Analisis Estructural
24
FORMACION DE LA MATRIZ DE RIGIDEZ 1. Datos E1 A E L ANGULO (°) ANG (RAD) Rigidez Datos 10 2000 800 90 1.570796327 25 E2 A E L ANGULO (°) ANG (RAD) Rigidez Datos 5 2000 1000 -143 -2.49582083 10 E3 A E L ANGULO (°) ANG (RAD) Rigidez Datos 6 2000 600 -90 -1.57079633 20 E4 A E L ANGULO (°) ANG (RAD) Rigidez Datos 5 2000 1000 -37 -0.64577182 10 2. Matriz de Conectividad 1 2 3 1 12.756 0.000 -6.378 4.806 0.000 0.000 0.000 52.244 4.806 -3.622 0.000 -20.000 2 -6.378 4.806 6.378 -4.806 4.806 -3.622 -4.806 3.622 3 0.000 0.000 0.000 0.000 0.000 -20.000 0.000 20.000 4 -6.378 -4.806 -4.806 -3.622 5 0.000 0.000 0.000 -25.000 3. Fuerzas de Empotramiento E1 A E L ANGULO (°) ANG (RAD) Rigidez Datos 10 2000 800 90 1.570796327 25 E2 A E L ANGULO (°) ANG (RAD) Rigidez Datos 5 2000 1000 -143 -2.49582083 10 E3 A E L ANGULO (°) ANG (RAD) Rigidez Datos 6 2000 600 -90 -1.57079633 20 E4 A E L ANGULO (°) ANG (RAD) Rigidez Datos 5 2000 1000 -37 -0.64577182 10 3.1 VECTOR DE CARGAS P Pn FEn ∑ 0 = - 0 P=Pn - ∑FEn
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Transcript of Analisis Estructural
FORMACION DE LA MATRIZ DE RIGIDEZ
1. Datos
E1 A E L ANGULO (°) ANG (RAD) RigidezK1
Datos 10 2000 800 90 1.57079632679 25
E2 A E L ANGULO (°) ANG (RAD) RigidezK2
Datos 5 2000 1000 -143 -2.4958208304 10
E3 A E L ANGULO (°) ANG (RAD) RigidezK3
Datos 6 2000 600 -90 -1.5707963268 20
E4 A E L ANGULO (°) ANG (RAD) RigidezK4
Datos 5 2000 1000 -37 -0.6457718232 10
2. Matriz de Conectividad
1 2 3 4
112.756 0.000 -6.378 4.806 0.000 0.000 -6.378 -4.806
0.000 52.244 4.806 -3.622 0.000 -20.000 -4.806 -3.622
2-6.378 4.806 6.378 -4.806
4.806 -3.622 -4.806 3.622
30.000 0.000 0.000 0.000
0.000 -20.000 0.000 20.000
4-6.378 -4.806 6.378 4.806
-4.806 -3.622 4.806 3.622
50.000 0.000
0.000 -25.000
3. Fuerzas de Empotramiento
E1 A E L ANGULO (°) ANG (RAD) Rigidez Seno Coseno
Datos 10 2000 800 90 1.57079632679 25 1 6.1257423E-17
E2 A E L ANGULO (°) ANG (RAD) Rigidez Seno Coseno
Datos 5 2000 1000 -143 -2.4958208304 10 -0.6018150232 -0.79863551
E3 A E L ANGULO (°) ANG (RAD) Rigidez Seno Coseno
Datos 6 2000 600 -90 -1.5707963268 20 -1 6.1257423E-17
E4 A E L ANGULO (°) ANG (RAD) Rigidez Seno Coseno
Datos 5 2000 1000 -37 -0.6457718232 10 -0.6018150232 0.79863551005
3.1 VECTOR DE CARGAS
P Pn ∑FEn
0 = - 0
P=Pn - ∑FEn
7.03630046304= -
-7.036300463
3.2 NUDOS
F.E. N1
Salen de 1 Llegan a 1 F.E. N1
-0
=0
7.03630046304 -7.036300463
4. Planteamos la Ecuacion P=KxU
P = K U
0 12.76 0.00 U1
-7.036300463 0.00 52.24 V1
U = K^(-1) P
U1 0.07839218532 0 0
V1 0 0.01914109085 7.03630046304
U
U1 0
V1 0.1346824664
5. Calculando Fuerzas Internas
Km () F o,m Fuerza Real
F1 3.36706166008 -25 28.367
F2 -0.8105393164 -10 9.189
F3 -2.6936493281 -20 17.306
F4 -0.8105393164 -10 9.189
Coseno Director0.00 0.00 3.752472E-33 6.125742E-17
0.00 25.00 6.125742E-17 1
Coseno Director6.38 4.81 0.6378186779 0.480630848
4.81 3.62 0.480630848 0.3621813221
Coseno Director0.00 0.00 3.752472E-33 -6.12574E-17
0.00 20.00 -6.12574E-17 1
Coseno Director6.38 -4.81 0.6378186779 -0.480630848
-4.81 3.62 -0.480630848 0.3621813221
50.000 0.000
0.000 -25.000
0.000 0.000
0.000 25.000
∆T αK1 x E 0,1
F.E. ∆L F.E. ∆TF 0,1
-1 0 6.00E-06 -25 0.00E+00
∆T αK2 x E 0,2
F.E. ∆L F.E. ∆TF 0,2
-1 0 6.00E-06 -10 0.00E+00
∆T αK3 x E 0,3
F.E. ∆L F.E. ∆TF 0,3
-1 0 6.00E-06 -20 0.00E+00
∆T αK4 x E 0,4
F.E. ∆L F.E. ∆TF 0,4
-1 0 6.00E-06 -10 0.00E+00
∆L
∆L
∆L
∆L
-1.53144E-15
-25
7.9863551005
6.0181502315
-1.22515E-15
20
-7.9863551
6.0181502315
FORMACION DE LA MATRIZ DE RIGIDEZ
1. Datos
E1 A E L ANGULO (°) ANG (RAD) RigidezK1
Datos 5 200 565.685425 135 2.35619449019 1.76776695281
E2 A E L ANGULO (°) ANG (RAD) RigidezK2
Datos 5 200 400 90 1.57079632679 2.5
E3 A E L ANGULO (°) ANG (RAD) RigidezK3
Datos 5 200 565.685425 45 0.7853981634 1.76776695281
E4 A E L ANGULO (°) ANG (RAD) RigidezK4
Datos 5 200 400 90 1.57079632679 2.5
2. Matriz de Conectividad
1 2 3 4
10.884 -0.884
-0.884 0.884
20.000 0.000
0.000 2.500
30.884 0.884
0.884 0.884
40.000 0.000
0.000 2.500
5-0.884 0.884 0.000 0.000 -0.884 -0.884 0.000 0.000
0.884 -0.884 0.000 -2.500 -0.884 -0.884 0.000 -2.500
3. Fuerzas de Empotramiento
E1 A E L ANGULO (°) ANG (RAD) Rigidez Seno Coseno
Datos 5 200 565.685425 135 2.35619449019 1.76776695281 0.70710678119 -0.7071067812
E2 A E L ANGULO (°) ANG (RAD) Rigidez Seno Coseno
Datos 5 200 400 90 1.57079632679 2.5 1 6.1257423E-17
E3 A E L ANGULO (°) ANG (RAD) Rigidez Seno Coseno
Datos 5 200 565.685425 45 0.7853981634 1.76776695281 0.70710678119 0.70710678119
E4 A E L ANGULO (°) ANG (RAD) Rigidez Seno Coseno
Datos 5 200 400 90 1.57079632679 2.5 1 6.1257423E-17
3.1 VECTOR DE CARGAS
P Pn ∑FEn
0 0.000000 ∆T = - 0 0.000000
P=Pn - ∑FEn
5 -0.008485 ∆T= -
-5 0.008485
3.1 NUDO 5
F.E. N5
Salen de 5 Llegan a 5
0 0.000000 ∆T-
0 0.000000 ∆T
-4.9999999998 0.014485 ∆T 0 0.006000 ∆T
4. Planteamos la Ecuacion P=KxU
P = K U
0 0.000000 ∆T 1.77 0.00 U5
-5 0.008485 ∆T 0.00 6.77 V5
U = K^(-1) P
U5 0.565685425 -2.208037E-17 0 0.000000 ∆TV5 -2.208037E-17 0.14775922501 5 -0.008485 ∆T
5. Condicion de la Ecuacion
Condicion Valor ∆T
V5 0 -589.256
Coseno Director0.884 -0.884 0.5 -0.5
-0.884 0.884 -0.5 0.5
Coseno Director0.000 0.000 3.752472E-33 6.125742E-17
0.000 2.500 6.125742E-17 1
Coseno Director0.884 0.884 0.5 0.5
0.884 0.884 0.5 0.5
Coseno Director0.000 0.000 3.752472E-33 6.125742E-17
0.000 2.500 6.125742E-17 1
5-0.884 0.884
0.884 -0.884
0.000 0.000
0.000 -2.500
-0.884 -0.884
-0.884 -0.884
0.000 0.000
0.000 -2.500
1.768 0.000
0.000 6.768
∆T αK1 x E 0,1
F.E. ∆L F.E. ∆TF 0,1
-1 0 6.00E-06 -1.7677669528 6.00E-03 ∆T
∆T αK2 x E 0,2
F.E. ∆L F.E. ∆TF 0,2
-1 0 6.00E-06 -2.5 6.00E-03 ∆T
∆T αK3 x E 0,3
F.E. ∆L F.E. ∆TF 0,3
-1 0 6.00E-06 -1.7677669528 6.00E-03 ∆T
∆T αK4 x E 0,4
F.E. ∆L F.E. ∆TF 0,4
0 0 6.00E-06 0 6.00E-03 ∆T
∑FEn
∆T
∆L
∆L
∆L
∆L
∆T
F.E. N5
=0 0.000000 ∆T
-5 0.008485 ∆T
1.2499999999 + -0.004243 ∆T
-1.25 + 0.004243 ∆T
-1.53144E-16 + 0.000000 ∆T
-2.5 + 0.006000 ∆T
-1.25 + 0.004243 ∆T
-1.25 + 0.004243 ∆T
0 + 0.000000 ∆T
0 + 0.006000 ∆T
FORMACION DE LA MATRIZ DE RIGIDEZ
1. Datos
E1 A E L ANGULO (°) ANG (RAD) Rigidez Inclinacion (α) Inclin (RAD)
Datos 5 200 800 0 0 1.25 0 0
E2 A E L ANGULO (°) ANG (RAD) Rigidez Inclinacion (α) Inclin (RAD)
Datos 7.071068 200 565.685425 45 0.7853981634 2.50000006629 0 0
E3 A E L ANGULO (°) ANG (RAD) Rigidez Inclinacion (α) Inclin (RAD)
Datos 7.071068 200 565.685425 135 2.35619449019 2.50000006629 0 0
E4 A E L ANGULO (°) ANG (RAD) Rigidez Inclinacion (α) Inclin (RAD)
Datos 5 200 400 -90 -1.5707963268 2.5 30 0.5235987756
2. Matriz de Conectividad
1 2 3 4
12.500 0.000 0.000 0.000 0.000 -2.500 -1.250 1.250
0.000 5.000 0.000 -2.500 -1.250 -1.250 1.250 -1.250
20.000 0.000 0.000 0.000
0.000 -2.500 0.000 2.500
3-1.250 -1.250 2.500 1.250 -1.250 0.000
-1.250 -1.250 1.250 1.250 0.000 0.000
4-1.250 1.250 -1.250 0.000 2.500 -1.250
1.250 -1.250 0.000 0.000 -1.250 1.250
3. Fuerzas de Empotramiento
E1 A E L ANGULO (°) ANG (RAD) Rigidez Seno Coseno
Datos 5 200 800 0 0 1.25 0 1
E2 A E L ANGULO (°) ANG (RAD) Rigidez Seno Coseno
Datos 7.071068 200 565.685425 45 0.7853981634 2.50000006629 0.70710678119 0.70710678119
E3 A E L ANGULO (°) ANG (RAD) Rigidez Seno Coseno
Datos 7.071068 200 565.685425 135 2.35619449019 2.50000006629 0.70710678119 -0.7071067812
E4 A E L ANGULO (°) ANG (RAD) Rigidez Seno Coseno
Datos 5 200 400 -90 -1.5707963268 2.5 -1 6.1257423E-17
3.1 VECTOR DE CARGAS
P Pn ∑FEn
-11.76777
=
-10
-
1.76777
-12.99223 -15 -2.00777
-0.86603 P -0.25223 -0.8660 P 0.25223
P=Pn - ∑FEn
-0.50000 P -2.00777
=
-0.5 P
-
2.00777
3.2 NUDOS
F.E. N1
Salen de 1 Llegan a 1 F.E. N1
--1.7678
=1.76776699984
2.0078 -2.0077670126
F.E. N4
Salen de 4 Llegan a 4 F.E. N4
-2.0077670062-
-2.26=
0.25223299377
2.00776700623 0 2.00776700623
4. Planteamos la Ecuacion P=KxU
P = K
-11.76777 2.500 0.000 -1.250 1.250
-12.99223 0.000 5.000 1.250 -1.250
-0.86603 P -0.25223 -1.250 1.250 2.500 -1.250
-0.50000 P -2.00777 1.250 -1.250 -1.250 1.250
Rotamos a Coordenadas Locales
R RT0.86602540378 0.5 0.86602540378 -0.5 1.54006352159 -0.4575317669
-0.5 0.86602540378 0.5 0.86602540378 -2.33253180001 1.70753180001
P = K
-11.76777 2.500 0.000 -0.45753176686 1.70753180001
-12.99223 0.000 5.000 0.45753176686 -1.7075318
-1.00000 P -1.22232 -0.4575317669 0.45753176686 1.10496824971 -1.1662658939
0.00000 P -1.61266 1.70753180001 -1.7075318 -1.16626589394 2.64503181658
U = K^(-1) PU1 0.43419927009 -0.0170996406 0.18686834489 - -11.76777V1 -0.0170996406 0.20854981775 -0.0934341737 - -12.99223U4 0.18686834489 -0.0934341737 1.02106762513 - -1.00000 P- - - - - -
5. Condicion de la Ecuacion
Condicion Valor P
U4 local 0 -2.187
Coseno DirectorCarga X Carga Y K1 1.25 0.00 1 0
0 0 0.00 0.00 0 0
Coseno DirectorCarga X Carga Y K2 1.25 1.25 0.5 0.5
0 0 1.25 1.25 0.5 0.5
Coseno DirectorCarga X Carga Y K3 1.25 -1.25 0.5 -0.5
0 0 -1.25 1.25 -0.5 0.5
Coseno DirectorCarga X Carga Y K4 0.00 0.00 3.752472E-33 -6.125742E-17
-1 -1 0.00 2.50 -6.12574E-17 1
∆T αK1 x E 0,1
F.E. ∆L F.E. ∆TF 0,1
-2 40 6.00E-06 -2.5 2.40E-01
∆T αK2 x E 0,2
F.E. ∆L F.E. ∆TF 0,2
0 40 6.00E-06 0 3.39E-01
∆T αK3 x E 0,3
F.E. ∆L F.E. ∆TF 0,3
1 40 6.00E-06 2.50000006629 3.39E-01
∆T αK4 x E 0,4
F.E. ∆L F.E. ∆TF 0,4
0 40 6.00E-06 0 2.40E-01
∆L
∆L
∆L
∆L
U
U1
V1
U4
V4
U
U1
V1
U4 localV4 local
P
-11.76777
-12.99223
-1.22232
-
-2.26
0
0.2400000064
0.2400000064
-2.007767006
2.0077670062
1.470178E-17
-0.24
FORMACION DE LA MATRIZ DE RIGIDEZ
1. Datos
E1 A E L ANGULO (°) ANG (RAD) Rigidez ∆T
Datos 7.07106781187 200000 500 37 0.64577182324 2828.42712475 -2 45
E2 A E L ANGULO (°) ANG (RAD) Rigidez ∆T
Datos 5 200000 565.685 0 0 1767.767 -2 45
E3 A E L ANGULO (°) ANG (RAD) Rigidez ∆T
Datos 5 200000 565.685 90 1.57079632679 1767.767 0 45
E4 A E L ANGULO (°) ANG (RAD) Rigidez ∆T
Datos 5.00000 200000 400 0 0 2500.000 0 45
E5 A E L ANGULO (°) ANG (RAD) Rigidez ∆T
Datos 7.07106781187 200000 400 143 2.49582083035 3535.53390593 0 45
E6 A E L ANGULO (°) ANG (RAD) Rigidez ∆T
Datos 7.07106781187 200000 400 37 0.64577182324 3535.534 0 45
E7 A E L ANGULO (°) ANG (RAD) Rigidez ∆T
Datos 0 200000 0 0 0 #DIV/0! 0 45
E8 A E L ANGULO (°) ANG (RAD) Rigidez ∆T
Datos 0.00000 200000 0 0 0 #DIV/0! 0 45
E9 A E L ANGULO (°) ANG (RAD) Rigidez ∆T
Datos 0.00000 200000 0 0 0 #DIV/0! 0 45
E10 A E L ANGULO (°) ANG (RAD) Rigidez ∆T
Datos 0.00000 200000 0 0 0 #DIV/0! 0 45
2. Matriz de Conectividad
1 2 3 4
13571.79 1359.43 -1804.02 -1359.43 -1767.77 0.00 0.00 0.00
1359.43 1024.40 -1359.43 -1024.40 0.00 0.00 0.00 0.00
2-1804.02 -1359.43 4059.05 -339.86 0.00 0.00 -2255.03 -1699.29
-1359.43 -1024.40 -339.86 4072.67 0.00 -1767.77 -1699.29 -1280.50
3-1767.77 0.00 0.00 0.00 4267.77 0.00 0.00 0.00
0.00 0.00 0.00 -1767.77 0.00 1767.77 0.00 0.00
40.00 0.00 -2255.03 -1699.29 0.00 0.00 2255.03 1699.29
0.00 0.00 -1699.29 -1280.50 0.00 0.00 1699.29 1280.50
50.00 0.00 -2255.03 1699.29 0.00 0.00 0.00 0.00
0.00 0.00 1699.29 -1280.50 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
3. Vector de Cargas
∆L
∆L
∆L
∆L
∆L
∆L
∆L
∆L
∆L
∆L
P=Pn - ∑FEn
Km Eo,m ∆T Eo,m ∆L Coseno Seno Fo,m Matriz
1 2828.42712475 0.13500 -2 0.80 0.60 -5275.0165877 -4212.81556299
-3174.58422983
2 1767.76695281 0.15274 -2 1.00 0.00 -3265.5339056 -3265.53390562
0
3 1767.76695281 0.15274 0 0.00 1.00 270 0.00
270.00
4 2500 0.10800 0 1.00 0.00 270 270.00
0.00
5 3535.53390593 0.10800 0 -0.80 0.60 381.837661841 -304.95
229.80
6 3535.53390593 0.10800 0 0.80 0.60 381.837661841 304.95
229.80
7 #DIV/0! 0.00000 0 1.00 0.00 #DIV/0! #DIV/0!
#DIV/0!
8 #DIV/0! 0.00000 0 1.00 0.00 #DIV/0! #DIV/0!
#DIV/0!
9 #DIV/0! 0.00000 0 1.00 0.00 #DIV/0! #DIV/0!
#DIV/0!
10 #DIV/0! 0.00000 0 1.00 0.00 #DIV/0! #DIV/0!
#DIV/0!
Fuerzas de Empotramiento
1
Salen "1" - Llegan "1" FE "1"
-7478.3494686 -7478.3494686
-3174.5842298 -3174.5842298
2
Salen "2" - Llegan "2" FE "2"
304.95 -4517.76 4822.71379463
229.80 -2674.79 2904.58422983
3
Salen "3" - Llegan "3" FE "3"
270.00 -3265.5339056 3535.53390562
270.00 0 270
4
Salen "4" - Llegan "4" FE "4"
0
0
5
Salen "5" - Llegan "5" FE "5"
-304.95 270.00 -574.94911582
229.80 0.00 229.795641301
6
Salen "6" - Llegan "6" FE "6"
0
6
0
7
Salen "7" - Llegan "7" FE "7"
0
0
Vector de Cargas Inclinacion del Apoyo
Pn - ∑FEn = P
-
-7478.3494686
=
7478.3494686
-3174.5842298 3174.58422983
15 4822.71379463 -4807.7137946
-10 2904.58422983 -2914.5842298
0 3535.53390562 -3535.5339056
0 270 -270
0 0 0
0 0 0
0 -574.94911582 574.949115819 0 00 229.795641301 -229.7956413
0 0 0 00 0
0 0 0 00 0
3. Ecuacion U = K-1 . P
U1 V1 U2 V2 U3 V3
U1 3571.79 1359.43 -1804.02 -1359.43 -1767.77 0.00V1 1359.43 1024.40 -1359.43 -1024.40 0.00 0.00U2 -1804.02 -1359.43 4059.05 -339.86 0.00 0.00V2 -1359.43 -1024.40 -339.86 4072.67 0.00 -1767.77U3 -1767.77 0.00 0.00 0.00 4267.77 0.00V3 0.00 0.00 0.00 -1767.77 0.00 1767.77U5 0.00 0.00 -2255.03 1699.29 0.00 0.00V5 0.00 0.00 1699.29 -1280.50 0.00 0.00
4. Condiciones del Problema
a) V5 = (-2)
Inclin. (α) Inclin (RAD)
U130 0.5235987756 R
V1 0.86602540378 0.5
U20 0
-0.5 0.86602540378
V2
U30 0 RT
V3 0.86602540378 -0.5
U50 0
0.5 0.86602540378
P=Pn - ∑FEn
Restriccion Local
V5 -20 0
αK1
1804.0236 1359.4293
6.00E-06 1359.4293 1024.4035
αK2
1767.7670 0.0000
6.00E-06 0.0000 0.0000
αK3
0.0000 0.0000
6.00E-06 0.0000 1767.7670
αK4
2500.0000 0.0000
6.00E-06 0.0000 0.0000
αK5
2255.0296 -1699.2867
6.00E-06 -1699.2867 1280.5043
αK6
2255.0296 1699.2867
6.00E-06 1699.2867 1280.5043
αK7
#DIV/0! #DIV/0!
6.00E-06 #DIV/0! #DIV/0!
αK8
#DIV/0! #DIV/0!
6.00E-06 #DIV/0! #DIV/0!
αK9
#DIV/0! #DIV/0!
6.00E-06 #DIV/0! #DIV/0!
αK10
#DIV/0! #DIV/0!
6.00E-06 #DIV/0! #DIV/0!
5
0.00 0.00
0.00 0.00
-2255.03 1699.29
1699.29 -1280.50
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
4755.03 -1699.29
-1699.29 1280.50
0.00 0.00
0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
U5 V5 P
0.00 0.00 7478.349
0.00 0.00 3174.584
-2255.03 1699.29 -4807.714
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