Ingenieria

ANALISIS VIGA HIPERESTATICA POR METODO MATRICIAL.

FUERZAS Y MOMENTOS DE FIJACIÓN
Y12 M12 Y21 M21 Y23 M23 Y32 M32 Y34 M34 Y43 M43 Y4V M4V 1.50 Ton 1.50 Ton-m 1.50 Ton -3.50 Ton-m 6.00 Ton 2.00Ton-m 6.00 Ton -4.00 Ton-m 7.50 Ton 6.25 Ton-m 7.50 Ton -6.25 Ton-m -3.00 Ton -6.00 Ton-m

DESPLAZAMIENTOS Y GIROS
V1 θ1 V2 θ2 V3 θ3 V4 θ4 0 -0.02 0 ? -0.02 ? 0 ?

MATRIZ DE RIGIDEZ DE CADA ELEMENTOV1 Y12 M12 = Y21 M21 0 0 0 0 V2 Y23 M23 = Y32 M32 0 0 0 0 θ1 1200 3200 -1200 1600 θ2 1200 V2 0 0 0 0 V3 -600 θ2 1200 V1 0 1.5 1.5 1.5 -3.5 1600 θ1 -0.02 * + -1200 V2 0 3200 θ2 θ2 θ3 1200 V2 0 6 2 6-4

3200 -1200 1600 θ2 θ2 * + -1200 600 -1200 V3 -0.02 1600 -1200 3200 θ3 θ3

V3 Y34 307.2

θ3 768

V4 0 0 0 0

θ4 768 V3 -0.02 θ3 0 θ4 7.5 6.25 + 7.5 -6.25 1280 θ3 * -768 V4 2560 θ4

M34768 2560 = Y43 -307.2 -768 M43 768 1280

ENSAMBLAJE DE LA MATRIZ Y ORDENAMIENTO DE FILAS Y COLUMNNAS

[Fn]
M2 M3 M4 Y1 M1 Y2 Y3 Y4 0 0 -6 Y1 M1 Y2 Y3 Y4 θ2 6400 1600 0 1200 1600 0 -1200 0[Knn]
θ3 θ4 V1 1600 0 0 5760 1280 0 1280 2560 0 0 0 0 0 0 0 1200 0 0 -432 768 0 -768 -768 0 θ1 1600 0 0 1200 3200 -1200 0 0

[Kna]
V2 0 0 0 0 0 0 0 0 V3 -1200 -432 768 0 0 -600 907.2 -307.2 V4 0 0 00 0 0 0 0 θ2 θ3 θ4 V1 θ1 V2 V3 V4

{δn}
θ2 θ3 θ4 0 -0.02 0 -0.02 0

{FFn}
-1.5 2.25 -6.25 1.5 1.5 7.5 13.5 7.5

=

*

+

CALCULO DE GIROS

{δn}
θ2 θ3 θ4 θ2 θ3 θ4 = 0.0001695 -5.3E-052.648E-05 0.0026 Rad -0.0045 Rad 0.0083 Rad

[Knn]

-1

[Fn]-{FFn}
2.648E-05 -0.000106 0.0004436 * 1.5 -2.25 0.25 +

[Kna]*{δa}
-8 8.64 -15.36

-5.3E-05 0.0002119 -0.000106

CALCULO DEFUERZAS Y MOMENTOS

[Fa]
Y1 M1 Y2 Y3 Y4 Y1 M1 Y2 Y3 Y4 = 1200 1600 0 -1200 0

[Kan]
0 0 1200 -432 -768 0 0 0 768 -768 *

{δn}
0.0026004 -0.004464 0.0083296 +

[Kaa]*{δa}
-24 -64 36 -18.1446.144 +

{FFn}
1.5 1.5 7.5 13.5 7.5

-19.38 Ton -56.34 Ton-m 38.14 Ton 0.56 Ton 13.68 Ton

FUERZA Y MOMENTOS INTERNOS
Y21 M21 = -1200 1600 -1200 3200 * -0.02 0.0026004 + 1.5 -3.5 = 22.38 Ton...