Mecánica GGB

William Haynes, Manuel Moncada, Dec 28, 2017

Table of Contents

  1. Repaso Álgebra Vectorial
    1. Elementos de un vector
    2. Regla del paralelogramo
    3. Vector unitario
    4. Descomposición de un vector en 3D
    5. Producto Vectorial
    6. Cap_0_Ej2
  2. Fuerza
    1. Rectangular Components in Rotated Coordinates
    2. Tip-to-tail Vector Addition
    3. Addition of Rectangular Components
    4. 3d Visualizer
  3. Momento
    1. Moment of Force about a point
    2. Definition of a Moment
    3. Moments - Verignon's Theorem
    4. Moments - Horizontal and Vertical Components
    5. Moment Visualizer
    6. Cálculo de momento
    7. Par de fuerzas
    8. Equivalent Force-Couple System
    9. 3D Moment
  4. Equilibrio
    1. Resultant vs. Equilibrant
    2. Example - Inclined Plane 1
    3. Example - Inclined Plane 2
    4. Three Force Body Example
    5. 3d Particle Equilibrium Problem 2.113
  5. Centroides
    1. Centroids of common shapes
    2. Centroids: Composite Area Method
    3. Centroid by composite area - shape with hole
    4. Parabolic Spandrel
    5. General Spandrel y=kx^n
    6. Center of Gravity
    7. double integration - polar coordinates - r dθ dr
    8. double integration - polar coordinates - r dr dθ
  6. Momento de Inercia
    1. Moment of Inertia of a Rectangle
    2. Moment of Inertia of T shape
    3. Moment of Inertia of a Semi-circle
    4. Polar Moment of Inertia
  7. Diagrama de fuerza de corte y momento flector
    1. Shear and Moment Building Blocks
    2. Shear and Bending Moment Diagram - Distributed Load
    3. Viga simplemente apoyada (Simply-supported beam)
    4. V-M: carga parabólica
    5. V-M: cargas combinadas
    6. V-M: cargas puntuales
    7. V-M: momento puntual
    8. V-M: cargas distribuidas
  8. Fricción
    1. Bloque en plano inclinado
  9. Homework Problems (Beer & Johnston, Statics 5th. ed.)
    1. Problem 2.1
    2. Problem 2.5
    3. Problem 2.6
    4. Problem 2.7
    5. Problem 2.19 & 2.29
    6. Problem 2.30
    7. Problem 2.32
    8. Problem 2.33
    9. Problem 2.35
    10. Review Problem 3
    11. Problem 2.101 & 102
    12. Problem 2.101 Rotated
    13. Moment Example 1
    14. Problem 3.7
    15. Problem 3.56
    16. Problem 3.68
    17. Problem 3.78
    18. Oven Door Example
    19. Backpack Example
  10. Anexo

1.

Repaso Álgebra Vectorial

  • 1. Elementos de un vector
  • 2. Regla del paralelogramo
  • 3. Vector unitario
  • 4. Descomposición de un vector en 3D
  • 5. Producto Vectorial
  • 6. Cap_0_Ej2

1.1.

Elementos de un vector

– Antonio González García

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

2.

Fuerza

  • 1. Rectangular Components in Rotated Coordinates
  • 2. Tip-to-tail Vector Addition
  • 3. Addition of Rectangular Components
  • 4. 3d Visualizer

2.1.

Rectangular Components in Rotated Coordinates

– William Haynes

2.2.

–

2.3.

–

2.4.

–

3.

Momento

  • 1. Moment of Force about a point
  • 2. Definition of a Moment
  • 3. Moments - Verignon's Theorem
  • 4. Moments - Horizontal and Vertical Components
  • 5. Moment Visualizer
  • 6. Cálculo de momento
  • 7. Par de fuerzas
  • 8. Equivalent Force-Couple System
  • 9. 3D Moment

3.1.

Moment of Force about a point

– William Haynes

3.2.

–

3.3.

–

3.4.

–

3.5.

–

3.6.

–

3.7.

–

3.8.

–

3.9.

–

4.

Equilibrio

  • 1. Resultant vs. Equilibrant
  • 2. Example - Inclined Plane 1
  • 3. Example - Inclined Plane 2
  • 4. Three Force Body Example
  • 5. 3d Particle Equilibrium Problem 2.113

4.1.

Resultant vs. Equilibrant

– William Haynes

4.2.

–

4.3.

–

4.4.

–

4.5.

–

5.

Centroides

  • 1. Centroids of common shapes
  • 2. Centroids: Composite Area Method
  • 3. Centroid by composite area - shape with hole
  • 4. Parabolic Spandrel
  • 5. General Spandrel y=kx^n
  • 6. Center of Gravity
  • 7. double integration - polar coordinates - r dθ dr
  • 8. double integration - polar coordinates - r dr dθ

5.1.

Centroids of common shapes

Determine the coordinates of the centroids of each of these shapes.
Centroids of common shapes
– William Haynes

5.2.

–

5.3.

–

5.4.

–

5.5.

–

5.6.

–

5.7.

–

5.8.

–

6.

Momento de Inercia

  • 1. Moment of Inertia of a Rectangle
  • 2. Moment of Inertia of T shape
  • 3. Moment of Inertia of a Semi-circle
  • 4. Polar Moment of Inertia

6.1.

Moment of Inertia of a Rectangle

Change rectangle dimensions and location. See how moments of inertia change.
Moment of Inertia of a Rectangle
– William Haynes

6.2.

–

6.3.

–

6.4.

–

7.

Diagrama de fuerza de corte y momento flector

  • 1. Shear and Moment Building Blocks
  • 2. Shear and Bending Moment Diagram - Distributed Load
  • 3. Viga simplemente apoyada (Simply-supported beam)
  • 4. V-M: carga parabólica
  • 5. V-M: cargas combinadas
  • 6. V-M: cargas puntuales
  • 7. V-M: momento puntual
  • 8. V-M: cargas distribuidas

7.1.

Shear and Moment Building Blocks

Shear and Bending Moment Diagrams
– William Haynes

7.2.

–

7.3.

–

7.4.

–

7.5.

–

7.6.

–

7.7.

–

7.8.

–

8.

Fricción

  • 1. Bloque en plano inclinado

8.1.

Bloque en plano inclinado

– Manuel Moncada

9.

Homework Problems (Beer & Johnston, Statics 5th. ed.)

These problems were taken from the textbook [i]Mechanics for Engineers: Statics[/i], 5th Edition, by Ferdinand P. Beer, and E. Russell Johnston.

  • 1. Problem 2.1
  • 2. Problem 2.5
  • 3. Problem 2.6
  • 4. Problem 2.7
  • 5. Problem 2.19 & 2.29
  • 6. Problem 2.30
  • 7. Problem 2.32
  • 8. Problem 2.33
  • 9. Problem 2.35
  • 10. Review Problem 3
  • 11. Problem 2.101 & 102
  • 12. Problem 2.101 Rotated
  • 13. Moment Example 1
  • 14. Problem 3.7
  • 15. Problem 3.56
  • 16. Problem 3.68
  • 17. Problem 3.78
  • 18. Oven Door Example
  • 19. Backpack Example

9.1.

Problem 2.1

Example 2.1 Determine graphically, the magnitude and direction of the resultant of the two forces shown. Find the exact answer using trigonometry.
– William Haynes

9.2.

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9.3.

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9.4.

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9.5.

–

9.6.

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9.7.

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9.8.

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9.9.

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9.10.

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9.11.

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9.12.

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9.13.

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9.14.

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9.15.

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9.16.

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9.17.

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9.18.

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9.19.

–

10.

Anexo


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