Consideramos positivo positivo: Valor del esfuerzo

M. Flector

Cortante

Axil

X

Ejemplo 1:

400 Kg/ m

6000 Kg- m

MA A

Ax Ay

C

B 20 m

15 m

Bx

En el segmento BC: +∑Mc: 0

6000 – 15 By = 0 …………………… By = 400 Kg

+∑Fy: 0

-400 400 + Cy = 0

+∑Fx: 0

Bx = 0

………………….. Cy = 400 Kg

En el segmento AB: +∑MA: 0

Cy

-MA + 400 (20)(10) – By (20) = 0 …………………… MA = 72000 Kg-m

+∑Fy: 0

Ay – 400 (20) + 400 = 0

………………….. Ay = 7600 Kg

+∑Fx: 0

Ax – Bx = 0

………………………Ax = 0

By

B

Bx By

400 Kg/ m 72000 Kg-m

K m 6000 Kg-

A

C

B 20 m

7600 Kg

15 m

400 Kg

X 400

X

En el segmento AB: 0 ≤ X < 20 m Momento

7600X – 72000 – 400X2/2

Cortante

7600 – 400X

En el segmento BC: 0 ≤ X < 15 m Momento

-400X

Cortante

-400

Bx By

B

Bx By

2000 Kg/ m

Ejemplo 2:

B

6m

C 8000 Kg

6m

A

3m

D

Ay

1.5 m

3m

Dx 7.0 m

Dy

Cálculo de reacciones: +∑Mc: 0

7Ay- 8000 (6) – 2000(8.5)(8.5)/2 = 0 …………………… Ay = 17,178 Kg

+∑Fy: 0

Ay + Dy - 2000(8.5) = 0

+∑Fx: 0

Dx = 8000

………………….. Dy = -178 Kg …………………… Dx = 8000 Kg

2000 Kg/ m

2.25 Tn-m

2.25 Tn-m

2000 Kg/ m

14.178 Tn

3 Tn

48 Tn-m

0.178 Tn

0.178 Tn

17 178 Tn 17.178

4 Tn-m 48 B

6m

C 8000 Kg

A 17.178 Tn

1.5 m

3m

6m D 7.0 m

0.178 Tn

8 Tn

Ejemplo 3:

1.5 Tn/ m 1 A

2

B

2m

A

γ =1.0 Tn/ m 0

3

6m C Cx 4.0 m

6 Tn/ m

Cy

Cálculo de reacciones: +∑Mc: 0

8Acos θ + 4Asen θ – (1.5) (4) (2) -(6)(6)(0.5)(6/3) = 0 …………………… A = 6.7 Tn

+∑Fy: 0

Cy + Asen θ - (1.5)(4) = 0

………………….. Cy = 0 Tn

+∑Fx: 0

Cx + Acos θ - (6)(6)(0.5) = 0

…………………… Cx = 15 Tn

1 5 Tn/ m 1.5 3 Tn

A cos θ A Asen θ

12 Tn-m 40m 4.0 3 Tn 12 Tn-m B

2m

γ =1.0 Tn/ m 0

3

6m C 15 Tn

6 Tn/ m

2.5 Tn/ m

Ejemplo 4: 2.5 m 1.5 m

θ 5 Tn

C

B 6m

1.5 m A Ay D 6.0 m

Dx Dy

C B

30 Tn-m 7.5 Tn-m 5 Tn

C B

9.58 Tn

5.42 Tn 7.5 Tn-m

9.58 Tn

30 Tn-m 6.0 m

5.42 Tn

5 Tn

5 Tn C

5 Tn 1.5 m

5 Tn

B

6m

1.5 m 5.42 Tn

D 5 Tn 9.58 Tn