Chapter 1

Introduction

Application of Trigonometry: Laws of Right-, Oblique-, Acute-, Obtuse-Triangle. Pythagorean Theory, Sine Law, and Cosine Law.

1. Trigonometry | Application

2. Right Triangle Formula | Application

3. Pythagorean Formula | Application

4. Sine Law | Application 1

5. Sine Law | Application 2

6. Cosine Law | Application

7. Trigonometric Application Measuring the Height of a Pyramid Without Climbing It

8. Measuring the Depth of a River Without Diving An Application of Trigonometry

9. How to Round Numbers in Practical Situations

Chapter 2

Principles

Resolve Forces using the Right Triangle & Sine Law. Application of Trigonometry in Solving Engineering Mechanics Problems

1. The Most Useful Technique

2. Resolve Force Running Application

3. Resolve Force Vehicle Climbing Hill Application

4. Sine Law Short Cut in Resolving Forces

5. Resolve Force Sine Law Application 1

6. Resolve Force Sine Law Application 2

7. Resolve Force Sine Law Application 3

8. Common Mistakes in Resolving Forces including the Use of Right Triangle Laws & Sine Rule

9. Basic Force Resolution and Sine Law Application | Pull-up Exercise Example

10. Basic Force Resolution | Tow Truck Pulling a Large Load from the Side of the Road

Chapter 3

Moments

Theory of Parallelogram, Moment/Torque, Principle of Moments (Varignon’s Theorem), Resultant by Resolving Forces, Resultant of Multiple Forces, including Parallel, Concurrent, Nonconcurrent, Uniform & Nonuniformly Distributed Load

Basics

1. Theory of Parallelogram Proof Using Cosine Law

2. Law of Parallelogram Proof by Resolving Forces

3. Moment Torque Explained

4. Understanding Moment Signs | Clarifying the Common Misconception

5. Resultant of Multiple Forces

6. Moment Calculation Basics

7. Principle of Moments (Varignon’s Theorem)

8. Moments using the Force Resolving Technique

9. Moments Using the Shortest Distance Technique

10. Moments from Multiple Forces by the Resultant and Resolving it

11. Moments from Multiple Forces by the Resultant Force and its Shortest Distance

Application

12. Resultants of Parallel Force Systems

13. Resultants of Uniform Force Systems

14. Resultants of Nonuniform Froce Systems

15. Resultants of Noncurrent Force Systems

16. Surprising Results! The Location of Resultant Forces

Common Mistakes

17. Moment Calculation in Statics Common Mistakes

18. Force Resultant Moment in Statics Common Mistakes

19. Force Moment Calculation Basics & Common Mistakes

20. How to Correctly Apply Force Equilibrium Principles in Solving Problems

21. How to Correctly Apply Force Resolution Techniques: Understanding Force Equilibrium Basics

22. When to Apply Sine Law in Finding Unknown Forces

23. Simple Application of Force Moment Concept

24. Moment Concept Application

Chapter 4

Reactions

Free-Body Diagram, Reaction Force Calculations for Various types of Forces, including Parallel, Concurrent, Nonconcurrent, Uniform & Nonuniformly Distributed Load

1. Free-Body Diagram

2. Reaction Force Calculation

3. Reaction Force Calculation for Uniform Force Systems

4. Reaction Force Calculation Nonuniform Force Systems

5. Reaction Force Calculation Nonconcurrent Force Systems

Common Mistakes

6. Foundations for Solving Problems in Mechanics, Statics, and Dynamics

Chapter 5

Structure

Analysis of Trusses, Frames, and Machine Members | Method of Joints and Sections

1. Introduction

2. Analysis Basics

3. Method of Joints

4. Method of Sections

5. Frame Analysis

6. Reaction Forces

Chapter 6

Friction

Friction, Friction Coefficient, Friction Force, Tension, Torque & Power, Rope, Flat Belt, V Belt, Tension, Torque, Square Threaded Screw, Ladder, & Wedge

1. Introduction

2. Inclined Surface

3. Rope/Belt

4. Pulley

5. V-Belt

6. Ladder

7. Jackscrew

Chapter 7

Centroid and Center of Gravity

Centroid, Center of Gravity, CG, mass moment & area moment 

1. Center of Gravity

2. Centroid

Chapter 8

Inertia

Inertia, Transfer Formula, Radius Gyration, Polar Moment of Inertia, 

1. Area Moment of Inertia | Radius Gyration | Polar Moment of Inertia

Reference

1. Limbrunner, G. F., D'Allaird, C., & Spiegel, L. Applied Statics and Strength of Materials

2. Beer, F. P.,‎ Johnston E. R., DeWolf, J. T., & Mazurek, D. Statics and mechanics of materials

3. Hibbeler, R. C. Mechanics of materials