MATRICES RIGIDEZ, TRANSFORMACION

ELEMENTO PORTICO 1

L1 = 14.142

0.7071 0.7071 0.0000-0.7071 0.7071 0.0000

T1 = 0.0000 0.0000 1.00000.0000 0.0000 0.00000.0000 0.0000 0.00000.0000 0.0000 0.0000

54094.0 0.0 0.00.0 357020.0 2524500.0

KL1 = 0.0 2524500.0 23801000.0-54094.0 0.0 0.00.0 -357020.0 -2524500.00.0 2524500.0 11901000.0

10 11 12205560.0 -151460.0 -1785100.0-151460.0 205560.0 1785100.0

K1 = -1785100.0 1785100.0 23801000.0-205560.0 151460.0 1785100.0151460.0 -205560.0 -1785100.0

-1785100.0 1785100.0 11901000.0

ELEMENTO PORTICO 2

L2 = 14.142

0 1 0-1 0 0

T2 = 0 0 10 0 00 0 00 0 0

72125.0 0.0 0.00.0 357020.0 2524500.0

KL2 = 0.0 2524500.0 23801000.0-72125.0 0.0 0.00.0 -357020.0 -2524500.00.0 2524500.0 11901000.0

8 9 6357020.0 0.0 -2524500.0

0.0 72125.0 0.0

K2 = -2524500.0 0.0 23801000.0252450.0 -51000.0 -1785100.0252450.0 51000.0 -1785100.0

-2524500.0 0.0 11901000.0

ELEMENTO PORTICO 3

L3 = 14.142

0.70711 0.70711 0-0.70711 0.70711 0

T3 = 0 0 10 0 00 0 00 0 0

54094.0 0.0 0.00.0 357020.0 2524500.0

KL3 = 0.0 2524500.0 23801000.0-54094.0 0.0 0.00.0 -357020.0 -2524500.00.0 2524500.0 11901000.0

1 2 3205560.0 -151460.0 -1785100.0-151460.0 205560.0 1785100.0

K3 = -1785100.0 1785100.0 23801000.0252450.0 -252450.0 -2524500.038250.0 38250.0 0.0

-1785100.0 1785100.0 11901000.0

ELEMENTO PORTICO 4

L4 = 14.142

0.7071 -0.7071 0.00000.7071 0.7071 0.0000

T4 = 0.0000 0.0000 1.00000.0000 0.0000 0.0000

0.0000 0.0000 0.00000.0000 0.0000 0.0000

72125.0 0.0 0.00.0 357020.0 2524500.0

KL4 = 0.0 2524500.0 23801000.0-72125.0 0.0 0.00.0 -357020.0 -2524500.00.0 2524500.0 11901000.0

1 2 3214570.0 142450.0 1785100.0142450.0 214570.0 1785100.0

K4 = 1785100.0 1785100.0 23801000.0-214570.0 -142450.0 -1785100.0-142450.0 -214570.0 -1785100.01785100.0 1785100.0 11901000.0

ELEMENTOBIARTICULADO 5

L5 = 20

T5 = -0.70711 0.70711 00 0 -0.70711

KL5 = 40000 -40000-40000 40000

8 9 420000 -20000 -20000

K5 = -20000 20000 20000-20000 20000 20000-20000 20000 20000

Matriz de Rigidez de toda la Estructura

1 2 3 4 5840250.0 -18031.0 0.0 252450.0 -1785100.0-18031.0 840250.0 0.0 -252450.0 1785100.0

Kuu = 0.0 0.0 95205000.0 -2524500.0 11901000.0252450.0 -252450.0 -2524500.0 377020.0 -2524500.0-1785100.0 1785100.0 11901000.0 -2524500.0 23801000.0-1785100.0 -1785100.0 11901000.0 0.0 0.0

7 8 9 10 1138250.0 252450.0 -51000.0 -205560.0 151460.038250.0 252450.0 51000.0 151460.0 -205560.0

Kur = 0.0 -2524500.0 0.0 -1785100.0 1785100.020000.0 -20000.0 20000.0 0.0 0.00.0 0.0 0.0 0.0 0.00.0 -2524500.0 0.0 0.0 0.0

1 2 3 4 538250.0 38250.0 0.0 20000.0 0.0

252450.0 252450.0 -2524500.0 -20000.0 0.0-51000.0 51000.0 0.0 20000.0 0.0

-205560.0 151460.0 -1785100.0 0.0 0.0Kru = 151460.0 -205560.0 1785100.0 0.0 0.0

1785100.0 -1785100.0 11901000.0 0.0 0.0-214570.0 -142450.0 -1785100.0 0.0 0.0-142450.0 -214570.0 -1785100.0 0.0 0.01785100.0 1785100.0 11901000.0 0.0 0.0

7 8 9 10 1174094.0 -20000.0 20000.0 0.0 0.0-20000.0 377020.0 -20000.0 0.0 0.020000.0 -20000.0 92125.0 0.0 0.0

0.0 0.0 0.0 205560.0 -151460.0Krr = 0.0 0.0 0.0 -151460.0 205560.0

0.0 0.0 0.0 -1785100.0 1785100.00.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0

VECTORES DE CARGA " FUERZAS "

Fuerzas Nodales

12 10 22 30 40 50 60 7

Fn = 0 80 90 100 110 120 130 140 15

FUERZAS DE EMPOTRAMIENTO LOCAL

-14.142014.1420

FEL1 = 33.3330-14.142014.1420-33.3330

00

FEL2 = 0000

00

FEL3 = 0000

00

FEL4 = 0000

FUERZAS DE EMPOTRAMIENTO GLOBAL

-20 100 11

FEG1 = 33.333 12-20 10 2

-33.333 3

0 80 9

FEG2 = 0 60 10 20 3

0 10 2

FEG3 = 0 30 40 70 5

0 10 2

FEG4 = 0 30 130 140 15

Vector de Fuerzas de Empotramiento Ensamblado

-20 10 2

-33.333 30 40 50 60 7

Fe = 0 80 9

-20 100 11

33.333 120 130 140 15

FUERZAS DE TODA LA ESTRUCTURA

Fuerzas Libres

32 10 2

Fu = 35.333 30 40 50 6

Fuerzas Restringidas

0 70 80 9

20 10Fre = 0 11

-33.333 120 130 140 15

Desplazamientos Restringidos

0 70 80 90 10

Dr = 0 110 120 130 140 15

RESULTADOS

Desplazamientos Libres

0.000069686 1-5.2398E-006 2

Du = -2.0910E-006 3-6.7439E-005 4-4.8814E-007 55.8789E-006 6

Reacciones =

1.1163 78.0555 8-5.17 9

-31.385 10

Fr = 7.8992 11142.2 12-10.474 13-5.0696 1490.158 15

Desplazamientos de toda la Estructura

0.000069686 1-5.2398E-006 2-2.0910E-006 3-6.7439E-005 4-4.8814E-007 55.8789E-006 6

0 7

D = 0 80 90 100 110 120 130 140 15

Fuerzas Internas

-16.60727.778

Fi 1 = 142.2-11.6770.5058950.648

-3.8212-6.7067

Fi 2 = -7.1054E-0153.82126.7067-94.847

2.465-1.3488

Fi 3 = -19.075-2.4651.3488

-1.0303E-013

3.821210.991

Fi 4 = 65.274-3.8212-10.99190.158

Fi 5 = 2.6976-2.6976

MATRICES RIGIDEZ, TRANSFORMACION

0.0000 0.0000 0.00000.0000 0.0000 0.00000.0000 0.0000 0.00000.7071 0.7071 0.0000-0.7071 0.7071 0.00000.0000 0.0000 1.0000

-54094.0 0.0 0.00.0 -357020.0 2524500.00.0 -2524500.0 11901000.0

54094.0 0.0 0.00.0 357020.0 -2524500.00.0 -2524500.0 23801000.0

1 2 3-205560.0 151460.0 -1785100.0 10151460.0 -205560.0 1785100.0 11

1785100.0 -1785100.0 11901000.0 12205560.0 -151460.0 1785100.0 1-151460.0 205560.0 -1785100.0 21785100.0 -1785100.0 23801000.0 3

0 0 00 0 00 0 0

0.70711 -0.70711 00.70711 0.70711 0

0 0 1

-72125.0 0.0 0.00.0 -357020.0 2524500.0

0.0 -2524500.0 11901000.072125.0 0.0 0.0

0.0 357020.0 -2524500.00.0 -2524500.0 23801000.0

1 2 3252450.0 252450.0 -2524500.0 8-51000.0 51000.0 0.0 9

-1785100.0 -1785100.0 11901000.0 6214570.0 142450.0 -1785100.0 1142450.0 214570.0 -1785100.0 2

-1785100.0 -1785100.0 23801000.0 3

0 0 00 0 00 0 00 -1 01 0 00 0 1

-54094.0 0.0 0.00.0 -357020.0 2524500.00.0 -2524500.0 11901000.0

54094.0 0.0 0.00.0 357020.0 -2524500.00.0 -2524500.0 23801000.0

4 7 5252450.0 38250.0 -1785100.0 1-252450.0 38250.0 1785100.0 2

-2524500.0 0.0 11901000.0 3357020.0 0.0 -2524500.0 4

0.0 54094.0 0.0 7-2524500.0 0.0 23801000.0 5

0.0000 0.0000 0.00000.0000 0.0000 0.00000.0000 0.0000 0.00000.7071 -0.7071 0.0000

0.7071 0.7071 0.00000.0000 0.0000 1.0000

-72125.0 0.0 0.00.0 -357020.0 2524500.00.0 -2524500.0 11901000.0

72125.0 0.0 0.00.0 357020.0 -2524500.00.0 -2524500.0 23801000.0

13 14 15-214570.0 -142450.0 1785100.0 1-142450.0 -214570.0 1785100.0 2

-1785100.0 -1785100.0 11901000.0 3214570.0 142450.0 -1785100.0 13142450.0 214570.0 -1785100.0 14

-1785100.0 -1785100.0 23801000.0 15

0-0.70711

7-20000 820000 920000 420000 7

6-1785100.0 1-1785100.0 211901000.0 3

0.0 40.0 5

23801000.0 6

12 13 14 151785100.0 -214570.0 -142450.0 1785100.0 1-1785100.0 -142450.0 -214570.0 1785100.0 211901000.0 -1785100.0 -1785100.0 11901000.0 3

0.0 0.0 0.0 0.0 40.0 0.0 0.0 0.0 50.0 0.0 0.0 0.0 6

60.0 7

-2524500.0 80.0 90.0 100.0 110.0 120.0 130.0 140.0 15

12 13 14 150.0 0.0 0.0 0.0 70.0 0.0 0.0 0.0 80.0 0.0 0.0 0.0 9

-1785100.0 0.0 0.0 0.0 101785100.0 0.0 0.0 0.0 11

23801000.0 0.0 0.0 0.0 120.0 214570.0 142450.0 -1785100.0 130.0 142450.0 214570.0 -1785100.0 140.0 -1785100.0 -1785100.0 23801000.0 15

VECTORES DE CARGA " FUERZAS "

FUERZAS DE EMPOTRAMIENTO GLOBAL

Vector de Fuerzas de Empotramiento Ensamblado

F = Fn-Fe

32 10 2

35.333 30 40 50 60 7

F = 0 80 9

20 100 11

-33.333 120 130 140 15

RESULTADOS

Desplazamientos de toda la Estructura

Ejercicio