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MÉTODO DE LA DISTRIBUCIÓN DE MOMENTOS
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UNPRGING. CIVIL
2010
AUTOR:
CÉSAR JESÚS
DÍAZ CORONELEST. ING. CIVIL – UNPRG - LAMBAYEQUE
CURSO:
ANÁLISIS ESTRUCTURAL I
DOCENTE:
ING. SERGIO BRAVO IDROGO
Ejercicio: MÉTODO DE LADISTRIBUCIÓN DE MOMENTOS
ANALISIS ESTRUCTURAL I
CÉSAR JESÚS DÍAZ CORONEL
EST. ING. CIVIL - UNPRG - 2 -
PROBLEMA 1: En la viga cargada como se muestra, por el método de ladistribución de momentos con KR, determinar:
a.- Los momentos de continuidadb.- Las reacciones en los apoyos (esquema)c.- Los diagramas de V y Md.- La deflexión en el extremo centro del tramo 23e.- La deflexión en el extremo centro del tramo 56F.- La deflexión en el extremo libre
ANALISIS ESTRUCTURAL I
CÉSAR JESÚS DÍAZ CORONEL
EST. ING. CIVIL - UNPRG - 3 -
PROBLEMA 1:
A) CALCULO DE LOS MOMENTOS DE CONTINUIDAD1.-Factores de Distribución
NUDO 2:
NUDO 3:
NUDO 4:
IK
IK
I
IFDI
I
I
IFDI
I
36.0
795.0
159
79
795.0
395.0395.0
6
37.2K
159
80
795.0
4.035.0
6
4.2K
2123
2121
IK
IK
I
IFDI
I
I
IFDI
I
36.0
772.0
772
377
772.0
377.03771.0
7
64.2K
772
395
772.0
395.0395.0
6
37.2K
3434
3232
IK
I
IFDI
I
I
IFDI
I
747.0
57
28
741.0
364.0364.0
7
55.2K
57
29
7414.0
377.03771.0
7
64.2K
4545
4343
ANALISIS ESTRUCTURAL I
CÉSAR JESÚS DÍAZ CORONEL
EST. ING. CIVIL - UNPRG - 4 -
NUDO 5:
NUDO 6:
NUDO 7:
2.- Momentos de Empotramiento
M12 = -5.048Tm M21 = +14.519Tm
M23 = -15.233Tm M32 = +15.100Tm
M34 = -12.990Tm M43 = +18.981Tm
M45 = -17.897Tm M54 = +12.246Tm
M56 = -15.480Tm M65 = +18.720Tm
M67 = -21.420Tm M76 = +19.530Tm
M78 = -9.100Tm
IK
I
IFDI
I
I
IFDI
I
774.0
387
205
774.0
41.041.0
6
46.2K
387
182
774.0
364.0364.0
7
55.2K
4545
5443
IK
I
IFDI
I
I
IFDI
I
725.0
145
63
725.0
315.0315.0
6
5.2
4
3K
145
82
725.0
41.041.0
6
46.2K
67R67
5656
IK
FDIIR
315.0
1315.0
315.0.315.0
6
5.2
4
3K 7676
ANALISIS ESTRUCTURAL I
CÉSAR JESÚS DÍAZ CORONEL
EST. ING. CIVIL - UNPRG - 5 -
3.- Distribución de Momentos
1º 7º 5º 6º 3º 4º 2º1 2 3 4 5 6 7
0 80/158 79/158 395/772 377/772 29/57 28/57 182/387 205/387 82/145 63/145 1 ∞-15.048 14.519 -15.233 15.1 -12.99 18.981 -17.897 12.246 -15.48 18.72 -21.42 19.53 -9.1
-0.54 -1.08 -1.03 -0.515 0.76 1.521 1.713 0.857 -5.215 -10.43
0.315 0.631 0.623 0.312 -0.338 -0.676 -0.653 -0.326 1.996 3.991 3.067
0.007 0.013 0.013 0.006 -0.393 -0.785 -0.885 -0.442
-0.002 -0.004 -0.003 -0.002 0.098 0.197 0.19 0.095 0.125 0.25 0.192
-0.025 -0.049 -0.047 -0.023 -0.052 -0.103 -0.117 -0.058
0.006 0.013 0.012 0.006 0.019 0.038 0.037 0.01 0.016 0.033 0.025
-0.006 -0.013 -0.012 -0.006 -0.006 -0.012 -0.014 -0.007
0.001 0.003 0.003 0.001 0.003 0.006 0.006 0.003 0.002 0.004 0.003
-0.001 -0.002 -0.002 -0.001 -0.001 -0.002 -0.003 -0.001
0.001 0.001 0.001 0.001 0.001
-0.001
-14.72 15.175 -1750 14.232 -14.232 18.034 -18.034 12.624 -12.624 23.392 -23.392 9.1 -9.1
Momentos: M1 = - 14.720TmM2 = - 15.175Tm
M3 = - 14.232Tm
M4 = - 18.034Tm
M5 = - 12.624Tm
M6 = - 23.392Tm
M7 = - 9.100Tm
ANALISIS ESTRUCTURAL I
CÉSAR JESÚS DÍAZ CORONEL
EST. ING. CIVIL - UNPRG - 6 -
B) ALCULO DE LAS REACCIONES EN LOS APOYOS
TRAMO 1-2:
TR
R
M
TR
XR
M
576.13
23
449.3
2
14437720.14175.156
0
224.13
43
249.3
2
12435715175720.146
0
2
2
1
1
1
2
ANALISIS ESTRUCTURAL I
CÉSAR JESÚS DÍAZ CORONEL
EST. ING. CIVIL - UNPRG - 7 -
TRAMO 2-3:
TR
R
M
TR
R
M
843.12
43
245.4
2
124356175.15232.146
0
157.14
23
445.4
2
144316232.14175.156
0
3
3
2
2
2
3
ANALISIS ESTRUCTURAL I
CÉSAR JESÚS DÍAZ CORONEL
EST. ING. CIVIL - UNPRG - 8 -
TRAMO 3-4:
TR
R
M
TR
R
M
843.12
43
245.4
2
124356175.15232.146
0
157.14
23
445.4
2
144316232.14175.156
0
3
3
2
2
2
3
ANALISIS ESTRUCTURAL I
CÉSAR JESÚS DÍAZ CORONEL
EST. ING. CIVIL - UNPRG - 9 -
TRAMO 4-5:
TR
R
M
TR
R
M
684.8
3
442.4
2
1243665034.18624.127
0
716.17
343
242.4
2
1543165624.12034.187
0
5
5
4
4
4
5
ANALISIS ESTRUCTURAL I
CÉSAR JESÚS DÍAZ CORONEL
EST. ING. CIVIL - UNPRG - 10 -
TRAMO 5-6:
TR
R
M
TR
R
M
684.8
3
442.4
2
1243665034.18624.127
0
716.17
343
242.4
2
1543165624.12034.187
0
5
5
4
4
4
5
ANALISIS ESTRUCTURAL I
CÉSAR JESÚS DÍAZ CORONEL
EST. ING. CIVIL - UNPRG - 11 -
TRAMO 6-7:
TR
R
M
TR
R
M
518.16
3
6615.3
2
136
4
21392.231.96
0
432.24
63
2615.3
2
136
4
211.9392.236
0
7
7
2
6
6
7
ANALISIS ESTRUCTURAL I
CÉSAR JESÚS DÍAZ CORONEL
EST. ING. CIVIL - UNPRG - 12 -
TRAMO 7-8:
Reacciones:
R1 = 13.224 T
R2 = 13.576 + 14.157 = 27.733T
R3 = 12.843 + 9.371 = 22.214T
R4 = 18.229 + 17.716 = 35.945T
R5 = 8.684 + 12.605 = 21.289T
R6 = 21.595 + 24.432 = 46.027T
R7 = 16.518 + 9.45 = 26.022T
TR
R
M
TR
xxxxR
M P
518.16
3
6615.3
2
136
4
21392.231.96
0
45.9
3
4
2
1205.1122.41.92
0
7
7
2
7
7
ANALISIS ESTRUCTURAL I
CÉSAR JESÚS DÍAZ CORONEL
EST. ING. CIVIL - UNPRG - 13 -
C) ESQUEMA DE REACCIONES Y DIAGRAMA DE V Y M
7T 6 .9T /m
3T/m
7.5T /m
6T 6T
3 .6T /m
7.2 T/m
3T/m
6T/m
3T/m
8.4T/m
4 .2T/m
5Tm5Tm14 .72 Tm
13 .224Tm 27.733Tm 22 .2 14Tm 35.94 5Tm 2 1.2 89Tm 46.02 7Tm 2 6.022Tm
V ( T )
+ + + + + + +
- - - - --
M ( T m )+ + + + + +
- - - - - --
1 3 . 2 2 7
1 4 . 7 2 6 1 5 . 1 6 31 4 . 2 8 7
1 8 . 0 0 8
1 2 . 6 5 0
2 3 . 3 4 6
9 . 1 0 0
1 . 4 9 6
4 . 7 2 9
6 . 8 8 1
1 . 5 0
3 . 5 05 . 4 5 3
6 . 4 2 9
3 . 7 4 5
1 . 2 5 5
1 4 . 1 5 7
9 . 3 7 1
1 7 . 7 1 6
1 2 . 6 0 5
2 4 . 4 3 2
9 . 4 5
6 . 2 2 4
1 3 . 5 7 6
6 . 8 4 3
2 . 8 4 3
3 . 3 7 1
1 8 . 2 2 9
2 . 6 8 4
8 . 6 8 4
2 1 . 5 9 5
1 6 . 5 1 8
V ( T )
+ + + + + + +
- - - - --
M ( T m )+ + + + + +
- - - - - --
1 3 . 2 2 7
1 4 . 7 2 6 1 5 . 1 6 31 4 . 2 8 7
1 8 . 0 0 8
1 2 . 6 5 0
2 3 . 3 4 6
9 . 1 0 0
1 . 4 9 6
4 . 7 2 9
6 . 8 8 1
1 . 5 0
3 . 5 05 . 4 5 3
6 . 4 2 9
3 . 7 4 5
1 . 2 5 5
1 4 . 1 5 7
9 . 3 7 1
1 7 . 7 1 6
1 2 . 6 0 5
2 4 . 4 3 2
9 . 4 5
6 . 2 2 4
1 3 . 5 7 6
6 . 8 4 3
2 . 8 4 3
3 . 3 7 1
1 8 . 2 2 9
2 . 6 8 4
8 . 6 8 4
2 1 . 5 9 5
1 6 . 5 1 8
ANALISIS ESTRUCTURAL I
CÉSAR JESÚS DÍAZ CORONEL
EST. ING. CIVIL - UNPRG - 14 -
D) CALCULO DE LA FLECHA EN EL CENTRO DEL TRAMO 2-3:
1 2
TmM
TmM
TmM
E 734.8
175.15
720.14
2
1
2
1
11 513.2646
TmL
aA
2881.306
TmL
bA
E
EE
3
1
111211
468.19
337.36881.30513.2643734.89175.1526720.14
666
2
TmEI
IE
LEI
L
bA
L
aALMLLMLM
E
E
E
E
E
EEEEE
ANALISIS ESTRUCTURAL I
CÉSAR JESÚS DÍAZ CORONEL
EST. ING. CIVIL - UNPRG - 15 -
E) CALCULO DE LA FLECHA EN EL CENTRO DEL TRAMO 5-6:
4 5
TmM
TmM
TmM
F 642.7
624.12
034.18
5
4
2
4
44 720.2966
TmL
aA
2755.286
TmL
bA
F
FF
3
4
444544
482.15
346.26755.2872.2963642.710624.1227034.18
666
2
TmEI
IE
LEI
L
bA
L
aALMLLMLM
F
F
F
F
F
FFFFF
ANALISIS ESTRUCTURAL I
CÉSAR JESÚS DÍAZ CORONEL
EST. ING. CIVIL - UNPRG - 16 -
F) CALCULO DE LA FLECHA EN EL EXTREMO LIBRE:
6 7
TmM
TmM
TmM
0
10.9
392.23
8
7
6
2
6
66 880.3626
TmL
aA
2
7
77 520.96
TmL
bA
38
8
7
8
7
77
6
668876766
211.19
25.16520.988.36220810.926392.23
666
2
TmEI
IE
LEI
L
bA
L
aALMLLMLM