1.-PROBLEMA 01: ANALIZAR LA PARRILLA MOSTRADA

Solucin1.-Determinar el nmero de grados de libertad 2.-Definir {Q}-{D}

3.- Definir {q}-{d}

4.-Matriz de Rigidez del elemento en direccin del sistema local de coordenadas [k]

BARRA 1100.26721900-100.26721900

01311.099172622.198330-1311.099172622.19833

[k']=02622.198337819.357660-2622.198333588.82373

-100.26721900100.26721900

0-1311.09917-2622.1983301311.09917-2622.19833

02622.198333588.823730-2622.198337189.19377

BARRA 266.844812800-66.844812800

0409.38451228.15350-409.38451228.1535

[k']=01228.15355471.423840-1228.15352634.38926

-66.84481280066.844812800

0-409.3845-1228.15350409.3845-1228.1535

01228.15352634.389260-1228.15354974.02167

BARRA 3100.26721900-100.26721900

01311.099172622.198330-1311.099172622.19833

[k']=02622.198337819.357660-2622.198333588.82373

-100.26721900100.26721900

0-1311.09917-2622.1983301311.09917-2622.19833

02622.198333588.823730-2622.198337189.19377

5.-Matriz de Rigidez del elemento en direccin del sistema global de coordenadas

Esta matriz se determina usando la matriz de transformacin de fuerzas.

Dnde:

BARRA 1

=0

100000

010000

[B]1 =001000

000100

000010

000001

100.2670.0000.000-100.2670.0000.000

0.0001311.0992622.1980.000-1311.0992622.198

[K]1 =0.0002622.1987819.3580.000-2622.1983588.824

-100.2670.0000.000100.2670.0000.000

0.000-1311.099-2622.1980.0001311.099-2622.198

0.0002622.1983588.8240.000-2622.1987189.194

BARRA 2

=90

00-1000

010000

[B]2 =100000

00000-1

000010

000100

5471.424-1228.1530.0002634.3891228.1530.000

-1228.153409.3840.000-1228.153-409.3840.000

[K]2 =0.0000.00066.8450.0000.000-66.845

2634.389-1228.1530.0004974.0221228.1530.000

1228.153-409.3840.0001228.153409.3840.000

0.0000.000-66.8450.0000.00066.845

BARRA 3

=0

100000

010000

[B]1 =001000

000100

000010

000001

100.2670.0000.000-100.2670.0000.000

0.0001311.0992622.1980.000-1311.0992622.198

[K]3 =0.0002622.1987819.3580.000-2622.1983588.824

-100.2670.0000.000100.2670.0000.000

0.000-1311.099-2622.1980.0001311.099-2622.198

0.0002622.1983588.8240.000-2622.1987189.194

5.- Solucin del Problema.5. a.- Solucin del Problema Primario y determinacin de las fuerzas de fijacin:

BARRA 1

{q}emp =[R]*{q'}

00

00

{q'}1 =0{q}emp =0

00

00

00

BARRA 2

{q}emp =[R]*{q'}

030

-30-30

{q'}1 =-30{q}emp =0

0-30

-30-30

300

BARRA 3

{q}emp =[R]*{q'}

00

00

{q'}1 =0{q}emp =0

00

00

00

-EnsamblajeDeterminacin de

Por lo tanto

5. b Solucin del Problema Complementario:-Determinacin de {Q}

-Determinacin de {K}

5571.691-1228.1530.0002634.3891228.1530.000

-1228.1531720.484-2622.198-1228.153-409.3840.000

K=0.000-2622.1987256.0390.0000.000-66.845

2634.389-1228.1530.0005074.2891228.1530.000

1228.153-409.3840.0001228.1531720.484-2622.198

0.0000.000-66.8450.000-2622.1987256.039

5571.691-1228.1530.0002634.3891228.1530.000

-1228.1531740.484-2622.198-1228.153-409.3840.000

K=0.000-2622.1987256.0390.0000.000-66.845

2634.389-1228.1530.0005074.2891228.1530.000

1228.153-409.3840.0001228.1531720.484-2622.198

0.0000.000-66.8450.000-2622.1987256.039

L5571.691-1228.1530.0002634.3890.000

-1228.1531740.484-2622.198-1228.1530.000

K=0.000-2622.1987256.0390.000-66.845

2634.389-1228.1530.0005074.2890.000

0.0000.000-66.8450.0007256.039

5571.691-1228.1530.0002634.3890.000

-1228.1531740.484-2622.198-1228.1530.000

K=0.000-2622.1987256.0390.000-66.845

2634.389-1228.1530.0005074.2890.000

0.0000.000-66.8450.0007256.039

-Determinacin de {D}

-30D4-0.000334257

30D50.074795432

{Q}=0{D}=D60.027031982

30D70.024188776

0D90.000249027

-Determinacin de {d}BARRA 1

{d}00

00

{d}==0=0

{d}D4-0.000334257

D50.074795432

D60.027031982

BARRA 2

{d}D4-0.000334257

D50.074795432

{d}==D6=0.027031982

{d}D70.024188776

D80

D90.000249027

BARRA 3

{d}D100

D110

{d}==D12=0

{d}D70.024188776

D80

D90.000249027

-Determinacin de {d}

BARRA 1

0.00000000

0.00000000

{d'}=0.00000000

-0.00033426

0.07479543

0.02703198

BARRA 2

0.02703198

0.07479543

{d'}=0.00033426

0.00024903

0.00000000

0.02418878

BARRA 3

0.00000000

0.00000000

{d'}=0.00000000

0.02418878

0.00000000

0.00024903

-Determinacin de {q}

0.03351506

-27.18101088

{q'}1compl=-99.1154396

-0.03351506

27.18101088

-1.79030163

1.79030163

1.323080475

{q'}2compl=29.96648494

-1.79030163

-1.323080475

-27.57465872

-2.425341282

0.652997555

{q'}3compl=0.893713146

2.425341282

-0.652997555

1.79030163

6.-RESPUESTA ESTRUCTURAL

0.0335151

-27.1810109

-99.1154396

{q'}1=-0.0335151

27.1810109

-1.7903016

1.7903016

-28.6769195

-0.0335151

{q'}2=-1.7903016

-31.3230805

2.4253413

-2.4253413

0.6529976

0.8937131

{q'}3=2.4253413

-0.6529976

1.7903016