Ejemplo Resuelto de PÓRTICO "MÉTODO DE RIGIDEZ" 01
-
Upload
yanaroquenilver -
Category
Documents
-
view
14 -
download
4
description
Transcript of Ejemplo Resuelto de PÓRTICO "MÉTODO DE RIGIDEZ" 01
a.- Módulo de Elasticidad del Concreto [f'c]
b.- Momentos de Inercia [ I ]
c. Rigidez Axial [AE] y a la Flexión [EI]
d. Determinación de Constantes de Rigideces
L
6
8
6
6
e. Constantes de Carga
M'ij (Kg-m) M'ji (Kg-m) Rij Rji R'ij
V 2-4 6 12000.000 -12000.000 12000.000 12000.000 0
V 4-5 8 5333.333 -10666.667 3333.333 10000.000 -666.667
C 1-2 6 12000.000 -12000.000 -12000.000 -12000.000 0
C 3-4 6 0.000 0.000 0.000 0.000 0.000
Suma vertical de fuerza aplicada (Ton)
Suma horizontal de fuerza aplicada (Ton)
f. Planteamiento de Ecuaciones
Viga 2-4 u2 v2 ө2 u4 v4 ө4
X 2-4 41666.67 0.00 0.00 -41666.667 0 0 u2 0.000 13.991
Ec (Kg/cm2)
200000.000
200000.000
Elemento
Vigas
I Cm^4
260416.667
260416.667
Area(cm^2)
1250.000
5208.333
AE Ton
250000
250000Rectangular
1250.000
Sección EI Ton-m2
5208.333
Columnas
Sección
Rectangular
Rectangular
Elemento
Viga
Columnas
Rectangular
0.000
666.667
Y'ji / X'ij (Kg)
12000.000
10666.667
868.056
868.056
Y'ij / X'ij (Kg)
Reacción Total
289.352
-45333.333
Tramo LMom. Resistentes
6EI/L^2
C 1-2
C 3-4
1736.111
1302.083
1736.111
V 2-4
V 4-5
AE/L 2EI/L 4EI/L
0.000
41666.667
31250.000
41666.667
Reac. Hiperestática
24000.000
Reac. Isostática
R'ji
1736.111
Tramo
41666.667
3472.222
2604.167
3472.222
3472.222
0.000
12000.000
2666.666
-12000.000
12EI/L^3
289.352
122.070
868.056
488.281
289.352
0.000
ANALISIS DE UNA VIGA CONTINUA POR EL METODO DE RIGIDECES [SECCION CONTINUA]
Ton
Ton
-45.333
24.000
Kg
Kg
-12000.000
0.000
Y 2-4 0.00 289.35 868.06 0.000 -289.352 868.056 v2 12.000 14.098
M 2-4 = 0.00 868.06 3472.22 0.000 -868.056 1736.111 ө2 + 12.000 = 19.944
X 4-2 -41666.67 0.00 0.00 41666.667 0 0 u4 0.000 -13.991
Y 4-2 0.00 -289.35 -868.06 0.000 289.352 -868.056 v4 12.000 9.902
M 4-2 0.00 868.06 1736.11 0.000 -868.056 3472.222 ө4 -12.000 -7.357
Viga 4-5 u4 v4 ө4 u5=0 v5=0 ө5=0
X 4-5 31250.00 0.00 0.00 0.000 0.000 0.000 u4 0.000 13.608
Y 4-5 0.00 122.07 488.28 0.000 0.000 0.000 v4 2.667 2.774
M 4-5 = 0.00 488.28 2604.17 0.000 0.000 0.000 ө4 + 5.333 = 5.954
X 5-4 -31250.00 0.00 0.00 0.000 0.000 0.000 u5=0 0.000 -13.608
Y 5-4 0.00 -122.07 -488.28 0.000 0.000 0.000 v5=0 10.667 10.560
M 5-4 0.00 488.28 1302.08 0.000 0.000 0.000 ө5=0 -10.667 -10.431
Col 1-2 u1=0 v1=0 ө1=0 u2 v2 ө2
X 1-2 0.00 0.00 -868.06 -289.352 0.000 -868.056 u1=0 -12.000 -10.009
Y 1-2 0.00 0.00 0.00 0.000 -41666.667 0 v1=0 0.000 22.098
M 1-2 = 0.00 0.00 3472.22 868.056 0.00 1736.111 ө1=0 + 12.000 = 0.000
X 2-1 0.00 0.00 868.06 289.352 0.00 868.056 u2 -12.000 -13.991
Y 2-1 0.00 0.00 0.00 0.000 41666.667 0 v2 0.000 -22.098
M 2-1 0.00 0.00 1736.11 868.056 0.00 3472.222 ө2 -12.000 -11.944
Col 3-4 u3=0 v3=0 ө3=0 u4 v4 ө4
X 3-4 0.00 0.00 0.00 -289.352 0.00 -868.056 u3=0 0.000 -0.382
Y 3-4 0.00 0.00 0.00 0.000 -41666.667 0.000 v3=0 0.000 12.676
M 3-4 = 0.00 0.00 0.00 868.056 0.00 1736.111 ө3=0 + 0.000 = 0.891
X 4-3 0.00 0.00 0.00 289.352 0.00 868.056 u4 0.000 0.382
Y 4-3 0.00 0.00 0.00 0.000 41666.667 0.000 v4 0.000 -12.676
M 4-3 0.00 0.00 0.00 868.056 0.00 3472.222 ө4 0.000 1.403
g. Condiciones de Continuidad
X1 = X1-2 = -10.009 Ton Verificación
Y1 = Y1-2 = 22.098 Ton
M1 = M1-2 = 0.000 Ton-m
X2 = X2-1 + X2-4 = 0 0.000
Y2 = Y2-1 + Y2-4 + Y2vol = 0 0.000
M2 = M2-1 + M2-4 + M2vol = 0 0.000
X3 = X3-4 = -0.382 Ton
Y3 = Y3-4 = 12.676 Ton
M3 = M3-4 = 0.891 Ton-m
X4 = X4-3 + X4-2 + X4-5 = 0 0.000
Y4 = Y4-3 + Y4-2 + Y4-5 = 0 0.000
M4 = M4-3 + M4-2 + M4-5 = 0 0.000
X5 = X5-4 = -13.608 Ton
Y5 = Y5-4 = 10.560 Ton
M5 = M5-4 = -10.431 Ton-m
Y2vol = 8.000 Ton 8000 Kg
M2vol = -8 Ton-m -8000 Kg-m
Suma de Fuerzas Reactivas Verticales 45.333 Ton
Suma de Fuerzas Reactivas Horizontales -24.000 Ton
Por consiguiente:
ө1 u2 v2 ө2 u4 v4 ө4
M1=0 3472.22 868.056 0.00 1736.111 0 0 0 ө1 12.000
X2=0 868.06 41956.019 0.000 868.056 -41666.667 0 0 u2 -12.000
Y2=0 0 0.000 41956.019 868.056 0.000 -289.352 868.056 v2 20.000
M2=0 = 1736.11 868.056 868.056 6944.444 0.000 -868.056 1736.111 ө2 + -8.000
X4=0 0 -41666.67 0.000 0.000 73206.019 0.00 868.056 u4 0.000
Y4=0 0 0.00 -289.352 -868.056 0.000 42078.09 -379.774 v4 14.667
M4=0 0 0.00 868.056 1736.111 868.056 -379.77 9548.611 ө4 -6.667
INVERSA 0.000334294 -1.22318E-05 1.44317E-06 -8.64727E-05 -7.1538E-06 -1.628E-06 1.62E-05 -12.000
-1.22319E-05 5.56262E-05 1.15978E-07 -3.34946E-06 3.1688E-05 -8.893E-08 -2.3E-06 12.000
1.44317E-06 1.15979E-07 2.393E-05 -2.94433E-06 8.551E-08 8.8974E-08 -1.6E-06 -20.000
-8.64727E-05 -3.34949E-06 -2.9443E-06 0.00017462 -1.5363E-06 3.3004E-06 -3.1E-05 8.000
-7.15384E-06 3.16878E-05 8.55097E-08 -1.53633E-06 3.1727E-05 -5.471E-08 -2.6E-06 0.000
-1.62797E-06 -8.89315E-08 8.89743E-08 3.30041E-06 -5.4707E-08 2.3837E-05 3.45E-07 -14.667
1.61767E-05 -2.2858E-06 -1.6444E-06 -3.12105E-05 -2.6149E-06 3.4488E-07 0.000111 6.667
ө1 -0.004747237
u2 0.000771247
v2 = -0.000530349 Luego reemplace en las ecuaciones del ítem f
ө2 0.002196849
u4 0.000435469
v4 -0.00030422
ө4 0.00029528