Course: Mastering Statics
Modules:
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
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)
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
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
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
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
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