Ejercicio desarrollado del estructura 2

EJEMPLO DE CALCULO POR EL METODO MATRICIAL DE LA RIGIDEZ
ANALIZAR BIEN LA ESTRUCTURA, FIJANDO CONDICIONES DE APOYO Y DIRECCION DE LAS BARRAS
NUMERACION DE NUDOS ETC.
PASO 01 ORDENAR NUDOS Y BARRAS, FIJAR COORDENADAS LOCALES Y GLOBALES
PASO 02 TRASLADO DE FUERZAS EN BARRAS HACIA LOS NUDOS CON MEP Y REACCIONES
BARRA 7 Y 10 BARRA 8 Y 11 BARRA 8 Y 11
Carga 700 Kg/m Carga 700 Kg/m Carga 700 Kg/m
Longitud 5 m. Longitud 4 m. Longitud 1.5 m.
Cortante 1750 kg. Cortante 1400 kg. Cortante 525 kg.
Momento 145833.33 kg-cm Momento 93333.33 kg-cm Momento 13125.00 kg-cm
Fuerzas actuantes en BARRA 7 Fuerzas actuantes en BARRA 8 Fuerzas actuantes en BARRA 9
Nudo inicial 4 Nudo inicial 5 Nudo inicial 6
Nudo Final 5 Nudo Final 6 Nudo Final 7
F4x= 0.00 Kg. F5x= 0.00 Kg. F6x= 0.00 Kg.
F4y= -1750.00 Kg. F5y= -1400.00 Kg. F6y= -525.00 Kg.
M4= -145833.33 Kg-cm M5= -93333.33 Kg-cm M6= -13125.00 Kg-cm
F5x= 0.00 Kg. F6x= 0.00 Kg. F7x= 0.00 Kg.
F5y= -1750.00 Kg. F6y= -1400.00 Kg. F7y= -525.00 Kg.
M5= 145833.33 Kg-cm M6= 93333.33 Kg-cm M7= 13125.00 Kg-cm
Fuerzas actuantes en BARRA 10 Fuerzas actuantes en BARRA 11 Fuerzas actuantes en BARRA 12
Nudo inicial 8 Nudo inicial 9 Nudo inicial 10
Nudo Final 9 Nudo Final 10 Nudo Final 11
F8x= 0.00 Kg. F9x= 0.00 Kg. F10x= 0.00 Kg.
F8y= -1750.00 Kg. F9y= -1400.00 Kg. F10y= -525.00 Kg.
M8= -145833.33 Kg-cm M9= -93333.33 Kg-cm M10= -13125.00 Kg-cm
F9x= 0.00 Kg. F10x= 0.00 Kg. F11x= 0.00 Kg.
F9y= -1750.00 Kg. F10y= -1400.00 Kg. F11y= -525.00 Kg.
M9= 145833.33 Kg-cm M10= 93333.33 Kg-cm M11= 13125.00 Kg-cm
PASO 03 CALCULO DE LA MATRIZ DE TRANSFORMACION DE CADA BARRA
MATRIZ DE TRANSFORMACION DE VIGAS:
VIGAS angulo= 0 º Su transpuesta es:
1.000 0.000 0 0 0 0 1.000 0.000 0 0 0 0
0.000 1.000 0 0 0 0 0.000 1.000 0 0 0 0
L = 0 0 1 0 0 0 L (T) = 0 0 1 0 0 0
0 0 0 1.000 0.000 0 0 0 0 1.000 0.000 0.000
0 0 0 0.000 1.000 0 0 0 0 0.000 1.000 0.000
0 0 0 0 0 1 0 0 0 0.000 0.000 1.000
MATRIZ DE TRANSFORMACION DE COLUMNAS:
COLUMNAS angulo= 90 º Su transpuesta es:
0.00 -1.000 0 0 0 0 0.000 1.000 0 0 0 0
1.000 0.000 0 0 0 0 -1.000 0.000 0 0 0 0
L = 0 0 1 0 0 0 L (T) = 0 0 1 0 0 0
0 0 0 0.000 -1.000 0 0 0 0 0.000 1.000 0.000
0 0 0 1.000 0.000 0 0 0 0 -1.000 0.000 0.000
0 0 0 0 0 1 0 0 0 0.000 0.000 1.000
PASO 04 PASO DE COORDENADAS LOCALES A GLOBALES DE LAS FUERZAS ACTUANTES EN LAS BARRAS
PASO DE LA FUERZA EN LA BARRA 7 FZAS. EN BARRA SIST. LOCAL FUERZAS EN BARRAS EN SISTEMA GLOBAL
1.000 0.000 0 0 0 0 0.00 0.00 F4x=
0.000 1.000 0 0 0 0 -1750.00 -1750.00 F4y=
0 0 1 0 0 0 X -145833.33 = -145833.33 M4=
0 0 0 1.000 0.000 0.000 0.00 0.00 F5x=
0 0 0 0.000 1.000 0.000 -1750.00 -1750.00 F5y=
0 0 0 0.000 0.000 1.000 145833.33 145833.33 M5=
PASO DE LA FUERZA EN LA BARRA 8
1.000 0.000 0 0 0 0 0.00 0.00 F5x= MATRIZ ENSAMBLADADE FUERZAS EN BARRAS
0.000 1.000 0 0 0 0 -1400.00 -1400.00 F5y= F4x= 0.00
0 0 1 0 0 0 X -93333.33 = -93333.33 M5= F4y= -1750.00
0 0 0 1.000 0.000 0.000 0.00 0.00 F6x= M4= -145833.33
0 0 0 0.000 1.000 0.000 -1400.00 -1400.00 F6y= F5x= 0.00
0 0 0 0.000 0.000 1.000 93333.33 93333.33 M6= F5y= -3150.00
M5= 52500.00
PASO DE LA FUERZA EN LA BARRA 9 FZAS. EN BARRA SIST. LOCAL FUERZAS EN BARRAS EN SISTEMA GLOBAL F6x= 0.00
1.000 0.000 0 0 0 0 0.00 0.00 F6x= F6y= -1925.00
0.000 1.000 0 0 0 0 -525.00 -525.00 F6y= M6= 80208.33
0 0 1 0 0 0 X -13125.00 = -13125.00 M6= F7x= 0.00
0 0 0 1.000 0.000 0.000 0.00 0.00 F7x= F7y= -525.00
0 0 0 0.000 1.000 0.000 -525.00 -525.00 F7y= M7= 13125.00
0 0 0 0.000 0.000 1.000 13125.00 13125.00 M7= F8x= 0.00
F8y= -1750.00
PASO DE LA FUERZA EN LA BARRA 10 FZAS. EN BARRA SIST. LOCAL FUERZAS EN BARRAS EN SISTEMA GLOBAL M8= -145833.33
1.000 0.000 0 0 0 0 0.00 0.00 F8x= F9x= 0.00
0.000 1.000 0 0 0 0 -1750.00 -1750.00 F8y= F9y= -3150.00
0 0 1 0 0 0 X -145833.33 = -145833.33 M8= M9= 52500.00
0 0 0 1.000 0.000 0.000 0.00 0.00 F9x= F10x= 0.00
0 0 0 0.000 1.000 0.000 -1750.00 -1750.00 F9y= F10y= -1925.00
0 0 0 0.000 0.000 1.000 145833.33 145833.33 M9= M10= 80208.33
1 2 3
4 5 6 7
8 9 10 12
1 2 3
4 5 6
7 8 9
10 11 12
1 2 3
4 5 6 7
8 9 10 12
1 2 3
4 5 6
7 8 9
10 11 12
Las cargas actuantes en la estructura,
soin transformados en cargas
equivalentes en cada nudo, actuando en
la direccion indicada en cada nudo.
Además en la estructura la direccion de
las barras esta dada desde el nudo
menor al nudo mayor correspondiente.
Además considerar que, en las barras
no actua fuerzas axiales, por lo cual no
existtirá Fx,
+ +
+
ENREALIDADESTEPADOYANOESNECESARIOPORCUANTO,LASFUERZASENESTE
EJERCICIOTODOSACTÚANENDIRECCION-YTANTOENCOORDENADASGLOBALESY
LOCALES.LOCUALNOSUCEDERÍASISEAPLICACENFUERZASENLASCOLUMNAS,POR
CUANTONOCOENCIDIRIANLASDIRECCIONESLOCALCONLAGLOBAL..

F11x= 0.00
PASO DE LA FUERZA EN LA BARRA 11 F11y= -525.00
1.000 0.000 0 0 0 0 0.00 0.00 F9x= M11= 13125.00
0.000 1.000 0 0 0 0 -1400.00 -1400.00 F9y=
0 0 1 0 0 0 X -93333.33 = -93333.33 M9=
0 0 0 1.000 0.000 0.000 0.00 0.00 F10x=
0 0 0 0.000 1.000 0.000 -1400.00 -1400.00 F10y=
0 0 0 0.000 0.000 1.000 93333.33 93333.33 M10=
PASO DE LA FUERZA EN LA BARRA 12 FZAS. EN BARRA SIST. LOCAL FUERZAS EN BARRAS EN SISTEMA GLOBAL
1.000 0.000 0 0 0 0 0.00 0.00 F10x=
0.000 1.000 0 0 0 0 -525.00 -525.00 F10y=
0 0 1 0 0 0 X -13125.00 = -13125.00 M10=
0 0 0 1.000 0.000 0.000 0.00 0.00 F11x=
0 0 0 0.000 1.000 0.000 -525.00 -525.00 F11y=
0 0 0 0.000 0.000 1.000 13125.00 13125.00 M11=
PASO 05: CALCULO DE LA MATRIZ DE RIGIDEZ LOCAL DE CADA ELEMENTO
Inicio 1 Final 4
BARRA base (cm) alto (cm) L (cm.) A I E AE/L 12EI/L^3 6EI/L^2 4EI/L 2EI/L
1 25 25 400 625.00 32552.08 217370.6512 339641.64 1326.73 265345.03 70758675.52 35379337.76
U1x U1y G1 U4x U4y G4
339641.64 0.00 0.00 -339641.64 0.00 0.00 U1x
0.00 1326.73 265345.03 0.00 -1326.73 265345.03 U1y
0.00 265345.03 70758675.52 0.00 -265345.03 35379337.76 G1
-339641.64 0.00 0.00 339641.64 0.00 0.00 U4x
0.00 -1326.73 -265345.03 0.00 1326.73 -265345.03 U4y
0.00 265345.03 35379337.76 0.00 -265345.03 70758675.52 G4
Inicio 2 Final 5
2 25 25 400 625.00 32552.08 217370.6512 339641.64 1326.73 265345.03 70758675.52 35379337.76
339641.64 0.00 0.00 -339641.64 0.00 0.00 U2x
0.00 1326.73 265345.03 0.00 -1326.73 265345.03 U2y
0.00 265345.03 70758675.52 0.00 -265345.03 35379337.76 G2
-339641.64 0.00 0.00 339641.64 0.00 0.00 U5x
0.00 -1326.73 -265345.03 0.00 1326.73 -265345.03 U5y
0.00 265345.03 35379337.76 0.00 -265345.03 70758675.52 G5
Inicio 3 Final 6
3 25 25 400 625.00 32552.08 217370.6512 339641.64 1326.73 265345.03 70758675.52 35379337.76
339641.64 0.00 0.00 -339641.64 0.00 0.00 U3x
0.00 1326.73 265345.03 0.00 -1326.73 265345.03 U3y
0.00 265345.03 70758675.52 0.00 -265345.03 35379337.76 G3
-339641.64 0.00 0.00 339641.64 0.00 0.00 U6x
0.00 -1326.73 -265345.03 0.00 1326.73 -265345.03 U6y
0.00 265345.03 35379337.76 0.00 -265345.03 70758675.52 G6
Inicio 4 Final 8
4 25 25 300 625.00 32552.08 217370.6512 452855.52 3144.83 471724.50 94344900.69 47172450.35
452855.52 0.00 0.00 -452855.52 0.00 0.00 U4x
0.00 3144.83 471724.50 0.00 -3144.83 471724.50 U4y
0.00 471724.50 94344900.69 0.00 -471724.50 47172450.35 G4
-452855.52 0.00 0.00 452855.52 0.00 0.00 U8x
0.00 -3144.83 -471724.50 0.00 3144.83 -471724.50 U8y
0.00 471724.50 47172450.35 0.00 -471724.50 94344900.69 G8
Inicio 5 Final 9
5 25 25 300 625.00 32552.08 217370.6512 452855.52 3144.83 471724.50 94344900.69 47172450.35
452855.52 0.00 0.00 -452855.52 0.00 0.00 U5x
0.00 3144.83 471724.50 0.00 -3144.83 471724.50 U5y
0.00 471724.50 94344900.69 0.00 -471724.50 47172450.35 G5
-452855.52 0.00 0.00 452855.52 0.00 0.00 U9x
0.00 -3144.83 -471724.50 0.00 3144.83 -471724.50 U9y
0.00 471724.50 47172450.35 0.00 -471724.50 94344900.69 G9
Inicio 6 Final 10
6 25 25 300 625.00 32552.08 217370.6512 452855.52 3144.83 471724.50 94344900.69 47172450.35
452855.52 0.00 0.00 -452855.52 0.00 0.00 U6x
0.00 3144.83 471724.50 0.00 -3144.83 471724.50 U6y
0.00 471724.50 94344900.69 0.00 -471724.50 47172450.35 G6
-452855.52 0.00 0.00 452855.52 0.00 0.00 U10x
0.00 -3144.83 -471724.50 0.00 3144.83 -471724.50 U10y
0.00 471724.50 47172450.35 0.00 -471724.50 94344900.69 G10
Inicio 4 Final 5
7 25 50 500 1250.00 260416.67 217370.6512 543426.63 5434.27 1358566.57 452855523.32 226427761.66
543426.63 0.00 0.00 -543426.63 0.00 0.00 U4x
0.00 5434.27 1358566.57 0.00 -5434.27 1358566.57 U4y
0.00 1358566.57 452855523.32 0.00 -1358566.57 226427761.66 G4
-543426.63 0.00 0.00 543426.63 0.00 0.00 U5x
0.00 -5434.27 -1358566.57 0.00 5434.27 -1358566.57 U5y
0.00 1358566.57 226427761.66 0.00 -1358566.57 452855523.32 G5
Inicio 5 Final 6
8 25 50 400 1250.00 260416.67 217370.6512 679283.28 10613.80 2122760.27 566069404.15 283034702.07
679283.28 0.00 0.00 -679283.28 0.00 0.00 U5x
0.00 10613.80 2122760.27 0.00 -10613.80 2122760.27 U5y
0.00 2122760.27 566069404.15 0.00 -2122760.27 283034702.07 G5
-679283.28 0.00 0.00 679283.28 0.00 0.00 U6x
0.00 -10613.80 -2122760.27 0.00 10613.80 -2122760.27 U6y
0.00 2122760.27 283034702.07 0.00 -2122760.27 566069404.15 G6
Inicio 6 Final 7
9 25 50 150 1250.00 260416.67 217370.6512 1811422.09 201269.12 15095184.11 1509518411.06 754759205.53
1811422.09 0.00 0.00 -1811422.09 0.00 0.00 U6x
0.00 201269.12 15095184.11 0.00 -201269.12 15095184.11 U6y
0.00 15095184.11 1509518411.06 0.00 -15095184.11 754759205.53 G6
-1811422.09 0.00 0.00 1811422.09 0.00 0.00 U7x
0.00 -201269.12 -15095184.11 0.00 201269.12 -15095184.11 U7y
0.00 15095184.11 754759205.53 0.00 -15095184.11 1509518411.06 G7
Inicio 8 Final 9
10 25 50 500 1250.00 260416.67 217370.6512 543426.63 5434.27 1358566.57 452855523.32 226427761.66
543426.63 0.00 0.00 -543426.63 0.00 0.00 U8x
0.00 5434.27 1358566.57 0.00 -5434.27 1358566.57 U8y
0.00 1358566.57 452855523.32 0.00 -1358566.57 226427761.66 G8
-543426.63 0.00 0.00 543426.63 0.00 0.00 U9x
0.00 -5434.27 -1358566.57 0.00 5434.27 -1358566.57 U9y
0.00 1358566.57 226427761.66 0.00 -1358566.57 452855523.32 G9
Inicio 9 Final 10
11 25 50 400 1250.00 260416.67 217370.6512 679283.28 10613.80 2122760.27 566069404.15 283034702.07
679283.28 0.00 0.00 -679283.28 0.00 0.00 U9x
0.00 10613.80 2122760.27 0.00 -10613.80 2122760.27 U9y
0.00 2122760.27 566069404.15 0.00 -2122760.27 283034702.07 G9
-679283.28 0.00 0.00 679283.28 0.00 0.00 U10x
0.00 -10613.80 -2122760.27 0.00 10613.80 -2122760.27 U10y
0.00 2122760.27 283034702.07 0.00 -2122760.27 566069404.15 G10
Inicio 10 Final 11
12 25 50 150 1250.00 260416.67 217370.6512 1811422.09 201269.12 15095184.11 1509518411.06 754759205.53
U10x U10y G10 U11x U11y G11
1811422.09 0.00 0.00 -1811422.09 0.00 0.00 U10x
0.00 201269.12 15095184.11 0.00 -201269.12 15095184.11 U10y
0.00 15095184.11 1509518411.06 0.00 -15095184.11 754759205.53 G10
-1811422.09 0.00 0.00 1811422.09 0.00 0.00 U11x
0.00 -201269.12 -15095184.11 0.00 201269.12 -15095184.11 U11y
ENREALIDADESTEPADOYANOESNECESARIO
EJERCICIOTODOSACTÚANENDIRECCION
LOCALES.LOCUALNOSUCEDERÍASISEAPLICACENFUERZASENLASCO
CUANTONOCOENCIDIRIANLASDIRECCIONESLOCALCONLAGLOBAL..

0.00 15095184.11 754759205.53 0.00 -15095184.11 1509518411.06 G11
PASO 06: CONVERSION DE LAS MATRICES DE RIGIDEZ LOCAL A MATRIZ DE RIGIDEZ GLOBAL
col Barra 1 U1x U1y G1 U4x U4y G4
0 -1327 -265345 0 1327 -265345 1327 0 -265345 -1327 0 -265345 U1x
339642 0 0 -339642 0 0 0 339642 0 0 -339642 0 U1y
0 265345 70758676 0 -265345 35379338 -265345 0 70758676 265345 0 35379338 G1
0 1327 265345 0 -1327 265345 -1327 0 265345 1327 0 265345 U4x
-339642 0 0 339642 0 0 0 -339642 0 0 339642 0 U4y
0 265345 35379338 0 -265345 70758676 -265345 0 35379338 265345 0 70758676 G4
0 -1327 -265345 0 1327 -265345 1327 0 -265345 -1327 0 -265345 U2x
339642 0 0 -339642 0 0 0 339642 0 0 -339642 0 U2y
0 265345 70758676 0 -265345 35379338 -265345 0 70758676 265345 0 35379338 G2
0 1327 265345 0 -1327 265345 -1327 0 265345 1327 0 265345 U5x
-339642 0 0 339642 0 0 0 -339642 0 0 339642 0 U5y
0 265345 35379338 0 -265345 70758676 -265345 0 35379338 265345 0 70758676 G5
col BARRA 3 U3x U3y G3 U6x U6y G6
0 -1327 -265345 0 1327 -265345 1327 0 -265345 -1327 0 -265345 U3x
339642 0 0 -339642 0 0 0 339642 0 0 -339642 0 U3y
0 265345 70758676 0 -265345 35379338 -265345 0 70758676 265345 0 35379338 G3
0 1327 265345 0 -1327 265345 -1327 0 265345 1327 0 265345 U6x
-339642 0 0 339642 0 0 0 -339642 0 0 339642 0 U6y
0 265345 35379338 0 -265345 70758676 -265345 0 35379338 265345 0 70758676 G6
0 -3145 -471725 0 3145 -471725 3145 0 -471725 -3145 0 -471725 U4x
452856 0 0 -452856 0 0 0 452856 0 0 -452856 0 U4y
0 471725 94344901 0 -471725 47172450 -471725 0 94344901 471725 0 47172450 G4
0 3145 471725 0 -3145 471725 -3145 0 471725 3145 0 471725 U8x
-452856 0 0 452856 0 0 0 -452856 0 0 452856 0 U8y
0 471725 47172450 0 -471725 94344901 -471725 0 47172450 471725 0 94344901 G8
0 -3145 -471725 0 3145 -471725 3145 0 -471725 -3145 0 -471725 U5x
452856 0 0 -452856 0 0 0 452856 0 0 -452856 0 U5y
0 471725 94344901 0 -471725 47172450 -471725 0 94344901 471725 0 47172450 G5
0 3145 471725 0 -3145 471725 -3145 0 471725 3145 0 471725 U9x
-452856 0 0 452856 0 0 0 -452856 0 0 452856 0 U9y
0 471725 47172450 0 -471725 94344901 -471725 0 47172450 471725 0 94344901 G9
0 -3145 -471725 0 3145 -471725 3145 0 -471725 -3145 0 -471725 U6x
452856 0 0 -452856 0 0 0 452856 0 0 -452856 0 U6y
0 471725 94344901 0 -471725 47172450 -471725 0 94344901 471725 0 47172450 G6
0 3145 471725 0 -3145 471725 -3145 0 471725 3145 0 471725 U10x
-452856 0 0 452856 0 0 0 -452856 0 0 452856 0 U10y
0 471725 47172450 0 -471725 94344901 -471725 0 47172450 471725 0 94344901 G10
vig Barra 7 U4x U4y G4 U5x U5y G5
543427 0 0 -543427 0 0 543427 0 0 -543427 0 0 U4x
0 5434 1358567 0 -5434 1358567 0 5434 1358567 0 -5434 1358567 U4y
0 1358567 452855523 0 -1358567 226427762 0 1358567 452855523 0 -1358567 226427762 G4
-543427 0 0 543427 0 0 -543427 0 0 543427 0 0 U5x
0 -5434 -1358567 0 5434 -1358567 0 -5434 -1358567 0 5434 -1358567 U5y
0 1358567 226427762 0 -1358567 452855523 0 1358567 226427762 0 -1358567 452855523 G5
vig BARRA 8 U5x U5y G5 U6x U6y G6
679283 0 0 -679283 0 0 679283 0 0 -679283 0 0 U5x
0 10614 2122760 0 -10614 2122760 0 10614 2122760 0 -10614 2122760 U5y
0 2122760 566069404 0 -2122760 283034702 0 2122760 566069404 0 -2122760 283034702 G5
-679283 0 0 679283 0 0 -679283 0 0 679283 0 0 U6x
0 -10614 -2122760 0 10614 -2122760 0 -10614 -2122760 0 10614 -2122760 U6y
0 2122760 283034702 0 -2122760 566069404 0 2122760 283034702 0 -2122760 566069404 G6
1811422 0 0 -1811422 0 0 1811422 0 0 -1811422 0 0 U6x
0 201269 15095184 0 -201269 15095184 0 201269 15095184 0 -201269 15095184 U6y
0 15095184 1509518411 0 -15095184 754759206 0 15095184 1509518411 0 -15095184 754759206 G6
-1811422 0 0 1811422 0 0 -1811422 0 0 1811422 0 0 U7x
0 -201269 -15095184 0 201269 -15095184 0 -201269 -15095184 0 201269 -15095184 U7y
0 15095184 754759206 0 -15095184 1509518411 0 15095184 754759206 0 -15095184 1509518411 G7
543427 0 0 -543427 0 0 543427 0 0 -543427 0 0 U8x
0 5434 1358567 0 -5434 1358567 0 5434 1358567 0 -5434 1358567 U8y
0 1358567 452855523 0 -1358567 226427762 0 1358567 452855523 0 -1358567 226427762 G8
-543427 0 0 543427 0 0 -543427 0 0 543427 0 0 U9x
0 -5434 -1358567 0 5434 -1358567 0 -5434 -1358567 0 5434 -1358567 U9y
0 1358567 226427762 0 -1358567 452855523 0 1358567 226427762 0 -1358567 452855523 G9
679283 0 0 -679283 0 0 679283 0 0 -679283 0 0 U9x
0 10614 2122760 0 -10614 2122760 0 10614 2122760 0 -10614 2122760 U9y
0 2122760 566069404 0 -2122760 283034702 0 2122760 566069404 0 -2122760 283034702 G9
-679283 0 0 679283 0 0 -679283 0 0 679283 0 0 U10x
0 -10614 -2122760 0 10614 -2122760 0 -10614 -2122760 0 10614 -2122760 U10y
0 2122760 283034702 0 -2122760 566069404 0 2122760 283034702 0 -2122760 566069404 G10
1811422 0 0 -1811422 0 0 1811422 0 0 -1811422 0 0 U10x
0 201269 15095184 0 -201269 15095184 0 201269 15095184 0 -201269 15095184 U10y
0 15095184 1509518411 0 -15095184 754759206 0 15095184 1509518411 0 -15095184 754759206 G10
-1811422 0 0 1811422 0 0 -1811422 0 0 1811422 0 0 U11x
0 -201269 -15095184 0 201269 -15095184 0 -201269 -15095184 0 201269 -15095184 U11y
0 15095184 754759206 0 -15095184 1509518411 0 15095184 754759206 0 -15095184 1509518411 G11
PASO 07: ENSAMBLAJE DE LAS MATRICES DE RIGIDEZ DEL SISTEMA Y REDUCCION SEGÚN LOS GRADOS DE LIBERTAD
U1x U1y G1 U2x U2y G2 U3x U3y G3 U4x U4y G4 U5x U5y G5 U6x U6y G6 U7x U7y G7 U8x U8y G8 U9x U9y G9 U10x U10y G10 U11x U11y G11 DESPLAZAMIENTOS RESTRINGIDOS
1326.73 0.00 -265345.03 0.00 0.00 0.00 0.00 0.00 0.00 -1326.73 0.00 -265345.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U1x 0
0.00 339641.64 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -339641.64 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U1y 0
-265345.03 0.00 70758675.52 0.00 0.00 0.00 0.00 0.00 0.00 265345.03 0.00 35379337.76 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 G1 0
0.00 0.00 0.00 1326.73 0.00 -265345.03 0.00 0.00 0.00 0.00 0.00 0.00 -1326.73 0.00 -265345.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U2x 0
0.00 0.00 0.00 0.00 339641.64 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -339641.64 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U2y 0
0.00 0.00 0.00 -265345.03 0.00 70758675.52 0.00 0.00 0.00 0.00 0.00 0.00 265345.03 0.00 35379337.76 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 G2 0
0.00 0.00 0.00 0.00 0.00 0.00 1326.73 0.00 -265345.03 0.00 0.00 0.00 0.00 0.00 0.00 -1326.73 0.00 -265345.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U3x 0
0.00 0.00 0.00 0.00 0.00 0.00 0.00 339641.64 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -339641.64 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U3y 0
0.00 0.00 0.00 0.00 0.00 0.00 -265345.03 0.00 70758675.52 0.00 0.00 0.00 0.00 0.00 0.00 265345.03 0.00 35379337.76 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 G3 0
-1326.73 0.00 265345.03 0.00 0.00 0.00 0.00 0.00 0.00 547898.18 0.00 -206379.47 -543426.63 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -3144.83 0.00 -471724.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U4x 1
0.00 -339641.64 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 797931.43 1358566.57 0.00 -5434.27 1358566.57 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -452855.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U4y 1
-265345.03 0.00 35379337.76 0.00 0.00 0.00 0.00 0.00 0.00 -206379.47 1358566.57 617959099.53 0.00 -1358566.57 226427761.66 0.00 0.00 0.00 0.00 0.00 0.00 471724.50 0.00 47172450.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 G4 1
0.00 0.00 0.00 -1326.73 0.00 265345.03 0.00 0.00 0.00 -543426.63 0.00 0.00 1227181.47 0.00 -206379.47 -679283.28 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -3144.83 0.00 -471724.50 0.00 0.00 0.00 0.00 0.00 0.00 U5x 1
0.00 0.00 0.00 0.00 -339641.64 0.00 0.00 0.00 0.00 0.00 -5434.27 -1358566.57 0.00 808545.23 764193.70 0.00 -10613.80 2122760.27 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -452855.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U5y 1
0.00 0.00 0.00 -265345.03 0.00 35379337.76 0.00 0.00 0.00 0.00 1358566.57 226427761.66 -206379.47 764193.70 1184028503.68 0.00 -2122760.27 283034702.07 0.00 0.00 0.00 0.00 0.00 0.00 471724.50 0.00 47172450.35 0.00 0.00 0.00 0.00 0.00 0.00 G5 1
0.00 0.00 0.00 0.00 0.00 0.00 -1326.73 0.00 265345.03 0.00 0.00 0.00 -679283.28 0.00 0.00 2495176.93 0.00 -206379.47 -1811422.09 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -3144.83 0.00 -471724.50 0.00 0.00 0.00 U6x 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 -339641.64 0.00 0.00 0.00 0.00 0.00 -10613.80 -2122760.27 0.00 1004380.09 12972423.85 0.00 -201269.12 15095184.11 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -452855.52 0.00 0.00 0.00 0.00 U6y 1
0.00 0.00 0.00 0.00 0.00 0.00 -265345.03 0.00 35379337.76 0.00 0.00 0.00 0.00 2122760.27 283034702.07 -206379.47 12972423.85 2240691391.42 0.00 -15095184.11 754759205.53 0.00 0.00 0.00 0.00 0.00 0.00 471724.50 0.00 47172450.35 0.00 0.00 0.00 G6 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -1811422.09 0.00 0.00 1811422.09 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U7x 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -201269.12 -15095184.11 0.00 201269.12 -15095184.11 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U7y 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 15095184.11 754759205.53 0.00 -15095184.11 1509518411.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 G7 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -3144.83 0.00 471724.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 546571.46 0.00 471724.50 -543426.63 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U8x 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -452855.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 458289.79 1358566.57 0.00 -5434.27 1358566.57 0.00 0.00 0.00 0.00 0.00 0.00 U8y 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -471724.50 0.00 47172450.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 471724.50 1358566.57 ############ 0.00 -1358566.57 226427761.66 0.00 0.00 0.00 0.00 0.00 0.00 G8 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -3144.83 0.00 471724.50 0.00 0.00 0.00 0.00 0.00 0.00 -543426.63 0.00 0.00 1225854.74 0.00 471724.50 -679283.28 0.00 0.00 0.00 0.00 0.00 U9x 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -452855.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -5434.27 -1358566.57 0.00 468903.59 764193.70 0.00 -10613.80 2122760.27 0.00 0.00 0.00 U9y 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -471724.50 0.00 47172450.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1358566.57 ############ 471724.50 764193.70 1113269828.16 0.00 -2122760.27 283034702.07 0.00 0.00 0.00 G9 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -3144.83 0.00 471724.50 0.00 0.00 0.00 0.00 0.00 0.00 -679283.28 0.00 0.00 2493850.21 0.00 471724.50 -1811422.09 0.00 0.00 U10x 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -452855.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -10613.80 -2122760.27 0.00 664738.45 12972423.85 0.00 -201269.12 15095184.11 U10y 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -471724.50 0.00 47172450.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2122760.27 283034702.07 471724.50 ########### ############# 0.00 -15095184.11 754759205.53 G10 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -1811422.09 0.00 0.00 1811422.09 0.00 0.00 U11x 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -201269.12 -15095184.11 0.00 201269.12 -15095184.11 U11y 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ########### 754759205.53 0.00 -15095184.11 1509518411.06 G11 1
LA MATRIZ REDUCIDA ES LA SIGUIENTE
U4x U4y G4 U5x U5y G5 U6x U6y G6 U7x U7y G7 U8x U8y G8 U9x U9y G9 U10x U10y G10 U11x U11y G11
547898.18 0.00 -206379.47 -543426.63 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -3144.83 0.00 -471724.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U4x 1
0.00 797931.43 1358566.57 0.00 -5434.27 1358566.57 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -452855.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U4y 2
-206379.47 1358566.57 617959099.53 0.00 -1358566.57 226427761.66 0.00 0.00 0.00 0.00 0.00 0.00 471724.50 0.00 47172450.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 G4 3
-543426.63 0.00 0.00 1227181.47 0.00 -206379.47 -679283.28 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -3144.83 0.00 -471724.50 0.00 0.00 0.00 0.00 0.00 0.00 U5x 4
0.00 -5434.27 -1358566.57 0.00 808545.23 764193.70 0.00 -10613.80 2122760.27 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -452855.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U5y 5
0.00 1358566.57 226427761.66 -206379.47 764193.70 ############# 0.00 -2122760.27 283034702.07 0.00 0.00 0.00 0.00 0.00 0.00 471724.50 0.00 47172450.35 0.00 0.00 0.00 0.00 0.00 0.00 G5 6
0.00 0.00 0.00 -679283.28 0.00 0.00 2495176.93 0.00 -206379.47 -1811422.09 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -3144.83 0.00 -471724.50 0.00 0.00 0.00 U6x 7
0.00 0.00 0.00 0.00 -10613.80 -2122760.27 0.00 1004380.09 12972423.85 0.00 -201269.12 15095184.11 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -452855.52 0.00 0.00 0.00 0.00 U6y 8
0.00 0.00 0.00 0.00 2122760.27 283034702.07 -206379.47 12972423.85 ############# 0.00 -15095184.11 754759205.53 0.00 0.00 0.00 0.00 0.00 0.00 471724.50 0.00 47172450.35 0.00 0.00 0.00 G6 9
0.00 0.00 0.00 0.00 0.00 0.00 -1811422.09 0.00 0.00 1811422.09 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U7x 10

0.00 0.00 0.00 0.00 0.00 0.00 0.00 -201269.12 -15095184.11 0.00 201269.12 -15095184.11 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U7y 11
K = 0.00 0.00 0.00 0.00 0.00 0.00 0.00 15095184.11 754759205.53 0.00 -15095184.11 1509518411.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 G7 12
-3144.83 0.00 471724.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 546571.46 0.00 471724.50 -543426.63 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 U8x 13
0.00 -452855.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 458289.79 1358566.57 0.00 -5434.27 1358566.57 0.00 0.00 0.00 0.00 0.00 0.00 U8y 14
-471724.50 0.00 47172450.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 471724.50 1358566.57 547200424.01 0.00 -1358566.57 226427761.66 0.00 0.00 0.00 0.00 0.00 0.00 G8 15
0.00 0.00 0.00 -3144.83 0.00 471724.50 0.00 0.00 0.00 0.00 0.00 0.00 -543426.63 0.00 0.00 1225854.74 0.00 471724.50 -679283.28 0.00 0.00 0.00 0.00 0.00 U9x 16
0.00 0.00 0.00 0.00 -452855.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -5434.27 -1358566.57 0.00 468903.59 764193.70 0.00 -10613.80 2122760.27 0.00 0.00 0.00 U9y 17
0.00 0.00 0.00 -471724.50 0.00 47172450.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1358566.57 226427761.66 471724.50 764193.70 1113269828.16 0.00 -2122760.27 283034702.07 0.00 0.00 0.00 G9 18
0.00 0.00 0.00 0.00 0.00 0.00 -3144.83 0.00 471724.50 0.00 0.00 0.00 0.00 0.00 0.00 -679283.28 0.00 0.00 2493850.21 0.00 471724.50 -1811422.09 0.00 0.00 U10x 19
0.00 0.00 0.00 0.00 0.00 0.00 0.00 -452855.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -10613.80 -2122760.27 0.00 664738.45 12972423.85 0.00 -201269.12 15095184.11 U10y 20
0.00 0.00 0.00 0.00 0.00 0.00 -471724.50 0.00 47172450.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2122760.27 283034702.07 471724.50 12972423.85 2169932715.90 0.00 -15095184.11 754759205.53 G10 21
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -1811422.09 0.00 0.00 1811422.09 0.00 0.00 U11x 22
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -201269.12 -15095184.11 0.00 201269.12 -15095184.11 U11y 23
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 15095184.11 754759205.53 0.00 -15095184.11 1509518411.06 G11 24
PASO 08: CALCULO DE DESPLAZAMIENTOS EN LOS NUDOS F=KxU
FUERZAS EXTERNAS (F)
F4x= 0.00
F4y= -1750.00
M4= -145833.33
F5x= 0.00
F5y= -3150.00
M5= 52500.00
F6x= 0.00
F6y= -1925.00
M6= 80208.33
F7x= 0.00
F7y= -525.00
M7= 13125.00 = K x U
F8x= 0.00
F8y= -1750.00
M8= -145833.33
F9x= 0.00
F9y= -3150.00
M9= 52500.00
F10x= 0.00
F10y= -1925.00
M10= 80208.33
F11x= 0.00
F11y= -525.00
M11= 13125.00
MATRIZ INVERSA DE K
1.00 2 3.00 4 5.00 6 7.00 8 9.00 10 11.00 12 13.00 14 15.00 16 17.00 18 19.00 20 21.00 22 23.00 24
0.000268029 0.000000556 -0.000000117 0.000266821 0.000000191 -0.000000020 0.000266329 -0.000000747 -0.000000100 0.000266329 -0.000015698 -0.000000100 0.000279277 0.000000564 0.000000002 0.000279242 0.000000201 -0.000000007 0.000279253 -0.000000766 -0.000000002 0.000279253 -0.000001130 -0.000000002 1
0.000000556 0.000002922 -0.000000006 0.000000560 0.000000049 -0.000000003 0.000000563 -0.000000027 0.000000000 0.000000563 -0.000000017 0.000000000 0.000001418 0.000002915 -0.000000006 0.000001413 0.000000065 -0.000000003 0.000001409 -0.000000036 0.000000000 0.000001409 -0.000000001 0.000000000 2
-0.000000117 -0.000000006 0.000000002 -0.000000118 0.000000006 0.000000000 -0.000000118 0.000000000 0.000000000 -0.000000118 0.000000033 0.000000000 -0.000000206 -0.000000006 0.000000000 -0.000000204 0.000000005 0.000000000 -0.000000204 0.000000000 0.000000000 -0.000000204 0.000000000 0.000000000 3
0.000266821 0.000000560 -0.000000118 0.000267444 0.000000182 -0.000000020 0.000266948 -0.000000742 -0.000000100 0.000266948 -0.000015677 -0.000000100 0.000279320 0.000000571 0.000000001 0.000279291 0.000000187 -0.000000006 0.000279304 -0.000000758 -0.000000002 0.000279304 -0.000001080 -0.000000002 4
0.000000191 0.000000049 0.000000006 0.000000182 0.000002835 -0.000000001 0.000000175 0.000000061 -0.000000007 0.000000175 -0.000001035 -0.000000007 0.000000435 0.000000065 0.000000007 0.000000447 0.000002797 -0.000000001 0.000000456 0.000000082 -0.000000008 0.000000456 -0.000001099 -0.000000008 5
-0.000000020 -0.000000003 0.000000000 -0.000000020 -0.000000001 0.000000001 -0.000000020 0.000000004 0.000000000 -0.000000020 -0.000000051 0.000000000 -0.000000040 -0.000000003 0.000000000 -0.000000041 -0.000000001 0.000000000 -0.000000040 0.000000004 0.000000000 -0.000000040 0.000000016 0.000000000 6
0.000266329 0.000000563 -0.000000118 0.000266948 0.000000175 -0.000000020 0.000267918 -0.000000738 -0.000000099 0.000267918 -0.000015628 -0.000000099 0.000279294 0.000000575 0.000000001 0.000279267 0.000000177 -0.000000006 0.000279285 -0.000000752 -0.000000001 0.000279285 -0.000000941 -0.000000001 7
-0.000000747 -0.000000027 0.000000000 -0.000000742 0.000000061 0.000000004 -0.000000738 0.000002910 0.000000007 -0.000000738 0.000003997 0.000000007 -0.000001853 -0.000000036 0.000000000 -0.000001860 0.000000082 0.000000004 -0.000001865 0.000002898 0.000000008 -0.000001865 0.000004045 0.000000008 8
-0.000000100 0.000000000 0.000000000 -0.000000100 -0.000000007 0.000000000 -0.000000099 0.000000007 0.000000002 -0.000000099 0.000000253 0.000000002 -0.000000175 0.000000000 0.000000000 -0.000000175 -0.000000007 0.000000000 -0.000000176 0.000000007 0.000000000 -0.000000176 -0.000000001 0.000000000 9
0.000266329 0.000000563 -0.000000118 0.000266948 0.000000175 -0.000000020 0.000267918 -0.000000738 -0.000000099 0.000268470 -0.000015628 -0.000000099 0.000279294 0.000000575 0.000000001 0.000279267 0.000000177 -0.000000006 0.000279285 -0.000000752 -0.000000001 0.000279285 -0.000000941 -0.000000001 10
-0.000015698 -0.000000017 0.000000033 -0.000015677 -0.000001035 -0.000000051 -0.000015628 0.000003997 0.000000253 -0.000015628 0.000061878 0.000000452 -0.000028094 -0.000000072 -0.000000001 -0.000028138 -0.000000939 0.000000016 -0.000028255 0.000003956 0.000000000 -0.000028255 0.000003929 0.000000000 11
-0.000000100 0.000000000 0.000000000 -0.000000100 -0.000000007 0.000000000 -0.000000099 0.000000007 0.000000002 -0.000000099 0.000000452 0.000000004 -0.000000175 0.000000000 0.000000000 -0.000000175 -0.000000007 0.000000000 -0.000000176 0.000000007 0.000000000 -0.000000176 -0.000000001 0.000000000 12
0.000279277 0.000001418 -0.000000206 0.000279320 0.000000435 -0.000000040 0.000279294 -0.000001853 -0.000000175 0.000279294 -0.000028094 -0.000000175 0.000417445 0.000001756 -0.000000095 0.000416144 0.000000531 -0.000000022 0.000415692 -0.000002287 -0.000000084 0.000415692 -0.000014952 -0.000000084 13
0.000000564 0.000002915 -0.000000006 0.000000571 0.000000065 -0.000000003 0.000000575 -0.000000036 0.000000000 0.000000575 -0.000000072 0.000000000 0.000001756 0.000005110 -0.000000011 0.000001748 0.000000094 -0.000000005 0.000001743 -0.000000051 0.000000001 0.000001743 0.000000060 0.000000001 14
0.000000002 -0.000000006 0.000000000 0.000000001 0.000000007 0.000000000 0.000000001 0.000000000 0.000000000 0.000000001 -0.000000001 0.000000000 -0.000000095 -0.000000011 0.000000002 -0.000000094 0.000000012 0.000000000 -0.000000094 -0.000000001 0.000000000 -0.000000094 0.000000032 0.000000000 15
0.000279242 0.000001413 -0.000000204 0.000279291 0.000000447 -0.000000041 0.000279267 -0.000001860 -0.000000175 0.000279267 -0.000028138 -0.000000175 0.000416144 0.000001748 -0.000000094 0.000416677 0.000000548 -0.000000023 0.000416223 -0.000002297 -0.000000085 0.000416223 -0.000015004 -0.000000085 16
0.000000201 0.000000065 0.000000005 0.000000187 0.000002797 -0.000000001 0.000000177 0.000000082 -0.000000007 0.000000177 -0.000000939 -0.000000007 0.000000531 0.000000094 0.000000012 0.000000548 0.000004941 -0.000000002 0.000000561 0.000000117 -0.000000014 0.000000561 -0.000002034 -0.000000014 17
-0.000000007 -0.000000003 0.000000000 -0.000000006 -0.000000001 0.000000000 -0.000000006 0.000000004 0.000000000 -0.000000006 0.000000016 0.000000000 -0.000000022 -0.000000005 0.000000000 -0.000000023 -0.000000002 0.000000001 -0.000000022 0.000000007 0.000000000 -0.000000022 -0.000000061 0.000000000 18
0.000279253 0.000001409 -0.000000204 0.000279304 0.000000456 -0.000000040 0.000279285 -0.000001865 -0.000000176 0.000279285 -0.000028255 -0.000000176 0.000415692 0.000001743 -0.000000094 0.000416223 0.000000561 -0.000000022 0.000417238 -0.000002304 -0.000000086 0.000417238 -0.000015141 -0.000000086 19
-0.000000766 -0.000000036 0.000000000 -0.000000758 0.000000082 0.000000004 -0.000000752 0.000002898 0.000000007 -0.000000752 0.000003956 0.000000007 -0.000002287 -0.000000051 -0.000000001 -0.000002297 0.000000117 0.000000007 -0.000002304 0.000005086 0.000000014 -0.000002304 0.000007126 0.000000014 20
-0.000000002 0.000000000 0.000000000 -0.000000002 -0.000000008 0.000000000 -0.000000001 0.000000008 0.000000000 -0.000000001 0.000000000 0.000000000 -0.000000084 0.000000001 0.000000000 -0.000000085 -0.000000014 0.000000000 -0.000000086 0.000000014 0.000000002 -0.000000086 0.000000293 0.000000002 21
0.000279253 0.000001409 -0.000000204 0.000279304 0.000000456 -0.000000040 0.000279285 -0.000001865 -0.000000176 0.000279285 -0.000028255 -0.000000176 0.000415692 0.000001743 -0.000000094 0.000416223 0.000000561 -0.000000022 0.000417238 -0.000002304 -0.000000086 0.000417790 -0.000015141 -0.000000086 22
-0.000001130 -0.000000001 0.000000000 -0.000001080 -0.000001099 0.000000016 -0.000000941 0.000004045 -0.000000001 -0.000000941 0.000003929 -0.000000001 -0.000014952 0.000000060 0.000000032 -0.000015004 -0.000002034 -0.000000061 -0.000015141 0.000007126 0.000000293 -0.000015141 0.000070924 0.000000492 23
-0.000000002 0.000000000 0.000000000 -0.000000002 -0.000000008 0.000000000 -0.000000001 0.000000008 0.000000000 -0.000000001 0.000000000 0.000000000 -0.000000084 0.000000001 0.000000000 -0.000000085 -0.000000014 0.000000000 -0.000000086 0.000000014 0.000000002 -0.000000086 0.000000492 0.000000005 24
(MATRIZ INVERSA DE K) x (matriz de fuerzas externas F) U=K-1xF
MANUAL ROBOT DIFERENCIA
U4x 0.014 0.014 0.000
U4y -0.009 -0.009 0.000 UX (cm) UZ (cm) RY (Rad)
G4 0.000 0.000 -0.001 8 1 0.03796 -0.01217 0.00034
U5x 0.015 0.015 0.000 11 2 0.03746 -0.02791 0.00008
U5y -0.020 -0.020 0.000 4 3 0.01424 -0.00887 0.00029
G5 0.000 0.000 0.000 7 4 0.01461 -0.02351 0.00008
U6x 0.015 0.015 0.000 1 5 0 0 0
U6y -0.014 -0.014 0.000 2 6 0 0 0
G6 0.000 0.000 0.000 9 7 0.03755 -0.02789 -0.0001
U7x 0.015 0.015 0.000 3 8 0 0 0
U7y -0.024 -0.024 0.000 10 9 0.03746 -0.01887 0.00001
G7 0.000 0.000 0.000 5 10 0.01454 -0.02025 -0.00008
U8x = 0.038 0.038 0.000 2 11 0.01461 -0.01374 0.00001
U8y -0.012 -0.012 0.000
G8 0.000 0.000 -0.001
U9x 0.038 0.038 0.000
U9y -0.028 -0.028 0.000
G9 0.000 0.000 0.000
U10x 0.038 0.037 0.000
U10y -0.019 -0.019 0.000
G10 0.000 0.000 0.000
U11x 0.038 0.037 0.000
U11y -0.028 -0.028 0.000
G11 0.000 0.000 0.000
PASO 09: CONVERSION DE LOS DESPLAZAMIENTOS GLOBALES A DESPLAZAMIENTOS LOCALES EN CADA BARRA.
Col 1
TRANSPUESTA DE LA MATRIZ DE TRANSFORMACION Desplaz. Local
U1x 0 1 0 0 0 0 0.00000 U1x 0.0000000
U1y -1 0 0 0 0 0 0.00000 U1y 0.0000000
G1 = 0 0 1 0 0 0 X 0.00000 G1 = 0.0000000
U4x 0 0 0 0 1 0 0.01438 U4x -0.0089586
U4y 0 0 0 -1 0 0 -0.00896 U4y -0.0143791
G4 0 0 0 0 0 1 -0.00029 G4 -0.0002906
Col 2
U2x 0 1 0 0 0 0 0.00000 U2x 0.0000000
U2y -1 0 0 0 0 0 0.00000 U2y 0.0000000
G2 = 0 0 1 0 0 0 X 0.00000 G2 = 0.0000000
U5x 0 0 0 0 1 0 0.01469 U5x -0.0204476
U5y 0 0 0 -1 0 0 -0.02045 U5y -0.0146851
G5 0 0 0 0 0 1 0.00009 G5 0.0000851
Col 3
U3x 0 1 0 0 0 0 0.00000 U3x 0.0000000
U3y -1 0 0 0 0 0 0.00000 U3y 0.0000000
G3 = 0 0 1 0 0 0 X 0.00000 G3 = 0.0000000
U6x 0 0 0 0 1 0 0.01475 U6x -0.0138748
U6y 0 0 0 -1 0 0 -0.01387 U6y -0.0147529
G6 0 0 0 0 0 1 -0.00001 G6 -0.0000136
Col 4
U4x 0 1 0 0 0 0 0.01438 U4x -0.0089586
U4y -1 0 0 0 0 0 -0.00896 U4y -0.0143791
G4 = 0 0 1 0 0 0 X -0.00029 G4 = -0.0002906
U8x 0 0 0 0 1 0 0.03833 U8x -0.0122918
U8y 0 0 0 -1 0 0 -0.01229 U8y -0.0383281
G8 0 0 0 0 0 1 -0.00034 G8 -0.0003446
Col 5
U5x 0 1 0 0 0 0 0.01469 U5x -0.0204476
U5y -1 0 0 0 0 0 -0.02045 U5y -0.0146851
G5 = 0 0 1 0 0 0 X 0.00009 G5 = 0.0000851
U9x 0 0 0 0 1 0 0.03792 U9x -0.0281677
U9y 0 0 0 -1 0 0 -0.02817 U9y -0.0379154
G9 0 0 0 0 0 1 0.00010 G9 0.0001040
Col 6
U6x 0 1 0 0 0 0 0.01475 U6x -0.0138748
U6y -1 0 0 0 0 0 -0.01387 U6y -0.0147529
G6 = 0 0 1 0 0 0 X -0.00001 G6 = -0.0000136
esto hay que
poner en
minusculas las U
y G por que son
locales.

U10x 0 0 0 0 1 0 0.03782 U10x -0.0190518
U10y 0 0 0 -1 0 0 -0.01905 U10y -0.0378241
G10 0 0 0 0 0 1 -0.00001 G10 -0.0000087
Viga 7
U4x 1 0 0 0 0 0 0.01438 U4x 0.0143791
U4y 0 1 0 0 0 0 -0.00896 U4y -0.0089586
G4 = 0 0 1 0 0 0 X -0.00029 G4 = -0.0002906
U5x 0 0 0 1 0 0 0.01469 U5x 0.0146851
U5y 0 0 0 0 1 0 -0.02045 U5y -0.0204476
G5 0 0 0 0 0 1 0.00009 G5 0.0000851
Viga 8
U5x 1 0 0 0 0 0 0.01469 U5x 0.0146851
U5y 0 1 0 0 0 0 -0.02045 U5y -0.0204476
G5 = 0 0 1 0 0 0 X 0.00009 G5 = 0.0000851
U6x 0 0 0 1 0 0 0.01475 U6x 0.0147529
U6y 0 0 0 0 1 0 -0.01387 U6y -0.0138748
G6 0 0 0 0 0 1 -0.00001 G6 -0.0000136
Viga 9
U6x 1 0 0 0 0 0 0.01475 U6x 0.0147529
U6y 0 1 0 0 0 0 -0.01387 U6y -0.0138748
G6 = 0 0 1 0 0 0 X -0.00001 G6 = -0.0000136
U7x 0 0 0 1 0 0 0.01475 U7x 0.0147529
U7y 0 0 0 0 1 0 -0.02374 U7y -0.0237368
G7 0 0 0 0 0 1 -0.00008 G7 -0.0000831
Viga 10
U8x 1 0 0 0 0 0 0.03833 U8x 0.0383281
U8y 0 1 0 0 0 0 -0.01229 U8y -0.0122918
G8 = 0 0 1 0 0 0 X -0.00034 G8 = -0.0003446
U9x 0 0 0 1 0 0 0.03792 U9x 0.0379154
U9y 0 0 0 0 1 0 -0.02817 U9y -0.0281677
G9 0 0 0 0 0 1 0.00010 G9 0.0001040
Viga 11
U9x 1 0 0 0 0 0 0.03792 U9x 0.0379154
U9y 0 1 0 0 0 0 -0.02817 U9y -0.0281677
G9 = 0 0 1 0 0 0 X 0.00010 G9 = 0.0001040
U10x 0 0 0 1 0 0 0.03782 U10x 0.0378241
U10y 0 0 0 0 1 0 -0.01905 U10y -0.0190518
G10 0 0 0 0 0 1 -0.00001 G10 -0.0000087
Viga 12
U10x 1 0 0 0 0 0 0.03782 U10x 0.0378241
U10y 0 1 0 0 0 0 -0.01905 U10y -0.0190518
G10 = 0 0 1 0 0 0 X -0.00001 G10 = -0.0000087
U11x 0 0 0 1 0 0 0.03782 U11x 0.0378241
U11y 0 0 0 0 1 0 -0.02818 U11y -0.0281825
G11 0 0 0 0 0 1 -0.00008 G11 -0.0000783
PASO 10: CALCULO DE ESFUERZOS EN CADA BARRA (SISTEMA LOCAL) N=k x u + f
Inicio 1 Final 4 0 0
BARRA base (cm) alto (cm) L (cm.) A I
1 25 25 400 625 32552.08333 DESP. LOCALES Fzas externas (Local) se ha convertido los signos por que ahora son reacciones internas BARRA
U1x U1y G1 U4x U4y G4 1
V1 339641.64 0.00 0.00 -339641.64 0.00 0.00 0.0000000 0.0 F1x 3042.71 0.0 3042.71 Kg
N1 0.00 1326.73 265345.03 0.00 -1326.73 265345.03 0.0000000 0.0 F1y -58.02 0.0 -58.02 Kg
M1 = 0.00 265345.03 70758675.52 0.00 -265345.03 35379337.76 X 0.0000000 + 0.0 M1 = -6464.83 + 0.0 = -6464.83 Kg-cm
V4 -339641.64 0.00 0.00 339641.64 0.00 0.00 -0.0089586 0.0 F4x -3042.71 0.0 -3042.71 Kg
N4 0.00 -1326.73 -265345.03 0.00 1326.73 -265345.03 -0.0143791 0.0 F4y 58.02 0.0 58.02 Kg
M4 0.00 265345.03 35379337.76 0.00 -265345.03 70758675.52 -0.0002906 0.0 M4 -16745.10 0.0 -16745.10 Kg-cm
0 0 0 0 0 0
2 25 25 400 625 32552.08333 BARRA
U2x U2y G2 U5x U5y G5 DESP. LOCALES Fzas externas (Local) 2
V2 339641.64 0.00 0.00 -339641.64 0.00 0.00 0.0000000 0.0 F2x 6944.84 0.0 6944.84 Kg
N2 0.00 1326.73 265345.03 0.00 -1326.73 265345.03 0.0000000 0.0 F2y 42.05 0.0 42.05 Kg
M2 = 0.00 265345.03 70758675.52 0.00 -265345.03 35379337.76 X 0.0000000 + 0.0 M2 = 6906.16 + 0.0 = 6906.16 Kg-cm
V5 -339641.64 0.00 0.00 339641.64 0.00 0.00 -0.0204476 0.0 F5x -6944.84 0.0 -6944.84 Kg
N5 0.00 -1326.73 -265345.03 0.00 1326.73 -265345.03 -0.0146851 0.0 F5y -42.05 0.0 -42.05 Kg
M5 0.00 265345.03 35379337.76 0.00 -265345.03 70758675.52 0.0000851 0.0 M5 9915.70 0.0 9915.70 Kg-cm
0 0 0 0 0 0
3 25 25 400 625 32552.08333 BARRA
U3x U3y G3 U6x U6y G6 DESP. LOCALES Fzas externas (Global) 3
V3 339641.64 0.00 0.00 -339641.64 0.00 0.00 0.0000000 0.0 F3x 4712.45 0.0 4712.45 Kg
N3 0.00 1326.73 265345.03 0.00 -1326.73 265345.03 0.0000000 0.0 F3y 15.97 0.0 15.97 Kg
M3 = 0.00 265345.03 70758675.52 0.00 -265345.03 35379337.76 X 0.0000000 + 0.0 M3 = 3434.23 + 0.0 = 3434.23 Kg-cm
V6 -339641.64 0.00 0.00 339641.64 0.00 0.00 -0.0138748 0.0 F6x -4712.45 0.0 -4712.45 Kg
N6 0.00 -1326.73 -265345.03 0.00 1326.73 -265345.03 -0.0147529 0.0 F6y -15.97 0.0 -15.97 Kg
M6 0.00 265345.03 35379337.76 0.00 -265345.03 70758675.52 -0.0000136 0.0 M6 2953.85 0.0 2953.85 Kg-cm
0 0 0 0 0 0
4 25 25 300 625 32552.08333 BARRA
U4x U4y G4 U8x U8y G8 DESP. LOCALES Fzas externas (Global) 4
V4 452855.52 0.00 0.00 -452855.52 0.00 0.00 -0.0089586 0.0 F4x 1509.47 0.0 1509.47 Kg
N4 0.00 3144.83 471724.50 0.00 -3144.83 471724.50 -0.0143791 0.0 F4y -224.29 0.0 -224.29 Kg
M4 = 0.00 471724.50 94344900.69 0.00 -471724.50 47172450.35 X -0.0002906 + 0.0 M4 = -32370.41 + 0.0 = -32370.41 Kg-cm
V8 -452855.52 0.00 0.00 452855.52 0.00 0.00 -0.0122918 0.0 F8x -1509.47 0.0 -1509.47 Kg
N8 0.00 -3144.83 -471724.50 0.00 3144.83 -471724.50 -0.0383281 0.0 F8y 224.29 0.0 224.29 Kg
M8 0.00 471724.50 47172450.35 0.00 -471724.50 94344900.69 -0.0003446 0.0 M8 -34917.10 0.0 -34917.10 Kg-cm
0 0 0 0 0 0
5 25 25 300 625 32552.08333 BARRA
V5 452855.52 0.00 0.00 -452855.52 0.00 0.00 -0.0204476 0.0 F5x 3496.09 0.0 3496.09 Kg
N5 0.00 3144.83 471724.50 0.00 -3144.83 471724.50 -0.0146851 0.0 F5y 162.25 0.0 162.25 Kg
M5 = 0.00 471724.50 94344900.69 0.00 -471724.50 47172450.35 X 0.0000851 + 0.0 M5 = 23890.21 + 0.0 = 23890.21 Kg-cm
V9 -452855.52 0.00 0.00 452855.52 0.00 0.00 -0.0281677 0.0 F9x -3496.09 0.0 -3496.09 Kg
N9 0.00 -3144.83 -471724.50 0.00 3144.83 -471724.50 -0.0379154 0.0 F9y -162.25 0.0 -162.25 Kg
M9 0.00 471724.50 47172450.35 0.00 -471724.50 94344900.69 0.0001040 0.0 M9 24783.94 0.0 24783.94 Kg-cm
0 0 0 0 0 0
6 25 25 300 625 32552.08333 BARRA
U6x U6y G6 U10x U10y G10 6
V6 452855.52 0.00 0.00 -452855.52 0.00 0.00 -0.0138748 0.0 F6x 2344.44 0.0 2344.44 Kg
N6 0.00 3144.83 471724.50 0.00 -3144.83 471724.50 -0.0147529 0.0 F6y 62.04 0.0 62.04 Kg
M6 = 0.00 471724.50 94344900.69 0.00 -471724.50 47172450.35 X -0.0000136 + 0.0 M6 = 9191.69 + 0.0 = 9191.69 Kg-cm
V10 -452855.52 0.00 0.00 452855.52 0.00 0.00 -0.0190518 0.0 F10x -2344.44 0.0 -2344.44 Kg
N10 0.00 -3144.83 -471724.50 0.00 3144.83 -471724.50 -0.0378241 0.0 F10y -62.04 0.0 -62.04 Kg
M10 0.00 471724.50 47172450.35 0.00 -471724.50 94344900.69 -0.0000087 0.0 M10 9421.68 0.0 9421.68 Kg-cm
0 0 0 0 0 0
7 25 50 500 1250 260416.6667 BARRA
V4 543426.63 0.00 0.00 -543426.63 0.00 0.00 0.0143791 0.0 F4x -166.27 0.0 -166.27 Kg
N4 0.00 5434.27 1358566.57 0.00 -5434.27 1358566.57 -0.0089586 1750.0 F4y -216.76 1750.0 1533.24 Kg
M4 = 0.00 1358566.57 452855523.32 0.00 -1358566.57 226427761.66 X -0.0002906 + 145833.3 M4 = -96717.82 + 145833.3 = 49115.51 Kg-cm
V5 -543426.63 0.00 0.00 543426.63 0.00 0.00 0.0146851 0.0 F5x 166.27 0.0 166.27 Kg
N5 0.00 -5434.27 -1358566.57 0.00 5434.27 -1358566.57 -0.0204476 1750.0 F5y 216.76 1750.0 1966.76 Kg
M5 0.00 1358566.57 226427761.66 0.00 -1358566.57 452855523.32 0.0000851 -145833.3 M5 -11663.07 -145833.3 -157496.40 Kg-cm
0 0 0 0 0 0
8 25 50 400 1250 260416.6667 BARRA
V5 679283.28 0.00 0.00 -679283.28 0.00 0.00 0.0146851 0.0 F5x -46.07 0.0 -46.07 Kg
N5 0.00 10613.80 2122760.27 0.00 -10613.80 2122760.27 -0.0204476 1400.0 F5y 81.99 1400.0 1481.99 Kg
M5 = 0.00 2122760.27 566069404.15 0.00 -2122760.27 283034702.07 X 0.0000851 + 93333.3 M5 = 30357.16 + 93333.3 = 123690.50 Kg-cm
V6 -679283.28 0.00 0.00 679283.28 0.00 0.00 0.0147529 0.0 F6x 46.07 0.0 46.07 Kg
N6 0.00 -10613.80 -2122760.27 0.00 10613.80 -2122760.27 -0.0138748 1400.0 F6y -81.99 1400.0 1318.01 Kg
M6 0.00 2122760.27 283034702.07 0.00 -2122760.27 566069404.15 -0.0000136 -93333.3 M6 2437.79 -93333.3 -90895.54 Kg-cm
0 0 0 0 0 0

9 25 50 150 1250 260416.6667 BARRA
V6 1811422.09 0.00 0.00 -1811422.09 0.00 0.00 0.0147529 0.0 F6x 0.00 0.0 0.00 Kg
N6 0.00 201269.12 15095184.11 0.00 -201269.12 15095184.11 -0.0138748 525.0 F6y 525.00 525.0 1050.00 Kg
M6 = 0.00 15095184.11 1509518411.06 0.00 -15095184.11 754759205.53 X -0.0000136 + 13125.0 M6 = 65625.00 + 13125.0 = 78750.00 Kg-cm
V7 -1811422.09 0.00 0.00 1811422.09 0.00 0.00 0.0147529 0.0 F7x 0.00 0.0 0.00 Kg
N7 0.00 -201269.12 -15095184.11 0.00 201269.12 -15095184.11 -0.0237368 525.0 F7y -525.00 525.0 0.00 Kg
M7 0.00 15095184.11 754759205.53 0.00 -15095184.11 1509518411.06 -0.0000831 -13125.0 M7 13125.00 -13125.0 0.00 Kg-cm
0 0 0 0 0 0
10 25 50 500 1250 260416.6667 BARRA
V8 543426.63 0.00 0.00 -543426.63 0.00 0.00 0.0383281 0.0 F8x 224.29 0.0 224.29 Kg
N8 0.00 5434.27 1358566.57 0.00 -5434.27 1358566.57 -0.0122918 1750.0 F8y -240.53 1750.0 1509.47 Kg
M8 = 0.00 1358566.57 452855523.32 0.00 -1358566.57 226427761.66 X -0.0003446 + 145833.3 M8 = -110916.24 + 145833.3 = 34917.10 Kg-cm
V9 -543426.63 0.00 0.00 543426.63 0.00 0.00 0.0379154 0.0 F9x -224.29 0.0 -224.29 Kg
N9 0.00 -5434.27 -1358566.57 0.00 5434.27 -1358566.57 -0.0281677 1750.0 F9y 240.53 1750.0 1990.53 Kg
M9 0.00 1358566.57 226427761.66 0.00 -1358566.57 452855523.32 0.0001040 -145833.3 M9 -9347.46 -145833.3 -155180.79 Kg-cm
0 0 0 0 0 0
11 25 50 400 1250 260416.6667 BARRA
U9x U9y G9 U10x U10y G10 11
V9 679283.28 0.00 0.00 -679283.28 0.00 0.00 0.0379154 0.0 F9x 62.04 0.0 62.04 Kg
N9 0.00 10613.80 2122760.27 0.00 -10613.80 2122760.27 -0.0281677 1400.0 F9y 105.56 1400.0 1505.56 Kg
M9 = 0.00 2122760.27 566069404.15 0.00 -2122760.27 283034702.07 X 0.0001040 + 93333.3 M9 = 37063.52 + 93333.3 = 130396.85 Kg-cm
V10 -679283.28 0.00 0.00 679283.28 0.00 0.00 0.0378241 0.0 F10x -62.04 0.0 -62.04 Kg
N10 0.00 -10613.80 -2122760.27 0.00 10613.80 -2122760.27 -0.0190518 1400.0 F10y -105.56 1400.0 1294.44 Kg
M10 0.00 2122760.27 283034702.07 0.00 -2122760.27 566069404.15 -0.0000087 -93333.3 M10 5161.66 -93333.3 -88171.68 Kg-cm
0 0 0 0 0 0
12 25 50 150 1250 260416.6667 BARRA
U10x U10y G10 U11x U11y G11 12
V10 1811422.09 0.00 0.00 -1811422.09 0.00 0.00 0.0378241 0.0 F10x 0.00 0.0 0.00 Kg
N10 0.00 201269.12 15095184.11 0.00 -201269.12 15095184.11 -0.0190518 525.0 F10y 525.00 525.0 1050.00 Kg
M10 = 0.00 15095184.11 1509518411.06 0.00 -15095184.11 754759205.53 X -0.0000087 + 13125.0 M10 = 65625.00 + 13125.0 = 78750.00 Kg-cm
V11 -1811422.09 0.00 0.00 1811422.09 0.00 0.00 0.0378241 0.0 F11x 0.00 0.0 0.00 Kg
N11 0.00 -201269.12 -15095184.11 0.00 201269.12 -15095184.11 -0.0281825 525.0 F11y -525.00 525.0 0.00 Kg
M11 0.00 15095184.11 754759205.53 0.00 -15095184.11 1509518411.06 -0.0000783 -13125.0 M11 13125.00 -13125.0 0.00 Kg-cm
POR CONVENSION DE SIGNOS LAS CELDAS VERDES DE LAS RESPUESTAS SE DEBEN CAMBIAR DE SIGNO PARA
QUE LA GRÁFICA SEA IGUAL QUE LOS RESULTADOS MOSTRADOS EN LAS GRAFICAS OBTENIDAS EN AUTODESK ROBOT.

Ejercicio desarrollado del estructura 2

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