Mechanics GGB

William Haynes, Mar 22, 2015

Table of Contents

  1. Forces and Vectors
    1. Parallelogram Rule - General Components
    2. Rectangular Components in Rotated Coordinates
    3. Tip-to-tail Vector Addition
    4. Addition of Rectangular Components
    5. 3d Visualizer
    6. Parallelogram Rule - step by step
    7. Parallelogram rule, one component and resultant known.
  2. Moments
    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. Moment 3 Methods
    7. Couples
    8. Equivalent Force-Couple System
    9. 3D Moment
    10. Perpendicular Distance
  3. Equilibrium
    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
    6. Force Triangle
  4. Centroids
    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. Moment of Inertia
    1. Differential Strip for rectangle
    2. Moment of Inertia of a Rectangle
    3. Moment of Inertia of T shape
    4. Moment of Inertia of a Semi-circle
    5. Polar Moment of Inertia
  6. Shear and Bending Moment Diagrams
    1. Shear and Moment Building Blocks
    2. Shear and Bending Moment Diagram - Distributed Load
    3. V-M 1: concentrated forces
    4. V-M 2: concentrated moments
    5. V-M 3: distributed loads
    6. V-M 4: combined loads
    7. V-M 5: arbitrary parabolic loading
  7. 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
    20. Copy of Problem 3.56
  8. Friction
    1. block-incline - numbas

1.

Forces and Vectors

  • 1. Parallelogram Rule - General Components
  • 2. Rectangular Components in Rotated Coordinates
  • 3. Tip-to-tail Vector Addition
  • 4. Addition of Rectangular Components
  • 5. 3d Visualizer
  • 6. Parallelogram Rule - step by step
  • 7. Parallelogram rule, one component and resultant known.

1.1.

Parallelogram Rule - General Components

– William Haynes

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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2.

Moments

  • 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. Moment 3 Methods
  • 7. Couples
  • 8. Equivalent Force-Couple System
  • 9. 3D Moment
  • 10. Perpendicular Distance

2.1.

Moment of Force about a point

– William Haynes

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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3.

Equilibrium

  • 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
  • 6. Force Triangle

3.1.

Resultant vs. Equilibrant

– William Haynes

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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4.

Centroids

  • 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

4.1.

Centroids of common shapes

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

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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5.

Moment of Inertia

  • 1. Differential Strip for rectangle
  • 2. Moment of Inertia of a Rectangle
  • 3. Moment of Inertia of T shape
  • 4. Moment of Inertia of a Semi-circle
  • 5. Polar Moment of Inertia

5.1.

Differential Strip for rectangle

– William Haynes

5.2.

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5.3.

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5.4.

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5.5.

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6.

Shear and Bending Moment Diagrams

  • 1. Shear and Moment Building Blocks
  • 2. Shear and Bending Moment Diagram - Distributed Load
  • 3. V-M 1: concentrated forces
  • 4. V-M 2: concentrated moments
  • 5. V-M 3: distributed loads
  • 6. V-M 4: combined loads
  • 7. V-M 5: arbitrary parabolic loading

6.1.

Shear and Moment Building Blocks

Shear and Bending Moment Diagrams
– William Haynes

6.2.

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6.3.

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6.4.

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6.5.

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6.6.

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6.7.

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7.

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
  • 20. Copy of Problem 3.56

7.1.

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

7.2.

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7.3.

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7.4.

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7.5.

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7.6.

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7.7.

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7.8.

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7.9.

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7.10.

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7.11.

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7.12.

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7.13.

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7.14.

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7.15.

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7.16.

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7.17.

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7.18.

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7.19.

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7.20.

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8.

Friction

  • 1. block-incline - numbas

8.1.

block-incline - numbas

– William Haynes

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