LINEAS DE INFLUENCIA

Longitud de tramo L= 14m= 0.65

MOMENTO

Ra Re Rc

-Ra= 2651.03 Re= 2814.36 Rc= 32.67

Tramo0.00 ≤ x ≤ 0.65

LONGITUD MOMENTO0.00 0.000.07 -0.060.13 -0.120.20 -0.180.26 -0.240.33 -0.310.39 -0.370.45 -0.430.52 -0.490.59 -0.550.65 -0.61

Tramo0.65 ≤ x ≤ 14

LONGITUD MOMENTO0.65 -0.612.13 -0.533.62 -0.445.10 -0.366.58 -0.288.07 -0.219.55 -0.1511.03 -0.0912.52 -0.0414.00 0.00

Tramo14.00 ≤ x ≤ 28

LONGITUD MOMENTO14.00 0.0015.40 0.0316.80 0.0518.20 0.0619.60 0.0621.00 0.0622.40 0.0523.80 0.0425.20 0.0326.60 0.0228.00 0.00

m

L L

m

L L

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

-0.80

-0.60

-0.40

-0.20

0.00

0.20

DIAGRAMA DE MOMENTO DE L.D.I.

LONGITUD

MO

ME

NT

O

Rc=L2

6

Re=2×L3

3×m

Ra=56L2−2×L

3

3×m

M PI=1Re (RaX− X

3

6 )

M PI=1Re (RaX− X

3

6+Re×(X−m ))

M PI=1Re (Rc×(2 L−X )−

(2L−X )3

6 )

CORTANTE

Ra Me Rc

Ra= 163.33 -Me= 1829.33 Rc= 32.67

Tramo0.00 ≤ x ≤ 0.65

LONGITUD CORTANTE0.00 0.000.07 -0.010.13 -0.010.20 -0.020.26 -0.020.33 -0.030.39 -0.030.45 -0.040.52 -0.050.59 -0.050.65 -0.06

Tramo0.65 ≤ x ≤ 14

LONGITUD CORTANTE0.65 0.942.13 0.813.62 0.685.10 0.566.58 0.448.07 0.339.55 0.2311.03 0.1412.52 0.0614.00 0.00

Tramo14.00 ≤ x ≤ 28

LONGITUD CORTANTE14.00 0.0015.40 -0.0416.80 -0.0718.20 -0.0919.60 -0.1021.00 -0.0922.40 -0.0823.80 -0.0725.20 -0.0526.60 -0.0228.00 0.00

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

m

L L

Me=−23L3

Ra=56L2

Rc=L2

6

V I=1Me (RaX− X

3

6 )

V I=1Me (RaX− X

3

6+Me)

V I=1Me (Rc×(2L−X )−

(2 L−X )3

6 )

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

-0.80

-0.60

-0.40

-0.20

0.00

0.20

DIAGRAMA DE MOMENTO

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

DIAGRAMA DE CORTANTE

DEDUCCIONDE FORMULA DE LINEA DE INFLUENCIA PARA VIGA HIPEESTATICA DE DOS TRAMOS

MOMENTO

DEDUCCION DE FORMULA DE MOMENTO

1) 0.00 ≤ x ≤ m

2) m ≤ x ≤ L

3) L ≤ x ≤ 2L

CORTANTE

DEDUCCION DE FORMULA DE CORTANTE

1) 0.00 ≤ x ≤ m

2) m ≤ x ≤ L

3) L ≤ x ≤ 2L

m

L L

Rc=L2

6

m

L L

Me=−23L3Ra=

56L2 Rc=L

2

6

Re=2×L3

3×mRa=5

6L2−2×L

3

3×m

M PI=1Re (RaX− X

3

6 )

M PI=1Re (RaX− X

3

6+Re×(X−m ))

M PI=1Re (Rc×(2 L−X )−

(2L−X )3

6 )

V I=1Me (RaX− X

3

6 )V I=

1Me (RaX− X

3

6+Me)

V I=1Me (Rc×(2L−X )−

(2 L−X )3

6 )