Trabajo Ing. de La Construcción (Matriz de Rigidez de Placa Idealizada)
2
USANDO IDEALIZACION DE PUNTALES DATOS t (cm)= 15 1. COORDENADAS NUDO X Y 1 0 0 2 0 300 3 100 300 4 100 0 5 600 300 6 600 0 2. TABLA DE PROPIEDADES ELEMENTO Ni Nj Lij (cm) B (cm) H (cm) 1 1 2 300 90 1 0 15 30 450 33750 220000 2 2 3 100 0 0 1 25 60 1500 450000 220000 3 3 5 500 0 0 1 25 60 1500 450000 220000 4 5 6 300 270 -1 0 25 25 625 32552.08333 220000 5 3 4 300 270 -1 0 15 30 450 33750 220000 6 2 4 316.227766 288.4349488 -0.949 0.316 1185.854123 0 220000 7 1 3 316.227766 71.56505118 0.949 0.316 1185.854123 0 220000 3. RIGIDECES POR ELEMENTOS PARA EL ELEMENTO 1 0 K1 = 330000 K2 = 3300 K3 = 495000 K4 = 99000000 K5 = 49500000 3300 0 -495000 -3300 0 -495000 0 330000 0 0 -330000 0 -495000 0 99000000 495000 0 49500000 -3300 0 495000 3300 0 495000 0 -330000 0 0 330000 0 -495000 0 49500000 495000 0 99000000 PARA EL ELEMENTO 2 0 K1 = 3300000 K2 = 1188000 K3 = 59400000 K4 = 3960000000 K5 = 1980000000 3300000 0 0 -3300000 0 0 0 1188000 59400000 0 -1188000 59400000 0 59400000 3960000000 0 -59400000 1980000000 -3300000 0 0 3300000 0 0 0 -1188000 -59400000 0 1188000 -59400000 0 59400000 1980000000 0 -59400000 3960000000 PARA EL ELEMENTO 3 0 K1 = 660000 K2 = 9504 K3 = 2376000 K4 = 792000000 K5 = 396000000 660000 0 0 -660000 0 0 0 9504 2376000 0 -9504 2376000 0 2376000 792000000 0 -2376000 396000000 -660000 0 0 660000 0 0 0 -9504 -2376000 0 9504 -2376000 0 2376000 396000000 0 -2376000 792000000 PARA EL ELEMENTO 4 0 K1 = 458333.3333 K2 = 3182.87037 K3 = 477430.55556 K4 = 95486111.11 K5 = 47743055.56 3182.87037 0 477430.5556 -3182.87037 0 477430.55556 0 458333.3333 0 0 -458333.333 0 477430.5556 0 95486111.11 -477430.556 0 47743055.556 -3182.87037 0 -477430.556 3182.87037 0 -477430.5556 0 -458333.333 0 0 458333.3333 0 477430.5556 0 47743055.56 -477430.556 0 95486111.111 PARA EL ELEMENTO 5 0 K1 = 330000 K2 = 3300 K3 = 495000 K4 = 99000000 K5 = 49500000 3300 0 495000 -3300 0 495000 0 330000 0 0 -330000 0 495000 0 99000000 -495000 0 49500000 -3300 0 -495000 3300 0 -495000 0 -330000 0 0 330000 0 495000 0 49500000 -495000 0 99000000 PARA EL ELEMENTO 6 0 K1 = 825000 K2 = 0 K3 = 0 K4 = 0 K5 = 0 82381.2 -247404.3 0 -82381.2 247404.3 0 -247404.3 742995.825 0 247404.3 -742995.825 0 0 0 0 0 0 0 -82381.2 247404.3 0 82381.2 -247404.3 0 247404.3 -742995.825 0 -247404.3 742995.825 0 0 0 0 0 0 0 PARA EL ELEMENTO 7 0 K1 = 825000 K2 = 0 K3 = 0 K4 = 0 K5 = 0 82381.2 247404.3 0 -82381.2 -247404.3 0 247404.3 742995.825 0 -247404.3 -742995.825 0 0 0 0 0 0 0 -82381.2 -247404.3 0 82381.2 247404.3 0 -247404.3 -742995.825 0 247404.3 742995.825 0 0 0 0 0 0 0 4. RIGIDEZ DEL SISTEMA 1 2 3 4 5 6 1 0 0 0 P1 2 0 0 P2 3 0 X = P3 4 0 0 0 P4 5 0 0 0 P5 6 0 0 0 0 P6 4. RIGIDEZ DEL SISTEMA SIMPLIFICADO Y DESARROLLADO 3385681.2 -247404.3 495000 -3300000 0 0 0 0 0 -247404.3 2260995.825 59400000 0 -1188000 59400000 0 0 0 495000 59400000 4059000000 0 -59400000 1980000000 0 0 0 -3300000 0 0 4045681.2 247404.3 495000 -660000 0 0 0 -1188000 -59400000 247404.3 2270499.825 -57024000 0 -9504 2376000 0 59400000 1980000000 495000 -57024000 4851000000 0 -2376000 396000000 0 0 0 -660000 0 0 663182.8704 0 477430.5556 0 0 0 0 -9504 -2376000 0 467837.3333 -2376000 0 0 0 0 2376000 396000000 477430.5556 -2376000 887486111 5. VECTOR CARGA P1=P3=P4 = 0 P5=P6 0 0 P2 = 10000 1 0 0 0 0 + -1 0 1 0 X 0 0 0 0 1 0 (N,V,M) P2 = 10000 0 0 6. SOLUCION DEL SISTEMA LINEAL SEN COS Area (cm2) I (cm4) E (kg/cm2) K11 1+K11 7 K12 1 K12 7 1 K21 1 K22 1+K11 2+ K11 6 K12 2 K12 6 2 K21 7 K21 2 K22 2+K11 3+ K11 5+K22 7 K12 5 K12 3 3 K21 6 K21 5 K22 5+K22 6 4 K21 3 K22 3+K11 4 K12 4 5 K21 4 K22 4 6 P0 RT 1 V1 Ø1 1 V1 Ø1 1 V1 Ø1 1 2 3 4 5 6 1 2 3 4 5 6 7 Y X 100 cm 500 cm 300 cm 10000 kg
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Hoja de Calculo para Placa idealizada usando matrices
Transcript of Trabajo Ing. de La Construcción (Matriz de Rigidez de Placa Idealizada)
USANDO IDEALIZACION DE PUNTALES
DATOS
t (cm)= 15
1. COORDENADAS
NUDO X Y1 0 02 0 3003 100 3004 100 05 600 3006 600 0
2. TABLA DE PROPIEDADES
ELEMENTO Ni Nj Lij (cm) B (cm) H (cm)1 1 2 300 90 1 0 15 30 450 33750 2200002 2 3 100 0 0 1 25 60 1500 450000 2200003 3 5 500 0 0 1 25 60 1500 450000 2200004 5 6 300 270 -1 0 25 25 625 32552.08333 2200005 3 4 300 270 -1 0 15 30 450 33750 2200006 2 4 316.227766 288.4349488 -0.949 0.316 1185.854123 0 2200007 1 3 316.227766 71.56505118 0.949 0.316 1185.854123 0 220000
3. RIGIDECES POR ELEMENTOS
PARA EL ELEMENTO 1 0
K1 = 330000 K2 = 3300 K3 = 495000K4 = 99000000 K5 = 49500000
3300 0 -495000 -3300 0 -4950000 330000 0 0 -330000 0
-495000 0 99000000 495000 0 49500000-3300 0 495000 3300 0 495000
0 -330000 0 0 330000 0-495000 0 49500000 495000 0 99000000
PARA EL ELEMENTO 2 0
K1 = 3300000 K2 = 1188000 K3 = 59400000K4 = 3960000000 K5 = 1980000000
3300000 0 0 -3300000 0 00 1188000 59400000 0 -1188000 594000000 59400000 3960000000 0 -59400000 1980000000
-3300000 0 0 3300000 0 00 -1188000 -59400000 0 1188000 -594000000 59400000 1980000000 0 -59400000 3960000000
PARA EL ELEMENTO 3 0
K1 = 660000 K2 = 9504 K3 = 2376000K4 = 792000000 K5 = 396000000
660000 0 0 -660000 0 00 9504 2376000 0 -9504 23760000 2376000 792000000 0 -2376000 396000000
-660000 0 0 660000 0 00 -9504 -2376000 0 9504 -23760000 2376000 396000000 0 -2376000 792000000
PARA EL ELEMENTO 4 0
K1 = 458333.3333 K2 = 3182.87037 K3 = 477430.55556K4 = 95486111.11 K5 = 47743055.56
3182.87037 0 477430.5556 -3182.87037 0 477430.555560 458333.3333 0 0 -458333.333 0
477430.5556 0 95486111.11 -477430.556 0 47743055.556-3182.87037 0 -477430.556 3182.87037 0 -477430.5556
0 -458333.333 0 0 458333.3333 0477430.5556 0 47743055.56 -477430.556 0 95486111.111
PARA EL ELEMENTO 5 0
K1 = 330000 K2 = 3300 K3 = 495000K4 = 99000000 K5 = 49500000
3300 0 495000 -3300 0 4950000 330000 0 0 -330000 0
495000 0 99000000 -495000 0 49500000-3300 0 -495000 3300 0 -495000
0 -330000 0 0 330000 0495000 0 49500000 -495000 0 99000000
PARA EL ELEMENTO 6 0
K1 = 825000 K2 = 0 K3 = 0K4 = 0 K5 = 0
82381.2 -247404.3 0 -82381.2 247404.3 0-247404.3 742995.825 0 247404.3 -742995.825 0
0 0 0 0 0 0-82381.2 247404.3 0 82381.2 -247404.3 0247404.3 -742995.825 0 -247404.3 742995.825 0
0 0 0 0 0 0
PARA EL ELEMENTO 7 0
K1 = 825000 K2 = 0 K3 = 0K4 = 0 K5 = 0
82381.2 247404.3 0 -82381.2 -247404.3 0247404.3 742995.825 0 -247404.3 -742995.825 0
0 0 0 0 0 0-82381.2 -247404.3 0 82381.2 247404.3 0
-247404.3 -742995.825 0 247404.3 742995.825 00 0 0 0 0 0
4. RIGIDEZ DEL SISTEMA
1 2 3 4 5 6
10 0 0 P1
20 0 P2
30 X = P3
40 0 0 P4
50 0 0 P5
60 0 0 0 P6
4. RIGIDEZ DEL SISTEMA SIMPLIFICADO Y DESARROLLADO
3385681.2 -247404.3 495000 -3300000 0 0 0 0 0-247404.3 2260995.825 59400000 0 -1188000 59400000 0 0 0
495000 59400000 4059000000 0 -59400000 1980000000 0 0 0-3300000 0 0 4045681.2 247404.3 495000 -660000 0 0
0 -1188000 -59400000 247404.3 2270499.825 -57024000 0 -9504 23760000 59400000 1980000000 495000 -57024000 4851000000 0 -2376000 3960000000 0 0 -660000 0 0 663182.8704 0 477430.55560 0 0 0 -9504 -2376000 0 467837.3333 -23760000 0 0 0 2376000 396000000 477430.5556 -2376000 887486111
5. VECTOR CARGA
P1=P3=P4 = 0P5=P6 0
0
P2 = 10000 1 0 0 00 + -1 0 1 0 X 00 0 0 1 0
(N,V,M)
P2 = 1000000
6. SOLUCION DEL SISTEMA LINEAL
SEN COS Area (cm2) I (cm4) E (kg/cm2)
K11
1+K11
7 K12
1 K12
7 1
K21
1
K22
1+K11
2+ K
116
K12
2 K12
6 2
K21
7 K21
2K22
2+K113+
K11
5+K22
7K
125 K
123 3
K21
6 K21
5 K22
5+K22
6 4
K21
3 K22
3+K11
4 K12
4 5
K21
4 K22
4 6
P0 RT
1
V1
Ø1
1
V1
Ø1
1
V1
Ø1
1
2 3
4
5
6
1
2 3
45
6 7
Y
X
100 cm 500 cm
300 cm
10000 kg
USANDO IDEALIZACION DE BRAZO RIGIDO
DATOS
t (cm)= 15
1. COORDENADAS
NUDO X Y1 0 02 0 3003 550 3004 550 0
2. TABLA DE PROPIEDADES
ELEMENTO Ni Nj Lij (cm) B (cm) H (cm) a b1 1 2 300 90 1 0 15 100 1500 1250000 2200002 2 3 500 0 0 1 25 60 1500 450000 220000 500 03 3 4 300 270 -1 0 25 25 625 32552.0833 220000
3. RIGIDECES POR ELEMENTOS
PARA EL ELEMENTO 1 0
K1 = 1100000 K2 = 122222.222 K3 = 18333333.333K4 = 3666666667 K5 = 1833333333
122222.222 0 -18333333 -122222.222 0 -18333333.330 1100000 0 0 -1100000 0
-18333333 0 3666666667 18333333.3 0 1833333333-122222.222 0 18333333.3 122222.222 0 3333.333
0 -1100000 0 0 1100000 0-18333333 0 1833333333 18333333.3 0 3666666667
PARA EL ELEMENTO 2 0
660000 0 0 -660000 0 00 9504 7128000 0 -660000 71280000 7128000 5544000000 0 -7128000 1584000000
-660000 0 0 660000 0 00 -660000 -7128000 0 9504 -71280000 7128000 1584000000 0 -7128000 792000000
PARA EL ELEMENTO 3 0
K1 = 458333.333 K2 = 3182.87037 K3 = 477430.55556K4 = 95486111.1 K5 = 47743055.6
3182.87037 0 477430.556 -3182.87037 0 30.555560 458333.333 0 0 -458333.333 0
477430.556 0 95486111.1 -477430.556 0 3055.556-3182.87037 0 -477430.556 3182.87037 0 -477430.5556
0 -458333.333 0 0 458333.333 0477430.556 0 47743055.6 -477430.556 0 95486111.111
4. RIGIDEZ DEL SISTEMA
1 2 3 4
10 0 P1
20 P2
30 X = P3
40 0 P4
4. RIGIDEZ DEL SISTEMA SIMPLIFICADO Y DESARROLLADO
782222.222 0 18333333.3 -660000 0 00 1109504 7128000 0 -660000 7128000
18333333.3 7128000 9210666667 0 -7128000 1584000000-660000 0 0 663182.87 0 30.55556
0 -660000 -7128000 0 467837.333 -71280000 7128000 1584000000 477430.556 -7128000 887486111.11
5. VECTOR CARGA
P1=P3=P4 = 0P5=P6 0
0
P2 = 0 1 0 0 -100000 + -1 0 1 0 X 00 0 0 1 0
(N,V,M)
P2 = 1000000
SEN COS Area (cm2) I (cm4) E (kg/cm2)
K111 K12
1 1
K211 K22
1+K112
K12
2 2
K212 K22
2+K113 K12
3 3
K213 K22
3 4
P0 RT
1
2 3
4
1
2
3
Y
X
50 cm 500 cm
300 cm
10000 kg
