Porticos Ejercicios Resueltos

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UNIVERSIDAD NACIONAL DE SAN ANTONIO ABAD DEL CUSCOFACULTAD DE INGENIERIA CIVILEJERCICIOS RESUELTOS

ASIGNATURA: ANALISIS MATRICIAL DE ESRUCTURASESTUDIANTE: TORRES APAZA DIEGO ARMANDO 111845

1. Resolver por el mtodo de rigidez, para el siguiente prtico que se muestra en la figura: Considere I=500in^4, A=10in^2, E=29(10^3)ksi

AE/L00-AE/L00

012EI/L^36EI/L^20-12EI/L^36EI/L^2

K=06EI/L^24EI/L0-6EI/L^22EI/L

-AE/L00AE/L00

0-12EI/L^3-6EI/L^2012EI/L^3-6EI/L^2

06EI/L^22EI/L0-6EI/L^24EI/L

0000

0000

T=001000

000

0

000

0

000001

Solucin

1.1. Matriz de rigidez en coordenadas locales para la barra 1

E(ksi)A(in^2)I(in^4)L(in)

2900010500240

AE/L12EI/L^36EI/L^24EI/L2EI/L

1208.3333312.58680561510.41667241666.667120833.333

NodosXY

100(240-0)/240(0-0)/240

2240010

465123

1208.3300-1208.33004100000

012.58681510.420-12.58681510.426010000

K1=01510.422416670-1510.421208335T=001000

-1208.33001208.33001000100

0-12.5868-1510.42012.5868-1510.422000010

01510.421208330-1510.422416673000001

465123

1000001208.300-1208004

010000012.5871510.40-12.591510.46

=00100001510.42416670-15101208335

000100-1208001208.3001

0000100-12.59-1510012.587-15102

00000101510.41208330-15102416673

1.2. MATRIZ DE RIGIDEZ EN COORDENADAS LOCALES PARA LA BARRA 2

123789

1208.3300-1208.330010-10000

012.58681510.420-12.58681510.422100000

K=01510.422416670-1510.421208333T=001000

-1208.33001208.330070000-10

0-12.5868-1510.42012.5868-1510.428000100

01510.421208330-1510.422416679000001

123789

01000012.58701510.4-12.5901510.41

-10000001208.300-120802

0010001510.40241667-151001208333

000010-12.590-151012.5870-15107

000-1000-1208001208.308

0000011510.40120833-151002416679

1.3. MATRIZ DE RIGIDEZ EN COORDENADAS GLOBALES

123456789

1220.9201401510.41667-1208.333300-12.58680601510.416671

01220.92014-1510.41670-1510.4167-12.5868060-1208.333302

1510.41667-1510.4167483333.3330120833.3331510.41667-1510.41670120833.3333

KCG=-1208.3333001208.33333000004

0-1510.4167120833.3330241666.6671510.416670005

0-12.5868061510.4166701510.4166712.58680560006

-12.5868060-1510.416700012.58680560-1510.41677

0-1208.3333000001208.3333308

1510.416670120833.333000-1510.41670241666.6679

1.4. CALCULO DE LOS DESPLAZAMIENTOS DESCONOCIDOS

51220.9201401510.41667-1208.33330D1

001220.92014-1510.41670-1510.4167D2

0=1510.41667-1510.4167483333.3330120833.333D3

0-1208.3333001208.333330D4

00-1510.4167120833.3330241666.667D5

D10.69575393

D2-0.00155071

D3=-0.0024876

D40.69575393

D5,0.00123411

1.5. CALCULO DE LAS REACCIONES DESCONOCIDAS

Q6-1.87378009K

Q7=-5K

Q81.873780091K

Q9750.2927781K.in

1.6. CALCULO DE FUERZAS PARA LA BARRA 1

q1KTD

N41208.3300-1208.33001000000.695754

N6012.58681510.420-12.58681510.420100000

N5=01510.422416670-1510.421208330010000.001234

F1-1208.33001208.33000001000.695754

F20-12.5868-1510.42012.5868-1510.42000010-0.00155

F301510.421208330-1510.42241667000001-0.00249

q1

N40

N6-1.8737801

N5=5.6843E-14

F10

F21.87378009

F3-449.70722

1.7. CALCULO DE FUERZAS PARA LA BARRA 2

q2KTD

N11208.3300-1208.33000-100000.695754

N2012.58681510.420-12.58681510.42100000-0.00155

N3=01510.422416670-1510.42120833001000-0.00249

F7-1208.33001208.33000000-100

F80-12.5868-1510.4012.5868-1510.420001000

F901510.421208330-1510.422416670000010

q2

N11.87378

N25

N3=449.707

F7-1.8738

F8-5

F9750.293

1.8. GRAFICA DE LA SOLUCION

2. ANALICE EL PORTICO DE LA FIGURA POR EL METODO MATRICIAL DE LOS DESPLAZAMIENTOS.

Dimensiones bxh (mm) Viga 300x500Columna 300x300E=19KN/mm^2

Solucin

2.1. Matriz de rigidez en coordenadas locales para la barra 1

E(KN/m2)A(m2)I(m^4)L(m)

190000000.150.0031256

AE/L(KN/m)12EI/L^3(KN/m)6EI/L^2(KN)4EI/L(KN.m)2EI/L(KN.m)

4750003298.6111119895.83333339583.3333319791.66667

NodosXY

103(6-0)/6(3-3)/6

26310

123456

47500000-47500000100000

03298.619895.830-3298.69895.83010000

[K]=09895.8339583.30-9895.819791.7[T]=001000

-4750000047500000000100

0-3298.6-9895.803298.61-9895.8000010

09895.8319791.70-9895.839583.3000001

123456

10000047500000-475000001

01000003298.61119895.83330-3298.6119895.83332

[T]t=001000[KCG]=09895.833339583.3330-9895.83319791.6673

000100-47500000475000004

0000100-3298.611-9895.83303298.6111-9895.8335

00000109895.833319791.6670-9895.83339583.3336

2.2. Matriz de rigidez en coordenadas locales para la barra 2

E(KN/m2)A(m2)I(m^4)L(m)

190000000.090.0006753

AE/L(KN/m)12EI/L^3(KN/m)6EI/L^2(KN)4EI/L(KN.m)2EI/L(KN.m)

57000057008550171008550

NodosXY

300(0-0)/3(3-0)/3

10301

57000000-57000000010000

0570085500-57008550-100000

[K]=08550171000-85508550[T]=001000

-5700000057000000000010

0-5700-855005700-8550000-100

0855085500-855017100000001

789123

0-1000057000-8550-57000-85507

100000057000000-57000008

[T]t=001000[KCG]=-85500171008550085509

0000-10-5700085505700085501

0001000-5700000057000002

000001-85500855085500171003

2.3. Matriz de rigidez en coordenadas locales para la barra 3

E(KN/m2)A(m2)I(m^4)L(m)

190000000.090.0006753

AE/L(KN/m)12EI/L^3(KN/m)6EI/L^2(KN)4EI/L(KN.m)2EI/L(KN.m)

57000057008550171008550

NodosXY

263(6-6)/3(0-3)/3

4600-1

57000000-570000000-10000

0570085500-57008550100000

[K]=08550171000-85508550[T]=001000

-57000000570000000000-10

0-5700-855005700-8550000100

0855085500-855017100000001

456101112

010000570008550-5700085504

-100000057000000-57000005

[T]t=001000[KCG]=8550017100-8550085506

000010-57000-855057000-855010

000-1000-57000000570000011

000001855008550-855001710012

2.4. MATRIZ DE RIGIDEZ EN COORDENADAS GLOBALES123456789101112

48070008550-47500000-5700085500001

0573298.69895.8330-3298.619895.8330-57000000002

85509895.83356683.330-9895.8319791.67-8550085500003

-4750000048070008550000-5700085504

0-3298.61-9895.830573298.6-9895.830000-57000005

[KCG]=09895.83319791.678550-9895.8356683.33000-8550085506

-57000-855000057000-85500007

0-5700000000057000000008

855008550000-85500171000009

000-57000-855000057000-855010

0000-57000000000570000011

000855008550000-855001710012

2.5. CALCULO DE LOS DESPLAZAMIENTOS DESCONOCIDOS 048070008550-47500000D1

-750573298.69895.8330-3298.6119895.833D2

-75=85509895.83356683.330-9895.83319791.67D3

0-4750000048070008550D4

-750-3298.611-9895.8330573298.6-9895.833D5

7509895.83319791.678550-9895.83356683.33D6

D11.8225E-05m

D2-0.0001316m

D3=-0.0020372rad

D4-1.823E-05m

D5-0.0001316m

D60.0020372rad

2.6. CALCULO DE LAS REACCIONES DESCONOCIDAS Q7-57000-85500001.8225E-0517.314KN

Q80-5700000000-0.0001315875.000KN

Q9=855008550000-0.0020372=-17.262KN.m

Q10000-57000-8550-1.8225E-05-17.314KN

Q110000-5700000-0.0001315875.000KN

Q120008550085500.002037217.262KN.m

2.7. CALCULO DE FUERZAS PARA LA BARRA 1q1KTD

N147500000-475000001000001.8225E-0517.314KN

N203298.6119895.8330-3298.6119895.833010000-0.00013160KN

N3=09895.83339583.330-9895.83319791.67001000-0.0020372=-40.32KN.m

F4-4750000047500000000100-1.823E-05-17.314KN

F50-3298.611-9895.83303298.611-9895.833000010-0.00013160KN

F609895.83319791.670-9895.83339583.330000010.002037240.32KN.m

2.8. CALCULO DE FUERZAS PARA LA BARRA 2q2KTD

N757000000-57000000010000075KN

N80570085500-57008550-1000000-17.314KN

N9=08550171000-855085500010000=-17.262KN.m

F1-57000000570000000000101.8225E-05-75KN

F20-5700-855005700-8550000-100-0.000131617.314KN

F30855085500-855017100000001-0.0020372-34.68KN.m

2.9. CALCULO DE FUERZAS PARA LA BARRA 3q3KTD

N457000000-570000000-10000-1.823E-0575KN

N50570085500-57008550100000-0.000131617.314KN

N6=08550171000-855085500010000.0020372=34.68KN.m

F10-57000000570000000000-100-75KN

F110-5700-855005700-85500001000-17.314KN

F120855085500-855017100000001017.262KN.m

2.10. GRAFICA DE LA SOLUCION

3. RESOLVER EL SIGUIENTE PORTICO

3.1. Matriz de rigidez en coordenadas locales para la barra 1123456

0.1666700-0.166700100000

00.111110.333330-0.11110.33333010000

[K]=00.333331.333330-0.33330.66667[T]=001000

-0.1667000.1666700000100

0-0.1111-0.333300.11111-0.3333000010

00.333330.666670-0.33331.33333000001

123456

1000000.16666700-0.166667001

01000000.1111110.3333330-0.1111110.3333332

[T]t=001000[KCG]=00.3333331.3333330-0.3333330.6666673

000100-0.166667000.166667004

0000100-0.111111-0.33333300.111111-0.3333335

00000100.3333330.6666670-0.3333331.3333336

3.2. Matriz de