3...Jacinto Aquino Jorge Desplazamiento
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![Page 1: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/1.jpg)
2.- ENUMERACION DE DEFORMACIONESDef. 1 2ux 1 4uy 2 5Øz 3 6
12 incógnitas
VECTOR DESPLAZAMIENTOS EN LOS APOYOS
U5x{Ua} U5y
{Us}= {Ub} = Ø5zU6xU6yØ6z
8.0 m
4.0 m
3.0 m
4.0 m
7.5 tn
5.0 tn
5
3
1 2
4
6
1 2
3 4
6
5
7.5 tn
nudo
= 5 cm
3 tn/m
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3.-FUERZAS EFECTIVAS EN COORD. GLOBALES
FUERZAS EXT. EN NUDOS
f1xf1yM1zf2xf2y
F= M2zf3xf3yM3zf4xf4yM4z
4.-FUERZAS DE EMPOTRAMIENTO PERFECTO DE BARRAS
FUERZAS EXT. EN NUDOS
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1 7.5 f1x2 0 f1y3 0 M1z4 7.5 f2x5 0 f2y
F= 6 0 M2z7 5 f3x8 0 f3y9 0 M3z
10 5 f4x11 0 f4y12 0 M4z
Matriz de Rigides de cada Barra
Barra 1
A 20I 3E 200L 400phi 90
matriz de rigidez en coordenadas locales
13 14 1510 0 00 0.0001125 0.0225
k'= 0 0.0225 6-10 0 00 -0.0001125 -0.02250 0.0225 3
Matriz de TransformaciónT= 0 1 0
-1 0 00 0 10 0 00 0 00 0 0
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matriz de rigidez en coordenadas globales
13 14 150.000 0.000 -0.0230.000 10.000 0.000
k= -0.023 0.000 6.0000.000 0.000 0.0230.000 -10.000 0.000-0.023 0.000 3.000
MATRIZ DE RIGIDEZ TOTAL DE LA ESTRUCTURA (COORDENADAS GLOBALES)
1 2 31 5.000 0.000 0.0272 0.000 13.333 0.0023 0.027 0.002 6.3334 -5.000 0.000 0.0005 0.000 0.000 -0.0026 0.000 0.002 0.5007 0.000 0.000 -0.0278 0.00 -13.33 0.00
9 0.03 0.00 2.6710 0.00 0.00 0.0011 0.00 0.00 0.0012 0.00 0.00 0.0013 0.00 0.00 0.0014 0.00 0.00 0.0015 0.00 0.00 0.0016 0.00 0.00 0.0017 0.00 0.00 0.0018 0.00 0.00 0.00
Ktotal=
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AHORA NECESITAMOS CALCULAR LAS FUERZAS EFECTIVAS EN LA ESTRUCTURA PARA RESOLVER EL SISTEMA
CALCULAMOS: {Fefect.}
F.EFECTIVA EN NUDOS
7.5 1 0.000-12.0 2 0.000
-1600.0 3 0.0007.5 4 0.000
-12.0 5 0.000
1600.0 6 - 0.000{Fefec.}= 5.0 7 0.000
-3.8 8 0.000-750.0 9 -0.023
5.0 10 0.000-3.8 11 0.000
750.0 12 0.000
00000
| 03.06284E-015
50-6.89146E-018
000
{Fefect.}={Fe}-[Kes]*{Us}
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7.5
-12.0-1600.0
7.5-12.0
1600.0
{Fefec.}= 5.0 --3.8
-750.05.0-3.8
750.0
RESOLVIENDO EL SISTEMA
{Ue}=INVERSA [Kee]*{Fefect.}
684349.60748-6.447841179-1198.092425684348.13958-3.502158821-651.1077149
{Ue}= 335316.23934-5.807885984-1122.779404335317.69936-2.342114016-1119.279179
{Fefect.}=[Kee]*{Ue}
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CÁLCULO DE LAS REACCIONES EN LOS APOYOS
0.00 0.00 0.000.00 0.00 0.00
{Fs}=E 0.00 0.00 0.000.00 0.00 0.000.00 0.00 0.000.00 0.00 0.00
0.00 0.00 -0.020.00 10.00 0.00
{Fs}=E -0.02 0.00 6.000.00 0.00 0.000.00 0.00 0.000.00 0.00 0.00
{Fs}= {Fa} ={Fb}
{Fs}=[Kse]{Ue}+[Kss]*{Us}
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PRIMERO SE CALCULARÁ LAS DEFORMACIONES EN COORDENDAS LOCALES PARA LA BARRA
BARRA 1
u1'xj 0.00 u1'yj -1.00
{u1'}= Ø1j = - u1'xk - u1'yk - Ø1k -
1{u1'}= EI
BARRA 1 AXIAL,CORTANTE Y MOMENTO
Barra 1
A 20I 3E 200L 400phi 90
matriz de rigidez en coordenadas locales
13 14 15 710 0 0 -10
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0 0.0001125 0.0225 0k'= 0 0.0225 6 0
-10 0 0 100 -0.0001125 -0.0225 00 0.0225 3 0
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3 4 5 67 10 13 168 11 14 179 12 15 18
VECTOR DEFORMACIONES DEL SISTEMA
0 13-5 14
= 0 150 160 170 18
7.5 tn
5.0 tn
1
14
15
8
9
2
33 tn/m
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3.-FUERZAS EFECTIVAS EN COORD. GLOBALES
FUERZA DE EMP. PERFECTO
f1xf1yM1zf2xf2y
+ M2zf3xf3yM3zf4xf4yM4z
FUERZAS DE EMPOTRAMIENTO PERFECTO DE BARRAS
BARRA 5
0.00 7-3.75 8
-750.00 9F5= 0.00 10 F6=
-3.75 11750.00 12
FUERZA DE EMP. PERFECTO
7.5 Tn
8.0 m
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0.0 f1x-12.0 f1y
-1600.0 M1z0.0 f2x
-12.0 f2y
+ 1600.0 M2z0.0 f3x-3.8 f3y
-750.0 M3z0.0 f4x-3.8 f4y
750.0 M4z
matriz de rigidez en coordenadas locales
7 8 9-10 0 0 130 -0.0001125 0.0225 140 -0.0225 3 15
10 0 0 70 0.0001125 -0.0225 80 -0.0225 6 9
Matriz de Transformación0 0 00 0 00 0 00 1 0-1 0 00 0 1
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matriz de rigidez en coordenadas globales
7 8 90.000 0.000 -0.023 130.000 -10.000 0.000 140.023 0.000 3.000 150.000 0.000 0.023 70.000 10.000 0.000 80.023 0.000 6.000 9
MATRIZ DE RIGIDEZ TOTAL DE LA ESTRUCTURA (COORDENADAS GLOBALES)
4 5 6 7-5.000 0.000 0.000 0.0000.000 0.000 0.002 0.0000.000 -0.002 0.500 -0.0275.000 0.000 0.027 0.000.000 13.333 -0.002 0.000.027 -0.002 6.333 0.000.00 0.00 0.00 5.0000.00 0.00 0.00 0.000
0.00 0.00 0.00 -0.0040.00 0.000 -0.027 -5.0000.00 -13.333 0.000 0.0000.03 0.000 2.667 0.0000.00 0.00 0.00 0.0000.00 0.00 0.00 0.0000.00 0.00 0.00 0.0230.00 0.00 0.00 0.000.00 0.00 0.00 0.000.00 0.00 0.00 0.00
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AHORA NECESITAMOS CALCULAR LAS FUERZAS EFECTIVAS EN LA ESTRUCTURA PARA RESOLVER EL SISTEMA
0.000 0.000 0.000 0.0000.000 0.000 0.000 0.0000.000 0.000 0.000 0.0000.000 0.000 0.000 0.0000.000 0.000 0.000 0.000
0.000 0.000 0.000 0.0000.000 0.023 0.000 0.000
-10.000 0.000 0.000 0.0000.000 3.000 0.000 0.0000.000 0.000 0.000 0.0000.000 0.000 0.000 -10.0000.000 0.000 -0.023 0.000
|
.}={Fe}-[Kes]*{Us}
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0 7.5
0 -120 -16000 7.50 -120 1600
3.062837E-015 = 550 -53.75
-6.89146E-018 -7500 50 -3.750 750
INVERSA [Kee]*{Fefect.}
cm 1cm 2
rad/cm 3cm 4cm 5
rad/cm 6
cm 7cm 8
rad/cm 9cm 10cm 11
rad/cm 12
.}=[Kee]*{Ue}
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0.00 0.00 0.00 0.000.00 0.00 0.00 0.00
0.00 0.00 0.00 0.020.00 0.00 0.00 0.000.00 0.00 0.00 0.000.00 0.00 0.00 0.00
0.00 0.00 0.000.00 0.00 0.00
0.00 0.00 0.000.00 0.00 -0.020.00 10.00 0.00
-0.02 0.00 6.00
-12.460540339 ton8.0788598418 ton
4176.27717361 ton-cm
-12.539459661 ton
23.4211401582 ton4186.81070002 ton-cm
}=[Kse]{Ue}+[Kss]*{Us}
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PRIMERO SE CALCULARÁ LAS DEFORMACIONES EN COORDENDAS LOCALES PARA LA BARRA
1.00 - - - 0.00 - - -
- 1.00 - - - - 0.00 1.00 - - -1.00 0.00 - - - -
0.00.00.0 deformaciones locales barra 1
-5.8-335316.2
-1122.8
8 90 0 13
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-0.0001125 0.0225 14-0.0225 3 15
0 0 7 *0.0001125 -0.0225 8
-0.0225 6 9
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VECTOR DEFORMACIONES DEL SISTEMA
U1x 1U1y 2
Ue= Ø1z 3U2x 4U2y 5Ø2z 6U3x 7U3y 8Ø3z 9U4x 10U4y 11Ø4z 12
5
3
1 2
4
6
1 2
3 4
6
5
13
7
1
5
46
11
10
12
16
17
18
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BARRA 6
0 1-12 2
-1600.00 30 4
-12 51600.00 6
F.EFECTIVA EN NUDOS
03 Tn/m
8.0 m
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7.5 1-12.0 2
-1600.0 37.5 4
-12.0 5
= 1600.0 65.0 7
-3.8 8-750.0 9
5.0 10-3.8 11
750.0 12
Matriz de Rigides de cada Barra
Barra 2
A 20I 3E 200L 400phi 90 °
matriz de rigidez en coordenadas locales
16 1710 00 0.0001125
k'= 0 0.0225-10 00 -0.00011250 0.0225
Matriz de TransformaciónT= 0.00 1
-1 0.000 00 00 00 0
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matriz de rigidez en coordenadas globales
16 170.000 0.0000.000 10.000
k= -0.023 0.0000.000 0.0000.000 -10.000-0.023 0.000
8 9 10 11 120.000 0.027 0.00 0.00 0.00
-13.333 0.000 0.00 0.00 0.000.000 2.667 0.00 0.00 0.000.00 0.00 0.000 0.000 0.0270.00 0.00 0.000 -13.333 0.0000.00 0.00 -0.027 0.000 2.6670.000 -0.004 -5.000 0.000 0.000
23.333 0.002 0.000 0.000 0.002
0.002 12.333 0.000 -0.002 0.5000.000 0.000 5.000 0.000 -0.0040.000 -0.002 0.000 23.333 -0.0020.002 0.500 -0.004 -0.002 12.3330.000 -0.023 0.00 0.00 0.00
-10.000 0.000 0.00 0.00 0.000.000 3.000 0.00 0.00 0.000.00 0.00 0.000 0.000 -0.0230.00 0.00 0.000 -10.000 0.0000.00 0.00 0.023 0.000 3.000
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0.000 0 130.000 -5 140.000 0 150.000 0 160.000 0 17
0.000 * 0 180.0000.0000.0000.0230.0003.000
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Tn 1
Tn 2Tn 3Tn 4Tn 5Tn 6
Tn 7Tn 8Tn 9Tn 10Tn 11Tn 12
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0.00 -0.02 0.00 0.00 0.00-10.00 0.00 0.00 0.00 0.00
0.00 3.00 0.00 0.00 0.000.00 0.00 0.00 0.00 -0.020.00 0.00 0.00 -10.00 0.000.00 0.00 0.02 0.00 3.00
0-5
*1/E 0000
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- 0.000 13 - 0.000 14
- 0.000 15 - x 335316.239 7 - -5.808 8 1.00 -1122.779 9
0.0 58.08tn 13
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0.0 12.46tn 140.0 4176.28tn 15
-5.8 = -58.08tn 7-335316.2 -12.46tn 8
-1122.8 807.94tn 9
5
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matriz de rigidez en coordenadas locales
18 10 11 120 -10 0 0 16
0.0225 0 -0.0001125 0.0225 176 0 -0.0225 3 180 10 0 0 10
-0.0225 0 0.0001125 -0.0225 113 0 -0.0225 6 12
Matriz de Transformación0 0 0 00 0 0 01 0 0 00 0.00 1 00 -1 0.00 00 0 0 1
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matriz de rigidez en coordenadas globales
18 10 11 12-0.023 0.000 0.000 -0.023 160.000 0.000 -10.000 0.000 176.000 0.023 0.000 3.000 180.023 0.000 0.000 0.023 100.000 0.000 10.000 0.000 113.000 0.023 0.000 6.000 12
13 14 15 16 170.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00
0.000 0.000 0.023 0.00 0.000.000 -10.000 0.000 0.00 0.00
-0.023 0.000 3.000 0.00 0.000.00 0.00 0.00 0.000 0.0000.00 0.00 0.00 0.000 -10.0000.00 0.00 0.00 -0.023 0.000
0.000 0.000 -0.023 0.00 0.000.000 10.000 0.000 0.00 0.00-0.023 0.000 6.000 0.00 0.000.00 0.00 0.00 0.000 0.0000.00 0.00 0.00 0.000 10.0000.00 0.00 0.00 -0.023 0.000
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684349.607483444-6.4478411789
*1/E -1198.0924252019684348.139575668
-3.5021588212-651.1077148555
335316.239340803-5.8078859842
-1122.7794038536335317.699356647
-2.3421140158-1119.2791785001
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BARRA 2
u1'xju1'yj
{u1'}= Ø1ju1'xku1'ykØ1k
{u1'}=
BARRA 2 AXIAL,CORTANTE Y MOMENTO
Barra 2
A 20I 3E 200L 400phi 90
matriz de rigidez en coordenadas locales
16 1710 0
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0 0.0001125k'= 0 0.0225
-10 00 -0.00011250 0.0225
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Matriz de Rigides de cada Barra
Barra 3
A 20I 2E 200L 300phi 90 °
matriz de rigidez en coordenadas locales
7 8 913.3333333 0 0
0 0.00017778 0.02666667k'= 0 0.02666667 5.33333333
-13.3333333 0 00 -0.00017778 -0.026666670 0.02666667 2.66666667
Matriz de TransformaciónT= 0.00 1 0
-1 0.00 00 0 10 0 00 0 00 0 0
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matriz de rigidez en coordenadas globales
7 8 90.000 0.000 -0.0270.000 13.333 0.000
k= -0.027 0.000 5.3330.000 0.000 0.0270.000 -13.333 0.000-0.027 0.000 2.667
180.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 8
0.00 90.023 100.000 113.000 120.00 130.00 140.00 15
-0.023 160.000 176.000 18
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+
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0.00 1.00 - - - -1.00 0.00 - - -
= - - 1.00 - - - - - 0.00 1.00 - - - -1.00 0.00 - - - - -
0.00.0
1 0.0 deformaciones locales barra 2EI -2.3
-335317.7-1119.3
BARRA 2 AXIAL,CORTANTE Y MOMENTO
matriz de rigidez en coordenadas locales
18 10 11 120 -10 0 0 16
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0.0225 0 -0.0001125 0.0225 176 0 -0.0225 3 18
0 10 0 0 10 *-0.0225 0 0.0001125 -0.0225 11
3 0 -0.0225 6 12
![Page 46: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/46.jpg)
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matriz de rigidez en coordenadas locales
1 2 3-13.3333333 0 0 7
0 -0.00017778 0.0266666667 80 -0.02666667 2.6666666667 9
13.3333333 0 0 10 0.00017778 -0.0266666667 20 -0.02666667 5.3333333333 3
Matriz de Transformación0 0 00 0 00 0 0
0.00 1 0-1 0.00 00 0 1
![Page 49: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/49.jpg)
matriz de rigidez en coordenadas globales
1 2 30.000 0.000 -0.027 70.000 -13.333 0.000 80.027 0.000 2.667 90.000 0.000 0.027 10.000 13.333 0.000 20.027 0.000 5.333 3
![Page 50: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/50.jpg)
![Page 51: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/51.jpg)
![Page 52: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/52.jpg)
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- 0.000 16 - 0.000 17
- 0.000 18 - x 335317.699 10 - -2.342 11 1.00 -1119.279 12
deformaciones locales barra 2
0.0 23.42tn 16
![Page 54: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/54.jpg)
0.0 12.54tn 170.0 4186.81tn 18
-2.3 = -23.42tn 10-335317.7 -12.54tn 11
-1119.3 828.97tn 12
![Page 55: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/55.jpg)
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Matriz de Rigides de cada Barra
Barra 4
A 20I 2E 200L 300phi 90 °
matriz de rigidez en coordenadas locales
10 11 12 4 513.3333333 0 0 -13.3333333 0
0 0.00017778 0.02666667 0 -0.00017778k'= 0 0.02666667 5.33333333 0 -0.02666667
-13.3333333 0 0 13.3333333 00 -0.00017778 -0.02666667 0 0.000177780 0.02666667 2.66666667 0 -0.02666667
Matriz de TransformaciónT= 0.00 1 0 0 0
-1 0.00 0 0 00 0 1 0 00 0 0 0.00 10 0 0 -1 0.000 0 0 0 0
![Page 58: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/58.jpg)
matriz de rigidez en coordenadas globales
10 11 12 4 50.000 0.000 -0.027 0.000 0.0000.000 13.333 0.000 0.000 -13.333
k= -0.027 0.000 5.333 0.027 0.0000.000 0.000 0.027 0.000 0.0000.000 -13.333 0.000 0.000 13.333-0.027 0.000 2.667 0.027 0.000
![Page 59: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/59.jpg)
![Page 60: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/60.jpg)
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BARRA 3
u1'xj 0.00 1.00 u1'yj -1.00 0.00
{u1'}= Ø1j = - - u1'xk - - u1'yk - - Ø1k - -
-5.8-335316.2
1 -1122.8{u1'}= EI -6.4
-684349.6-1198.1
BARRA 3 AXIAL,CORTANTE Y MOMENTO
Barra 3
A 20I 2E 200L 300phi 90 °
matriz de rigidez en coordenadas locales
7 8 9 1 213.3333333 0 0 -13.3333333 0
![Page 63: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/63.jpg)
0 0.00017778 0.02666667 0 -0.00017778k'= 0 0.02666667 5.33333333 0 -0.02666667
-13.3333333 0 0 13.3333333 00 -0.00017778 -0.02666667 0 0.000177780 0.02666667 2.66666667 0 -0.02666667
![Page 64: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/64.jpg)
![Page 65: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/65.jpg)
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Matriz de Rigides de cada Barra
Barra 5
A 20I 1E 200L 800phi 0
matriz de rigidez en coordenadas locales
6 70 10 5
0.02666667 11 02.66666667 12 k'= 0
0 4 -5-0.02666667 5 05.33333333 6 0
Matriz de Transformación0 T= 1.000 00 00 00 01 0
![Page 67: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/67.jpg)
matriz de rigidez en coordenadas globales
6 7-0.027 10 5.0000.000 11 0.0002.667 12 k= 0.0000.027 4 -5.0000.000 5 0.0005.333 6 0.000
![Page 68: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/68.jpg)
![Page 69: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/69.jpg)
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- - - - 335316.239 - - - - -5.808
1.00 - - - -1122.779 - 0.00 1.00 - x 684349.607 - -1.00 0.00 - -6.448 - - - 1.00 -1198.092
deformaciones locales barra 3
30 7 -5.8
![Page 72: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/72.jpg)
0.02666667 8 -335316.22.66666667 9 -1122.8
0 1 * -6.4 =-0.02666667 2 -684349.65.33333333 3 -1198.1
![Page 73: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/73.jpg)
![Page 74: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/74.jpg)
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Matriz de Rigides de cada Barra
°
matriz de rigidez en coordenadas locales
8 9 10 11 120 0 -5 0 0 7
4.6875E-006 0.001875 0 -4.688E-006 0.001875 80.001875 1 0 -0.001875 0.5 9
0 0 5 0 0 10-4.6875E-006 -0.001875 0 4.6875E-006 -0.001875 11
0.001875 0.5 0 -0.001875 1 12
Matriz de Transformación0 0 0 0 0
1.00 0 0 0 00 1 0 0 00 0 1.00 0 00 0 0 1.00 00 0 0 0 1
![Page 76: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/76.jpg)
matriz de rigidez en coordenadas globales
8 9 10 11 120.000 0.000 -5.000 0.000 0.000 70.000 0.002 0.000 0.000 0.002 80.002 1.000 0.000 -0.002 0.500 90.000 0.000 5.000 0.000 0.000 100.000 -0.002 0.000 0.000 -0.002 110.002 0.500 0.000 -0.002 1.000 12
![Page 77: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/77.jpg)
![Page 78: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/78.jpg)
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BARRA 4
78
9 {u1'}=123
BARRA 4 AXIAL,CORTANTE Y MOMENTO
Barra 4
A 20I 2E 200L 300phi 90
matriz de rigidez en coordenadas locales
108.53tn 7 13.3333333
![Page 81: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/81.jpg)
0.16tn 8 0124.49tn 9 k'= 0
-8.53tn 1 -13.3333333-0.16tn 2 0
-76.35tn 3 0
![Page 82: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/82.jpg)
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Matriz de Rigides de cada Barra
Barra 6
A 20 m2I 1 m4E 200 tn/m2L 800 cmphi 0 °
matriz de rigidez en coordenadas locales
1 2 35 0 00 4.6875E-006 0.001875
k'= 0 0.001875 1-5 0 00 -4.688E-006 -0.0018750 0.001875 0.5
Matriz de TransformaciónT= 1.00 0 0
0 1.00 00 0 10 0 00 0 00 0 0
![Page 85: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/85.jpg)
matriz de rigidez en coordenadas globales
1 2 35.000 0.000 0.0000.000 0.000 0.002
k= 0.000 0.002 1.000-5.000 0.000 0.0000.000 0.000 -0.0020.000 0.002 0.500
![Page 86: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/86.jpg)
![Page 87: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/87.jpg)
![Page 88: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/88.jpg)
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u1'xj 0.00 1.00 - - u1'yj -1.00 0.00 - -
Ø1j = - - 1.00 - u1'xk - - - 0.00 u1'yk - - - -1.00 Ø1k - - - -
-2.3-335317.7
1 -1119.3 deformaciones locales barra 4{u1'}= EI -3.5
-684348.1-651.1
BARRA 4 AXIAL,CORTANTE Y MOMENTO
°
matriz de rigidez en coordenadas locales
11 12 4 5 60 0 -13.3333333 0 0 10
![Page 90: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/90.jpg)
0.00017778 0.02666667 0 -0.00017778 0.02666667 110.02666667 5.33333333 0 -0.02666667 2.66666667 12
0 0 13.3333333 0 0 4-0.00017778 -0.02666667 0 0.00017778 -0.02666667 50.02666667 2.66666667 0 -0.02666667 5.33333333 6
![Page 91: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/91.jpg)
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matriz de rigidez en coordenadas locales
4 5 6-5 0 0 10 -4.688E-006 0.001875 20 -0.001875 0.5 35 0 0 40 4.6875E-006 -0.001875 50 -0.001875 1 6
Matriz de Transformación0 0 00 0 00 0 0
1.00 0 00 1.00 00 0 1
![Page 94: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/94.jpg)
matriz de rigidez en coordenadas globales
4 5 6-5.000 0.000 0.000 10.000 0.000 0.002 20.000 -0.002 0.500 35.000 0.000 0.000 40.000 0.000 -0.002 50.000 -0.002 1.000 6
![Page 95: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/95.jpg)
![Page 96: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/96.jpg)
![Page 97: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/97.jpg)
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- - 335317.699 10 - - -2.342 11
- - -1119.279 12 1.00 - x 684348.140 4 0.00 - -3.502 5 - 1.00 -651.108 6
deformaciones locales barra 4
-2.3 15.47tn 10
![Page 99: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/99.jpg)
-335317.7 14.84tn 11-1119.3 1601.70tn 12
* -3.5 = -15.47tn 4-684348.1 -14.84tn 5
-651.1 2850.16tn 6
![Page 100: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/100.jpg)
![Page 101: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/101.jpg)
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BARRA 5
u1'xju1'yj
{u1'}= Ø1j =u1'xku1'ykØ1k
{u1'}=
BARRA 5 AXIAL,CORTANTE Y MOMENTO
Barra 5
A 20I 1E 200L 800phi 0 °
matriz de rigidez en coordenadas locales
7 8 95 0 0
![Page 108: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/108.jpg)
0 4.6875E-006 0.001875k'= 0 0.001875 1
-5 0 00 -4.688E-006 -0.0018750 0.001875 0.5
![Page 109: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/109.jpg)
![Page 110: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/110.jpg)
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1.00 - - - - - - 1.00 - - - -
- - 1.00 - - - - - - 1.00 - - - - - - 1.00 - - - - - - 1.00
335316.2-5.8
1 -1122.8 deformaciones locales barra 5EI 335317.7
-2.3-1119.3
BARRA 5 AXIAL,CORTANTE Y MOMENTO
matriz de rigidez en coordenadas locales
10 11 12-5 0 0 7 335316.2
![Page 117: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/117.jpg)
0 -4.688E-006 0.001875 8 -5.80 -0.001875 0.5 9 -1122.8
5 0 0 10 * 335317.70 4.6875E-006 -0.001875 11 -2.30 -0.001875 1 12 -1119.3
![Page 118: 3...Jacinto Aquino Jorge Desplazamiento](https://reader030.fdocuments.net/reader030/viewer/2022020403/577c7c7e1a28abe0549ad22b/html5/thumbnails/118.jpg)
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335316.239 7-5.808 8
-1122.779 9x 335317.699 10
-2.342 11-1119.279 12
-7.30tn 7
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-4.20tn 8### 9
= 7.30tn 104.20tn 11
### 12
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BARRA 6
u1'xj 1.00 - u1'yj - 1.00
{u1'}= Ø1j = - - u1'xk - - u1'yk - - Ø1k - -
684349.6-6.4
1 -1198.1{u1'}= EI 684348.1
-3.5-651.1
BARRA 6 AXIAL,CORTANTE Y MOMENTO
Barra 6
A 20I 1E 200L 800phi 0 °
matriz de rigidez en coordenadas locales
1 2 3 4 55 0 0 -5 0
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0 4.6875E-006 0.001875 0 -4.688E-006k'= 0 0.001875 1 0 -0.001875
-5 0 0 5 00 -4.688E-006 -0.001875 0 4.6875E-0060 0.001875 0.5 0 -0.001875
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- - - - 684349.607 - - - - -6.448
1.00 - - - -1198.092 - 1.00 - - x 684348.140 - - 1.00 - -3.502 - - - 1.00 -651.108
deformaciones locales barra 5
60 1 684349.6
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0.001875 2 -6.40.5 3 -1198.1
0 4 * 684348.1 =-0.001875 5 -3.5
1 6 -651.1
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12
3456
7.34tn 1
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-3.47tn 2### 3
-7.34tn 43.47tn 5
### 6