matricial.docx

UNIVERSIDAD LAICA ELOY ALFARO DE MANABFACULTAD DE INGENIERACARRERA DE INGENIERA CIVIL

CARRERA DE INGENIERA CIVIL1.- Datos geomtricos de la estructura.

2.- Enumeracin de los elementos de prticos: nudos, elementos y grados de libertad.

3.- Establecimiento de las secciones de vigas y columnas para el prtico

5.- Establecimiento de los ngulos y cada una de las caractersticas que integran al prtico

6.- Clculo de la matriz de rigidez de cada elemento.ELEMENTO 1663,4900-663,4900

05,411048,140-5,411048,14

k'=01048,14270924,730-1048,14135462,37

-663,4900663,4900

0-5,41-1048,1405,41-1048,14

01048,14135462,370-1048,14270924,73

0,199-0,9800000

0,9800,1990000

RT=001000

0000,199-0,9800

0000,9800,1990

000001

0,1990,9800000

-0,9800,1990000

R=00,0001000

00,00000,1985130,9800

00,0000-0,9800,1985130

00,0000001

k= (RT k) R31,36128,09-1027,26-31,36-128,09-1027,2613

128,09637,53208,16-128,09-637,53208,1614

k=-1027,26208,16270924,731027,26-208,16135462,3715

-31,36-128,091027,2631,36128,091027,261

-128,09-637,53-208,16128,09637,53208,162

-1027,26208,16135462,371027,26-208,16270924,733

131415123

ELEMENTO 2700,3300-700,3300

06,361167,770-6,361167,77

k'=01167,77285967,950-1167,77142983,98

-700,3300700,3300

0-6,36-1167,7706,36-1167,77

01167,77142983,980-1167,77142983,98

0,199-0,9800000

0,9800,1990000

RT=001000

0000,199-0,9800

0000,9800,1990

000001

0,1985130,9800980000

-0,9800980,1985130000

R=001000

0000,1985130,9800980

000-0,9800980,1985130

000001

k= (RT k) R33,77135,16-1144,47-33,77-135,16-1144,471

135,16672,92232,07-135,16-672,92232,072

k=-1144,47232,07285967,951144,47-232,07142983,983

-33,77-135,161144,4733,77135,161144,474

-135,16-672,92-232,07135,16672,92-232,075

-1144,47232,07142983,981144,47-232,07285967,956

123456

ELEMENTO 342000-42000

01,864200-1,86420

k'=0420126000,000-42063000,00

-4200042000

0-1,86-42001,86-420

042063000,000-420126000,00

100000

010000

RT=001000

000100

000010

000001

100000

010000

R=001000

000100

000010

000001

k= (RT k) R42000-420004

01,864200-1,864205

k=04201260000-420630006

-42000420007

0-1,86-42001,86-4208

0420630000-4201260009

456789

ELEMENTO 4700,3300-700,3300

06,361167,770-6,361167,77

k'=01167,77285967,950-1167,77142983,98

-700,3300700,3300

0-6,36-1167,7706,36-1167,77

01167,77142983,980-1167,77142983,98

0,199-0,9800000

0,9800,1990000

RT=001000

0000,199-0,9800

0000,9800,1990

000001

0,1985130,9800980000

-0,9800980,1985130000

R=001000

0000,1985130,9800980

000-0,9800980,1985130

000001

k= (RT k) R33,77135,16-1144,47-33,77-135,16-1144,471

135,16672,92232,07-135,16-672,92232,072

k=-1144,47232,07285967,951144,47-232,07142983,983

-33,77-135,161144,4733,77135,161144,474

-135,16-672,92-232,07135,16672,92-232,075

-1144,47232,07142983,981144,47-232,07285967,956

123456

ELEMENTO 5663,4900-663,4900

05,411048,140-5,411048,14

k'=01048,14270924,730-1048,14135462,37

-663,4900663,4900

0-5,41-1048,1405,41-1048,14

01048,14135462,370-1048,14270924,73

0,199-0,9800000

0,9800,1990000

RT=001000

0000,199-0,9800

0000,9800,1990

000001

0,1990,9800000

-0,9800,1990000

R=00,0001000

00,00000,1985130,9800

00,0000-0,9800,1985130

00,0000001

k= (RT k) R31,36128,09-1027,26-31,36-128,09-1027,2613

128,09637,53208,16-128,09-637,53208,1614

k=-1027,26208,16270924,731027,26-208,16135462,3715

-31,36-128,091027,2631,36128,091027,261

-128,09-637,53-208,16128,09637,53208,162

-1027,26208,16135462,371027,26-208,16270924,733

131415123

ELEMENTO 6369,9700-369,9700

01,28380,210-1,28380,21

k'=0380,21151069,60-380,210

-369,9700369,9700

0-1,28-380,2101,28-380,21

0380,2175534,820-380,21151069,6

100000

010000

RT=001000

000100

000010

000001

100000

010000

R=001000

000100

000010

000001

k= (RT k) R369,9700-369,970016

01,28380,210-1,28380,2117

k=0380,21151069,60-380,2175543,8218

-369,9700369,970010

0-1,28-380,2101,28-380,2111

0380,2175543,820-380,21151069,612

161718101112

MATRIZ DE RIGIDEZ DE TODO EL ELEMENTO

K-1LL

7.- Clculo de los vectores de carga de todos los elementosELEMENTO 3

Donde:

Se procede a calcular el vector P0f4

4,5f5

f=3,37500f6

0f7

4,5f8

-3,37500f9

-100000

0-10000

RT=00-1000

000-100

0000-10

00000-1

P= f RT0,00

-4,50

P=-3,38

0,00

-4,50

3,38

Reacciones respectiva a cada nudo

VOLADIZO

Donde:


ELEMENTO 6

Donde:

Se procede a calcular el vector P0f1

5,959459459f2

f=5,91919f3

0f10

5,959459459f11

-5,91919f12

-100000

0-10000

RT=00-1000

000-100

0000-10

00000-1

P= f RTP=0

-5,95945946

-5,91919284

0

-5,95945946

5,919192841


VOLADIZO

Donde:


8.- Resumen de reacciones en los nudos

9.- Determinacin de los desequilibrantes de nudos.4,00001

-5,962

-5,923

6,00004

-4,50005

Q=-3,37506

0,00007

-7,30008

1,429

0,000010

-8,7611

3,9612

1,1206412121

-0,234769922

-0,00266623

2,1100810284

-0,437986635

-1-0,000968326

D=KLL*Q2,1000397527

0,37679928

-0,000961499

1,11132471810

0,1912829511

-0,0026148712

ELEMENTO 1 (Coordenadas globales)013

014

d=015

1,1205786211

-0,234633342

-0,002689183

0

0

p=0

0

0

0

-2,334673

5,5770487

kd=838,88948

2,334673

-5,5770487

477,718997

q= k d -p-2,33467313

5,577048714

q838,8894815

2,3346731

-5,57704872

477,7189973

ELEMENTO 21,1206412121

-0,234769922

-0,00266623

d=2,1100810284

-0,437986635

-0,000968326

0

0

p=0

0

0

0

-1,78700976

2,172439393

kd=278,6416789

1,787009765

-2,17243939

521,4121474

q= k d -p-1,787009761

2,1724393932

q=278,641678883

1,787009764

-2,172439395

521,412147456

ELEMENTO 32,1100810284

-0,437986635

d=-0,000968326

2,1000397527

0,37679928

-0,000961499

0,00

-4,50

p=-3,38

0,00

-4,50

3,38

4,217335928

-2,33145168

kd=-524,791831

-4,21733593

2,331451679

-524,361425

q= k d -p4,21734

2,16855

q=-521,41686

-4,21737

6,83158

-527,73649

ELEMENTO 41,11132471810

0,1912829511

d=-0,0026148712

2,1000397527

0,37679928

-0,000961499

0

0

p=0

0

0

0

-4,21733593

9,631451694

kd=289,3685311

4,21733593

-9,63145169

525,7764295

q= k d -p

-4,2173359310

9,63145169411

q=289,368531112

4,217335937

-9,6314516948

525,77642959

ANLISIS MATRICIAL21

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