quinta-practica-calificada-analisis-estrucctural-i (1).pdf
TRANSCRIPT
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA
ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
PREGUNTA:
En el prtico calcular:
A. Los momentos en las barras
B. Las reacciones en los apoyos
C. Diagramas de N, V, y M.
D. Las deflexiones en el centro de las vigas.
P = 4.0, w = 4.0, H = 22, a = 3.4, b = 4.1
PRTICO
1.7 1.73.4 1.7 1.7 3.4
4.92
4.1
4T 4T
4 T/m
6T 6T
6 T/m
4.8T 4.8T
4.8 T/m
22 T
33 T
1 2
3 5
6
4
7 8
a/2 a/2a a/2 a/2 a
1.2b
b
P
w
1.5P
1.5w
1.2P
1.2w
H
1.5H
1 2
3 5
6
4
7 8
P
1.5P1.2P
30x55
40x70 35x65
30x30
30x30
40x30
40x50
40x28
30x55
40x70 35x65
30x30
30x30
40x30
40x50
40x28
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA
ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
SOLUCIN:
A. CALCULO DE MOMENTOS.
1. PORTICO SIN DESLIZAMIENTO
1.1. MOMENTOS DE EMPOTRAMIENTO
ME12 = -20.513 Tm ME21 = 20.513 Tm ME34 = -30.770 Tm
ME43 = 30.770 Tm ME45 = -24.616 Tm ME54 = 24.616 Tm
4T 4T
4 T/m
6T 6T
6 T/m
4.8T 4.8T
4.8 T/m
22 T
33 T
6 7 8
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA
ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
1.2. FACTORES DE DISTRIBUCION
Nudo 1
Nudo 2
Nudo 3
Nudo 4
Nudo 5
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA
ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
1.3. PROCESO ITERATIVO
1 5
2 4
0.212 0.788 0.788 0.212
-20.513
20.513 -0.165
1.246 -8.017
-16.034 -4.314
5.784 21.500
10.750 0.046
-0.050 -4.254
-8.507 -2.289
0.912 3.391
1.695 0.036
-0.037 -0.682
-1.364 -0.367
0.153 0.567
0.283 0.010
-0.018 -0.116
-0.232 -0.062
0.028 0.105
0.053 0.002
-0.005 -0.022
-0.043 -0.012
0.006 0.021
0.010 0.001
-0.001 -0.005
-0.009 -0.002
0.001 0.005
0.002 0.000
-0.001 -0.002
-0.003 0.000
0.001 0.002
8.020 -8.020
7.115 -7.115
3 1
4 3
5 2
0.081 0.090 0.829 0.434 0.219 0.043 0.304 0.913 0.087
-30.770
30.770
-24.616
24.616
2.492 2.769 25.508
12.754
-11.237
-22.474 -2.142
2.892 -1.665
-3.329 -1.680 -0.330 -2.332
-1.166
-0.099 -0.110 -1.018
-0.509
-2.157 0.532
1.065 0.101
0.456 0.463
0.926 0.467 0.092 0.649
0.324
-0.074 -0.083 -0.762
-0.381
-1.144 -0.148
-0.296 -0.028
0.076 0.363
0.726 0.366 0.072 0.509
0.254
-0.036 -0.040 -0.364
-0.182
-0.184 -0.116
-0.232 -0.022
0.014 0.105
0.209 0.106 0.021 0.146
0.073
-0.010 -0.011 -0.098
-0.049
-0.031 -0.033
-0.067 -0.006
0.003 0.025
0.049 0.025 0.005 0.035
0.017
-0.002 -0.002 -0.023
-0.011
-0.006 -0.008
-0.016 -0.002
0.001 0.005
0.011 0.006 0.001 0.008
0.004
-0.001 0.000 -0.005
-0.003 -0.001 -0.002
-0.004 0.000
0.002 0.002 0.000 0.002
5.712 2.523 -8.236
2.098 -2.098
40.984 -0.708 -3.662 -36.612
1.262
-0.354
0.000
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA
ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
1.4. CORTANTES EN LAS COLUMNAS
( )
( )
2. PORTICO CON DESPLAZAMIENTO EN PRIMER NIVEL (3-4-5)
2.1. MOMENTOS EMPOTRAMIENTO
(
)(
)
22 T
33 T H1
3.349
3.349
3.349
0.769
0.769
0.769
8.020
5.712
2.523
1.262
3.349
2.629
2.629
2.629
0.216
0.216
0.216
7.115
3.662
0.708
0.354
2.629
0.426
0.426
0.426
2.098
H2
1
3 54
? ?
2
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA
ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
(
)(
)
(
)(
)
SI
2.2. PROCESO ITERATIVO
1 5
2
4
0.212 0.788 0.788 0.212
9.035
19.327
-7.615
-15.229 -4.097
-0.301 -1.119
-0.559 3.122
-7.894 -1.010
-2.019 -0.543
1.888 7.016
3.508 0.512
-1.314 -1.584
-3.168 -0.852
0.614 2.284
1.142 0.093
-0.222 -0.487
-0.973 -0.262
0.150 0.558
0.279 0.018
-0.041 -0.117
-0.234 -0.063
0.034 0.125
0.062 0.004
-0.008 -0.026
-0.052 -0.014
0.007 0.027
0.013 0.001
-0.002 -0.006
-0.011 -0.003
0.002 0.006
0.003 0.000
0.000 -0.001
-0.002 -0.001
0.000 0.001
-17.242 17.242
1.947 -1.947
3 1
4 3
5 2
0.081 0.090 0.829 0.434 0.219 0.043 0.304 0.913 0.087
-223.081
-1032.785
-181.374
18.070 20.077 184.934
92.467
41.399
90.687
-0.151 195.065
390.131 196.863 38.654 273.271
82.797 7.890
-15.788 -17.542 -161.585
-80.792
-2.049 -62.374
136.636
0.944 31.512
63.023 31.802 6.244 44.145
-124.748 -11.887
-2.629 -2.921 -26.906
-13.453
-0.272 -10.076
22.073
0.307 5.165 10.329 5.212 1.023 7.235 -20.152 -1.920
-0.443 -0.492 -4.536
-2.268
-0.426 -1.651
3.618
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA
ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
0.075 0.943
1.886 0.952 0.187 1.321
-3.303 -0.315
-0.082 -0.092 -0.844
-0.422
-0.131 -0.302
0.661
0.017 0.185
0.371 0.187 0.037 0.260
-0.603 -0.057
-0.016 -0.018 -0.168
-0.084
-0.032 -0.059
0.130
0.004 0.038
0.076 0.038 0.008 0.053
-0.119 -0.011
-0.003 -0.004 -0.034
-0.017
-0.007 -0.013
0.027
0.001 0.008
0.016 0.008 0.002 0.011
-0.025 -0.002
-0.001 -0.001 -0.007
-0.004
-0.002 -0.003
0.006
0.303 -224.074 223.771
0.004 0.002 0.000 0.003
-0.005 0.001
461.264 -797.720 43.237 293.221
96.990 -96.990
-223.081
-1032.785
-181.374
-0.496
117.532
181.374
-223.577
-915.253
0.000
2.3. CORTANTES EN LAS COLUMNAS
( )
( )
H'20.549
0.549
0.549
90.986
90.986
90.986
1.947
0.303
224.074
223.577
0.549
14.751
14.751
14.751
348.165
348.165
348.165
17.242
43.237
797.720
915.253
14.751
19.713
19.713
19.713
96.990
H'1
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA
ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
3. PORTICO CON DESPLAZAMIENTO EN EL SEGUNDO NIVEL (1-2)
3.1. MOMENTOS DE EMPOTRAMIENTO
(
)(
)
(
)(
)
SI
1
3 54
2
??
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA
ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
3.2. PROCESO ITERATIVO
1 2 2
1
0.212 0.788 0.788 0.212
-240.928
-240.928
94.926
189.851 51.077
30.953 115.050
57.525 2.622
9.131 -23.698
-47.396 -12.751
3.088 11.479
5.739 0.569
-1.134 -2.485
-4.971 -1.337
0.767 2.852
1.426 0.108
-0.248 -0.605
-1.209 -0.325
0.181 0.672
0.336 0.022
-0.048 -0.141
-0.282 -0.076
0.040 0.149
0.074 0.004
-0.010 -0.031
-0.062 -0.017
0.009 0.032
0.016 0.001
-0.002 -0.007
-0.013 -0.004
0.002 0.007
0.003 0.000
0.000 -0.001
-0.003 -0.001
0.000 0.001
201.036 -201.036
-198.200 198.200
3 3
4 4
5 5
0.081 0.090 0.829 0.434 0.219 0.043 0.304 0.913 0.087
-240.928
-240.928
15.476
25.538
18.262 20.291 186.899
93.450
1.544 26.461
52.922 26.705 5.243 37.070
18.535
-2.268 -2.520 -23.216
-11.608
-6.376 -8.461
-16.922 -1.613
0.384 5.739
11.477 5.791 1.137 8.039
4.020
-0.496 -0.551 -5.075
-2.538
-0.669 -1.835
-3.670 -0.350
0.090 1.094
2.188 1.104 0.217 1.533
0.766
-0.096 -0.107 -0.982
-0.491
-0.163 -0.350
-0.700 -0.067
0.020 0.218
0.435 0.220 0.043 0.305
0.153
-0.019 -0.021 -0.197
-0.099
-0.038 -0.070
-0.139 -0.013
0.004 0.045
0.089 0.045 0.009 0.063
0.031
-0.004 -0.004 -0.041
-0.020
-0.008 -0.014
-0.029 -0.003
0.001 0.009
0.019 0.009 0.002 0.013
0.007
-0.001 -0.001 -0.008
-0.004
-0.002 -0.003
-0.006 -0.001
0.000 0.002
0.004 0.002 0.000 0.003
0.001
0.000 0.000 -0.002
-0.001
0.000 -0.001
-0.001 0.000
-208.031 17.086 190.945
0.001 0.000 0.000 0.001
0.000
145.824 33.877 -215.993 36.292
0.000 0.000
2.046 -2.046
8.543
16.938
0.000
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA
ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
3.3. CORTANTES EN COLUMNA
( )
( )
4. CALCULO DE LAS CONSTANTES
H"2
5.209
198.200
208.031
17.086
8.543
101.714
99.081
10.328
10.328
201.036
215.993
33.877
16.938
99.081
0.416
0.416
0.416
2.046
H"1
10.328
5.209
5.209
99.081
99.081
101.714
101.714
101.714
H2 = 22.720
H1 = 32.406
H'2 = 15.300
H'1 = 474.164
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA
ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
( ) ( )
( ) ( )
5. CALCULOS DE LOS MOMENTOS FINALES
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
H"2 = 200.795
H"1 = 215.917
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
B. CALCULO DE LAS REACCIONES
22 T
33 T
4T
4 T/m
6T 6T
6 T/m4.8 T/m
4.8T 4.8T
10.885 24.315
22.61319.62749.7933.007
93.73515.913
19.757
42.953116.120
23.193
25.444
25.444
25.444
111.888
4.235
24.778
24.778
14.388
42.167
13.269
31.845
16.040
2.9249.886
8.731
16.040
16.040
29.623
29.623
29.623
95.576
19.757
23.193
14.388
14.388
13.269
9.886
8.731
8.731
8.731
13.269
13.269
13.269
13.269
31.845
24.315
24.315
24.315
49.7935.028
10.885
10.885
10.885
15.913
15.913
4T
13.269+31.845 = 45.114
2.924 +42.167 = 45.091el error es 0.023
9.886
9.886
9.886
2.924
2.924
2.924
2.924
2.9242.924
22.613
22.613
22.613
22.613
19.627
111.888
111.888
95.576
42.167
42.167
42.167
42.167
93.735
93.735
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA
ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
C. DIAGRAMAS N, V, y M.
--
-
-
13.269
31.845
93.73515.913
10.885 13.269
2.924
22.613
DIAGRAMA DE FUERZAS NORMALES
-
-
--
+
++
++
+
10.885
24.315
13.269
19.627
22.613
2.92442.16749.793
3.007
8.731
9.886
DIAGRAMA DE FUERZAS CORTANTES
-
--
+
+
++
+
+
+
+
+
-
-
-
--
-
29.623
29.623
24.778 95.5764.235
14.388
14.388
111.88825.444
42.953
19.75723.193
16.040 16.040
DIAGRAMA DE MOMENTOS FLECTORES
116.120
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA
ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
D. CALCULO DE LA DEFLEXION EN LOS CENTROS DE LAS VIGAS TRAMO 1-2
(
)
(
) ( )
(
)
(
) ( )
( ) (
)
( ( )) (
)
( )
(
)
( ( ))
(
)
T/m
4T
4 T/m
10.885 +Q/2 24.315+ Q/2
13.269
16.040 29.623
13.268
4T
Q
1A C B
2
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA
ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
TRAMO 3-4
(
)
(
) ( )
(
)
(
) ( )
( ) (
)
( ( )) (
)
( )
(
)
( ( ))
(
)
T/m
6 T/m
49.793 +Q/23.007 +Q/2
Q
3 A C B 442.953116.120
31.845 31.845
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UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA
ESCUELA PROFESIONAL DE INGENIERIA CIVIL
ANALISIS ESTRUCTURAL I
TRAMO 4-5
(
)
(
) ( )
(
)
(
) ( )
( ) (
)
( ( )) (
)
( )
(
)
( ( ))
(
)
T/m
4.8 T/m
4.8T 4.8T
22.613 +Q/219.627 +Q/2
Q
4A C B
54.235 14.388
2.9242.924