 < 𝑃_𝑛𝑏
Pn = 197.81006 0.7 Pn = 282.5858 Tn
* 10 * 0.24
282.5858
<
Cumple
571.2
* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0
�_2=𝑇 ∗𝑋_1
√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:
𝑋_1=𝑇 ∗𝑡_2/𝑡_1
X1
√(�_2/�_1 ) >2 → �_0=2∗�_1
T Donde:
A2 = A2 =
4.4000 * 2.9333 12.9067 m2 A0 =
Pnb = Pnb =
0.85 * 210 856.8 Tn
* 10 * 0.48
2 * 0.24 𝑃_𝑛𝑏 > 𝑃_𝑛
856.8 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏
〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1
4.4000 0.24
>
282.5858
= 18.3333
A0 =
0.48
Cumple
ok !!
>
m2
2
X1 =
4.40
X1 =
2.9333
*
0.40 0.60 m
ok !!
〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2400 As min = 12 cm2 Diametro(ø) = 4
1
* 5.0671
Pulg. =
20.2683
cm2
Cumple
ok !!
* PLANOS DE PLANTA Y PERFIL:
20 ø3/4" @ 22
S = 4.20 19
ø3/4" @
T = 4.40
DOWELLS
4 ø 1"
VARILLAS TRANSVERSALES 20 ø3/4" @ 22 cm
VARILLAS LONGITUDINALES 19 ø3/4" @ 22 cm
22
d = 0.42
hz = 0.50
T = 4.40
* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 5: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P
45.58 17.69 2.30 1.95 210.00 500.00 3.50 4200.00 63.27
* Datos de la Columna: F'c: t1 t2
280.00 70.00 40.00
GRAFICA
Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn
N.P.T + 0.30
N.T.N ± 0.00 0.15
hf: 2.00
Df:
Kg/cm2 cm cm
* Datos de la Terreno:
N.F.C-1.95 σ(ult):
NPT NTN NFC
0.15 0.00 -1.85
m m m
* Esfuezo neto del terreno:
* Dimenciones de la Zapata:
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =
7.2142
* Area de la Zapata:
3.50
Tn/m2
𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2
T= 3.1116
≈
T=
3.15
m
S= 2.8116
≈
S=
2.85
m
Az =
8.9775
m2
* Nueva Area de la Zapata: * Debe Cumplir: �_𝑣1= (𝑇 − 𝑡_1)/2
1.85
�_𝑣1= �_𝑣2
�_𝑍 = 𝑃/�_𝑛 Az =
8.7709
m2
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
1.225
m Cumple
�_𝑣2= (𝑆 − 𝑡_1)/2
Lv2 =
1.225
ok !!
m
* EFECTOS DE CARGA EXCENTRICA: e1 = 0.86 e2 = 0.72
e1
�_2= �/6
T 6
= 0.5250
e2
>
T 6
�_1= 𝑆/6
S 6
= 0.4750
e1
>
T 6
�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇)
e2
σ1 = T = 3.15
63.27 ( 1 8.9775
+ 6 *
0.86 2.85
+ 6 * 0.72 ) 3.15
σ1 = 29.4750 Tn/m2 �_1 < �_� 29.4750
P
7.2142 No Cumple
<
* POR TANTEO e
�_1= �/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/� + 〖 6� 〗 _2/�) σ1 =
63.27 ( 1 T*S
+ 6 *
0.86 S
+ 6 * 0.72 ) T
T=
5.2
m
σ1 =
6.9669
Tn/m2
S=
5
m
σ2 =
-2.0997
Tn/m2
σ2
σ1
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
2.25
m
* DISEÑO POR PUNZONAMIENTO: 0.70 +d
�_𝑛𝑢= 𝑃_𝑢/�_𝑧
m
𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣
Pu = 93.892442 Tn
S = 5.00
0.40
n
0.40 +d Wnu = σ1
0.70
Wnu =
6.9669
Tn/m2
T = 5.20 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶
Ø = 0.85
* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =
93.892442 − 93.892442 − 93.892442 − 91.9417 −
6.9669 x (0.70 + d ) ( 0.40 + d ) 6.9669 x (0.28 + 1.10 d + d² ) 1.9507 − 7.6636 d − 6.9669 d² 7.6636 d − 6.9669 d² 1
2
0.27 x
+
4 0.70 0.40
* bo = 2m + 2n
Vc = Vc = Vc =
x 2 (0.70 +d + 0.40 + d ) d 1.06 210 x 10 307.2172 ( 1.10 + 2 d ) d 337.9389 d 614.4344 d² 2 +
* Reemplazando 1 y 2
d²
+
( 337.9389d 287.2481 d d
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!
= 1.1571429 * Usamos:
91.9417 − 7.6636 d − 6.9669 d² ≤ 91.9417 − 7.6636 d − 6.9669 d² ≤
^
−
+ +
614.4344 d² ) * 0.85 522.2692 d²
529.2362 d²
+
294.9117 d
−
d= d=
ℎ_𝑧 = d + ∅/2 +r
91.9417 ≥ 0 0.2227 -0.7800
ℎ_𝑧 = d + ∅/2 +r
hz = 0.2227 + (3/4") 0.0254 + 0.07 2 hz = 0.30223 hz = ≈
0.35
m
𝑑 = ℎ_𝑧 − ∅/2 −r d= d=
0.35 − (3/4") 0.0254 − 0.07 2 0.27 m
* VERIFICACION POR CORTANTE: �_𝑛 ≤ �_�
�_𝑛= �_𝑢𝑑/∅
Ø = 0.85
σx =
3.5147
�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑
�_𝑢𝑑=((�_1+ �_𝑥)/2)∗� ∗(�_�−�)
�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2
Vud = Vud =
5.2408 51.8840
* 5.00 Tn
* ( 2.25
−
0.27 )
Vc = Vc =
Vn = 51.88396 0.85 Vn = 61.0400 Tn
0.53 210 x 10 x 5.00 x 0.27 103.6858 Tn
�_𝑛 ≤ �_�
61.0400
≤
103.6858
Cumple
ok !!
* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2
σx =
3.0439
�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =
8.4889
* 5.00 *
Mu =
71.6251
Tn - m
Ø = 0.9
( 2.25)² 3
𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2
a= a=
0.5047 0.0353
a=
0.0353
m
〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑
�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 71.6251
As = 0.9
*
4.2 *
As =
As min = 0.27 − 0.0353 2
75.0936
0.22 *
210 10.197 4200 10.197
* 5.00
* 0.27
As min = 0.003272 m2 As min = 32.72 cm2
cm2
�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛
75.0936 > 32.72
*VARILLAS LONGITUDINALES Diametro(ø) =
0.75
〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅
n°v =
Cumple
Pulg.
75.0936 2.8502
n°v = 26.3465
≈
n°v =
27
varillas
* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
5.00 − 0.75 * 0.0254 − 2* 0.07 − 27 1
s= s=
0.1862 18.6190
m
≈
*VARILLAS TRANSVERSALES Diametro(ø) =
0.75
Pulg.
�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =
As(T) =
75.0936 *
78.0973 2.8502
5.20 5.00 n°v = 27.4004
* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
−
* 0.0254 − 2*
As(T) =
≈
78.0973
n°v =
cm2
28
varillas
s=
18
cm
ok !!
𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
5.20 − 0.75 * 0.0254 − 2* 0.07 − 28 1
s= s=
0.1867
m
18.6702
s=
≈
18
cm
* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =
0.85 * 280 666.4 Tn
𝑃_𝑛= 𝑃_𝑢/∅
�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.70 * 0.40 A1 = 0.28 m2
Ø = 0.7
𝑃_𝑛 < 𝑃_𝑛𝑏
𝑃_𝑛 < 𝑃_𝑛𝑏
134.1321 < 666.4
Pn = 93.892442 0.7 Pn = 134.1321 Tn
* 10 * 0.28
Cumple
* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0
�_2=𝑇 ∗𝑋_1
√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:
𝑋_1=𝑇 ∗𝑡_2/𝑡_1
X1
√(�_2/�_1 ) >2 → �_0=2∗�_1
X1 =
X1 =
T Donde:
A2 = A2 =
3.1500 5.6700
1.8000 * m2
A0 = Pnb = Pnb =
0.85 * 210 999.6 Tn
* 10 * 0.56
2 * 0.28 𝑃_𝑛𝑏 > 𝑃_𝑛
999.6 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏
> 134.1321
3.1500 0.28
= 11.2500
A0 =
0.56
Cumple
ok !!
>
m2
2
3.15 *
1.8000
0.40 0.70 m
ok !!
〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2800 As min = 14 cm2 Diametro(ø) = 4
1
Pulg.
* 5.0671
=
20.2683
cm2
Cumple
ok !!
* PLANOS DE PLANTA Y PERFIL:
28 ø 3/4" @ 18
S = 5.00 27 ø 3/4" @ 18
T = 5.20
DOWELLS
4
VARILLAS TRANSVERSALES 28 ø 3/4" @ 18
ø 1"
VARILLAS LONGITUDINALES 27 ø 3/4" @ 18
d = 0.27
hz = 0.35
T = 5.20
* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 6: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P
69.71 33.98 2.30 1.95 210.00 500.00 3.50 4200.00 103.69
GRAFICA
Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn
N.P.T + 0.30
N.T.N ± 0.00 0.15
* Datos de la Columna: hf: 2.00 F'c: t1 t2
280.00 60.00 40.00
Df:
Kg/cm2 cm cm
* Datos de la Terreno:
N.F.C-1.95 σ(ult):
NPT NTN NFC
0.15 0.00 -1.85
m m m
* Esfuezo neto del terreno:
* Dimenciones de la Zapata:
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =
7.2142
* Area de la Zapata:
3.50
Tn/m2
𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2
T= 3.8912
≈
T=
3.90
m
S= 3.6912
≈
S=
3.70
m
Az =
14.43
m2
* Nueva Area de la Zapata: * Debe Cumplir: �_𝑣1= (𝑇 − 𝑡_1)/2
1.85
�_𝑍 = 𝑃/�_𝑛 Az = 14.3729 m2
�_𝑣1= �_𝑣2
�_𝑣1= (𝑇 − 𝑡_1)/2 �_𝑣2= (𝑆 − 𝑡_1)/2
Lv1 =
1.65
m Cumple ok !!
Lv2 =
1.65
m
* EFECTOS DE CARGA EXCENTRICA: �_2= 𝑇/6
T 6
= 0.6500
e2
>
T 6
�_1= 𝑆/6
S 6
= 0.6167
e1
<
T 6
e1 = 0.00 e2 = 0.79
e1
�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇)
e2
σ1 = T = 3.90
103.69 ( 1 14.43
+ 6 *
0.00 3.70
+ 6 * 0.79 ) 3.90
σ1 = 15.9190 Tn/m2
15.9190
P
�_1 < �_𝑛 <
7.2142 No Cumple
* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)
e
σ1 =
σ2
103.69 ( 1 T*S
+ 6 *
0.00 S
+ 6 * 0.79 ) T
T=
5.4
m
σ1 =
6.9339
Tn/m2
S=
5.2
m
σ2 =
0.4513
Tn/m2
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
2.4
m
σ1
* DISEÑO POR PUNZONAMIENTO: 0.60 +d
�_𝑛𝑢= 𝑃_𝑢/�_𝑧
m
𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣
Pu = 155.35712 Tn
S = 5.20
0.40
n
0.40 +d Wnu = σ1
0.60
Wnu =
6.9339
Tn/m2
T = 5.40 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶
Ø = 0.85
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =
155.35712 − 155.35712 − 155.35712 − 153.6930 −
6.9339 x (0.60 + d ) ( 0.40 + d ) 6.9339 x (0.24 + 1.00 d + d² ) 1.6641 − 6.9339 d − 6.9339 d² 6.9339 d − 6.9339 d² 1
* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod 2
0.27 x
= * Usamos:
* Reemplazando 1 y 2
+
4 0.60 0.40
^
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !! * bo = 2m + 2n
1.26 Vc = Vc = Vc =
x 2 (0.60 +d + 0.40 + d ) d 1.06 210 x 10 307.2172 ( 1.00 + 2 d ) d 307.2172 d 614.4344 d² 2 +
153.6930 − 6.9339 d − 6.9339 d² ≤ 153.6930 − 6.9339 d − 6.9339 d² ≤ 529.2031 d²
+
( 307.2172d 261.1346 d
268.0685 d
−
+ +
614.4344 d² ) * 0.85 522.2692 d²
153.6930 ≥ 0
d= d=
0.3422 -0.8487
ℎ_𝑧 = d + ∅/2 +r
hz = 0.3422 + (3/4") 0.0254 + 0.07 2 hz = 0.42173 hz = ≈
0.45
m
𝑑 = ℎ_𝑧 − ∅/2 −r d= d=
0.45 − (3/4") 0.0254 − 0.07 2 0.37 m
* VERIFICACION POR CORTANTE: �_𝑛 ≤ �_�
�_𝑛= �_𝑢𝑑/∅
Ø = 0.85
�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2
σx =
4.4969
�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑
�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑) Vud = Vud =
5.7154 60.3321
* 5.20 Tn
* ( 2.4
Vn = 60.332109 0.85 Vn = 70.9790 Tn
−
0.37 )
Vc = Vc =
0.53 210 x 10 x 5.20 x 0.37 147.7715 Tn
�_𝑛 ≤ �_�
70.9790
≤
147.7715
Cumple ok !!
* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2
σx =
4.0528
�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =
8.9603
* 5.20 *
Mu =
89.4597
Tn - m
Ø = 0.9
( 2.4 )² 3
𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2
a= a=
0.7098 0.0302
a=
0.0302
m
〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑
�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 89.4597
As = 0.9
*
4.2 *
As =
As min = 0.37 − 0.0302 2
66.6827
0.22 *
210 10.197 4200 10.197
* 5.20
* 0.37
As min = 0.004664 m2 As min = 46.64 cm2
cm2
�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛
66.6827 > 46.64
*VARILLAS LONGITUDINALES Diametro(ø) =
0.75
〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅
n°v =
Cumple
Pulg.
66.6827 2.8502
n°v = 23.3956
≈
n°v =
24
varillas
* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
5.20 − 0.75 * 0.0254 − 2* 0.07 − 24 1
s= s=
0.2192 21.9172
m
≈
*VARILLAS TRANSVERSALES Diametro(ø) =
0.75
Pulg.
�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =
As(T) =
66.6827 *
69.2474 2.8502
5.40 5.20 n°v = 24.2954
* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
−
* 0.0254 − 2*
As(T) =
≈
69.2474
n°v =
cm2
25
varillas
s=
21
cm
ok !!
𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
5.40 − 0.75 * 0.0254 − 2* 0.07 − 25 1
s= s=
0.2184 21.8373
m
≈
s=
21
cm
* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =
0.85 * 280 571.2 Tn
𝑃_𝑛= 𝑃_𝑢/∅
�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.60 * 0.40 A1 = 0.24 m2
Ø = 0.7
𝑃_𝑛 < 𝑃_𝑛𝑏
𝑃_𝑛 < 𝑃_𝑛𝑏
221.9387 < 571.2
Pn = 155.35712 0.7 Pn = 221.9387 Tn
* 10 * 0.24
Cumple
* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛
�_2=𝑇 ∗𝑋_1
√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0
𝑋_1=𝑇 ∗𝑡_2/𝑡_1
X1
√(�_2/�_1 ) >2 → �_0=2∗�_1
X1 =
X1 =
T Donde:
A2 = A2 =
3.9000 * 2.6000 10.1400 m2 A0 =
Pnb = Pnb =
0.85 * 210 856.8 Tn
* 10 * 0.48
2 * 0.24 𝑃_𝑛𝑏 > 𝑃_𝑛
856.8 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏
〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2400 As min = 12 cm2
> 221.9387
3.9000 0.24
= 16.2500
A0 =
0.48
Cumple
ok !!
>
m2
2
3.90 *
2.6000
0.40 0.60 m
ok !!
Diametro(ø) = 4
1
Pulg.
* 5.0671
=
20.2683
cm2
Cumple
ok !!
* PLANOS DE PLANTA Y PERFIL:
25 ø 3/4" @ 21
S = 5.20 24 ø 3/4" @ 21
T = 5.40
DOWELLS
4
VARILLAS TRANSVERSALES 25 ø 3/4" @ 21
ø 1"
VARILLAS LONGITUDINALES 24 ø 3/4" @ 21
d = 0.37
hz = 0.45
T = 5.40
* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 8: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P
18.35 11.00 2.30 1.95 210.00 500.00 3.50 4200.00 29.35
GRAFICA
Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn
N.P.T + 0.30
N.T.N ± 0.00 0.15
* Datos de la Columna: hf: 2.00 F'c: t1 t2
280.00 40.00 40.00
Df:
Kg/cm2 cm cm
* Datos de la Terreno:
N.F.C-1.95 σ(ult):
NPT NTN NFC
0.15 0.00 -1.85
3.50
m m m
* Esfuezo neto del terreno:
* Dimenciones de la Zapata:
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
T= 2.0171
≈
T=
2.05
m
1.85
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶 �_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =
7.2142
Tn/m2
S= 2.0171
S=
2.05
m
Az =
4.2025
m2
≈
* Debe Cumplir: �_𝑣1= �_𝑣2
�_𝑍 = 𝑃/�_𝑛 4.0685
𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2 * Nueva Area de la Zapata:
* Area de la Zapata:
Az =
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
m2
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
0.825
m Cumple ok !!
�_𝑣2= (𝑆 − 𝑡_1)/2
Lv2 =
0.825
m
* EFECTOS DE CARGA EXCENTRICA: e1 = 0.39 e2 = 0.81 e2 e1
�_2= 𝑇/6
T 6
= 0.3417
e2
>
T 6
�_1= 𝑆/6
S 6
= 0.3417
e1
>
T 6
�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 = T = 2.05
29.35 ( 1 4.2025
+ 6 *
0.39 2.05
σ1 = 31.5142 Tn/m2
31.5142
P
�_1 < �_𝑛 <
7.2142 No Cumple
* POR TANTEO e
�_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)
+ 6 * 0.81 ) 2.05
σ1 =
29.35 ( 1 T*S
+ 6 *
0.39 S
+ 6 * 0.81 ) T
T=
3.7
m
σ1 =
6.7589
Tn/m2
S=
3.5
m
σ2 =
-2.2259
Tn/m2
σ2
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
σ1
* DISEÑO POR PUNZONAMIENTO: 0.40 +d
�_𝑛𝑢= 𝑃_𝑢/�_𝑧
m
𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣
Pu = 44.392191 Tn
S = 3.50
0.40
n
0.40 +d Wnu = σ1
0.40
Wnu =
6.7589
Tn/m2
T = 3.70 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶
Ø = 0.85
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛
* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod
^
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d
1.65
m
Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =
44.392191 − 44.392191 − 44.392191 − 43.3108 −
6.7589 x (0.40 + d ) ( 0.40 + d ) 6.7589 x (0.16 + 0.80 d + d² ) 1.0814 − 5.4071 d − 6.7589 d² 5.4071 d − 6.7589 d² 1
2
0.27 x
=
+
4 0.40 0.40
* bo = 2m + 2n
1.62 Vc = Vc = Vc =
* Usamos:
x 2 (0.40 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 0.80 245.7737 d + 614.4344 d² 2
* Reemplazando 1 y 2 43.3108 − 5.4071 d − 6.7589 d² ≤ 43.3108 − 5.4071 d − 6.7589 d² ≤ 529.0281 d²
+
( 245.7737d 208.9077 d
214.3148 d
−
d= d=
+ +
614.4344 d² ) * 0.85 522.2692 d²
43.3108 ≥ 0 0.1480 -0.5531
ℎ_𝑧 = d + ∅/2 +r
hz = 0.1480 + (3/4") 0.0254 + 0.07 2 hz = 0.22753 hz = ≈
𝑑 = ℎ_𝑧 − ∅/2 −r d= d=
0.25 − (3/4") 0.0254 − 0.07 2 0.17 m
* VERIFICACION POR CORTANTE: �_𝑛 ≤ �_�
�_𝑛= �_𝑢𝑑/∅
Ø = 0.85
0.25
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!
m
σx =
3.1650
�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑
�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)
�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2
Vud = Vud =
4.9619 25.7028
* 3.50 Tn
* ( 1.65
−
0.17 )
Vc = Vc =
Vn = 25.702847 0.85 Vn = 30.2386 Tn
0.53 210 x 10 x 3.50 x 0.17 45.6986 Tn
�_𝑛 ≤ �_�
30.2386
≤
45.6986
Cumple ok !!
* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2
σx =
2.7522
�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =
8.1350
* 3.50 *
Mu =
25.8387
Tn - m
Ø = 0.9
( 1.65)² 3
𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2
a= a=
0.3104 0.0296
a=
0.0296
m
〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑
�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 25.8387
As = 0.9
*
4.2 *
As =
As min = 0.17 − 0.0296 2
44.0456
0.22 *
210 10.197 4200 10.197
* 3.50
* 0.17
As min = 0.001442 m2 As min = 14.42 cm2
cm2
�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛
44.0456 > 14.42
*VARILLAS LONGITUDINALES Diametro(ø) =
0.75
〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅
n°v =
Cumple
Pulg.
44.0456 2.8502
n°v = 15.4533
≈
n°v =
16
varillas
* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
3.50 − 0.75 * 0.0254 − 2* 0.07 − 16 1
s= s=
0.2227 22.2730
m
≈
*VARILLAS TRANSVERSALES Diametro(ø) =
0.75
Pulg.
�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =
As(T) =
44.0456 *
46.5625 2.8502
3.70 3.50 n°v = 16.3364
* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
−
* 0.0254 − 2*
As(T) =
≈
46.5625
n°v =
cm2
17
varillas
s=
22
cm
ok !!
𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
3.70 − 0.75 * 0.0254 − 2* 0.07 − 17 1
s= s=
0.2213
m
22.1309
s=
≈
22
cm
* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =
0.85 * 280 380.8 Tn
𝑃_𝑛= 𝑃_𝑢/∅
�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.40 * 0.40 A1 = 0.16 m2
Ø = 0.7
𝑃_𝑛 < 𝑃_𝑛𝑏
𝑃_𝑛 < 𝑃_𝑛𝑏
Pn = 44.392191 0.7 Pn = 63.4174 Tn
* 10 * 0.16
63.4174
< 380.8
Cumple
* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0
�_2=𝑇 ∗𝑋_1
√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:
𝑋_1=𝑇 ∗𝑡_2/𝑡_1
X1
√(�_2/�_1 ) >2 → �_0=2∗�_1
X1 =
X1 =
T Donde:
A2 = A2 =
2.0500 4.2025
2.0500 * m2
A0 = Pnb = Pnb =
0.85 * 210 571.2 Tn
* 10 * 0.32
2 * 0.16 𝑃_𝑛𝑏 > 𝑃_𝑛
571.2 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏
> 63.4174
2.0500 0.16
= 12.8125
A0 =
0.32
Cumple
ok !!
>
m2
2
2.05 *
2.0500
0.40 0.40 m
ok !!
〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 1600 As min = 8 cm2 Diametro(ø) = 4
1
Pulg.
* 5.0671
=
20.2683
cm2
Cumple
ok !!
* PLANOS DE PLANTA Y PERFIL:
17 ø 3/4" @ 22
S = 3.50 16 ø 3/4" @ 22
T = 3.70
DOWELLS
4
VARILLAS TRANSVERSALES 17 ø 3/4" @ 22
ø 1"
VARILLAS LONGITUDINALES 16 ø 3/4" @ 22
d = 0.17
hz = 0.25
T = 3.70
* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 9: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P
18.52 11.11 2.30 1.95 210.00 500.00 3.50 4200.00 29.62
GRAFICA
Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn
N.P.T + 0.30
N.T.N ± 0.00 0.15
* Datos de la Columna: hf: 2.00 F'c: t1 t2
280.00 40.00 40.00
Df:
Kg/cm2 cm cm
* Datos de la Terreno:
N.F.C-1.95 σ(ult):
NPT NTN NFC
0.15 0.00 -1.85
m m m
3.50
1.85
* Esfuezo neto del terreno:
* Dimenciones de la Zapata:
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =
7.2142
Tn/m2
T=
2.05
m
S= 2.0264
≈
S=
2.05
m
Az =
4.2025
m2
* Debe Cumplir: �_𝑣1= �_𝑣2
�_𝑍 = 𝑃/�_𝑛 4.1064
≈
* Nueva Area de la Zapata:
* Area de la Zapata:
Az =
𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2
T= 2.0264
m2
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
0.825
m
Lv2 =
0.825
m
Cumple ok !!
�_𝑣2= (𝑆 − 𝑡_1)/2
* EFECTOS DE CARGA EXCENTRICA: e1 = 0.39 e2 = 0.83 e2 e1
�_2= 𝑇/6
T 6
= 0.3417
e2
>
T 6
�_1= 𝑆/6
S 6
= 0.3417
e1
>
T 6
�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 = T = 2.05
29.62 ( 1 4.2025
+ 6 *
0.39 2.05
σ1 = 32.2203 Tn/m2
32.2203
�_1 < �_𝑛 <
7.2142 No Cumple
+ 6 * 0.83 ) 2.05
P
* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)
e
σ1 =
σ2
29.62 ( 1 T*S
+ 6 *
0.39 S
T=
3.7
m
σ1 =
6.8960
Tn/m2
S=
3.5
m
σ2 =
-2.3208
Tn/m2
�_𝑣1= (𝑇 − 𝑡_1)/2
σ1
* DISEÑO POR PUNZONAMIENTO: 0.40 +d
�_𝑛𝑢= 𝑃_𝑢/�_𝑧
m
𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣
Pu = 44.805895 Tn
S = 3.50
0.40
n
0.40 +d Wnu = σ1
0.40
T = 3.70 * CONDICION DE DISEÑO:
+ 6 * 0.83 ) T
Wnu =
6.8960
Tn/m2
Lv1 =
1.65
m
�_𝑈/∅ ≤ �_𝐶
Ø = 0.85
* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =
44.805895 − 44.805895 − 44.805895 − 43.7025 −
6.8960 x (0.40 + d ) ( 0.40 + d ) 6.8960 x (0.16 + 0.80 d + d² ) 1.1034 − 5.5168 d − 6.8960 d² 5.5168 d − 6.8960 d² 1
2
0.27 x
=
+
4 0.40 0.40
* bo = 2m + 2n
Vc = Vc = Vc =
x 2 (0.40 +d + 0.40 + d ) d 1.06 210 x 10 307.2172 ( 0.80 + 2 d ) d 245.7737 d + 614.4344 d² 2
* Reemplazando 1 y 2
529.1652 d²
+
( 245.7737d 208.9077 d
214.4245 d
−
d= d=
+ +
614.4344 d² ) * 0.85 522.2692 d²
43.7025 ≥ 0 0.1490 -0.5542
ℎ_𝑧 = d + ∅/2 +r
hz = 0.1490 + (3/4") 0.0254 + 0.07 2 hz = 0.22853 hz = ≈
𝑑 = ℎ_𝑧 − ∅/2 −r d= d=
* VERIFICACION POR CORTANTE:
0.25 − (3/4") 0.0254 − 0.07 2 0.17 m
0.25
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!
1.62
* Usamos:
43.7025 − 5.5168 d − 6.8960 d² ≤ 43.7025 − 5.5168 d − 6.8960 d² ≤
^
m
�_𝑛 ≤ �_�
�_𝑛= �_𝑢𝑑/∅
Ø = 0.85
σx =
3.2093
�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑
�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)
�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2
Vud = Vud =
5.0527 26.1728
* 3.50 Tn
* ( 1.65
−
0.17 )
Vc = Vc =
Vn = 26.172784 0.85 Vn = 30.7915 Tn
0.53 210 x 10 x 3.50 x 0.17 45.6986 Tn
�_𝑛 ≤ �_�
30.7915
≤
45.6986
Cumple ok !!
* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2
σx =
2.7858
�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =
8.2889
* 3.50 *
Mu =
26.3277
Tn - m
Ø = 0.9
( 1.65)² 3
𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2
a= a=
0.3098 0.0302
a=
0.0302
m
〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑
�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 26.3277
As = 0.9
*
4.2 *
As =
As min = 0.17 − 0.0302 2
44.9691
0.22 *
210 10.197 4200 10.197
* 3.50
* 0.17
As min = 0.001442 m2 As min = 14.42 cm2
cm2
�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛
44.9691 > 14.42
*VARILLAS LONGITUDINALES Diametro(ø) =
0.75
〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅
n°v =
Cumple
Pulg.
44.9691 2.8502
n°v = 15.7774
≈
n°v =
16
varillas
* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
3.50 − 0.75 * 0.0254 − 2* 0.07 − 16 1
s= s=
0.2227 22.2730
m
≈
*VARILLAS TRANSVERSALES Diametro(ø) =
0.75
Pulg.
�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =
As(T) =
44.9691 *
47.5388 2.8502
3.70 3.50 n°v = 16.6789
* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
−
* 0.0254 − 2*
As(T) =
≈
47.5388
n°v =
cm2
17
varillas
s=
22
cm
ok !!
𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
3.70 − 0.75 * 0.0254 − 2* 0.07 − 17 1
s= s=
0.2213
m
22.1309
s=
≈
22
cm
* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =
0.85 * 280 380.8 Tn
𝑃_𝑛= 𝑃_𝑢/∅
�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.40 * 0.40 A1 = 0.16 m2
Ø = 0.7
𝑃_𝑛 < 𝑃_𝑛𝑏
𝑃_𝑛 < 𝑃_𝑛𝑏
Pn = 44.805895 0.7 Pn = 64.0084 Tn
* 10 * 0.16
64.0084
< 380.8
Cumple
* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0
�_2=𝑇 ∗𝑋_1
√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:
𝑋_1=𝑇 ∗𝑡_2/𝑡_1
X1
√(�_2/�_1 ) >2 → �_0=2∗�_1
X1 =
X1 =
T Donde:
A2 = A2 =
2.0500 4.2025
2.0500 * m2
A0 = Pnb = Pnb =
0.85 * 210 571.2 Tn
* 10 * 0.32
2 * 0.16 𝑃_𝑛𝑏 > 𝑃_𝑛
571.2 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏
> 64.0084
2.0500 0.16
= 12.8125
A0 =
0.32
Cumple
ok !!
>
m2
2
2.05 *
2.0500
0.40 0.40 m
ok !!
〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 1600 As min = 8 cm2 Diametro(ø) = 4
1
Pulg.
* 5.0671
=
20.2683
cm2
Cumple
ok !!
* PLANOS DE PLANTA Y PERFIL:
17 ø 3/4" @ 22
S = 3.50 16 ø 3/4" @ 22
T = 3.70
DOWELLS
4
VARILLAS TRANSVERSALES 17 ø 3/4" @ 22
ø 1"
VARILLAS LONGITUDINALES 16 ø 3/4" @ 22
d = 0.17
hz = 0.25
T = 3.70
* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 11: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P
70.37 34.07 2.30 1.95 210.00 500.00 3.50 4200.00 104.44
* Datos de la Columna: F'c: t1 t2
280.00 60.00 40.00
GRAFICA
Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn
N.P.T + 0.30
0.15
hf: 2.00
Df:
Kg/cm2 cm cm
* Datos de la Terreno:
N.F.C-1.95 σ(ult):
NPT NTN NFC
0.15 0.00 -1.85
N.T.N ± 0.00
m m m
3.50
1.85
* Esfuezo neto del terreno:
* Dimenciones de la Zapata:
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =
7.2142
Tn/m2
𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2
T= 3.9049
≈
T=
3.95
m
S= 3.7049
≈
S=
3.75
m
* Nueva Area de la Zapata:
* Area de la Zapata:
Az = 14.8125 m2
* Debe Cumplir: �_𝑣1= �_𝑣2
�_𝑍 = 𝑃/�_𝑛 Az = 14.4772 m2
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
1.675
m
Lv2 =
1.675
m
Cumple ok !!
�_𝑣2= (𝑆 − 𝑡_1)/2
* EFECTOS DE CARGA EXCENTRICA: e1 = 0.00 e2 = 0.84
e1
�_2= 𝑇/6
T 6
= 0.6583
e2
>
T 6
�_1= 𝑆/6
S 6
= 0.6250
e1
<
T 6
�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇)
e2
σ1 = T = 3.95
104.44 ( 1 14.8125
+ 6 *
0.00 3.75
σ1 = 16.0474 Tn/m2
16.0474
�_1 < �_𝑛 <
7.2142 No Cumple
+ 6 * 0.84 ) 3.95
P
* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)
e
σ1 =
σ2
104.44 ( 1 T*S
+ 6 *
0.00 S
T=
5.5
m
σ1 =
6.8661
Tn/m2
S=
5.3
m
σ2 =
0.2997
Tn/m2
�_𝑣1= (𝑇 − 𝑡_1)/2
σ1
* DISEÑO POR PUNZONAMIENTO: 0.60 +d
�_𝑛𝑢= 𝑃_𝑢/�_𝑧
m
𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣
Pu = 156.43861 Tn
S = 5.30
0.40
n
0.40 +d Wnu = σ1
0.60
T = 5.50 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶
+ 6 * 0.84 ) T
Wnu =
6.8661
Tn/m2
Lv1 =
2.45
m
�_𝑈/∅ ≤ �_𝐶
Ø = 0.85
* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =
156.43861 − 156.43861 − 156.43861 − 154.7907 −
6.8661 x (0.60 + d ) ( 0.40 + d ) 6.8661 x (0.24 + 1.00 d + d² ) 1.6479 − 6.8661 d − 6.8661 d² 6.8661 d − 6.8661 d² 1
2
0.27 x
=
+
4 0.60 0.40
* bo = 2m + 2n
Vc = Vc = Vc =
x 2 (0.60 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 1.00 307.2172 d + 614.4344 d² 2
* Reemplazando 1 y 2
529.1353 d²
+
( 307.2172d 261.1346 d
268.0007 d
−
d= d=
+ +
614.4344 d² ) * 0.85 522.2692 d²
154.7907 ≥ 0 0.3440 -0.8505
ℎ_𝑧 = d + ∅/2 +r
hz = 0.3440 + (3/4") 0.0254 + 0.07 2 hz = 0.42353 hz = ≈
𝑑 = ℎ_𝑧 − ∅/2 −r d= d=
* VERIFICACION POR CORTANTE:
0.45 − (3/4") 0.0254 − 0.07 2 0.37 m
0.45
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!
1.26
* Usamos:
154.7907 − 6.8661 d − 6.8661 d² ≤ 154.7907 − 6.8661 d − 6.8661 d² ≤
^
m
�_𝑛 ≤ �_�
�_𝑛= �_𝑢𝑑/∅
Ø = 0.85
σx =
4.3828
�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑
�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)
�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2
Vud = Vud =
5.6244 62.0038
* 5.30 Tn
* ( 2.45
−
0.37 )
Vc = Vc =
Vn = 62.003772 0.85 Vn = 72.9456 Tn
0.53 210 x 10 x 5.30 x 0.37 150.6132 Tn
�_𝑛 ≤ �_�
72.9456
≤
150.6132
Cumple ok !!
* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2
σx =
3.9410
�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =
8.8366
* 5.30 *
Mu =
93.7071
Tn - m
Ø = 0.9
( 2.45)² 3
𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2
a= a=
0.7090 0.0310
a=
0.0310
m
〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑
�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 93.7071
As = 0.9
*
4.2 *
As =
As min = 0.37 − 0.0310 2
69.9348
0.22 *
210 10.197 4200 10.197
* 5.30
* 0.37
As min = 0.004753 m2 As min = 47.53 cm2
cm2
�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛
69.9348 > 47.53
*VARILLAS LONGITUDINALES Diametro(ø) =
0.75
〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅
n°v =
Cumple
Pulg.
69.9348 2.8502
n°v = 24.5366
≈
n°v =
25
varillas
* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
5.30 − 0.75 * 0.0254 − 2* 0.07 − 25 1
s= s=
0.2142 21.4206
m
≈
*VARILLAS TRANSVERSALES Diametro(ø) =
0.75
Pulg.
�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =
As(T) =
69.9348 *
72.5739 2.8502
5.50 5.30 n°v = 25.4625
* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
−
* 0.0254 − 2*
As(T) =
≈
72.5739
n°v =
cm2
26
varillas
s=
21
cm
ok !!
𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
5.50 − 0.75 * 0.0254 − 2* 0.07 − 26 1
s= s=
0.2136 21.3638
m
≈
s=
21
cm
* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =
0.85 * 280 571.2 Tn
𝑃_𝑛= 𝑃_𝑢/∅
�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.60 * 0.40 A1 = 0.24 m2
Ø = 0.7
𝑃_𝑛 < 𝑃_𝑛𝑏
𝑃_𝑛 < 𝑃_𝑛𝑏
223.4837 < 571.2
Pn = 156.43861 0.7 Pn = 223.4837 Tn
* 10 * 0.24
Cumple
* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛
�_2=𝑇 ∗𝑋_1
√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0
𝑋_1=𝑇 ∗𝑡_2/𝑡_1
X1
√(�_2/�_1 ) >2 → �_0=2∗�_1
X1 =
X1 =
T Donde:
A2 = A2 =
3.9500 * 2.6333 10.4017 m2 A0 =
Pnb = Pnb =
0.85 * 210 856.8 Tn
* 10 * 0.48
2 * 0.24 𝑃_𝑛𝑏 > 𝑃_𝑛
856.8 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏
〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2400 As min = 12 cm2
> 223.4837
3.9500 0.24
= 16.4583
A0 =
0.48
Cumple
ok !!
>
m2
2
3.95 *
2.6333
0.40 0.60 m
ok !!
Diametro(ø) = 4
1
Pulg.
* 5.0671
=
20.2683
cm2
Cumple
ok !!
* PLANOS DE PLANTA Y PERFIL:
26 ø 3/4" @ 21
S = 5.30 25 ø 3/4" @ 21
T = 5.50
DOWELLS
4
VARILLAS TRANSVERSALES 26 ø 3/4" @ 21
ø 1"
VARILLAS LONGITUDINALES 25 ø 3/4" @ 21
d = 0.37
hz = 0.45
T = 5.50
* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 12: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P
47.77 19.84 2.30 1.95 210.00 500.00 3.50 4200.00 67.61
* Datos de la Columna: F'c: t1 t2
280.00 70.00 40.00
GRAFICA
Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn
N.P.T + 0.30
N.T.N ± 0.00 0.15
hf: 2.00
Df:
Kg/cm2 cm cm
* Datos de la Terreno:
N.F.C-1.95 σ(ult):
NPT NTN NFC
0.15 0.00 -1.85
3.50
m m m
* Esfuezo neto del terreno:
* Dimenciones de la Zapata:
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
T= 3.2113
≈
T=
3.25
m
1.85
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶
𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2
�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =
7.2142
Tn/m2
2.95
m
Az =
9.5875
m2
* Debe Cumplir: �_𝑣1= �_𝑣2
�_𝑍 = 𝑃/�_𝑛 9.3718
S=
≈
* Nueva Area de la Zapata:
* Area de la Zapata:
Az =
S= 2.9113
m2
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
1.275
m Cumple
�_𝑣2= (𝑆 − 𝑡_1)/2
Lv2 =
1.275
ok !!
m
* EFECTOS DE CARGA EXCENTRICA: e1 = 0.88 e2 = 0.75
e1 e2
�_2= 𝑇/6
T 6
= 0.5417
e2
>
T 6
�_1= 𝑆/6
S 6
= 0.4917
e1
>
T 6
�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 =
T = 3.25
67.61 ( 1 9.5875
+ 6 *
0.88 2.95
σ1 = 29.4375 Tn/m2
29.4375
P
�_1 < �_𝑛 <
7.2142 No Cumple
* POR TANTEO e
�_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)
+ 6 * 0.75 ) 3.25
σ1 =
67.61 ( 1 T*S
+ 6 *
0.88 S
+ 6 * 0.75 ) T
T=
5.5
m
σ1 =
6.6985
Tn/m2
S=
5.2
m
σ2 =
-1.9705
Tn/m2
σ2
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
σ1
* DISEÑO POR PUNZONAMIENTO: 0.70 +d
�_𝑛𝑢= 𝑃_𝑢/�_𝑧
m
𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣
Pu = 100.60583 Tn
S = 5.20
0.40
n
0.40 +d Wnu = σ1
0.70
Wnu =
6.6985
Tn/m2
T = 5.50 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶
Ø = 0.85
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛
* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod
^
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d
2.4
m
Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =
100.60583 − 100.60583 − 100.60583 − 98.7303 −
6.6985 x (0.70 + d ) ( 0.40 + d ) 6.6985 x (0.28 + 1.10 d + d² ) 1.8756 − 7.3683 d − 6.6985 d² 7.3683 d − 6.6985 d² 1
2
0.27 x
+
4 0.70 0.40
* bo = 2m + 2n
= 1.1571429 Vc = Vc = Vc =
* Usamos:
x 2 (0.70 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 1.10 337.9389 d + 614.4344 d² 2
* Reemplazando 1 y 2 98.7303 − 7.3683 d − 6.6985 d² ≤ 98.7303 − 7.3683 d − 6.6985 d² ≤ 528.9677 d²
+
( 337.9389d 287.2481 d
294.6164 d
−
d= d=
+ +
614.4344 d² ) * 0.85 522.2692 d²
98.7303 ≥ 0 0.2355 -0.7925
ℎ_𝑧 = d + ∅/2 +r
hz = 0.2355 + (3/4") 0.0254 + 0.07 2 hz = 0.31503 hz = ≈
𝑑 = ℎ_𝑧 − ∅/2 −r d= d=
0.35 − (3/4") 0.0254 − 0.07 2 0.27 m
* VERIFICACION POR CORTANTE: �_𝑛 ≤ �_�
�_𝑛= �_𝑢𝑑/∅
Ø = 0.85
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!
0.35
m
σx =
3.3412
�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑
�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)
�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2
Vud = Vud =
5.0198 55.5997
* 5.20 Tn
* ( 2.4
−
0.27 )
Vc = Vc =
Vn = 55.599663 0.85 Vn = 65.4114 Tn
0.53 210 x 10 x 5.20 x 0.27 107.8332 Tn
�_𝑛 ≤ �_�
65.4114
≤
107.8332
Cumple
ok !!
* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2
σx =
2.9156
�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =
8.1563
* 5.20 *
Mu =
81.4323
Tn - m
Ø = 0.9
( 2.4 )² 3
𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2
a= a=
0.5011 0.0389
a=
0.0389
m
〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑
�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 81.4323
As = 0.9
*
4.2 *
As =
As min = 0.27 − 0.0389 2
85.9837
0.22 *
210 10.197 4200 10.197
* 5.20
* 0.27
As min = 0.003403 m2 As min = 34.03 cm2
cm2
�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛
85.9837 > 34.03
*VARILLAS LONGITUDINALES Diametro(ø) =
0.75
〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅
n°v =
Cumple
Pulg.
85.9837 2.8502
n°v = 30.1673
≈
n°v =
31
varillas
* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
5.20 − 0.75 * 0.0254 − 2* 0.07 − 31 1
s= s=
0.1680 16.8032
m
≈
*VARILLAS TRANSVERSALES Diametro(ø) =
0.75
Pulg.
�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =
As(T) =
85.9837 *
90.9443 2.8502
5.50 5.20 n°v = 31.9077
* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
−
* 0.0254 − 2*
As(T) =
≈
90.9443
n°v =
cm2
32
varillas
s=
16
cm
ok !!
𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
5.50 − 0.75 * 0.0254 − 2* 0.07 − 32 1
s= s=
0.1723
m
17.2289
s=
≈
17
cm
* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =
0.85 * 280 666.4 Tn
𝑃_𝑛= 𝑃_𝑢/∅
�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.70 * 0.40 A1 = 0.28 m2
Ø = 0.7
𝑃_𝑛 < 𝑃_𝑛𝑏
𝑃_𝑛 < 𝑃_𝑛𝑏
143.7226 < 666.4
Pn = 100.60583 0.7 Pn = 143.7226 Tn
* 10 * 0.28
Cumple
* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0
�_2=𝑇 ∗𝑋_1
√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:
𝑋_1=𝑇 ∗𝑡_2/𝑡_1
X1
√(�_2/�_1 ) >2 → �_0=2∗�_1
X1 =
X1 =
T Donde:
A2 = A2 =
3.2500 6.0357
1.8571 * m2
A0 = Pnb = Pnb =
0.85 * 210 999.6 Tn
* 10 * 0.56
2 * 0.28 𝑃_𝑛𝑏 > 𝑃_𝑛
999.6 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏
> 143.7226
3.2500 0.28
= 11.6071
A0 =
0.56
Cumple
ok !!
>
m2
2
3.25 *
1.8571
0.40 0.70 m
ok !!
〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2800 As min = 14 cm2 Diametro(ø) = 4
1
Pulg.
* 5.0671
=
20.2683
cm2
Cumple
ok !!
* PLANOS DE PLANTA Y PERFIL:
32 ø 3/4" @ 17
S = 5.20 31 ø 3/4" @ 16
T = 5.50
DOWELLS
4
VARILLAS TRANSVERSALES 32 ø 3/4" @ 17
ø 1"
VARILLAS LONGITUDINALES 31 ø 3/4" @ 16
d = 0.27
hz = 0.35
T = 5.50
* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 13: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P
63.11 24.54 2.30 1.95 210.00 500.00 3.50 4200.00 87.65
GRAFICA
Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn
N.P.T + 0.30
N.T.N ± 0.00 0.15
* Datos de la Columna: hf: 2.00 F'c: t1 t2
280.00 70.00 40.00
Df:
Kg/cm2 cm cm
* Datos de la Terreno:
N.F.C-1.95 σ(ult):
NPT NTN NFC
0.15 0.00 -1.85
m m m
3.50
1.85
* Esfuezo neto del terreno:
* Dimenciones de la Zapata:
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2
�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =
7.2142
Tn/m2
T= 3.6357
≈
T=
3.65
m
S= 3.3357
≈
S=
3.35
m
* Nueva Area de la Zapata:
* Area de la Zapata:
Az = 12.2275 m2
* Debe Cumplir:
�_𝑍 = 𝑃/�_𝑛
�_𝑣1= �_𝑣2
Az = 12.1502 m2
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
1.475
m
Lv2 =
1.475
m
Cumple
�_𝑣2= (𝑆 − 𝑡_1)/2
ok !!
* EFECTOS DE CARGA EXCENTRICA: e1 = 0.77 e2 = 0.00
e1 e2
�_2= 𝑇/6
T 6
= 0.6083
e2
<
T 6
�_1= 𝑆/6
S 6
= 0.5583
e1
>
T 6
�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 =
T = 3.65
87.65 ( 1 12.2275
+ 6 *
0.77 3.35
σ1 = 17.0548 Tn/m2
17.0548
�_1 < �_𝑛 <
7.2142 No Cumple
+ 6 * 0.00 ) 3.65
P
* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)
e
σ1 =
σ2
87.65 ( 1 T*S
+ 6 *
0.77 S
T=
5
m
σ1 =
7.1675
Tn/m2
S=
4.8
m
σ2 =
0.1370
Tn/m2
�_𝑣1= (𝑇 − 𝑡_1)/2
σ1
* DISEÑO POR PUNZONAMIENTO: 0.70 +d
�_𝑛𝑢= 𝑃_𝑢/�_𝑧
m
𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣
Pu = 130.07753 Tn
S = 4.80
0.40
n
0.40 +d Wnu = σ1
0.70
T = 5.00 * CONDICION DE DISEÑO:
+ 6 * 0.00 ) T
Wnu =
7.1675
Tn/m2
Lv1 =
2.15
m
�_𝑈/∅ ≤ �_𝐶
Ø = 0.85
* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =
130.07753 − 130.07753 − 130.07753 − 128.0706 −
7.1675 x (0.70 + d ) ( 0.40 + d ) 7.1675 x (0.28 + 1.10 d + d² ) 2.0069 − 7.8843 d − 7.1675 d² 7.8843 d − 7.1675 d² 1
2
0.27 x
+
4 0.70 0.40
* bo = 2m + 2n
Vc = Vc = Vc =
x 2 (0.70 +d + 0.40 + d ) d 1.06 210 x 10 307.2172 ( 1.10 + 2 d ) d 337.9389 d + 614.4344 d² 2
* Reemplazando 1 y 2
529.4367 d²
+
( 337.9389d 287.2481 d
295.1323 d
−
d= d=
+ +
614.4344 d² ) * 0.85 522.2692 d²
128.0706 ≥ 0 0.2866 -0.8440
ℎ_𝑧 = d + ∅/2 +r
hz = 0.2866 + (3/4") 0.0254 + 0.07 2 hz = 0.36613 hz = ≈
𝑑 = ℎ_𝑧 − ∅/2 −r d= d=
* VERIFICACION POR CORTANTE:
0.40 − (3/4") 0.0254 − 0.07 2 0.32 m
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!
= 1.1571429 * Usamos:
128.0706 − 7.8843 d − 7.1675 d² ≤ 128.0706 − 7.8843 d − 7.1675 d² ≤
^
0.40
m
�_𝑛 ≤ �_�
�_𝑛= �_𝑢𝑑/∅
Ø = 0.85
σx =
4.5943
�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑
�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)
�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2
Vud = Vud =
5.8809 51.6580
* 4.80 Tn
* ( 2.15
−
0.32 )
Vc = Vc =
Vn = 51.658002 0.85 Vn = 60.7741 Tn
0.53 210 x 10 x 4.80 x 0.32 117.9714 Tn
�_𝑛 ≤ �_�
60.7741
≤
117.9714
Cumple
ok !!
* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2
σx =
4.1444
�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =
9.2397
* 4.80 *
Mu =
68.3368
Tn - m
Ø = 0.9
( 2.15)² 3
𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2
a= a=
0.6110 0.0290
a=
0.0290
m
〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑
�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 68.3368
As = 0.9
*
4.2 *
As =
As min = 0.32 − 0.0290 2
59.1777
0.22 *
210 10.197 4200 10.197
* 4.80
* 0.32
As min = 0.003723 m2 As min = 37.23 cm2
cm2
�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛
59.1777 > 37.23
*VARILLAS LONGITUDINALES Diametro(ø) =
0.75
〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅
n°v =
Cumple
Pulg.
59.1777 2.8502
n°v = 20.7624
≈
n°v =
21
varillas
* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
4.80 − 0.75 * 0.0254 − 2* 0.07 − 21 1
s= s=
0.2320 23.2048
m
≈
*VARILLAS TRANSVERSALES Diametro(ø) =
0.75
Pulg.
�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =
As(T) =
59.1777 *
61.6434 2.8502
5.00 4.80 n°v = 21.6275
* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
−
* 0.0254 − 2*
As(T) =
≈
61.6434
n°v =
cm2
22
varillas
s=
23
cm
ok !!
𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
5.00 − 0.75 * 0.0254 − 2* 0.07 − 22 1
s= s=
0.2305
m
23.0521
s=
≈
23
cm
* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =
0.85 * 280 666.4 Tn
𝑃_𝑛= 𝑃_𝑢/∅
�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.70 * 0.40 A1 = 0.28 m2
Ø = 0.7
𝑃_𝑛 < 𝑃_𝑛𝑏
𝑃_𝑛 < 𝑃_𝑛𝑏
185.8250 < 666.4
Pn = 130.07753 0.7 Pn = 185.8250 Tn
* 10 * 0.28
Cumple
* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0
�_2=𝑇 ∗𝑋_1
√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:
𝑋_1=𝑇 ∗𝑡_2/𝑡_1
X1
√(�_2/�_1 ) >2 → �_0=2∗�_1
X1 =
X1 =
T Donde:
A2 = A2 =
3.6500 7.6129
2.0857 * m2
A0 = Pnb = Pnb =
0.85 * 210 999.6 Tn
* 10 * 0.56
2 * 0.28 𝑃_𝑛𝑏 > 𝑃_𝑛
999.6 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏
> 185.8250
3.6500 0.28
= 13.0357
A0 =
0.56
Cumple
ok !!
>
m2
2
3.65 *
2.0857
0.40 0.70 m
ok !!
〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2800 As min = 14 cm2 Diametro(ø) = 4
1
Pulg.
* 5.0671
=
20.2683
cm2
Cumple
ok !!
* PLANOS DE PLANTA Y PERFIL:
22 ø 3/4" @ 23
S = 4.80 21 ø 3/4" @ 23
T = 5.00
DOWELLS
4
VARILLAS TRANSVERSALES 22 ø 3/4" @ 23
ø 1"
VARILLAS LONGITUDINALES 21 ø 3/4" @ 23
d = 0.32
hz = 0.40
T = 5.00
* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 16: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P
24.37 15.98 2.30 1.95 210.00 500.00 3.50 4200.00 40.35
* Datos de la Columna: F'c: t1 t2
280.00 40.00 40.00
GRAFICA
Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn
N.P.T + 0.30
0.15
hf: 2.00
Df:
Kg/cm2 cm cm
* Datos de la Terreno:
N.F.C-1.95 σ(ult):
NPT NTN NFC
0.15 0.00 -1.85
N.T.N ± 0.00
m m m
3.50
1.85
* Esfuezo neto del terreno:
* Dimenciones de la Zapata:
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =
7.2142
Tn/m2
T=
2.40
m
S= 2.3649
≈
S=
2.40
m
Az =
5.76
m2
* Debe Cumplir: �_𝑣1= �_𝑣2
�_𝑍 = 𝑃/�_𝑛 5.5928
≈
* Nueva Area de la Zapata:
* Area de la Zapata:
Az =
𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2
T= 2.3649
m2
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
1
m
Lv2 =
1
m
Cumple ok !!
�_𝑣2= (𝑆 − 𝑡_1)/2
* EFECTOS DE CARGA EXCENTRICA: e1 = 0.41 e2 = 0.02 e2 e1
�_2= 𝑇/6
T 6
= 0.4000
e2
<
T 6
�_1= 𝑆/6
S 6
= 0.4000
e1
>
T 6
�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 = T = 2.40
40.35 ( 1 5.76
+ 6 *
0.41 2.40
σ1 = 14.5348 Tn/m2
14.5348
�_1 < �_𝑛 <
7.2142 No Cumple
+ 6 * 0.02 ) 2.40
P
* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)
e
σ1 =
σ2
40.35 ( 1 T*S
+ 6 *
0.41 S
T=
3.5
m
σ1 =
6.4953
Tn/m2
S=
3.2
m
σ2 =
0.7095
Tn/m2
�_𝑣1= (𝑇 − 𝑡_1)/2
σ1
* DISEÑO POR PUNZONAMIENTO: 0.40 +d
�_𝑛𝑢= 𝑃_𝑢/�_𝑧
m
𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣
Pu = 61.280535 Tn
S = 3.20
0.40
n
0.40 +d Wnu = σ1
0.40
T = 3.50 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶
+ 6 * 0.02 ) T
Wnu =
6.4953
Tn/m2
Lv1 =
1.55
m
�_𝑈/∅ ≤ �_𝐶
Ø = 0.85
* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =
61.280535 − 61.280535 − 61.280535 − 60.2413 −
6.4953 x (0.40 + d ) ( 0.40 + d ) 6.4953 x (0.16 + 0.80 d + d² ) 1.0392 − 5.1962 d − 6.4953 d² 5.1962 d − 6.4953 d² 1
2
0.27 x
=
+
4 0.40 0.40
* bo = 2m + 2n
Vc = Vc = Vc =
x 2 (0.40 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 0.80 245.7737 d + 614.4344 d² 2
* Reemplazando 1 y 2
528.7645 d²
+
( 245.7737d 208.9077 d
214.1039 d
−
d= d=
+ +
614.4344 d² ) * 0.85 522.2692 d²
60.2413 ≥ 0 0.1911 -0.5961
ℎ_𝑧 = d + ∅/2 +r
hz = 0.1911 + (3/4") 0.0254 + 0.07 2 hz = 0.27063 hz = ≈
𝑑 = ℎ_𝑧 − ∅/2 −r d= d=
* VERIFICACION POR CORTANTE:
0.30 − (3/4") 0.0254 − 0.07 2 0.22 m
0.30
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!
1.62
* Usamos:
60.2413 − 5.1962 d − 6.4953 d² ≤ 60.2413 − 5.1962 d − 6.4953 d² ≤
^
m
�_𝑛 ≤ �_�
�_𝑛= �_𝑢𝑑/∅
Ø = 0.85
σx =
4.2967
�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑
�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)
�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2
Vud = Vud =
5.3960 22.9654
* 3.20 Tn
* ( 1.55
−
0.22 )
Vc = Vc =
Vn = 22.965404 0.85 Vn = 27.0181 Tn
0.53 210 x 10 x 3.20 x 0.22 54.0702 Tn
�_𝑛 ≤ �_�
27.0181
≤
54.0702
Cumple ok !!
* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2
σx =
3.9330
�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =
8.4618
* 3.20 *
Mu =
21.6848
Tn - m
Ø = 0.9
( 1.55)² 3
𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2
a= a=
0.4199 0.0201
a=
0.0201
m
〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑
�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 21.6848
As = 0.9
*
4.2 *
As =
As min = 0.22 − 0.0201 2
27.3237
0.22 *
210 10.197 4200 10.197
* 3.20
* 0.22
As min = 0.001706 m2 As min = 17.06 cm2
cm2
�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛
27.3237 > 17.06
*VARILLAS LONGITUDINALES Diametro(ø) =
0.75
〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅
n°v =
Cumple
Pulg.
27.3237 2.8502
n°v =
9.5865
≈
n°v =
10
varillas
* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
3.20 − 0.75 * 0.0254 − 2* 0.07 − 10 1
s= s=
0.3379 33.7883
m
≈
*VARILLAS TRANSVERSALES Diametro(ø) =
0.75
Pulg.
�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =
As(T) =
27.3237 *
29.8852 2.8502
3.50 3.20 n°v = 10.4852
* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
−
* 0.0254 − 2*
As(T) =
≈
29.8852
n°v =
cm2
11
varillas
s=
33
cm
ok !!
𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
3.50 − 0.75 * 0.0254 − 2* 0.07 − 11 1
s= s=
0.3341
m
33.4095
s=
≈
33
cm
* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =
0.85 * 280 380.8 Tn
𝑃_𝑛= 𝑃_𝑢/∅
�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.40 * 0.40 A1 = 0.16 m2
Ø = 0.7
𝑃_𝑛 < 𝑃_𝑛𝑏
𝑃_𝑛 < 𝑃_𝑛𝑏
Pn = 61.280535 0.7 Pn = 87.5436 Tn
* 10 * 0.16
87.5436
< 380.8
Cumple
* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0
�_2=𝑇 ∗𝑋_1
√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:
𝑋_1=𝑇 ∗𝑡_2/𝑡_1
X1
√(�_2/�_1 ) >2 → �_0=2∗�_1
X1 =
X1 =
T Donde:
A2 = A2 =
2.4000 5.7600
2.4000 * m2
A0 = Pnb = Pnb =
0.85 * 210 571.2 Tn
* 10 * 0.32
2 * 0.16 𝑃_𝑛𝑏 > 𝑃_𝑛
571.2 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏
> 87.5436
2.4000 0.16
= 15.0000
A0 =
0.32
Cumple
ok !!
>
m2
2
2.40 *
2.4000
0.40 0.40 m
ok !!
〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 1600 As min = 8 cm2 Diametro(ø) = 4
1
Pulg.
* 5.0671
=
20.2683
cm2
Cumple
ok !!
* PLANOS DE PLANTA Y PERFIL:
11 ø 3/4" @ 33
S = 3.20 10 ø 3/4" @ 33
T = 3.50
DOWELLS
4
VARILLAS TRANSVERSALES 11 ø 3/4" @ 33
ø 1"
VARILLAS LONGITUDINALES 10 ø 3/4" @ 33
d = 0.22
hz = 0.30
T = 3.50
* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 17: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P
18.44 11.06 2.30 1.95 210.00 500.00 3.50 4200.00 29.51
* Datos de la Columna: F'c: t1 t2
280.00 40.00 40.00
GRAFICA
Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn
N.P.T + 0.30
0.15
hf: 2.00
Df:
Kg/cm2 cm cm
* Datos de la Terreno:
N.F.C-1.95 σ(ult):
NPT NTN NFC
0.15 0.00 -1.85
N.T.N ± 0.00
m m m
3.50
1.85
* Esfuezo neto del terreno:
* Dimenciones de la Zapata:
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =
7.2142
Tn/m2
T=
2.05
m
S= 2.0224
≈
S=
2.05
m
Az =
4.2025
m2
* Debe Cumplir: �_𝑣1= �_𝑣2
�_𝑍 = 𝑃/�_𝑛 4.0902
≈
* Nueva Area de la Zapata:
* Area de la Zapata:
Az =
𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2
T= 2.0224
m2
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
0.825
m
Lv2 =
0.825
m
Cumple ok !!
�_𝑣2= (𝑆 − 𝑡_1)/2
* EFECTOS DE CARGA EXCENTRICA: e1 = 0.40 e2 = 0.80 e2 e1
�_2= 𝑇/6
T 6
= 0.3417
e2
>
T 6
�_1= 𝑆/6
S 6
= 0.3417
e1
>
T 6
�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 = T = 2.05
29.51 ( 1 4.2025
+ 6 *
0.40 2.05
σ1 = 31.6818 Tn/m2
31.6818
�_1 < �_𝑛 <
7.2142 No Cumple
+ 6 * 0.80 ) 2.05
P
* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)
e
σ1 =
σ2
29.51 ( 1 T*S
+ 6 *
0.40 S
T=
3.8
m
σ1 =
6.5424
Tn/m2
S=
3.5
m
σ2 =
-2.1052
Tn/m2
�_𝑣1= (𝑇 − 𝑡_1)/2
σ1
* DISEÑO POR PUNZONAMIENTO: 0.40 +d
�_𝑛𝑢= 𝑃_𝑢/�_𝑧
m
𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣
Pu = 44.629623 Tn
S = 3.50
0.40
n
0.40 +d Wnu = σ1
0.40
T = 3.80 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶
+ 6 * 0.80 ) T
Wnu =
6.5424
Tn/m2
Lv1 =
1.7
m
�_𝑈/∅ ≤ �_𝐶
Ø = 0.85
* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =
44.629623 − 44.629623 − 44.629623 − 43.5828 −
6.5424 x (0.40 + d ) ( 0.40 + d ) 6.5424 x (0.16 + 0.80 d + d² ) 1.0468 − 5.2339 d − 6.5424 d² 5.2339 d − 6.5424 d² 1
2
0.27 x
=
+
4 0.40 0.40
* bo = 2m + 2n
Vc = Vc = Vc =
x 2 (0.40 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 0.80 245.7737 d + 614.4344 d² 2
* Reemplazando 1 y 2
528.8116 d²
+
( 245.7737d 208.9077 d
214.1416 d
−
d= d=
+ +
614.4344 d² ) * 0.85 522.2692 d²
43.5828 ≥ 0 0.1488 -0.5538
ℎ_𝑧 = d + ∅/2 +r
hz = 0.1488 + (3/4") 0.0254 + 0.07 2 hz = 0.22833 hz = ≈
𝑑 = ℎ_𝑧 − ∅/2 −r d= d=
* VERIFICACION POR CORTANTE:
0.25 − (3/4") 0.0254 − 0.07 2 0.17 m
0.25
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!
1.62
* Usamos:
43.5828 − 5.2339 d − 6.5424 d² ≤ 43.5828 − 5.2339 d − 6.5424 d² ≤
^
m
�_𝑛 ≤ �_�
�_𝑛= �_𝑢𝑑/∅
Ø = 0.85
σx =
3.0606
�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑
�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)
�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2
Vud = Vud =
4.8015 25.7119
* 3.50 Tn
* ( 1.7
−
0.17 )
Vc = Vc =
Vn = 25.711875 0.85 Vn = 30.2493 Tn
0.53 210 x 10 x 3.50 x 0.17 45.6986 Tn
�_𝑛 ≤ �_�
30.2493
≤
45.6986
Cumple ok !!
* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2
σx =
2.6737
�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =
7.8792
* 3.50 *
Mu =
26.5661
Tn - m
Ø = 0.9
( 1.7 )² 3
𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2
a= a=
0.3095 0.0305
a=
0.0305
m
〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑
�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 26.5661
As = 0.9
*
4.2 *
As =
As min = 0.17 − 0.0305 2
45.4207
0.22 *
210 10.197 4200 10.197
* 3.50
* 0.17
As min = 0.001442 m2 As min = 14.42 cm2
cm2
�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛
45.4207 > 14.42
*VARILLAS LONGITUDINALES Diametro(ø) =
0.75
〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅
n°v =
Cumple
Pulg.
45.4207 2.8502
n°v = 15.9358
≈
n°v =
16
varillas
* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
3.50 − 0.75 * 0.0254 − 2* 0.07 − 16 1
s= s=
0.2227 22.2730
m
≈
*VARILLAS TRANSVERSALES Diametro(ø) =
0.75
Pulg.
�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =
As(T) =
45.4207 *
49.3139 2.8502
3.80 3.50 n°v = 17.3017
* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
−
* 0.0254 − 2*
As(T) =
≈
49.3139
n°v =
cm2
18
varillas
s=
22
cm
ok !!
𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
3.80 − 0.75 * 0.0254 − 2* 0.07 − 18 1
s= s=
0.2142
m
21.4174
s=
≈
21
cm
* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =
0.85 * 280 380.8 Tn
𝑃_𝑛= 𝑃_𝑢/∅
�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.40 * 0.40 A1 = 0.16 m2
Ø = 0.7
𝑃_𝑛 < 𝑃_𝑛𝑏
𝑃_𝑛 < 𝑃_𝑛𝑏
Pn = 44.629623 0.7 Pn = 63.7566 Tn
* 10 * 0.16
63.7566
< 380.8
Cumple
* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0
�_2=𝑇 ∗𝑋_1
√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:
𝑋_1=𝑇 ∗𝑡_2/𝑡_1
X1
√(�_2/�_1 ) >2 → �_0=2∗�_1
X1 =
X1 =
T Donde:
A2 = A2 =
2.0500 4.2025
2.0500 * m2
A0 = Pnb = Pnb =
0.85 * 210 571.2 Tn
* 10 * 0.32
2 * 0.16 𝑃_𝑛𝑏 > 𝑃_𝑛
571.2 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏
> 63.7566
2.0500 0.16
= 12.8125
A0 =
0.32
Cumple
ok !!
>
m2
2
2.05 *
2.0500
0.40 0.40 m
ok !!
〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 1600 As min = 8 cm2 Diametro(ø) = 4
1
Pulg.
* 5.0671
=
20.2683
cm2
Cumple
ok !!
* PLANOS DE PLANTA Y PERFIL:
18 ø 3/4" @ 21
S = 3.50 16 ø 3/4" @ 22
T = 3.80
DOWELLS
4
VARILLAS TRANSVERSALES 18 ø 3/4" @ 21
ø 1"
VARILLAS LONGITUDINALES 16 ø 3/4" @ 22
d = 0.17
hz = 0.25
T = 3.80
* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 19: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P
65.06 34.90 2.30 1.95 210.00 500.00 3.50 4200.00 99.96
* Datos de la Columna: F'c: t1 t2
280.00 60.00 40.00
GRAFICA
Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn
N.P.T + 0.30
0.15
hf: 2.00
Df:
Kg/cm2 cm cm
* Datos de la Terreno:
N.F.C-1.95 σ(ult):
NPT NTN NFC
0.15 0.00 -1.85
N.T.N ± 0.00
m m m
3.50
1.85
* Esfuezo neto del terreno:
* Dimenciones de la Zapata:
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =
7.2142
Tn/m2
𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2
T= 3.8223
≈
T=
3.85
m
S= 3.6223
≈
S=
3.65
m
* Nueva Area de la Zapata:
* Area de la Zapata:
Az = 14.0525 m2
* Debe Cumplir: �_𝑣1= �_𝑣2
�_𝑍 = 𝑃/�_𝑛 Az = 13.8558 m2
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
1.625
m
Lv2 =
1.625
m
Cumple ok !!
�_𝑣2= (𝑆 − 𝑡_1)/2
* EFECTOS DE CARGA EXCENTRICA: e1 = 0.01 e2 = 0.77 e2 e1
�_2= 𝑇/6
T 6
= 0.6417
e2
>
T 6
�_1= 𝑆/6
S 6
= 0.6083
e1
<
T 6
�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 = T = 3.85
99.96 ( 1 14.0525
+ 6 *
0.01 3.65
σ1 = 15.7659 Tn/m2
15.7659
�_1 < �_𝑛 <
7.2142 No Cumple
+ 6 * 0.77 ) 3.85
P
* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)
e
σ1 =
σ2
99.96 ( 1 T*S
+ 6 *
0.01 S
T=
5.4
m
σ1 =
6.9140
Tn/m2
S=
5
m
σ2 =
0.4903
Tn/m2
�_𝑣1= (𝑇 − 𝑡_1)/2
σ1
* DISEÑO POR PUNZONAMIENTO: 0.60 +d
�_𝑛𝑢= 𝑃_𝑢/�_𝑧
m
𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣
Pu = 150.41074 Tn
S = 5.00
0.40
n
0.40 +d Wnu = σ1
0.60
T = 5.40 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶
+ 6 * 0.77 ) T
Wnu =
6.9140
Tn/m2
Lv1 =
2.4
m
�_𝑈/∅ ≤ �_𝐶
Ø = 0.85
* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =
150.41074 − 150.41074 − 150.41074 − 148.7514 −
6.9140 x (0.60 + d ) ( 0.40 + d ) 6.9140 x (0.24 + 1.00 d + d² ) 1.6594 − 6.9140 d − 6.9140 d² 6.9140 d − 6.9140 d² 1
2
0.27 x
=
+
4 0.60 0.40
* bo = 2m + 2n
Vc = Vc = Vc =
x 2 (0.60 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 1.00 307.2172 d + 614.4344 d² 2
* Reemplazando 1 y 2
529.1832 d²
+
( 307.2172d 261.1346 d
268.0486 d
−
d= d=
+ +
614.4344 d² ) * 0.85 522.2692 d²
148.7514 ≥ 0 0.3343 -0.8408
ℎ_𝑧 = d + ∅/2 +r
hz = 0.3343 + (3/4") 0.0254 + 0.07 2 hz = 0.41383 hz = ≈
𝑑 = ℎ_𝑧 − ∅/2 −r d= d=
* VERIFICACION POR CORTANTE:
0.45 − (3/4") 0.0254 − 0.07 2 0.37 m
0.45
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!
1.26
* Usamos:
148.7514 − 6.9140 d − 6.9140 d² ≤ 148.7514 − 6.9140 d − 6.9140 d² ≤
^
m
�_𝑛 ≤ �_�
�_𝑛= �_𝑢𝑑/∅
Ø = 0.85
σx =
4.4992
�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑
�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)
�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2
Vud = Vud =
5.7066 57.9216
* 5.00 Tn
* ( 2.4
−
0.37 )
Vc = Vc =
Vn = 57.921611 0.85 Vn = 68.1431 Tn
0.53 210 x 10 x 5.00 x 0.37 142.0879 Tn
�_𝑛 ≤ �_�
68.1431
≤
142.0879
Cumple ok !!
* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2
σx =
4.0590
�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =
8.9435
* 5.00 *
Mu =
85.8574
Tn - m
Ø = 0.9
( 2.4 )² 3
𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2
a= a=
0.7099 0.0301
a=
0.0301
m
〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑
�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 85.8574
As = 0.9
*
4.2 *
As =
As min = 0.37 − 0.0301 2
63.9922
0.22 *
210 10.197 4200 10.197
* 5.00
* 0.37
As min = 0.004484 m2 As min = 44.84 cm2
cm2
�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛
63.9922 > 44.84
*VARILLAS LONGITUDINALES Diametro(ø) =
0.75
〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅
n°v =
Cumple
Pulg.
63.9922 2.8502
n°v = 22.4516
≈
n°v =
23
varillas
* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
5.00 − 0.75 * 0.0254 − 2* 0.07 − 23 1
s= s=
0.2200 22.0043
m
≈
*VARILLAS TRANSVERSALES Diametro(ø) =
0.75
Pulg.
�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =
As(T) =
63.9922 *
69.1116 2.8502
5.40 5.00 n°v = 24.2477
* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
−
* 0.0254 − 2*
As(T) =
≈
69.1116
n°v =
cm2
25
varillas
s=
22
cm
ok !!
𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
5.40 − 0.75 * 0.0254 − 2* 0.07 − 25 1
s= s=
0.2184
m
21.8373
s=
≈
21
cm
* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =
0.85 * 280 571.2 Tn
𝑃_𝑛= 𝑃_𝑢/∅
�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.60 * 0.40 A1 = 0.24 m2
Ø = 0.7
𝑃_𝑛 < 𝑃_𝑛𝑏
𝑃_𝑛 < 𝑃_𝑛𝑏
214.8725 < 571.2
Pn = 150.41074 0.7 Pn = 214.8725 Tn
* 10 * 0.24
Cumple
* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0
�_2=𝑇 ∗𝑋_1
√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:
𝑋_1=𝑇 ∗𝑡_2/𝑡_1
X1
√(�_2/�_1 ) >2 → �_0=2∗�_1
X1 =
X1 =
T Donde:
A2 = A2 =
3.8500 9.8817
2.5667 * m2
A0 = Pnb = Pnb =
0.85 * 210 856.8 Tn
* 10 * 0.48
2 * 0.24 𝑃_𝑛𝑏 > 𝑃_𝑛
856.8 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏
> 214.8725
3.8500 0.24
= 16.0417
A0 =
0.48
Cumple
ok !!
>
m2
2
3.85 *
2.5667
0.40 0.60 m
ok !!
〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2400 As min = 12 cm2 Diametro(ø) = 4
1
Pulg.
* 5.0671
=
20.2683
cm2
Cumple
ok !!
* PLANOS DE PLANTA Y PERFIL:
25 ø 3/4" @ 21
S = 5.00 23 ø 3/4" @ 22
T = 5.40
DOWELLS
4
VARILLAS TRANSVERSALES 25 ø 3/4" @ 21
ø 1"
VARILLAS LONGITUDINALES 23 ø 3/4" @ 22
d = 0.37
hz = 0.45
T = 5.40
* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 20: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P
47.65 19.97 2.30 1.95 210.00 500.00 3.50 4200.00 67.61
* Datos de la Columna: F'c: t1 t2
280.00 70.00 40.00
GRAFICA
Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn
N.P.T + 0.30
0.15
hf: 2.00
Df:
Kg/cm2 cm cm
* Datos de la Terreno:
N.F.C-1.95 σ(ult):
NPT NTN NFC
0.15 0.00 -1.85
N.T.N ± 0.00
m m m
3.50
1.85
* Esfuezo neto del terreno:
* Dimenciones de la Zapata:
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2
�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =
7.2142
Tn/m2
T=
3.25
m
S= 2.9114
≈
S=
2.95
m
Az =
9.5875
m2
* Debe Cumplir: �_𝑣1= �_𝑣2
�_𝑍 = 𝑃/�_𝑛 9.3721
≈
* Nueva Area de la Zapata:
* Area de la Zapata:
Az =
T= 3.2114
m2
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
1.275
m
Lv2 =
1.275
m
Cumple
�_𝑣2= (𝑆 − 𝑡_1)/2
ok !!
* EFECTOS DE CARGA EXCENTRICA: e1 = 0.88 e2 = 0.78
e1 e2
�_2= 𝑇/6
T 6
= 0.5417
e2
>
T 6
�_1= 𝑆/6
S 6
= 0.4917
e1
>
T 6
�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 =
T = 3.25
67.61 ( 1 9.5875
+ 6 *
0.88 2.95
σ1 = 29.8293 Tn/m2
29.8293
�_1 < �_𝑛 <
7.2142 No Cumple
+ 6 * 0.78 ) 3.25
P
* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)
e
σ1 =
σ1
67.61 ( 1 T*S
+ 6 *
0.88 S
T=
5.5
m
σ1 =
6.7761
Tn/m2
S=
5.2
m
σ2 =
-2.0480
Tn/m2
�_𝑣1= (𝑇 − 𝑡_1)/2
σ2
* DISEÑO POR PUNZONAMIENTO: 0.70 +d
�_𝑛𝑢= 𝑃_𝑢/�_𝑧
m
𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣
Pu = 100.64719 Tn
S = 5.20
0.40
n
0.40 +d Wnu = σ1
0.70
T = 5.50 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶
+ 6 * 0.78 ) T
Wnu =
6.7761
Tn/m2
Lv1 =
2.4
m
�_𝑈/∅ ≤ �_𝐶
Ø = 0.85
* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =
100.64719 − 100.64719 − 100.64719 − 98.7499 −
6.7761 x (0.70 + d ) ( 0.40 + d ) 6.7761 x (0.28 + 1.10 d + d² ) 1.8973 − 7.4537 d − 6.7761 d² 7.4537 d − 6.7761 d² 1
2
0.27 x
+
4 0.70 0.40
* bo = 2m + 2n
Vc = Vc = Vc =
x 2 (0.70 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 1.10 337.9389 d + 614.4344 d² 2
* Reemplazando 1 y 2
529.0453 d²
+
( 337.9389d 287.2481 d
294.7018 d
−
d= d=
+ +
614.4344 d² ) * 0.85 522.2692 d²
98.7499 ≥ 0 0.2355 -0.7926
ℎ_𝑧 = d + ∅/2 +r
hz = 0.2355 + (3/4") 0.0254 + 0.07 2 hz = 0.31503 hz = ≈
𝑑 = ℎ_𝑧 − ∅/2 −r d= d=
* VERIFICACION POR CORTANTE:
0.35 − (3/4") 0.0254 − 0.07 2 0.27 m
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!
= 1.1571429 * Usamos:
98.7499 − 7.4537 d − 6.7761 d² ≤ 98.7499 − 7.4537 d − 6.7761 d² ≤
^
0.35
m
�_𝑛 ≤ �_�
�_𝑛= �_𝑢𝑑/∅
Ø = 0.85
σx =
3.3588
�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑
�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)
�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2
Vud = Vud =
5.0674 56.1269
* 5.20 Tn
* ( 2.4
−
0.27 )
Vc = Vc =
Vn = 56.126914 0.85 Vn = 66.0317 Tn
0.53 210 x 10 x 5.20 x 0.27 107.8332 Tn
�_𝑛 ≤ �_�
66.0317
≤
107.8332
Cumple
ok !!
* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2
σx =
2.9256
�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =
8.2389
* 5.20 *
Mu =
82.2571
Tn - m
Ø = 0.9
( 2.4 )² 3
𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2
a= a=
0.5007 0.0393
a=
0.0393
m
〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑
�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 82.2571
As = 0.9
*
4.2 *
As =
As min = 0.27 − 0.0393 2
86.9288
0.22 *
210 10.197 4200 10.197
* 5.20
* 0.27
As min = 0.003403 m2 As min = 34.03 cm2
cm2
�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛
86.9288 > 34.03
*VARILLAS LONGITUDINALES Diametro(ø) =
0.75
〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅
n°v =
Cumple
Pulg.
86.9288 2.8502
n°v = 30.4989
≈
n°v =
31
varillas
* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
5.20 − 0.75 * 0.0254 − 2* 0.07 − 31 1
s= s=
0.1680 16.8032
m
≈
*VARILLAS TRANSVERSALES Diametro(ø) =
0.75
Pulg.
�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =
As(T) =
86.9288 *
91.9439 2.8502
5.50 5.20 n°v = 32.2584
* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
−
* 0.0254 − 2*
As(T) =
≈
91.9439
n°v =
cm2
33
varillas
s=
16
cm
ok !!
𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
5.50 − 0.75 * 0.0254 − 2* 0.07 − 33 1
s= s=
0.1669
m
16.6905
s=
≈
16
cm
* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =
0.85 * 280 666.4 Tn
𝑃_𝑛= 𝑃_𝑢/∅
�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.70 * 0.40 A1 = 0.28 m2
Ø = 0.7
𝑃_𝑛 < 𝑃_𝑛𝑏
𝑃_𝑛 < 𝑃_𝑛𝑏
143.7817 < 666.4
Pn = 100.64719 0.7 Pn = 143.7817 Tn
* 10 * 0.28
Cumple
* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0
�_2=𝑇 ∗𝑋_1
√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:
𝑋_1=𝑇 ∗𝑡_2/𝑡_1
X1
√(�_2/�_1 ) >2 → �_0=2∗�_1
X1 =
X1 =
T Donde:
A2 = A2 =
3.2500 6.0357
1.8571 * m2
A0 = Pnb = Pnb =
0.85 * 210 999.6 Tn
* 10 * 0.56
2 * 0.28 𝑃_𝑛𝑏 > 𝑃_𝑛
999.6 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏
> 143.7817
3.2500 0.28
= 11.6071
A0 =
0.56
Cumple
ok !!
>
m2
2
3.25 *
1.8571
0.40 0.70 m
ok !!
〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2800 As min = 14 cm2 Diametro(ø) = 4
1
Pulg.
* 5.0671
=
20.2683
cm2
Cumple
ok !!
* PLANOS DE PLANTA Y PERFIL:
33 ø 3/4" @ 16
S = 5.20 31 ø 3/4" @ 16
T = 5.50
DOWELLS
4
VARILLAS TRANSVERSALES 33 ø 3/4" @ 16
ø 1"
VARILLAS LONGITUDINALES 31 ø 3/4" @ 16
d = 0.27
hz = 0.35
T = 5.50
* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 21: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P
38.60 15.15 2.30 1.95 210.00 500.00 3.50 4200.00 53.75
* Datos de la Columna: F'c: t1 t2
280.00 70.00 40.00
GRAFICA
Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn
N.P.T + 0.30
0.15
hf: 2.00
Df:
Kg/cm2 cm cm
* Datos de la Terreno:
N.F.C-1.95 σ(ult):
NPT NTN NFC
0.15 0.00 -1.85
N.T.N ± 0.00
m m m
3.50
1.85
* Esfuezo neto del terreno:
* Dimenciones de la Zapata:
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2
�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =
7.2142
Tn/m2
T=
2.90
m
S= 2.5795
≈
S=
2.60
m
Az =
7.54
m2
* Debe Cumplir: �_𝑣1= �_𝑣2
�_𝑍 = 𝑃/�_𝑛 7.4501
≈
* Nueva Area de la Zapata:
* Area de la Zapata:
Az =
T= 2.8795
m2
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
1.1
m
Lv2 =
1.1
m
Cumple
�_𝑣2= (𝑆 − 𝑡_1)/2
ok !!
* EFECTOS DE CARGA EXCENTRICA: e1 = 0.82 e2 = 0.18
e1 e2
�_2= 𝑇/6
T 6
= 0.4833
e2
<
T 6
�_1= 𝑆/6
S 6
= 0.4333
e1
>
T 6
�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 =
T = 2.90
53.75 ( 1 7.54
+ 6 *
0.82 2.60
σ1 = 23.2714 Tn/m2
23.2714
�_1 < �_𝑛 <
7.2142 No Cumple
+ 6 * 0.18 ) 2.90
P
* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)
e
σ1 =
σ1
53.75 ( 1 T*S
+ 6 *
0.82 S
T=
4.5
m
σ1 =
6.8574
Tn/m2
S=
4.2
m
σ2 =
-1.1700
Tn/m2
�_𝑣1= (𝑇 − 𝑡_1)/2
σ2
* DISEÑO POR PUNZONAMIENTO: 0.70 +d
�_𝑛𝑢= 𝑃_𝑢/�_𝑧
m
𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣
Pu = 79.78838 Tn
S = 4.20
0.40
n
0.40 +d Wnu = σ1
0.70
T = 4.50 * CONDICION DE DISEÑO: �_𝑈/∅ ≤ �_𝐶
+ 6 * 0.18 ) T
Wnu =
6.8574
Tn/m2
Lv1 =
1.9
m
�_𝑈/∅ ≤ �_𝐶
Ø = 0.85
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =
79.78838 79.78838 79.78838 77.8683
x x − − 7.5431 d
− 6.8574 − 6.8574 − 1.9201
* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod
(0.70 + d ) ( 0.40 + d ) (0.28 + 1.10 d + d² ) 7.5431 d − 6.8574 d² 1 − 6.8574 d²
2
0.27 x
+
4 0.70 0.40
* bo = 2m + 2n
Vc = Vc = Vc =
x 2 (0.70 +d + 0.40 + d ) d 1.06 210 x 10 ( + 2 d ) d 307.2172 1.10 337.9389 d + 614.4344 d² 2
* Reemplazando 1 y 2
529.1266 d²
+
( 337.9389d 287.2481 d
294.7912 d
−
d= d=
+ +
614.4344 d² ) * 0.85 522.2692 d²
77.8683 ≥ 0 0.1955 -0.7527
ℎ_𝑧 = d + ∅/2 +r
hz = 0.1955 + (3/4") 0.0254 + 0.07 2 hz = 0.27503 hz = ≈
𝑑 = ℎ_𝑧 − ∅/2 −r d= d=
* VERIFICACION POR CORTANTE:
0.30 − (3/4") 0.0254 − 0.07 2 0.22 m
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!
= 1.1571429 * Usamos:
77.8683 − 7.5431 d − 6.8574 d² ≤ 77.8683 − 7.5431 d − 6.8574 d² ≤
^
0.30
m
�_𝑛 ≤ �_�
�_𝑛= �_𝑢𝑑/∅
Ø = 0.85
σx =
3.8605
�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑
�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)
�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2
Vud = Vud =
5.3590 37.8128
* 4.20 Tn
* ( 1.9
−
0.22 )
Vc = Vc =
Vn = 37.812829 0.85 Vn = 44.4857 Tn
0.53 210 x 10 x 4.20 x 0.22 70.9672 Tn
�_𝑛 ≤ �_�
44.4857
≤
70.9672
Cumple
ok !!
* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2
σx =
3.4681
�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =
8.5914
* 4.20 *
Mu =
43.4211
Tn - m
Ø = 0.9
( 1.9 )² 3
𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2
a= a=
0.4085 0.0315
a=
0.0315
m
〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑
�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2)) 43.4211
As = 0.9
*
4.2 *
As =
As min = 0.22 − 0.0315 2
56.2413
0.22 *
210 10.197 4200 10.197
* 4.20
* 0.22
As min = 0.002240 m2 As min = 22.40 cm2
cm2
�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛
56.2413 > 22.40
*VARILLAS LONGITUDINALES Diametro(ø) =
0.75
〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅
n°v =
Cumple
Pulg.
56.2413 2.8502
n°v = 19.7322
≈
n°v =
20
varillas
* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
4.20 − 0.75 * 0.0254 − 2* 0.07 − 20 1
s= s=
0.2127 21.2682
m
≈
*VARILLAS TRANSVERSALES Diametro(ø) =
0.75
Pulg.
�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆 〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =
As(T) =
56.2413 *
60.2586 2.8502
4.50 4.20 n°v = 21.1417
* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
−
* 0.0254 − 2*
As(T) =
≈
60.2586
n°v =
cm2
22
varillas
s=
21
cm
ok !!
𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
4.50 − 0.75 * 0.0254 − 2* 0.07 − 22 1
s= s=
0.2067
m
20.6712
s=
≈
20
cm
* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 Pnb = Pnb =
0.85 * 280 666.4 Tn
𝑃_𝑛= 𝑃_𝑢/∅
�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.70 * 0.40 A1 = 0.28 m2
Ø = 0.7
𝑃_𝑛 < 𝑃_𝑛𝑏
𝑃_𝑛 < 𝑃_𝑛𝑏
113.9834 < 666.4
Pn = 79.78838 0.7 Pn = 113.9834 Tn
* 10 * 0.28
Cumple
* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0
�_2=𝑇 ∗𝑋_1
√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:
𝑋_1=𝑇 ∗𝑡_2/𝑡_1
X1
√(�_2/�_1 ) >2 → �_0=2∗�_1
X1 =
X1 =
T Donde:
A2 = A2 =
2.9000 4.8057
1.6571 * m2
A0 = Pnb = Pnb =
0.85 * 210 999.6 Tn
* 10 * 0.56
2 * 0.28 𝑃_𝑛𝑏 > 𝑃_𝑛
999.6 * PARA ZONA SISMICA (DOWELLS) 𝑃_𝑛 ≤ 𝑃_𝑛𝑏
> 113.9834
2.9000 0.28
= 10.3571
A0 =
0.56
Cumple
ok !!
>
m2
2
2.90 *
1.6571
0.40 0.70 m
ok !!
〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2800 As min = 14 cm2 Diametro(ø) = 4
1
Pulg.
* 5.0671
=
20.2683
cm2
Cumple
ok !!
* PLANOS DE PLANTA Y PERFIL:
22 ø 3/4" @ 20
S = 4.20 20 ø 3/4" @ 21
T = 4.50
DOWELLS
4
VARILLAS TRANSVERSALES 22 ø 3/4" @ 20
ø 1"
VARILLAS LONGITUDINALES 20 ø 3/4" @ 21
d = 0.22
hz = 0.30
T = 4.50
* DISEÑO DE UNA ZAPATA AISLADA CON EXCENTRICIDADES * Datos de la Zapata N° 22: CM: CV: ɣc: ɣs: F'c: S/Cpiso: σ(ult): fy: P
58.03 26.00 2.30 1.95 210.00 500.00 3.50 4200.00 84.03
GRAFICA
Tn Tn Tn/m3 Tn/m3 Kg/cm2 Kg/cm2 Kg/cm2 Kg/cm2 Tn
N.P.T + 0.30
N.T.N ± 0.00 0.15
* Datos de la Columna: hf: 2.00 F'c: t1 t2
280.00 60.00 40.00
Df:
Kg/cm2 cm cm
* Datos de la Terreno:
N.F.C-1.95 σ(ult):
NPT NTN NFC
0.15 0.00 -1.85
m m m
3.50
1.85
* Esfuezo neto del terreno:
* Dimenciones de la Zapata:
�_𝑛 = �_𝑎𝑑𝑚 − ɣ𝑝𝑟𝑜𝑚 ∗ ℎ𝑓 − 𝑆/𝐶
𝑇 =√(�_𝑍 )+ (𝑡_1−𝑡_2)/2
�_𝑎𝑑𝑚 = �_𝑢𝑙𝑡/𝐹_𝑠 σn =
7.2142
Tn/m2
𝑆 =√(�_𝑍 ) − (𝑡_1−𝑡_2)/2
T= 3.5129
≈
T=
3.55
m
S= 3.3129
≈
S=
3.35
m
* Nueva Area de la Zapata:
* Area de la Zapata:
Az = 11.8925 m2
* Debe Cumplir: �_𝑣1= �_𝑣2
�_𝑍 = 𝑃/�_𝑛 Az = 11.6478 m2
�_𝑣1= (𝑇 − 𝑡_1)/2
Lv1 =
1.475
m
Lv2 =
1.475
m
Cumple ok !!
�_𝑣2= (𝑆 − 𝑡_1)/2
* EFECTOS DE CARGA EXCENTRICA: e1 = 0.00 e2 = 0.27 e2 e1
�_2= 𝑇/6
T 6
= 0.5917
e2
<
T 6
�_1= 𝑆/6
S 6
= 0.5583
e1
<
T 6
�_(1−2)= 𝑃/�_𝑍 (1 ± 〖 6� 〗 _1/𝑆 ± 〖 6� 〗 _2/𝑇) σ1 = T = 3.55
84.03 ( 1 11.8925
+ 6 *
0.00 3.35
σ1 = 10.2901 Tn/m2
10.2901
�_1 < �_𝑛 <
7.2142 No Cumple
+ 6 * 0.27 ) 3.55
P
* POR TANTEO �_1= 𝑃/(𝑇 ∗𝑆)(1 + 〖 6� 〗 _1/𝑆 + 〖 6� 〗 _2/𝑇)
e
σ1 =
σ2
84.03 ( 1 T*S
+ 6 *
0.00 S
T=
4.4
m
σ1 =
6.5322
Tn/m2
S=
4
m
σ2 =
3.0165
Tn/m2
�_𝑣1= (𝑇 − 𝑡_1)/2
σ1
* DISEÑO POR PUNZONAMIENTO: 0.60 +d
�_𝑛𝑢= 𝑃_𝑢/�_𝑧
m
𝑃_𝑢= 1.7 𝐶𝑚+1.4 𝐶𝑣
Pu = 125.44149 Tn
S = 4.00
0.40
n
0.40 +d Wnu = σ1
0.60
T = 4.40 * CONDICION DE DISEÑO:
+ 6 * 0.27 ) T
Wnu =
6.5322
Tn/m2
Lv1 =
1.9
m
�_𝑈/∅ ≤ �_𝐶
Ø = 0.85
* Escogemos el menor de los dos: Vc=0.27(2+4/β) √( 〖𝑓 _� 〗 ^′ ) bod
〖� _𝑈 = 𝑃 〗 _𝑈− �_𝑛𝑢 ∗𝑚 ∗𝑛 Vu = Vu = Vu = Vu =
125.44149 − 125.44149 − 125.44149 − 123.8738 −
6.5322 x (0.60 + d ) ( 0.40 + d ) 6.5322 x (0.24 + 1.00 d + d² ) 1.5677 − 6.5322 d − 6.5322 d² 6.5322 d − 6.5322 d² 1
2
0.27 x
=
+
4 0.60 0.40
* bo = 2m + 2n
Vc = Vc = Vc =
x 2 (0.60 +d + 0.40 + d ) d 1.06 210 x 10 307.2172 ( 1.00 + 2 d ) d 307.2172 d + 614.4344 d² 2
* Reemplazando 1 y 2
528.8014 d²
+
( 307.2172d 261.1346 d
267.6668 d
−
d= d=
+ +
614.4344 d² ) * 0.85 522.2692 d²
123.8738 ≥ 0 0.2931 -0.7993
ℎ_𝑧 = d + ∅/2 +r
hz = 0.2931 + (3/4") 0.0254 + 0.07 2 hz = 0.37263 hz = ≈
𝑑 = ℎ_𝑧 − ∅/2 −r d= d=
* VERIFICACION POR CORTANTE:
0.40 − (3/4") 0.0254 − 0.07 2 0.32 m
0.40
��=1.06√( 〖𝑓 _� 〗 ^′ ) 𝑏𝑜d = 1.06 ok !!
1.26
* Usamos:
123.8738 − 6.5322 d − 6.5322 d² ≤ 123.8738 − 6.5322 d − 6.5322 d² ≤
^
m
�_𝑛 ≤ �_�
�_𝑛= �_𝑢𝑑/∅
Ø = 0.85
σx =
5.2698
�_�=0.53 √( 〖𝑓 _� 〗 ^′ ) ∗𝑆 ∗𝑑
�_𝑢𝑑=((�_1+ �_𝑥)/2)∗𝑆 ∗(�_�−𝑑)
�_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1+𝑑))/𝑇+�_2
Vud = Vud =
5.9010 37.2943
* 4.00 Tn
* ( 1.9
−
Vc = Vc =
0.32 )
Vn = 37.294289 0.85 Vn = 43.8756 Tn
0.53 210 x 10 x 4.00 x 0.32 98.3095 Tn
�_𝑛 ≤ �_�
43.8756
≤
98.3095
Cumple ok !!
* DISEÑO POR FLEXION: �_𝑥=((�_1 − �_2)(�_𝑣+ 𝑡_1))/𝑇+�_2
σx =
5.0141
�_𝑠= �_𝑢/(∅ ∗ 〖𝑓 _� 〗 ^′∗(𝑑−𝑎/2))
�_𝑢=(�_𝑥/2+�_1) ∗ 𝑆∗ 〖� _𝑣 〗 ^2/3 Mu =
9.0393
* 4.00 *
Mu =
43.5090
Tn - m
Ø = 0.9
( 1.9 )² 3
As min = 0.9
*
4.2 *
As =
0.32 − 0.0219 2
37.2447
cm2
a= a=
0.6181 0.0219
a=
0.0219
m
〖�𝑠〗 _𝑚𝑖𝑛=0.22 ∗√( 〖𝑓 _� 〗 ^′/10.197)/( 〖𝑓 _� 〗 ^′/10.197) ∗𝑆 ∗𝑑
43.5090
As =
𝑎= (2𝑑 ± √(4 𝑑^2 −(8 �_𝑢)/(0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ ∅ ∗𝑆)))/2
0.22 *
210 10.197 4200 10.197
* 4.00
As min = 0.003103 m2 As min = 31.03 cm2
* 0.32
�_𝑠> 〖�𝑠〗 _𝑚𝑖𝑛
37.2447 > 31.03
Cumple
ok !!
*VARILLAS LONGITUDINALES Diametro(ø) =
0.75
〖𝑛 ^° 〗 _𝑣= �_𝑠/�_∅
n°v =
Pulg.
37.2447 2.8502
n°v = 13.0673
≈
n°v =
14
varillas
* Separación 𝑠= (𝑆 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
4.00 − 0.75 * 0.0254 − 2* 0.07 − 14 1
s= s=
0.2955
m
29.5458
≈
s=
29
cm
s=
30
cm
*VARILLAS TRANSVERSALES Diametro(ø) =
0.75
Pulg.
�_𝑠 (𝑇)= �_𝑠∗𝑇/𝑆
As(T) =
〖𝑛 ^° 〗 _𝑣= �_(𝑠(𝑇))/�_∅ n°v =
40.9692 2.8502
37.2447 *
4.40 4.00 n°v = 14.3740
As(T) =
≈
40.9692
n°v =
cm2
15
varillas
* Separación 𝑠= (𝑇 − ∅ −2𝑟)/( 〖𝑛 ^° 〗 _𝑣 −1)
s=
4.40 − 0.75 * 0.0254 − 2* 0.07 − 15 1
s= s=
0.3029 30.2925
m
≈
* VERIFICACION POR APLASTAMIENTO: *COLUMNA - ZAPATA Ø = 0.7
𝑃_𝑛 < 𝑃_𝑛𝑏
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_1 *
* 10 *
�_1= 𝑡_(1 )∗ 𝑡_2 A1 = 0.60 * 0.40 A1 = 0.24 m2
𝑃_𝑛= 𝑃_𝑢/∅
Pn = 125.44149 0.7
𝑃_𝑛 < 𝑃_𝑛𝑏
179.2021 < 571.2
Cumple
ok !!
Pnb = Pnb =
0.85 * 280 571.2 Tn
* 10 * 0.24
Pn = 179.2021 Tn
* ZAPATA - SUELO 𝑃_𝑛𝑏 > 𝑃_𝑛
�_2=𝑇 ∗𝑋_1
√(�_2/�_1 ) ≤2 → �_0= √(�_2/�_1 ) ∗ �_1 Si:
𝑃_𝑛𝑏=0.85 ∗ 〖𝑓 _� 〗 ^′ ∗ �_0
𝑋_1=𝑇 ∗𝑡_2/𝑡_1
X1
√(�_2/�_1 ) >2 → �_0=2∗�_1
X1 =
X1 =
T Donde:
A2 = A2 =
3.5500 8.4017
2.3667 * m2
A0 = Pnb = Pnb =
0.85 * 210 856.8 Tn
3.5500 0.24
2 * 0.24
* 10 * 0.48
𝑃_𝑛𝑏 > 𝑃_𝑛
856.8 * PARA ZONA SISMICA (DOWELLS)
> 179.2021
A0 =
0.48
Cumple
ok !!
𝑃_𝑛 ≤ 𝑃_𝑛𝑏
〖�𝑠〗 _𝑚𝑖𝑛=0.005 ∗ �_1 As min = 0.005 * 2400 As min = 12 cm2 Diametro(ø) = 4
1
* 5.0671
Pulg. =
20.2683
cm2
* PLANOS DE PLANTA Y PERFIL:
15 ø 3/4" @ 30
Cumple
= 14.7917
ok !!
>
m2
2
3.55 *
2.3667
0.40 0.60 m
S = 4.00 14 ø 3/4" @ 29
T = 4.40
DOWELLS
4
VARILLAS TRANSVERSALES 15 ø 3/4" @ 30
ø 1"
VARILLAS LONGITUDINALES 14 ø 3/4" @ 29
d = 0.32
hz = 0.40
T = 4.40