a.- Mdulo de Elasticidad del Concreto [f'c]

b.- Momentos de Inercia [ I ]

c. Rigidez Axial [AE] y a la Flexin [EI]

d. Determinacin de Constantes de Rigideces

L

4

4

3

e. Constantes de Carga

M'ij (Kg-m) M'ji (Kg-m)

V 1-2 4 2285.714 761.905

V 3-4 4 761.905 2285.714

C 1-2 3

f. Planteamiento de Ecuaciones

Viga 1-2 u1 v1 1 u2 v2 2

X 1-2 0.00 0.00 0.00 -50000.00 0.00 0.00 u1 0.0000000 0.000000 0.000 0.000

Y 1-2 0.00 0.00 0.00 0.00 -500.00 1000.00 v1 0.000000 0.685714 5.714 6.400

M 1-2 = 0.00 0.00 0.00 0.00 -1000.00 1333.33 X 1 0.000000 1.537662 + 2.286 = 3.823

X 2-1 0.00 0.00 0.00 50000.00 0.00 0.00 u2 -2.040E-14 0.000000 0.000 0.000

Y 2-1 0.00 0.00 0.00 0.00 500.00 -1000.00 v2 -1.870E-03 -0.685714 0.686 0.000

M 2-1 0.00 0.00 0.00 0.00 -1000.00 2666.67 2 -2.494E-04 1.205195 -0.762 0.443

Viga 3-4 u3 v3 3 u4 v4 4

X 3-4 50000.00 0.00 0.00 0.000 0.000 0.000 u3 2.040E-14 0.000000 0.000 0.000

Y 3-4 0.00 500.00 1000.00 0.000 0.000 0.000 v3 -1.870E-03 -0.685714 0.686 0.000

M 3-4 = 0.00 1000.00 2666.67 0.000 0.000 0.000 X 3 2.494E-04 -1.205195 + 0.762 = -0.443

X 4-3 -50000.00 0.00 0.00 0.000 0.000 0.000 u4 0.00000 0.000000 0.000 0.000

Y 4-3 0.00 -500.00 -1000.00 0.000 0.000 0.000 v4 0.00000 0.685714 5.714 6.400

M 4-3 0.00 1000.00 1333.33 0.000 0.000 0.000 4 0.00000 -1.537662 -2.286 -3.823

Col 2-3 u2 v2 2 u3 v3 3

X 2-3 1185.19 0.00 -1777.78 -1185.19 0.00 -1777.78 u2 -2.040E-14 0.000000 0.000 0.000

Ec (Kg/cm2)

200000.000

200000.000

Elemento

Vigas

I Cm^4

133333.333

133333.333

Area(cm^2)

1000.000

2666.667

AE Ton

200000

200000Rectangular

1000.000

Seccin EI Ton-m2

2666.667

Columnas

Seccin

Rectangular

Rectangular

Elemento

Viga

Columnas

Rectangular

685.714

5714.285

1777.778

Reaccin Total

1185.185

6EI/L^2

C 2-3

1333.333

1333.333

50000.000

50000.000

66666.667

AE/L 2EI/L 4EI/L

Tramo LMom. Resistentes

1000.000

1777.778

Tramo

2666.667

2666.667

3555.556

V 1-2

V 3-4

ANALISIS DE UNA VIGA CONTINUA POR EL METODO DE RIGIDECES [SECCION CONTINUA]

5714.285

685.714

12EI/L^3

500.000

500.000

1000.000

Y 2-3 0.00 66666.67 0.00 0.00 -66666.67 0.00 v2 -1.870E-03 0.000000 0.000 0.000

M 2-3 = -1777.78 0.00 3555.56 1777.78 0.00 1777.78 X e2 -2.494E-04 -0.443290 + 0.000 = -0.443

X 3-2 -1185.19 0.00 1777.78 1185.19 0.00 1777.78 u3 2.040E-14 0.000000 0.000 0.000

Y 3-2 0.00 -66666.67 0.00 0.00 66666.67 0.00 v3 -1.870E-03 0.000000 0.000 0.000

M 3-2 -1777.78 0.00 1777.78 1777.78 0.00 3555.56 3 2.494E-04 0.443290 0.000 0.443

g. Condiciones de Continuidad

X1 = X1-2 = 0.000 Ton

Y1 = Y1-2 = 6.400 Ton

M1 = M1-2 = 3.823 Ton-m

X2 = X2-1 + X2-3 = 0.000 Verificacin

Y2 = Y2-1 + Y2-3 = 0.000

M2 = M2-1 + M2-3 = 0.000

X3 = X3-4 +X 3-2 = 0.000 Ton

Y3 = Y3-4 + Y 3-2 = 0.000 Ton

M3 = M3-2+ M3-4 = 0.000 Ton-m

X4 = X4-3 = 0.000

Y4 = Y4-3 = 6.400

M4 = M4-3 = -3.823

Por consiguiente:

u2 v2 2 u3 v3 3

X2=0 51185.185 0.000 -1777.778 -1185.185 0.000 -1777.778 u2 0.000

Y2=0 0.000 67166.667 -1000.000 0.000 -66666.667 0.000 v2 0.686

M2=0 -1777.778 -1000.000 6222.223 1777.778 0.000 1777.778 2 -0.762

X3=0 = -1185.185 0.000 1777.778 51185.185 0.000 1777.778 u3 + 0.000

Y3=0 0.000 -66666.667 0.000 0.000 67166.667 1000.000 v3 0.686

M3=0 -1777.778 0.000 1777.778 1777.778 1000.000 6222.223 3 0.762

INVERSA 1.98447E-05 3.27237E-08 4.37952E-06 1.5528E-07 -3.27237E-08 4.37952E-06 0.000

3.27237E-08 0.001821922 0.000409573 -3.2724E-08 0.001814443 -0.00040861 -0.686

4.37952E-06 0.000409573 0.000269052 -4.3795E-06 0.000408609 -0.00014004 0.762

1.5528E-07 -3.27237E-08 -4.37952E-06 1.98447E-05 3.27237E-08 -4.3795E-06 0.000

-3.2724E-08 0.001814443 0.000408609 3.27237E-08 0.001821922 -0.00040957 -0.686

4.37952E-06 -0.000408609 -0.000140039 -4.3795E-06 -0.000409573 0.000269052 -0.762

u2 -2.0399184E-14

v2 -1.8701297E-03

2 = -2.4935052E-04 Luego reemplace en las ecuaciones del tem f

u3 2.0399185E-14

v3 -1.8701297E-03

3 2.4935052E-04