diseño de una zapata combinada
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PRACTICA CALIFICADA
TRABAJO DOMICILIARIO
EJERCICIO PRACTICO
Diseño de Zapata Combinada
6.00
6.00
5.60 5.60
40X6040X60
60X40
60X40
60X4060X40 60X40
60X40 60X40
WL=1800 kg/m
WD=2550 kg/m
WL=1800 kg/m
WD=2250 kg/m
A B C
40X60 40X80 40X60
40X6040X8040X60
30X50 30X50
30X5030X50
Portico 2
3.00
3.00
6.00 6.00
WL=1600 kg/m
WD=2550 kg/m
WL=1600 kg/m
WD=1980 kg/m
3.00
3.00
5.60 5.601 2 3
60X40
30X50 30X50
30X5030X50
60X4080X4060X40
60X40 80X40
Portico B
ANALISIS ESTRUCTURAL
PORTICO B
CARGA MUERTA
L1: 5.6 m
L2: 5.6 m
h1: 3 m
h2: 3 m
W1: 2.25 TON/m
W2: 1.98 TON/m
C1: 60 x 40
C2: 40 x 80
V1: 30 x 50
V2: 30 X 50
1. CALCULO DE RIGIDECES
NODO 1
k12= 558.03571
k14= 1066.6667
NODO 2
k21= 558.03571
k23= 558.03571
k25= 5688.8889
NODO3
k32= 558.03571
k36= 1066.6667
NODO 4
k41= 1066.6667
k45= 558.03571
k47= 1066.6667
NODO 5
k52= 5688.8889
k58= 5688.8889
k54= 558.03571
k56= 558.03571
NODO 6
k63= 1066.6667
k65= 558.03571
k69= 1066.6667
1 2 3
4 5 6
7 8 9
CARGA VIVA
NODO 1 NODO 4
d12= d41= 0.396
d14= d45= 0.207
d47= 0.396
NODO 2
d21= NODO 5
d23= d52= 0.455
d25= d58= 0.455
d54= 0.045
NODO3 d56= 0.045
d32=
d36= NODO 6
d63= 0.396
d65= 0.207
d69= 0.396
M1-2 Tn-m
M2-1 Tn-m
M2-3 Tn-m
M3-2 Tn-m
M4-5 Tn-m
M5-4 Tn-m
M5-6 Tn-m
M6-5 Tn-m
-5.88
5.88
-5.88
5.88
-5.1744
5.1744
-5.1744
5.1744
0.657
3.MOMENTOS DE EMPOTRAMIENTO
0.082
0.082
0.836
0.343
2. FACTORES DE DISTRIBUCION
0.343
0.657
L1: 5.6 m
L2: 5.6 m
h1: 3 m
h2: 3 m
W1: 1.60 TON/m
W2: 1.6 TON/m
C1: 60 x 40
C2: 40 x 80
V1: 30 x 50
V2: 30 X 50
M1-2 Tn-m
M2-1 Tn-m
M2-3 Tn-m
M3-2 Tn-m
M4-5 Tn-m
M5-4 Tn-m
M5-6 Tn-m
M6-5 Tn-m
-4.181333
4.1813333
-4.181333
4.1813333
-4.181333
4.1813333
4.1813333
3.MOMENTOS DE EMPOTRAMIENTO
-4.181333
HARDLY CROSS “CARGA MUERTA”
-0.0
00
8
-0.8
86
6
-1.1
65
2
0.2
61
3
0.0
18
1
0.0
12-4.953 6.344
-0.0
26
0.0
40
0.0
00
-0.0
02
0.00
3
0.0
52
0.8
30
0.8
86
0.0
00
0.0005 0.0002
-0.0002 -0.0004
0.0030 0.0015
-0.0011 -0.0023
-0.0025 -0.0050
0.0548 0.0274
0.0039 0.0078
-5.880 5.880
0.8689 0.4345
0.0
36
-0.0
02
-1.7
73
0.3
96
-2.3
30
0.5
23
-0.0
04
0.0
010.207 0.045
0.4
55
-0.0
51
0.0
79
-0.0
23
0.0
06
0.1
05
1.6
61
0.3
96
1.7
72
0.0
01
0.0
05
-0.0
02
-0.0
01
-3.1
80
0.3
96
-2.3
30
-1.3
16
0.5
23
-0.0
95
0.0
36
-0.3
38
-0.0
51
0.2
88
0.4
55 -5.880 5.880
0.045 0.207-0.0
01
-0.0
04
0.0
09
-0.0
23
0.0
40
0.0
79
-0.0
18
0.1
05
-0.2
62
1.6
61
1.6
89
0.3
96
3.1
80
0.0
01
-0.0
01
0.0
06
-0.0050 -0.0025
-0.6096 -1.2192
0.0078 0.0039
0.1367 0.2734
-0.0023 -0.0011
0.0095 0.0189
-0.0004 -0.0002
-0.0004 -0.0008
-0.0
02
-3.7
01
-6.344 4.952 -2.6
32
0.2
61
-0.1
90
0.0
18
0.0
10
-0.0
01
-0.6
76
-0.0
26
0.5
76
0.8
36
0.6
57
-1.1
65
-0.0
02
-0.0
02
0.0
18
-0.0
12
0.0
79
0.0
40
-0.0
37
0.0
52
-0.5
23
0.8
30
3.3
79
0.6
57
3.7
01
0.0
00
-0.0
02
0.00
3
-5.174 5.174 -5.174 5.174
0.343 0.082 0.082 0.343
0.0282 0.0565 -0.6885 -1.3770
-0.0331 -0.0663 -0.0497 -0.0994
1.7676 0.8838 0.0565 0.0282
0.0039 0.0078 0.0026 0.0052
-0.2738 -0.1369 -0.0663 -0.0331
0.0009 0.0018 -0.0005 -0.0011
-0.0193 -0.0097 0.0078 0.0039
-3.701 5.911 -5.911 3.702
-0.0013 -0.0006 0.0018 0.0009
1 2 3
4 5 6
987
Diagramas de Momentos y Cortantes
-3.70 5.91 -5.9 3.70
5.15 5.94
3.70 -3.70
0.00
-5.1
-5.94
-2.294 2.2938
-6.3
-5.0 6.34 4.95 6.05 6.55
1.77 3.18 -3.180 -1.773
0.00 0.00
-6.1
-6.55
-0.886 0.8866
0.89 0.01 -0.887
0.0
0.0
12
3
45 6
7 8 9
HARDLY CROSS “CARGA VIVA”
”
-0.0
00
4
-0.5
92
5
-0.8
28
6
0.2
18
5
0.0
17
9
0.0
07
-3.559 4.493
-0.0
23
0.0
31
0.0
00
-0.0
01
0.00
2
0.0
35
0.5
58
0.5
95
0.0
00
0.0003 0.0002
-0.0001 -0.0003
0.0019 0.0010
-0.0008 -0.0016
-0.0022 -0.0044
0.0367 0.0183
0.0030 0.0061
-4.181 4.181
0.5840 0.2920
0.0
36
-0.0
01
-1.1
85
0.3
96
-1.6
57
0.4
37
-0.0
03
-0.0
02
0.207 0.045
0.4
55
-0.0
45
0.0
62
-0.0
16
0.0
04
0.0
70
1.1
16
0.3
96
1.1
91
0.0
01
0.0
03
-0.0
01
-0.0
01
-2.2
91
0.3
96
-1.6
57
-1.1
01
0.5
23
-0.0
94
0.0
36
-0.2
69
-0.0
45
0.2
41
0.4
55 -4.181 4.181
0.045 0.2070.0
01
-0.0
03
0.0
06
-0.0
16
0.0
25
0.0
62
-0.0
12
0.0
70
-0.1
75
1.1
16
1.3
65
0.3
96
2.3
68
0.0
01
-0.0
01
0.0
04
-0.0044 -0.0022
-0.4335 -0.8670
0.0061 0.0030
0.1143 0.2287
-0.0016 -0.0008
0.0094 0.0188
-0.0003 -0.0001
-0.0002 -0.0004
-0.0
01
-2.9
34
-4.492 3.561 -2.2
01
0.2
61
-0.1
87
0.0
18
0.0
05
0.0
00
-0.5
37
-0.0
23
0.4
81
0.8
36
0.6
57
-0.8
29
0.0
05
-0.0
01
0.0
12
-0.0
08
0.0
49
0.0
31
-0.0
25
0.0
35
-0.3
49
0.5
58
2.7
30
0.6
57
2.9
49
0.0
00
-0.0
02
0.00
2
-4.181 4.181 -4.181 4.181
0.343 0.082 0.082 0.343
0.0236 0.0472 -0.5758 -1.1516
-0.0263 -0.0527 -0.0489 -0.0979
1.4281 0.7140 0.0472 0.0236
0.0024 0.0048 0.0014 0.0028
-0.1827 -0.0913 -0.0527 -0.0263
0.0006 0.0012 -0.0003 -0.0007
-0.0129 -0.0064 0.0048 0.0024
4.798 -4.804 2.934
-0.0008 -0.0004 0.0012 0.0006
-2.949
1 2 3
4 5 6
987
Diagramas de Momentos y Cortantes
-2.95 4.80 -4.8 2.93
2.95 -2.93
0.00
-4.5
-3.6 4.49 3.56
1.19 2.37 -2.291 -1.185
0.00 0.00
0.60 0.01 -0.593
4.15 4.81
-4.1
-4.81
-1.772 1.7417
4.31 4.65
-4.3
-4.65
-0.595 0.59250.0
0.0
12
3
45 6
7 8 9
PORTICO A
CARGA MUERTA
L1: 5.6 m
L2: 5.6 m
h1: 3 m
h2: 3 m
W1: 2.25 TON/m
W2: 1.98 TON/m
C1: 40 x 60
C2: 40 x 60
V1: 30 x 50
V2: 30 X 50
NODO 1
k12=
k14=
NODO 2
k21=
k23=
k25=
NODO3
k32=
k36=
NODO 4
k41=
k45=
k47=
NODO 5
k52=
k58=
k54=
k56=
NODO 6
k63=
k65=
k69=
2400
558.03571
2400
2400
2400
558.03571
558.03571
2400
2400
558.03571
2400
558.03571
558.03571
2400
558.03571
1. CALCULO DE RIGIDECES
558.03571
2400
1 2 3
4 5 6
7 8 9
NODO 1 NODO 4
d12= d41= 0.448
d14= d45= 0.104
d47= 0.448
NODO 2
d21= NODO 5
d23= d52= 0.406
d25= d58= 0.406
d54= 0.094
NODO3 d56= 0.094
d32=
d36= NODO 6
d63= 0.448
d65= 0.104
d69= 0.448
M1-2 Tn-m
M2-1 Tn-m
M2-3 Tn-m
M3-2 Tn-m
M4-5 Tn-m
M5-4 Tn-m
M5-6 Tn-m
M6-5 Tn-m
-5.88
5.88
-5.88
5.88
-5.1744
5.1744
-5.1744
5.1744
0.811
3.MOMENTOS DE EMPOTRAMIENTO
0.159
0.159
0.683
0.189
2. FACTORES DE DISTRIBUCION
0.189
0.811
M1-2 Tn-m
M2-1 Tn-m
M2-3 Tn-m
M3-2 Tn-m
M4-5 Tn-m
M5-4 Tn-m
M5-6 Tn-m
M6-5 Tn-m
-4.181333
4.1813333
-4.181333
4.1813333
-4.181333
4.1813333
4.1813333
3.MOMENTOS DE EMPOTRAMIENTO
-4.181333
PORTICO A
CARGA VIVA
L1: 5.6 m
L2: 5.6 m
h1: 3 m
h2: 3 m
W1: 1.60 TON/m
W2: 1.6 TON/m
C1: 40 x 60
C2: 40 x 60
V1: 30 x 50
V2: 30 X 50
HARDLY CROSS “CARGA MUERTA”
0.0
00
2
-0.9
32
1
-1.3
16
9
0.3
50
6
0.0
33
9
0.0
07-5.447 6.097
-0.0
03
0.0
11
0.0
00
-0.0
01
0.00
7
0.0
74
0.8
49
0.9
31
0.0
01
0.0005 0.0002
-0.0002 -0.0005
0.0031 0.0015
-0.0015 -0.0030
-0.0007 -0.0015
0.0345 0.0172
0.0025 0.0051
-5.880 5.880
0.3950 0.1975
0.0
68
0.0
00
-1.8
64
0.4
48
-2.6
34
0.7
01
-0.0
02
0.0
000.104 0.094
0.4
06
-0.0
06
0.0
22
-0.0
13
0.0
13
0.1
48
1.6
99
0.4
48
1.8
62
0.0
02
0.0
01
0.0
00
-0.0
02
-3.5
85
0.4
48
-2.6
34
-1.5
65
0.7
01
-0.1
54
0.0
68
-0.1
52
-0.0
06
0.1
24
0.4
06 -5.880 5.880
0.094 0.1040.0
00
-0.0
02
0.0
05
-0.0
13
0.0
22
0.0
22
-0.0
32
0.1
48
-0.3
30
1.6
99
2.0
87
0.4
48
3.5
84
0.0
02
-0.0
03
0.0
13
-0.0015 -0.0007
-0.3062 -0.6124
0.0051 0.0025
0.0815 0.1631
-0.0030 -0.0015
0.0079 0.0158
-0.0005 -0.0002
0.0000 0.0001
-0.0
04
-4.3
73
-6.097 5.447 -3.1
30
0.3
51
-0.3
08
0.0
34
0.0
01
0.0
00
-0.3
05
-0.0
03
0.2
48
0.6
83
0.8
11
-1.3
17
-0.0
01
-0.0
01
0.0
10
-0.0
06
0.0
45
0.0
11
-0.0
64
0.0
74
-0.6
60
0.8
49
4.1
75
0.8
11
4.3
74
0.0
00
-0.0
06
0.00
7
-5.174 5.174 -5.174 5.174
0.189 0.159 0.159 0.189
0.0289 0.0577 -0.3639 -0.7277
-0.0354 -0.0709 -0.0358 -0.0716
0.9707 0.4854 0.0577 0.0289
0.0052 0.0104 0.0001 0.0003
-0.1536 -0.0768 -0.0709 -0.0354
0.0011 0.0023 -0.0005 -0.0010
-0.0150 -0.0075 0.0104 0.0052
-4.374 5.574 -5.575 4.374
-0.0015 -0.0007 0.0023 0.0011
1 2 3
4 5 6
987
Diagramas de Momentos y Cortantes
-4.37 5.57 -5.6 4.37
5.33 5.76
4.37 -4.37
0.00
-5.3
-5.8
-2.653 2.6526
-6.1
-5.4 6.10 5.45 6.18 6.42
1.86 3.58 -3.585 -1.864
0.00 0.00
-6.2
-6.4
-0.931 0.9321
0.93 0.01 -0.932
0.0
0.0
12
3
45 6
7 8 9
HARDLY CROSS “CARGA VIVA”
0.0
00
8
-0.6
07
1
-0.9
36
5
0.2
95
0
0.0
33
6
0.0
04
-3.897 4.323
-0.0
03
0.0
08
0.0
00
-0.0
01
0.0
04
0.0
48
0.5
59
0.6
12
0.0
01
0.0003 0.0002
-0.0002 -0.0004
0.0020 0.0010
-0.0011 -0.0022
-0.0008 -0.0016
0.0225 0.0113
0.0019 0.0038
-4.181 4.181
0.2598 0.1299
0.0
67
0.0
02
-1.2
14
0.4
48
-1.8
73
0.5
90
-0.0
02
-0.0
01
0.104 0.094
0.4
06
-0.0
07
0.0
17
-0.0
09
0.0
09
0.0
97
1.1
18
0.4
48
1.2
24
0.0
01
-0.0
02
0.0
02
-0.0
02
-2.5
75
0.4
48
-1.8
73
-1.3
16
0.7
01
-0.1
52
0.0
68
-0.1
21
-0.0
07
0.1
04
0.4
06 -4.181 4.181
0.094 0.1040.0
01
-0.0
02
0.0
03
-0.0
09
0.0
14
0.0
17
-0.0
21
0.0
97
-0.2
15
1.1
18
1.6
86
0.4
48
2.6
72
0.0
01
-0.0
02
0.0
09
-0.0016 -0.0008
-0.2177 -0.4355
0.0038 0.0019
0.0686 0.1372
-0.0022 -0.0011
0.0078 0.0156
-0.0004 -0.0002
0.0002 0.0004
-0.0
03
-3.4
96
-4.323 3.899 -2.6
33
0.3
51
-0.3
04
0.0
34
-0.0
05
0.0
01
-0.2
41
-0.0
03
0.2
09
0.6
83
0.8
11
-0.9
36
0.0
03
-0.0
01
0.0
07
-0.0
05
0.0
29
0.0
08
-0.0
42
0.0
48
-0.4
31
0.5
59
3.3
73
0.8
11
3.5
08
0.0
00
-0.0
04
0.0
04
-4.181 4.181 -4.181 4.181
0.189 0.159 0.159 0.189
0.0243 0.0486 -0.3061 -0.6121
-0.0280 -0.0561 -0.0354 -0.0707
0.7842 0.3921 0.0486 0.0243
0.0034 0.0067 -0.0006 -0.0011
-0.1001 -0.0501 -0.0561 -0.0280
0.0008 0.0016 -0.0004 -0.0008
-0.0098 -0.0049 0.0067 0.0034
4.519 -4.523 3.497
-0.0010 -0.0005 0.0016 0.0008
-3.508
1 2 3
4 5 6
987
Diagramas de Momentos y Cortantes
-3.51 4.52 -4.5 3.50
4.3 4.66
3.51 -3.50
0.00
-4.3
-4.7
-2.06 2.0237
-4.3
-3.9 4.32 3.90 4.4 4.56
1.22 2.67 -2.575 -1.214
0.00 0.00
-4.4
-4.6
-0.612 0.6071
0.61 0.00 -0.607
0.0
0.0
12
3
45 6
7 8 9
PORTICO 2
CARGA MUERTA
L1: 6 m 1
L2: 6 m
h1: 3 m
h2: 3 m
W1: 2.55 TON/m 4
W2: 2.25 TON/m
C1: 60 x 40
C2: 80 x 40
V1: 30 x 50 7
V2: 30 X 50
NODO 1
k12=
k14=
NODO 2
k21=
k23=
k25=
NODO3
k32=
k36=
NODO 4
k41=
k45=
k47=
NODO 5
k52=
k58=
k54=
k56=
NODO 6
k63=
k65=
k69=
1066.6667
520.83333
1066.6667
1422.2222
1422.2222
520.83333
520.83333
1066.6667
1066.6667
520.83333
1066.6667
520.83333
520.83333
1422.2222
520.83333
520.83333
1066.6667
1. CALCULO DE RIGIDECES1 2 3
4 5 6
7 8 9
NODO 1 NODO 4
d12= d41= 0.402
d14= d45= 0.196
d47= 0.402
NODO 2
d21= NODO 5
d23= d52= 0.366
d25= d58= 0.366
d54= 0.134
NODO3 d56= 0.134
d32=
d36= NODO 6
d63= 0.402
d65= 0.196
d69= 0.402
M1-2 Tn-m
M2-1 Tn-m
M2-3 Tn-m
M3-2 Tn-m
M4-5 Tn-m
M5-4 Tn-m
M5-6 Tn-m
M6-5 Tn-m
3.MOMENTOS DE EMPOTRAMIENTO
-7.65
7.65
-7.65
7.65
-6.75
6.75
-6.75
6.75
0.672
0.211
0.211
0.577
0.328
0.328
0.672
2. FACTORES DE DISTRIBUCION
PORTICO 2
CARGA VIVA
L1: 6 m
L2: 6 m
h1: 3 m
h2: 3 m
W1: 1.80 TON/m
W2: 1.8 TON/m
C1: 60 x 40
C2: 80 x 40
V1: 30 x 50
V2: 30 X 50
M1-2 Tn-m
M2-1 Tn-m
M2-3 Tn-m
M3-2 Tn-m
M4-5 Tn-m
M5-4 Tn-m
M5-6 Tn-m
M6-5 Tn-m
3.MOMENTOS DE EMPOTRAMIENTO
5.4
5.4
-5.4
5.4
-5.4
5.4
-5.4
-5.4
HARDLY CROSS “CARGA MUERTA”
-6.750 6.750 -6.750 6.750
-0.0018-0.0037
0.328 0.211
-0.0037-0.0018
0.1808
-4.916
-0.0022
0.0026
-0.0264
0.0139
-0.3216
-0.1073
2.1849
0.0904
0.0904
7.667
-0.0011
0.0052
-0.0132
0.0279
-0.1608
-0.2145
1.0925
-1.7102
0.328
4.917
0.0026
-0.0031
0.0139
0.0258
-0.1073
-0.1452
0.211
-0.8551
-7.667
0.0052
-0.0015
0.0279
0.0129
-0.2145
-0.0726
0.1808
6.516
-0.0004
-0.0045
-0.0036
0.0280
0.0059
0.0140
0.0118
0.1720
-0.7506
0.196
7.650
0.3440
-1.5012
-0.0036
0.0012
-0.0004
-6.517
0.134
-7.650
0.196
-7.650
1.0621
0.0650
0.0059
0.0041
0.0118
0.0021
-0.0073
0.0006
-0.0007
8.216
0.3
660.134
7.650
0.5311
0.0325
-8.217
-0.0007
-0.0022
-0.0073
0.0
29
0.0
53
-0.0
05
-0.0
06
-4.9
14
-0.0
09
-0.0
03
-4.1
98
0.6
72
-1.5
37
-3.5
03
0.3
52
-0.2
97
-2.3
22
0.4
02
-3.0
74
-1.7
51
0.7
05
-0.1
49
0.0
57
0.0
26
-1.1
60
8
0.4
02
-3.0
74
0.7
05
0.0
57
-0.0
09
0.3
52
3
0.0
28
7
-0.0
04
6
0.0
67
1.0
88
-1.5
37
2
-0.3
29
2.1
75
2.2
37
0.4
02
1.1
60
0.0
01
0.00
4
0.1
33
2.1
75
0.4
02
4.1
98
0.0
02
-0.0
02
0.0
08
-0.0
27
0.1
33
-0.6
59
1.0
88
4.4
75
0.6
72
2.3
19
0.0
02
0.0
08
4.9
16
0.0
00
-0.0
05
0.00
4
-0.0
54
0.0
67
-0.0
05
0.0
16
0.0
00
-0.0
01
0.0
10
-0.0
10
0.0
32
-0.0
20
-0.0
02
0.0
01
0.0
00
-0.0
02
0.0
07
-0.0
20
0.0
38
0.0
32
0.0
76
0.0
16
-0.5
86
-0.0
05
0.4
94
0.3
66
0.2
47
-0.2
93
-0.0
10
0.5
77
-0.0
02
-0.0
01
0.0
14
-0.0
101 2 3
4 5 6
987
Diagramas de Momentos y Cortantes
-4.92 7.67 -7.7 4.92
6.29 7.21
4.92 -4.91
0.00
-6.3
-7.2
-3.038 3.0376
-8.2
-6.5 8.22 6.52 7.37 7.93
2.32 4.20 -4.198 -2.322
0.00 0.00
-7.4
-7.9
-1.16 1.1608
1.16 0.01 -1.161
0.0
0.0
12
3
45 6
7 8 9
HARDLY CROSS “CARGA VIVA”
-0.0
03
2
-0.7
68
7
-1.0
85
1
0.2
91
7
0.7
73
0.0
01
0.0
03
0.0
44
0.5
83
0.0
56
-0.0
06
0.0
87
1.4
51
0.4
02
0.3
66
-0.0
11
-0.0
06
-0.0
02
-2.9
91
1.5
45
0.0
02
-0.0
11
0.2
04
0.3
66
0.4
02
-2.1
70
-1.4
50
-0.2
15
1.4
51
1.7
89
0.4
02
0.0
01
-0.0
01
3.1
00
0.0
02
-0.0
01
0.0
05
-0.0
18
0.0
87
0.6
72
0.0
05
-0.0
01
0.0
10
-0.0
07
0.0
48
3.8
81
0.0
00
-0.0
03
0.7
26
-0.0
05
0.0
27
9
0.0
06
0.0
12
0.0
00
-0.0
01-4.646 5.777
-0.0026 -0.0052
0.0008 0.0004
-0.0002 -0.0005
0.0
05
-1.5
37
0.4
02
-2.1
70
-0.0
01
-0.0
02
0.0
24
-0.0
14
0.7
05
-0.1
43
0.0
57
0.0
19
0.134 0.196-0.0
14
0.0
24
0.0
24
-0.2
30
0.0
05 -5.400 5.400
-0.0039 -0.0019
-0.5298 -1.0597
0.6
72
-1.0
85
-2.8
99
0.3
52
-0.2
87
0.0
29
0.0
37
-0.0
05
0.4
09
0.5
77
0.0
12
-0.4
61
0.0
44
-0.4
31
0.7
26
3.5
78
0.0
03
-0.0
35
-5.400 5.400
0.328 0.211
-0.0
03
-0.0
04
-3.8
60
0.00130.0026
0.0045 0.0089
-0.0019 -0.0039
0.0427 0.0213
-5.400 5.400
0.7086 0.3543
0.196 0.134
0.1424 0.2848
0.0089 0.0045
0.0136 0.0273
-0.0005 -0.0002
-0.0016 -0.0032
-0.0052 -0.0026
0.211 0.328
-5.776 4.649
-0.7078 -1.4157
-5.400 5.400
0.1496 0.07480.8736
0.1496
1.7471
0.0748
-0.0844 -0.1687 -0.0701 -0.1401
0.0089 0.0177 0.0091 0.0183
-0.2104 -0.1052 -0.1687 -0.0844
0.0018 0.0035 -0.0009 -0.0018
-0.0172 -0.0086 0.0177 0.0089
-3.881 6.161 -6.168 3.862
-0.0014 -0.0007 0.0035 0.0018
1 2 3
4 5 6
987
Diagramas de Momentos y Cortantes
-3.88 6.16 -6.2 3.86
5.02 5.78
3.88 -3.86
0.00
-5.0
-5.8
-2.327 2.2837
-5.8
-4.6 5.78 4.65 5.21 5.59
1.55 3.10 -2.991 -1.537
0.00 0.00
-5.2
-5.6
-0.773 0.7687
0.77 0.01 -0.769
0.0
0.0
12
3
45 6
7 8 9
MOMENTOS
Portico 2 Portico A Portico B
Columna 1 Columna 1 Columna 2
MD= 2.32 Tn-m MD= 0.01 Tn-m MD= 0 Tn-m
ML= 1.55 Tn-m ML= 0.004 Tn-m ML= 0 Tn-m
Columna 2
MD= 0.01 Tn-m
ML= 0.01 Tn-m
CARGAS
Portico 2 Portico A Portico B
Columna 1 Columna 1 Columna 2
PD= 13.66 Tn PD= 24.36 Tn PD= 25 Tn
PL= 10.23 Tn PL= 18.44 Tn PL= 19 Tn
Columna 2
PD= 30.28 Tn
PL= 22.74 Tn
DISEÑO DE ZAPATA COMBINADA
σ=0.8 kg/cm2 0.8 fy (kg/cm2) 4200 f'c ( kg/cm2)= 210
COLUMNA 01: 60 x 40 COLUMNA 02: 80 x 60
Cargas:
PD= 38.02 Tn PD= 55.26 Tn
PL= 28.67 Tn PL= 41.66 Tn
Momentos:
Dirección Longitudinal
MD= 2.32 Tn-m MD= 0.01 Tn-m
ML= 1.55 Tn-m ML= 0.01 Tn-m
Dirección Transversal
MD= 0.01 Tn-m MD= 0.01 Tn-m
ML= 0.004 Tn-m ML= 0.01 Tn-m
DATOS DEL ANALISIS ESTRUCTURAL
B
0.4 0.4
5.4
0.6 0.8B
L
1 2
I. DIMENSIONAMIENTO
(38.02+28.67+55.26+41.66)x1.2x1.15
8
A= 28.22
SI L=10 m B= 2.82 m
L= 8.20 m √
B= 3.50 m √
Calculamos Xcg para Estados de Carga de Gravedad
ESTADO DE CARGA (Gravedad)
P1= 66.69 Tn M1= 3.87 Tn
P2= 96.92 Tn M2= 0.02 Tn
Xcg= 3.46 m L1= 5.80 m
Verificacion de Esfuerzos (Con Momentos Tranversales)
σ1= 6.84 < σt= 8 tn/m2 OK
RESUMEN DE PRESIONES
σ1= 6.84 Tn/m2 ⇒ σ1= 9.58 Tn/m2
Peso propio real: pp: 44.77 Tn h=0.65m
Peso propio considerado ppc: 32.72 Tn
Reajuste σ al Estado de Carga
σ1= 7.26 < σt= 8 tn/m2 OK
Presión sin considerar pp
σ1= 5.70 Tn/m2
σudiseño= 7.98 Tn/m2
A=
M2
P2
M1
P1
Xcg
R
VERIFICACION POR CORTANTE FLEXION (Considerado para el mayor volado)
d=h-7.5 x=2-0.575 = 1.725 m
d= 0.575 m
Vu= 48.20 Tn
Cortante que toma el concreto (Vc)
Vc= 154.57 Tn
ΦVc= 131.38 Tn
Debe cumplir que: Vu ≤ΦVc
48.20 < 131.38
Wu=σu x B= 27.94 Tn
Vu1= 5.59 Tn x1= 0.2 m
Vu2= 61.48 Tn x2= 2.2 m
Verificación del Cortante Flexión en Cara Interior Vux
Muij=Mu1= 0.56 Tn-m
Muji=Mu2= 67.62 Tn-m
Vuji= 92.60 Tn
Vuij= -69.47 Tn
Por semejanza de Triangulos
Vux= 70.94 Tn a= 5.025 m
ΦVc= 131.38 Tn
Debe cumplir que: Vux ≤ΦVc
70.94 < 131.38 OK
M2=[Wu*(x2^2)]/2
Vuij = 69.47 Tn
Vu2 = 61.48 Tn
5.025 d
M1=[Wu*(x1^2)]/2
Vu1 = 5.59 Tn
Vuji = 92.60 TnVux
5.025
Vuji = 92.60 TnVux
Vuij = 69.47 Tnd
d
x
d d
x
VERIFICACION DE CORTANTE DE PUNZONAMIENTO (Mayor volado Columna 02)
Pu2= 132.97 Tn
Ao= 1.34 m2
Vup= 122.26 Tn
Cortante que toma el Concreto Vcp
bo= 470.00 cm
Vup= 422.96 Tn √
Vup= 430.79 Tn
Tomamos el menor
ΦVcp= 359.52 Tn
Debe cumplir que: Vup ≤ΦVcp
122.26 < 359.52 OK
DISEÑO POR FLEXION
Volado Izquierdo
x'= 0.00
Muizq= 0.00 Tn-m < Mmin -----> Usar Asmin
Volado derecho
x''= 2.00 m
Muder= 55.89 Tn-m < Mmin -----> Usar Asmin
Momento Positivo
Mu=MPR-MQR=MPQ
MPR= 117.50 Tn-m
MQR= 34.09 Tn-m
Mu= 83.41 Tn-m < Mmin -----> Usar Asmin
Momento Transversal: Se calculará para el volado de 1.45 m
Mutrans= 29.38 Tn-m
Cálculo del Mmínimo
Asmin= 56.35 cm2
Calculo del amin
amin= 3.79 cm
Remplazando
Mmin= 118.44 Tn-m
Usando Asmin
Asmin= 56.35 cm2
Con Φ 3/4"
S= 17.64 ∽ 17.50 cm
C2+d
C1+d
x''
y
y
M1=0.56
M2=67.62
P
Q
R
ACERO TRANSVERSAL
Mutrans= 29.38 Tn-m
Suponiendo:a=d/5 11.50
As= 15.02 cm2
a= 0.43 cm
Entramos con: 0.43 cm
As= 13.57 cm2 < Asmin=56.35 cm2
a= 0.39 cm
Usando Asmin
As= 56.35 cm2
Con Φ 3/4"
S= 41.33 ∽ 40.00 cm
Con Φ 5/8"
S= 29.10 ∽ 30.00 cm
@ 0.175Ø3/4" :@
0
.40
Ø3/4" :
1 2
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