1. Nombre: Arias Gutierrez Dennis
Docente: Ing. Marcelo Pardo A.
Asignatura: Estructuras Hiperestáticas
Tema: Estructuras por el Método de Rigidez
Gestion: II/2021
INGENIERIA CIVIL
3. 20 [GPa]
135°
20 [GPa]
135°
3.0 [m]
1.0 [m]
6.0 [m]
1.0 [m]
4.0 [m]
RESOLVER MEDIANTE EL METODO MATRICIAL LA CERCHA
CORRESPONDIENTE CON LOS SIGUIENTES DATOS:
Barras de sección A =
0.0022 m²
Cargas verdes = 20 KN.
Dirección de carga = 315°
E = 200 GPa.
Distancias en metros.
6. Barra 1:
Barra 1: 1 2 3 4
x1: 0 A= 0.0022 m2
6.12574E-17 0 Klocal Transformacion B 1.6511E-27 2.6953E-11 -1.6511E-27 -2.6953E-11 1
y1: 0 L= 1 m 1 0 440000 -440000 6.1257E-17 1 0 0 2.6953E-11 440000 -2.6953E-11 -440000 2
x2: 0 E= 2.00E+08 Kpa 0 6.1257E-17 -440000 440000 0 0 6.1257E-17 1 -1.6511E-27 -2.6953E-11 1.6511E-27 2.6953E-11 3
y2: 1 Ang= 1.570796327 Rad 0 1 -2.6953E-11 -440000 2.6953E-11 440000 4
Angulo en Grados= 90 °
x2-x1: 0
y2-y1: 1 Cuadrante= 1
Barra 2:
Barra 2: 3 4 5 6
x1: 0 A= 0.0022 m2
6.12574E-17 0 Klocal Transformacion B 4.1277E-28 6.7383E-12 -4.1277E-28 -6.7383E-12 3
y1: 1 L= 4 m 1 0 110000 -110000 6.1257E-17 1 0 0 6.7383E-12 110000 -6.7383E-12 -110000 4
x2: 0 E= 2.00E+08 Kpa 0 6.1257E-17 -110000 110000 0 0 6.1257E-17 1 -4.1277E-28 -6.7383E-12 4.1277E-28 6.7383E-12 5
y2: 5 Ang= 1.570796327 Rad 0 1 -6.7383E-12 -110000 6.7383E-12 110000 6
Angulo en Grados= 90 °
x2-x1: 0
y2-y1: 4 Cuadrante= 1
Barra 3:
Barra 3: 5 6 7 8
x1: 0 A= 0.0022 m2
6.12574E-17 0 Klocal Transformacion B 1.6511E-27 2.6953E-11 -1.6511E-27 -2.6953E-11 5
y1: 5 L= 1 m 1 0 440000 -440000 6.1257E-17 1 0 0 2.6953E-11 440000 -2.6953E-11 -440000 6
x2: 0 E= 2.00E+08 Kpa 0 6.1257E-17 -440000 440000 0 0 6.1257E-17 1 -1.6511E-27 -2.6953E-11 1.6511E-27 2.6953E-11 7
y2: 6 Ang= 1.570796327 Rad 0 1 -2.6953E-11 -440000 2.6953E-11 440000 8
Angulo en Grados= 90 °
x2-x1: 0
y2-y1: 1 Cuadrante= 1
Barra 4:
Barra 4: 1 2 9 10
x1: 0 A= 0.0022 m2
1 0 Klocal Transformacion B 440000 0 -440000 0 1
y1: 0 L= 1 m 0 0 440000 -440000 1 0 0 0 0 0 0 0 2
x2: 1 E= 2.00E+08 Kpa 0 1 -440000 440000 0 0 1 0 -440000 0 440000 0 9
y2: 0 Ang= 0 Rad 0 0 0 0 0 0 10
Angulo en Grados= 0 °
x2-x1: 1
y2-y1: 0 Cuadrante= 1
Barra 5:
Barra 5: 3 4 9 10
x1: 0 A= 0.0022 m2
0.707106781 0 Klocal Transformacion B 155563.492 -155563.492 -155563.492 155563.492 3
y1: 1 L= 1.414213562 m -0.70710678 0 311126.984 -311126.984 0.70710678 -0.70710678 0 0 -155563.492 155563.492 155563.492 -155563.492 4
x2: 1 E= 2.00E+08 Kpa 0 0.70710678 -311126.984 311126.984 0 0 0.70710678 -0.70710678 -155563.492 155563.492 155563.492 -155563.492 9
y2: 0 Ang= 5.497787144 Rad 0 -0.70710678 155563.492 -155563.492 -155563.492 155563.492 10
Angulo en Grados= 315 °
x2-x1: 1
y2-y1: -1 Cuadrante= 4
Barra 6:
Barra 6: 3 4 11 12
x1: 0 A= 0.0022 m2
1 0 Klocal Transformacion B 440000 0 -440000 0 3
y1: 1 L= 1 m 0 0 440000 -440000 1 0 0 0 0 0 0 0 4
x2: 1 E= 2.00E+08 Kpa 0 1 -440000 440000 0 0 1 0 -440000 0 440000 0 11
y2: 1 Ang= 0 Rad 0 0 0 0 0 0 12
Angulo en Grados= 0 °
x2-x1: 1
y2-y1: 0 Cuadrante= 1
Barra 7:
Barra 7: 5 6 11 12
x1: 0 A= 0.0022 m2
0.242535625 0 Klocal Transformacion B 6277.39265 -25109.5706 -6277.39265 25109.5706 5
y1: 5 L= 4.123105626 m -0.9701425 0 106715.675 -106715.675 0.24253563 -0.9701425 0 0 -25109.5706 100438.282 25109.5706 -100438.282 6
x2: 1 E= 2.00E+08 Kpa 0 0.24253563 -106715.675 106715.675 0 0 0.24253563 -0.9701425 -6277.39265 25109.5706 6277.39265 -25109.5706 11
y2: 1 Ang= 4.957367644 Rad 0 -0.9701425 25109.5706 -100438.282 -25109.5706 100438.282 12
Angulo en Grados= 284.0362435 °
x2-x1: 1
y2-y1: -4 Cuadrante= 4
Barra 8:
Barra 8: 5 6 13 14
x1: 0 A= 0.0022 m2
1 0 Klocal Transformacion B 440000 0 -440000 0 5
y1: 5 L= 1 m 0 0 440000 -440000 1 0 0 0 0 0 0 0 6
x2: 1 E= 2.00E+08 Kpa 0 1 -440000 440000 0 0 1 0 -440000 0 440000 0 13
y2: 5 Ang= 0 Rad 0 0 0 0 0 0 14
Angulo en Grados= 0 °
x2-x1: 1
y2-y1: 0 Cuadrante= 1
Barra 9:
Barra 9: 7 8 13 14
x1: 0 A= 0.0022 m2
0.707106781 0 Klocal Transformacion B 155563.492 -155563.492 -155563.492 155563.492 7
y1: 6 L= 1.414213562 m -0.70710678 0 311126.984 -311126.984 0.70710678 -0.70710678 0 0 -155563.492 155563.492 155563.492 -155563.492 8
x2: 1 E= 2.00E+08 Kpa 0 0.70710678 -311126.984 311126.984 0 0 0.70710678 -0.70710678 -155563.492 155563.492 155563.492 -155563.492 13
y2: 5 Ang= 5.497787144 Rad 0 -0.70710678 155563.492 -155563.492 -155563.492 155563.492 14
Angulo en Grados= 315 °
x2-x1: 1
y2-y1: -1 Cuadrante= 4
Barra 10:
Barra 10: 7 8 21 22
x1: 0 A= 0.0022 m2
1 0 Klocal Transformacion B 146666.667 0 -146666.667 0 7
y1: 6 L= 3 m 0 0 146666.667 -146666.667 1 0 0 0 0 0 0 0 8
x2: 3 E= 2.00E+08 Kpa 0 1 -146666.667 146666.667 0 0 1 0 -146666.667 0 146666.667 0 21
y2: 6 Ang= 0 Rad 0 0 0 0 0 0 22
Angulo en Grados= 0 °
x2-x1: 3
y2-y1: 0 Cuadrante= 1
Barra 11:
Barra 11: 9 10 11 12
x1: 1 A= 0.0022 m2
6.12574E-17 0 Klocal Transformacion B 1.6511E-27 2.6953E-11 -1.6511E-27 -2.6953E-11 9
y1: 0 L= 1 m 1 0 440000 -440000 6.1257E-17 1 0 0 2.6953E-11 440000 -2.6953E-11 -440000 10
x2: 1 E= 2.00E+08 Kpa 0 6.1257E-17 -440000 440000 0 0 6.1257E-17 1 -1.6511E-27 -2.6953E-11 1.6511E-27 2.6953E-11 11
y2: 1 Ang= 1.570796327 Rad 0 1 -2.6953E-11 -440000 2.6953E-11 440000 12
Angulo en Grados= 90 °
x2-x1: 0
y2-y1: 1 Cuadrante= 1
Barra 12:
Barra 12: 11 12 13 14
x1: 1 A= 0.0022 m2
6.12574E-17 0 Klocal Transformacion B 4.1277E-28 6.7383E-12 -4.1277E-28 -6.7383E-12 11
y1: 1 L= 4 m 1 0 110000 -110000 6.1257E-17 1 0 0 6.7383E-12 110000 -6.7383E-12 -110000 12
x2: 1 E= 2.00E+08 Kpa 0 6.1257E-17 -110000 110000 0 0 6.1257E-17 1 -4.1277E-28 -6.7383E-12 4.1277E-28 6.7383E-12 13
y2: 5 Ang= 1.570796327 Rad 0 1 -6.7383E-12 -110000 6.7383E-12 110000 14
Angulo en Grados= 90 °
x2-x1: 0
y2-y1: 4 Cuadrante= 1
Barra 13:
Barra 13: 9 10 15 16
x1: 1 A= 0.0022 m2
1 0 Klocal Transformacion B 220000 0 -220000 0 9
y1: 0 L= 2 m 0 0 220000 -220000 1 0 0 0 0 0 0 0 10
x2: 3 E= 2.00E+08 Kpa 0 1 -220000 220000 0 0 1 0 -220000 0 220000 0 15
y2: 0 Ang= 0 Rad 0 0 0 0 0 0 16
Angulo en Grados= 0 °
x2-x1: 2
y2-y1: 0 Cuadrante= 1
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
7. Barra 12:
Barra 12: 11 12 13 14
x1: 1 A= 0.0022 m2
6.12574E-17 0 Klocal Transformacion B 4.1277E-28 6.7383E-12 -4.1277E-28 -6.7383E-12 11
y1: 1 L= 4 m 1 0 110000 -110000 6.1257E-17 1 0 0 6.7383E-12 110000 -6.7383E-12 -110000 12
x2: 1 E= 2.00E+08 Kpa 0 6.1257E-17 -110000 110000 0 0 6.1257E-17 1 -4.1277E-28 -6.7383E-12 4.1277E-28 6.7383E-12 13
y2: 5 Ang= 1.570796327 Rad 0 1 -6.7383E-12 -110000 6.7383E-12 110000 14
Angulo en Grados= 90 °
x2-x1: 0
y2-y1: 4 Cuadrante= 1
Barra 13:
Barra 13: 9 10 15 16
x1: 1 A= 0.0022 m2
1 0 Klocal Transformacion B 220000 0 -220000 0 9
y1: 0 L= 2 m 0 0 220000 -220000 1 0 0 0 0 0 0 0 10
x2: 3 E= 2.00E+08 Kpa 0 1 -220000 220000 0 0 1 0 -220000 0 220000 0 15
y2: 0 Ang= 0 Rad 0 0 0 0 0 0 16
Angulo en Grados= 0 °
x2-x1: 2
y2-y1: 0 Cuadrante= 1
Barra 14:
Barra 14: 9 10 17 18
x1: 1 A= 0.0022 m2
0.894427191 0 Klocal Transformacion B 157419.186 78709.5928 -157419.186 -78709.5928 9
y1: 0 L= 2.236067977 m 0.447213595 0 196773.982 -196773.982 0.89442719 0.4472136 0 0 78709.5928 39354.7964 -78709.5928 -39354.7964 10
x2: 3 E= 2.00E+08 Kpa 0 0.89442719 -196773.982 196773.982 0 0 0.89442719 0.4472136 -157419.186 -78709.5928 157419.186 78709.5928 17
y2: 1 Ang= 0.463647609 Rad 0 0.4472136 -78709.5928 -39354.7964 78709.5928 39354.7964 18
Angulo en Grados= 26.56505118 °
x2-x1: 2
y2-y1: 1 Cuadrante= 1
Barra 15:
Barra 15: 11 12 17 18
x1: 1 A= 0.0022 m2
1 0 Klocal Transformacion B 220000 0 -220000 0 11
y1: 1 L= 2 m 0 0 220000 -220000 1 0 0 0 0 0 0 0 12
x2: 3 E= 2.00E+08 Kpa 0 1 -220000 220000 0 0 1 0 -220000 0 220000 0 17
y2: 1 Ang= 0 Rad 0 0 0 0 0 0 18
Angulo en Grados= 0 °
x2-x1: 2
y2-y1: 0 Cuadrante= 1
Barra 16:
Barra 16: 13 14 19 20
x1: 1 A= 0.0022 m2
1 0 Klocal Transformacion B 220000 0 -220000 0 13
y1: 5 L= 2 m 0 0 220000 -220000 1 0 0 0 0 0 0 0 14
x2: 3 E= 2.00E+08 Kpa 0 1 -220000 220000 0 0 1 0 -220000 0 220000 0 19
y2: 5 Ang= 0 Rad 0 0 0 0 0 0 20
Angulo en Grados= 0 °
x2-x1: 2
y2-y1: 0 Cuadrante= 1
Barra 17:
Barra 17: 13 14 21 22
x1: 1 A= 0.0022 m2
0.894427191 0 Klocal Transformacion B 157419.186 78709.5928 -157419.186 -78709.5928 13
y1: 5 L= 2.236067977 m 0.447213595 0 196773.982 -196773.982 0.89442719 0.4472136 0 0 78709.5928 39354.7964 -78709.5928 -39354.7964 14
x2: 3 E= 2.00E+08 Kpa 0 0.89442719 -196773.982 196773.982 0 0 0.89442719 0.4472136 -157419.186 -78709.5928 157419.186 78709.5928 21
y2: 6 Ang= 0.463647609 Rad 0 0.4472136 -78709.5928 -39354.7964 78709.5928 39354.7964 22
Angulo en Grados= 26.56505118 °
x2-x1: 2
y2-y1: 1 Cuadrante= 1
Barra 18:
Barra 18: 15 16 17 18
x1: 3 A= 0.0022 m2
6.12574E-17 0 Klocal Transformacion B 1.6511E-27 2.6953E-11 -1.6511E-27 -2.6953E-11 15
y1: 0 L= 1 m 1 0 440000 -440000 6.1257E-17 1 0 0 2.6953E-11 440000 -2.6953E-11 -440000 16
x2: 3 E= 2.00E+08 Kpa 0 6.1257E-17 -440000 440000 0 0 6.1257E-17 1 -1.6511E-27 -2.6953E-11 1.6511E-27 2.6953E-11 17
y2: 1 Ang= 1.570796327 Rad 0 1 -2.6953E-11 -440000 2.6953E-11 440000 18
Angulo en Grados= 90 °
x2-x1: 0
y2-y1: 1 Cuadrante= 1
Barra 19:
Barra 19: 19 20 21 22
x1: 3 A= 0.0022 m2
6.12574E-17 0 Klocal Transformacion B 1.6511E-27 2.6953E-11 -1.6511E-27 -2.6953E-11 19
y1: 5 L= 1 m 1 0 440000 -440000 6.1257E-17 1 0 0 2.6953E-11 440000 -2.6953E-11 -440000 20
x2: 3 E= 2.00E+08 Kpa 0 6.1257E-17 -440000 440000 0 0 6.1257E-17 1 -1.6511E-27 -2.6953E-11 1.6511E-27 2.6953E-11 21
y2: 6 Ang= 1.570796327 Rad 0 1 -2.6953E-11 -440000 2.6953E-11 440000 22
Angulo en Grados= 90 °
x2-x1: 0
y2-y1: 1 Cuadrante= 1
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
Mat de transformacion Btranspuesta
MATRIZ DE RIGIDEZ GLOBAL
8. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
1 440000 2.69533E-11 -1.65109E-27 -2.69533E-11 0 0 0 0 -440000 0 0 0 0 0 0 0 0 0 0 0 0 0 1
2 2.69533E-11 440000 -2.69533E-11 -440000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
3 -1.65109E-27 -2.69533E-11 595563.4919 -155563.4919 -4.12772E-28 -6.73832E-12 0 0 -155563.4919 155563.4919 -440000 0 0 0 0 0 0 0 0 0 0 0 3
4 -2.69533E-11 -440000 -155563.4919 705563.4919 -6.73832E-12 -110000 0 0 155563.4919 -155563.4919 0 0 0 0 0 0 0 0 0 0 0 0 4
5 0 0 -4.12772E-28 -6.73832E-12 446277.3926 -25109.57059 -1.65109E-27 -2.69533E-11 0 0 -6277.392648 25109.57059 -440000 0 0 0 0 0 0 0 0 0 5
6 0 0 -6.73832E-12 -110000 -25109.57059 650438.2824 -2.69533E-11 -440000 0 0 25109.57059 -100438.2824 0 0 0 0 0 0 0 0 0 0 6
7 0 0 0 0 -1.65109E-27 -2.69533E-11 302230.1585 -155563.4919 0 0 0 0 -155563.4919 155563.4919 0 0 0 0 0 0 -146666.6667 0 7
8 0 0 0 0 -2.69533E-11 -440000 -155563.4919 595563.4919 0 0 0 0 155563.4919 -155563.4919 0 0 0 0 0 0 0 0 8
9 -440000 0 -155563.4919 155563.4919 0 0 0 0 972982.6775 -76853.89905 -1.65109E-27 -2.69533E-11 0 0 -220000 0 -157419.1856 -78709.59281 0 0 0 0 9
10 0 0 155563.4919 -155563.4919 0 0 0 0 -76853.89905 634918.2883 -2.69533E-11 -440000 0 0 0 0 -78709.59281 -39354.7964 0 0 0 0 10
11 0 0 -440000 0 -6277.392648 25109.57059 0 0 -1.65109E-27 -2.69533E-11 666277.3926 -25109.57059 -4.12772E-28 -6.73832E-12 0 0 -220000 0 0 0 0 0 11
12 0 0 0 0 25109.57059 -100438.2824 0 0 -2.69533E-11 -440000 -25109.57059 650438.2824 -6.73832E-12 -110000 0 0 0 0 0 0 0 0 12
13 0 0 0 0 -440000 0 -155563.4919 155563.4919 0 0 -4.12772E-28 -6.73832E-12 972982.6775 -76853.89905 0 0 0 0 -220000 0 -157419.1856 -78709.59281 13
14 0 0 0 0 0 0 155563.4919 -155563.4919 0 0 -6.73832E-12 -110000 -76853.89905 304918.2883 0 0 0 0 0 0 -78709.59281 -39354.7964 14
15 0 0 0 0 0 0 0 0 -220000 0 0 0 0 0 220000 2.69533E-11 -1.65109E-27 -2.69533E-11 0 0 0 0 15
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.69533E-11 440000 -2.69533E-11 -440000 0 0 0 0 16
17 0 0 0 0 0 0 0 0 -157419.1856 -78709.59281 -220000 0 0 0 -1.65109E-27 -2.69533E-11 377419.1856 78709.59281 0 0 0 0 17
18 0 0 0 0 0 0 0 0 -78709.59281 -39354.7964 0 0 0 0 -2.69533E-11 -440000 78709.59281 479354.7964 0 0 0 0 18
19 0 0 0 0 0 0 0 0 0 0 0 0 -220000 0 0 0 0 0 220000 2.69533E-11 -1.65109E-27 -2.69533E-11 19
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.69533E-11 440000 -2.69533E-11 -440000 20
21 0 0 0 0 0 0 -146666.6667 0 0 0 0 0 -157419.1856 -78709.59281 0 0 0 0 -1.65109E-27 -2.69533E-11 304085.8523 78709.59281 21
22 0 0 0 0 0 0 0 0 0 0 0 0 -78709.59281 -39354.7964 0 0 0 0 -2.69533E-11 -440000 78709.59281 479354.7964 22
3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 21 22
595563.4919 -155563.4919 -4.12772E-28 -6.73832E-12 0 0 -155563.4919 155563.4919 -440000 0 0 0 0 0 0 0 0 0 0
-155563.4919 705563.4919 -6.73832E-12 -110000 0 0 155563.4919 -155563.4919 0 0 0 0 0 0 0 0 0 0 0
-4.12772E-28 -6.73832E-12 446277.3926 -25109.57059 -1.65109E-27 -2.69533E-11 0 0 -6277.392648 25109.57059 -440000 0 0 0 0 0 0 0 0
-6.73832E-12 -110000 -25109.57059 650438.2824 -2.69533E-11 -440000 0 0 25109.57059 -100438.2824 0 0 0 0 0 0 0 0 0
0 0 -1.65109E-27 -2.69533E-11 302230.1585 -155563.4919 0 0 0 0 -155563.4919 155563.4919 0 0 0 0 0 -146666.6667 0
0 0 -2.69533E-11 -440000 -155563.4919 595563.4919 0 0 0 0 155563.4919 -155563.4919 0 0 0 0 0 0 0
-155563.4919 155563.4919 0 0 0 0 972982.6775 -76853.89905 -1.65109E-27 -2.69533E-11 0 0 -220000 -157419.1856 -78709.59281 0 0 0 0
155563.4919 -155563.4919 0 0 0 0 -76853.89905 634918.2883 -2.69533E-11 -440000 0 0 0 -78709.59281 -39354.7964 0 0 0 0
-440000 0 -6277.392648 25109.57059 0 0 -1.65109E-27 -2.69533E-11 666277.3926 -25109.57059 -4.12772E-28 -6.73832E-12 0 -220000 0 0 0 0 0
0 0 25109.57059 -100438.2824 0 0 -2.69533E-11 -440000 -25109.57059 650438.2824 -6.73832E-12 -110000 0 0 0 0 0 0 0
0 0 -440000 0 -155563.4919 155563.4919 0 0 -4.12772E-28 -6.73832E-12 972982.6775 -76853.89905 0 0 0 -220000 0 -157419.1856 -78709.59281
0 0 0 0 155563.4919 -155563.4919 0 0 -6.73832E-12 -110000 -76853.89905 304918.2883 0 0 0 0 0 -78709.59281 -39354.7964
0 0 0 0 0 0 -220000 0 0 0 0 0 220000 -1.65109E-27 -2.69533E-11 0 0 0 0
0 0 0 0 0 0 -157419.1856 -78709.59281 -220000 0 0 0 -1.65109E-27 377419.1856 78709.59281 0 0 0 0
0 0 0 0 0 0 -78709.59281 -39354.7964 0 0 0 0 -2.69533E-11 78709.59281 479354.7964 0 0 0 0
0 0 0 0 0 0 0 0 0 0 -220000 0 0 0 0 220000 2.69533E-11 -1.65109E-27 -2.69533E-11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.69533E-11 440000 -2.69533E-11 -440000
0 0 0 0 -146666.6667 0 0 0 0 0 -157419.1856 -78709.59281 0 0 0 -1.65109E-27 -2.69533E-11 304085.8523 78709.59281
0 0 0 0 0 0 0 0 0 0 -78709.59281 -39354.7964 0 0 0 -2.69533E-11 -440000 78709.59281 479354.7964
u3 0.001036731 u1 = 0 R1 = -28.28427125
u4 8.57099E-05 u2 = 0 R2 = -37.71236166
u5 0.018548596 u3 = 0.001036731 0 0.00000000
u6 0.001371359 u4 = 0.00008571 0 0.00000000
u7 0.022774606 u5 = 0.01854860 0 0.00000000
u8 0.001435641 u6 = 0.00137136 0 0.00000000
u9 6.42824E-05 u7 = 0.02277461 14.14213562 14.14213562
u10 -0.001553405 u8 = 0.00143564 -14.14213562 -14.14213562
u11 0.000801028 u9 = 0.00006428 0 0.000000
u12 -0.001939099 u10 = -0.00155340 0 0.0000000
u13 0.018612879 u11 0.00080103 0 0.0000000
u14 -0.002453359 u12 -0.00193910 0 0.0000000
u15 6.42824E-05 u13 0.01861288 0 0.0000000
u17 0.000201059 u14 -0.00245336 0 0.0000000
u18 -0.000149992 u15 0.00006428 0 0.0000000
u19 0.018677161 u16 0 R16 = 65.99663291
u20 -0.011553999 u17 0.00020106 0 0.0000000
u21 0.022967453 u18 -0.00014999 0 0.0000000
u22 -0.011521858 u19 0.01867716 14.14213562 14.14213562
u20 -0.01155400 -14.14213562 -14.14213562
u21 0.02296745 0 0.00000000
u22 -0.01152186 0 0.00000000
REACCIONES
RESOLVIENDO EL SISTEMA
=
VECTOR DESPLAZAMIENTOS COMPLETO
MATRIZ DE RIGIDEZ REDUCIDA
SISTEMA DE ECUACIONES CON INCOGNITAS
10. COORDENADAS DESPLA.
U1= 0 Xi despla = 0 Xi despla = 0 F1= -2.3102E-15 Cuadrante = 3
U2= 0 Yi despla = 0 Yi despla = 0 F2= -37.7123617 Ang Rad = 4.71238898
U3= 0.00103673 Xf despla = 0.00103673 Xf despla = 0.02073461 F3= 2.3102E-15 Ang Grados = 270
U4= 8.571E-05 Yf despla = 1.00008571 Yf despla = 1.0017142 F4= 37.7123617 Comp o Trac = 37.71236166
37.7123617
COORDENADAS DESPLA.
U3= 0.00103673 Xi despla = 0.00103673 Xi despla = 0.02073461 F3= -8.6631E-15 Cuadrante = 3
U4= 8.571E-05 Yi despla = 1.00008571 Yi despla = 1.0017142 F4= -141.421356 Ang Rad = 4.71238898
U5= 0.0185486 Xf despla = 0.0185486 Xf despla = 0.37097192 F5= 8.6631E-15 Ang Grados = 270
U6= 0.00137136 Yf despla = 5.00137136 Yf despla = 5.02742717 F6= 141.421356 Comp o Trac = 141.42135624
141.421356
COORDENADAS DESPLA.
U5= 0.0185486 Xi despla = 0.0185486 Xi despla = 0.37097192 F5= -1.7326E-15 Cuadrante = 3
U6= 0.00137136 Yi despla = 5.00137136 Yi despla = 5.02742717 F6= -28.2842712 Ang Rad = 4.71238898
U7= 0.02277461 Xf despla = 0.02277461 Xf despla = 0.45549212 F7= 1.7326E-15 Ang Grados = 270
U8= 0.00143564 Yf despla = 6.00143564 Yf despla = 6.02871282 F8= 28.2842712 Comp o Trac = 28.28427125
28.2842712
COORDENADAS DESPLA.
U1= 0 Xi despla = 0 Xi despla = 0 F1= -28.2842712 Cuadrante = 1
U2= 0 Yi despla = 0 Yi despla = 0 F2= 0 Ang Rad = 3.141592654
U9= 6.4282E-05 Xf despla = 1.00006428 Xf despla = 1.00128565 F9= 28.2842712 Ang Grados = 180
U10= -0.0015534 Yf despla = -0.0015534 Yf despla = -0.0310681 F10= 0 Comp o Trac = 28.28427125
28.2842712
COORDENADAS DESPLA.
U3= 0.00103673 Xi despla = 0.00103673 Xi despla = 0.02073461 F3= -103.708995 Cuadrante = 1
U4= 8.571E-05 Yi despla = 1.00008571 Yi despla = 1.0017142 F4= 103.708995 Ang Rad = 2.35619449
U9= 6.4282E-05 Xf despla = 1.00006428 Xf despla = 1.00128565 F9= 103.708995 Ang Grados = 135
U10= -0.0015534 Yf despla = -0.0015534 Yf despla = -0.0310681 F10= -103.708995 Comp o Trac = 146.66666667
146.666667
COORDENADAS DESPLA.
U3= 0.00103673 Xi despla = 0.00103673 Xi despla = 0.02073461 F3= 103.708995 Cuadrante = 1
U4= 8.571E-05 Yi despla = 1.00008571 Yi despla = 1.0017142 F4= 0 Ang Rad = 0
U11= 0.00080103 Xf despla = 1.00080103 Xf despla = 1.01602057 F11= -103.708995 Ang Grados = 0
U12= -0.0019391 Yf despla = 0.9980609 Yf despla = 0.96121801 F12= 0 Comp o Trac = -103.70899457
103.708995
COORDENADAS DESPLA.
U5= 0.0185486 Xi despla = 0.0185486 Xi despla = 0.37097192 F5= 28.2842712 Cuadrante = 4
U6= 0.00137136 Yi despla = 5.00137136 Yi despla = 5.02742717 F6= -113.137085 Ang Rad = 4.957367644
U11= 0.00080103 Xf despla = 1.00080103 Xf despla = 1.01602057 F11= -28.2842712 Ang Grados = 284.0362435
U12= -0.0019391 Yf despla = 0.9980609 Yf despla = 0.96121801 F12= 113.137085 Comp o Trac = -116.61903790
116.619038
COORDENADAS DESPLA.
U5= 0.0185486 Xi despla = 0.0185486 Xi despla = 0.37097192 F5= -28.2842712 Cuadrante = 1
U6= 0.00137136 Yi despla = 5.00137136 Yi despla = 5.02742717 F6= 0 Ang Rad = 3.141592654
U13= 0.01861288 Xf despla = 1.01861288 Xf despla = 1.37225757 F13= 28.2842712 Ang Grados = 180
U14= -0.00245336 Yf despla = 4.99754664 Yf despla = 4.95093282 F14= 0 Comp o Trac = 28.28427125
28.2842712
Solicitacion Barra =
Solicitacion Barra =
Solicitacion Barra =
Solicitacion Barra =
Solicitacion Barra =
Solicitacion Barra =
Solicitacion Barra =
Solicitacion Barra =
BARRA 1
BARRA 2
BARRA 3
BARRA 4
BARRA 5
BARRA 6
BARRA 7
BARRA 8
11. COORDENADAS DESPLA.
U7= 0.02277461 Xi despla = 0.02277461 Xi despla = 0.45549212 F7= 42.4264069 Cuadrante = 4
U8= 0.00143564 Yi despla = 6.00143564 Yi despla = 6.02871282 F8= -42.4264069 Ang Rad = 5.497787144
U13= 0.01861288 Xf despla = 1.01861288 Xf despla = 1.37225757 F13= -42.4264069 Ang Grados = 315
U14= -0.00245336 Yf despla = 4.99754664 Yf despla = 4.95093282 F14= 42.4264069 Comp o Trac = -60.000000
60
COORDENADAS DESPLA.
U7= 0.02277461 Xi despla = 0.02277461 Xi despla = 0.45549212 F7= -28.2842712 Cuadrante = 1
U8= 0.00143564 Yi despla = 6.00143564 Yi despla = 6.02871282 F8= 0 Ang Rad = 3.141592654
U21= 0.02296745 Xf despla = 3.02296745 Xf despla = 3.45934906 F21= 28.2842712 Ang Grados = 180
U22= -0.01152186 Yf despla = 5.98847814 Yf despla = 5.76956284 F22= 0 Comp o Trac = 28.28427125
28.2842712
COORDENADAS DESPLA.
U9= 6.4282E-05 Xi despla = 1.00006428 Xi despla = 1.00128565 F9= 1.0396E-14 Cuadrante = 1
U10= -0.0015534 Yi despla = -0.0015534 Yi despla = -0.0310681 F10= 169.705627 Ang Rad = 1.570796327
U11= 0.00080103 Xf despla = 1.00080103 Xf despla = 1.01602057 F11= -1.0396E-14 Ang Grados = 90
U12= -0.0019391 Yf despla = 0.9980609 Yf despla = 0.96121801 F12= -169.705627 Comp o Trac = -169.70562748
169.705627
COORDENADAS DESPLA.
U11= 0.00080103 Xi despla = 1.00080103 Xi despla = 1.01602057 F11= 3.4652E-15 Cuadrante = 1
U12= -0.0019391 Yi despla = 0.9980609 Yi despla = 0.96121801 F12= 56.5685425 Ang Rad = 1.570796327
U13= 0.01861288 Xf despla = 1.01861288 Xf despla = 1.37225757 F13= -3.4652E-15 Ang Grados = 90
U14= -0.00245336 Yf despla = 4.99754664 Yf despla = 4.95093282 F14= -56.5685425 Comp o Trac = -56.56854249
56.5685425
COORDENADAS DESPLA.
U9= 6.4282E-05 Xi despla = 1.00006428 Xi despla = 1.00128565 F9= -1.7764E-15 Cuadrante = 1
U10= -0.0015534 Yi despla = -0.0015534 Yi despla = -0.0310681 F10= 0 Ang Rad = 3.141592654
U15= 6.4282E-05 Xf despla = 3.00006428 Xf despla = 3.00128565 F15= 1.7764E-15 Ang Grados = 180
U16= 0 Yf despla = 0 Yf despla = 0 F16= 0 Comp o Trac = 0.00000
1.7764E-15
COORDENADAS DESPLA.
U9= 6.4282E-05 Xi despla = 1.00006428 Xi despla = 1.00128565 F9= -131.993266 Cuadrante = 3
U10= -0.0015534 Yi despla = -0.0015534 Yi despla = -0.0310681 F10= -65.9966329 Ang Rad = 3.605240263
U17= 0.00020106 Xf despla = 3.00020106 Xf despla = 3.00402118 F17= 131.993266 Ang Grados = 206.5650512
U18= -0.00014999 Yf despla = 0.99985001 Yf despla = 0.99700015 F18= 65.9966329 Comp o Trac = 147.57295747
147.572957
COORDENADAS DESPLA.
U11= 0.00080103 Xi despla = 1.00080103 Xi despla = 1.01602057 F11= 131.993266 Cuadrante = 1
U12= -0.0019391 Yi despla = 0.9980609 Yi despla = 0.96121801 F12= 0 Ang Rad = 0
U17= 0.00020106 Xf despla = 3.00020106 Xf despla = 3.00402118 F17= -131.993266 Ang Grados = 0
U18= -0.00014999 Yf despla = 0.99985001 Yf despla = 0.99700015 F18= 0 Comp o Trac = -131.99326582
131.993266
COORDENADAS DESPLA.
U13= 0.01861288 Xi despla = 1.01861288 Xi despla = 1.37225757 F13= -14.1421356 Cuadrante = 1
U14= -0.00245336 Yi despla = 4.99754664 Yi despla = 4.95093282 F14= 0 Ang Rad = 3.141592654
U19= 0.01867716 Xf despla = 3.01867716 Xf despla = 3.37354322 F19= 14.1421356 Ang Grados = 180
U20= -0.011554 Yf despla = 4.988446 Yf despla = 4.76892002 F20= 0 Comp o Trac = 14.14213562
14.1421356
Solicitacion Barra =
Solicitacion Barra =
Solicitacion Barra =
Solicitacion Barra =
Solicitacion Barra =
Solicitacion Barra =
Solicitacion Barra =
Solicitacion Barra =
BARRA 11
BARRA 12
BARRA 13
BARRA 14
BARRA 15
BARRA 9
BARRA 10
BARRA 16
12. COORDENADAS DESPLA.
U13= 0.01861288 Xi despla = 1.01861288 Xi despla = 1.37225757 F13= 28.2842712 Cuadrante = 1
U14= -0.00245336 Yi despla = 4.99754664 Yi despla = 4.95093282 F14= 14.1421356 Ang Rad = 0.463647609
U21= 0.02296745 Xf despla = 3.02296745 Xf despla = 3.45934906 F21= -28.2842712 Ang Grados = 26.56505118
U22= -0.01152186 Yf despla = 5.98847814 Yf despla = 5.76956284 F22= -14.1421356 Comp o Trac = -31.62277660
31.6227766
COORDENADAS DESPLA.
U15= 6.4282E-05 Xi despla = 3.00006428 Xi despla = 3.00128565 F15= 4.0428E-15 Cuadrante = 1
U16= 0 Yi despla = 0 Yi despla = 0 F16= 65.9966329 Ang Rad = 1.570796327
U17= 0.00020106 Xf despla = 3.00020106 Xf despla = 3.00402118 F17= -4.0428E-15 Ang Grados = 90
U18= -0.00014999 Yf despla = 0.99985001 Yf despla = 0.99700015 F18= -65.9966329 Comp o Trac = -65.99663291
65.9966329
COORDENADAS DESPLA.
U19= 0.01867716 Xi despla = 3.01867716 Xi despla = 3.37354322 F19= -8.6631E-16 Cuadrante = 3
U20= -0.011554 Yi despla = 4.988446 Yi despla = 4.76892002 F20= -14.1421356 Ang Rad = 4.71238898
U21= 0.02296745 Xf despla = 3.02296745 Xf despla = 3.45934906 F21= 8.6631E-16 Ang Grados = 270
U22= -0.01152186 Yf despla = 5.98847814 Yf despla = 5.76956284 F22= 14.1421356 Comp o Trac = 14.14213562
14.1421356
Solicitacion Barra =
Solicitacion Barra =
Solicitacion Barra =
BARRA 17
BARRA 18
BARRA 19
Barra 1 Barra 2 Barra 3 Barra 4 Barra 5 Barra 6 Barra 7 Barra 8 Barra 9 Barra 10 Barra 11 Barra 12 Barra 13 Barra 14 Barra 15 Barra 16 Barra 17 Barra 18 Barra 19
Xi 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 3 3
Xf 0 0 0 1 1 1 1 1 1 3 1 1 3 3 3 3 3 3 3
Yi 0 1 5 0 1 1 5 5 6 6 0 1 0 0 1 5 5 0 5
Yf 1 5 6 0 0 1 1 5 5 6 1 5 0 1 1 5 6 1 6
Xi despla = 0 0.001036731 0.018548596 0 0.001036731 0.001036731 0.018548596 0.018548596 0.022774606 0.022774606 1.000064282 1.000801028 1.000064282 1.000064282 1.000801028 1.018612879 1.018612879 3.000064282 3.018677161
Xf despla = 0.001036731 0.018548596 0.022774606 1.000064282 1.000064282 1.000801028 1.000801028 1.018612879 1.018612879 3.022967453 1.000801028 1.018612879 3.000064282 3.000201059 3.000201059 3.018677161 3.022967453 3.000201059 3.022967453
Yi despla = 0 1.00008571 5.001371359 0 1.00008571 1.00008571 5.001371359 5.001371359 6.001435641 6.001435641 -0.001553405 0.998060901 -0.001553405 -0.001553405 0.998060901 4.997546641 4.997546641 0 4.988446001
Yf despla = 1.00008571 5.001371359 6.001435641 -0.001553405 -0.001553405 0.998060901 0.998060901 4.997546641 4.997546641 5.988478142 0.998060901 4.997546641 0 0.999850008 0.999850008 4.988446001 5.988478142 0.999850008 5.988478142
COORDENADAS DE BARRAS
Solicitaciones Xi Yi Xf Yf Coord Xetiq Coord Yetiq Etiqueta
1 0 0 0 1 0 0.5 37.71236166
2 0 1 0 5 0 3 141.4213562
3 0 5 0 6 0 5.5 28.28427125
4 0 0 1 0 0.5 0 28.28427125
5 0 1 1 0 0.5 0.5 146.6666667
6 0 1 1 1 0.5 1 -103.7089946
7 0 5 1 1 0.5 3 -116.6190379
8 0 5 1 5 0.5 5 28.28427125
9 0 6 1 5 0.5 5.5 -60
10 0 6 3 6 1.5 6 28.28427125
11 1 0 1 1 1 0.5 -169.7056275
12 1 1 1 5 1 3 -56.56854249
13 1 0 3 0 2 0 0.000
14 1 0 3 1 2 0.5 147.5729575
15 1 1 3 1 2 1 -131.9932658
16 1 5 3 5 2 5 14.14213562
17 1 5 3 6 2 5.5 -31.6227766
18 3 0 3 1 3 0.5 -65.99663291
19 3 5 3 6 3 5.5 14.14213562
COORDENADAS DE BARRAS
COORDENADAS DE BARRAS
