Mastering Statics 

Course Overview

1-0 Introduction to Mechanics

1-1 Brief Introduction of Vectors

1-2 Basic Operations of Vectors: Vector Addition

1-3 Vector Addition: Triangle Rules

1-4 Cartesian Components (2D)

1-5 Cartesian Components (3D)

1-6 Decomposition of a Force into its Cartesian Components

1-7 Example: Cartesian Components

1-8 Introduction to Dot Product

1-9 Dot Product: Cartesian Components

1-10 Example: Dot Product

1-11 Introduction to Cross Product

1-12 Cross Product: Cartesian Components

1-13 Application of Cross Product: Calculating Area

1-14 Application of Cross Product: Moment of a Force

1-15 Example: Moment of a Force

1-16 Couple of Forces

1-17 Vector Operation: Mix or Triple (Scalar) Product

1-18 Application of Mix Product: Moment of a Force about an Axis

1-19 Example: Moment of a Force about an Axis

Grading Criteria

Quiz 1

2-1 Equivalent Systems of Forces

2-2 Simplified Equivalent System

2-3 Example: Simplified Equivalent System of Forces in 2D

2-4 Equilibrium of a Rigid Body

2-5 Reactions at Different Supports

2-6 Example: Calculating Reactions

2-7 Equilibrium of a System of Rigid Bodies

2-8 Example: Equilibrium of a System of Two Rigid Bodies

2.9 2-Force Members

2.10 Example: 2-Force Members

2-11 3-Force members (Optional)

Quiz 2

3-1 Stability - Static Point of View

3-2 Example: Static Determinacy

3-3 Example: Static Indeterminacy

3-4 Kinematic Considerations - Rigid Body Motion

3-5 Kinematic considerations - Infinitesimal Motions

3-6 Stability - Kinematic Approach

3-7 Kinematic considerations - Multiple rigid bodies

3.8 Stability - Kinematic approach for Multiple Rigid Bodies, Part 1

3.9 Stability - Kinematic approach for Multiple Rigid Bodies, Part 2

Quiz 3

4-1 Introduction to Trusses

4-2 Simple Trusses

4-3 Compound Trusses

4-4 Complex Trusses

4-5 Introduction to Method of Joints

4-6 Example: Method of Joints for Simple Trusses

4-7 Illustration: Method of Joints for Complex and Compound Trusses

4-8 Introduction to Method of Sections

4-9 Illustration: Computer-aided Analysis of Trusses

Quiz 4

5.1 Area and Centroid

5.2 Area and Centroid Examples

5.3 Example of a Half Circle

5.4 Example of Composite Areas

5.5 Distributed Loading

5.6 Example 1: Distributed Loading

5.7 Example 2: Distributed Loading

5.8 The First Theorem of Pappus-Guldiness

5.9 The Second Theorem of Pappus-Guldiness

5.10 Moments of Inertia - Part 1

5.11 Moments of Inertia - Part 2

5.12 Product Moment of Inertia

5.13 Radius of Gyration and Polar Moment of Inertia

5.14 Moments of inertia for Simple Geometric Shapes

5.15 Parallel Axis Theorem

5.16 Example: Moments of Inertia for a Combined Shape using Parallel Axis Theorem

5.17 Example: Proper Application of Parallel Axis Theorem for Shifted Axis

5.18 Transformation due to Rotated Axes

5.19 Moment of Inertia with respect to Rotated Axes

5.20 Mohr's circle

5.21 Example 1: Application of Mohr's Circle for Calculating Moments of Inertia with respect to Rotated Axes

5.22 Example 2: Special Cases regarding Mohr's Circle

Quiz 5

6-1 Introduction to Internal Forces

6-2 Sign Convention of Internal Forces

6-3 Understanding Axial Force

6-4 Understanding Shear Force

6-5 Understanding Bending Moments

6-6 Sign convention: A critical review

6-7 Introduction to Axial, Shear and Bending Moment Diagram

6-8 Rules of Shear Force Diagram (Part 1)

6-9 Rules of Shear Force Diagram (Part 2)

6-10 Rules of Shear Force Diagram (Part 3)

6-11 Rules of Axial Force Diagram

6-12 Example: Axial Force Diagram

6-13 Rules of Bending Moment Diagram

6-14 Example: Bending Moment Diagram

6-15 Example 2: Bending Moment Diagram

Please proceed to Module 7

7-1 Analyzing Joints in Frames based on Internal Forces Diagrams

7-2 Stability and Reaction of the structure

7-3 Axial Force Diagram

7-4 Shear Force Diagram

7-5 Bending Moment Diagram

7-6 Summary: Major Steps of performing Static Analysis of a structure

7-7 Remarks

7-8 Example: Drawing Bending Moment Diagram using Fast Track Approach

7-9 Reactions and Force Decomposition

7-10 Axial Force, Shear Force and Bending Moment Diagrams

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Quiz 6

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