Welcome to CE 221! This on-demand course was put together especially for CE 221 at MSU. Use the video lessons and notes to understand your lecture topics better, and the practice questions to cement your knowledge. And don't hesitate to leave a question in the Q&A box under each lesson if you need additional help with anything. Happy studying!
CE 221
MSU
Course Overview
Lessons & Practice
1. Scalars and Vectors
6hr1.2.1. Scalars & Vectors - Definitions & Examples3 min1.2.2. Vectors (2D)12 min1.2.3. Vectors (3D)6 min1.2.4. Examples: Scalars and Vectors (Sine and Cosine Laws)13 min1.2.5. Practice: Scalars and Vectors (Sine and Cosine Laws)10 min1.2.6. Practice: Scalars and Vectors (Catesian Format, Sine Law)16 min1.2.7. Example: Scalars and Vectors (Rectangular Components)13 min1.2.8. Practice: Scalars and Vectors (Rectangular Components) 11 min
1.6.1. Forces 3D Cartesian Form (IMPORTANT!)11 min1.6.2. Example 1 - Part 1: 3D Force Vectors 11 min1.6.3. Example 1 - Part 2: 3D Force Vectors 7 min1.6.4. Example 2: 3D Force Vectors13 min1.6.5. Example: Forces in Cartesian Vector Form16 min1.6.6. Practice 1: 3D Force Vectors10 min1.6.7. Practice: 3D Vector Practice Questions Part 15 min1.6.8. Practice: 3D Vector Practice Questions Part 26 min
2. Center of Gravity and Centriod
4hr2.1.1. Centroids of Area12 min2.1.2. Centroids of Area17 min2.1.3. Example: Centroids of Area - Geometric (DO THIS!)10 min2.1.4. Example: Centroids of Area - Integration (OPTIONAL)15 min2.1.5. Practice: Centroids Practice - Geometric (DO THIS!)11 min2.1.6. Practice: Centroids Geometric (DO THIS!)9 min2.1.7. Practice: Centroids Geometric10 min2.1.8. Quiz: Centroids Practice - Geometric Quiz (New)2 Qns2.1.9. Practice: Centroids - Geometric 3D (OPTIONAL)17 min2.1.10. Practice: Centroids - Integration16 min2.1.11. Practice: Centroids - Integration14 min2.1.12. Quiz: Centroids Practice - Integration Quiz (New)1 Qn
2.3.1. Hydrostatics20 min2.3.2. Example 1: Hydrostatics (IMPORTANT - EXAM LIKE!)18 min2.3.3. Example 2 - Part 1: Hydrostatics (IMPORTANT - EXAM LIKE!)15 min2.3.4. Example 2 - Part 2: Hydrostatics (IMPORTANT - EXAM LIKE!)18 min2.3.5. Practice 1: Hydrostatics (IMPORTANT - EXAM LIKE!)13 min2.3.6. Practice 2: Hydrostatics (IMPORTANT - EXAM LIKE!)14 min
3. Equilibrium of Particles
4hr3.3.1. Ropes, Cables, and Springs (2D Equilibrium)7 min3.3.2. Pulleys (2D Equilibrium)7 min3.3.3. Example 1: Ropes and Cables (2D)11 min3.3.4. Practice 1: Ropes and Cables (2D)13 min3.3.5. Example 2: Part 1 - Pulleys (2D) - IMPORTANT!12 min3.3.6. Example 2: Part 2 - Pulleys (2D) - IMPORTANT! 6 min3.3.7. Practice 2: Pulleys (2D) - IMPORTANT!13 min3.3.8. Example Question 1: Cables and Springs5 min3.3.9. Example Question 2: Cables and Hanging Weights3 min3.3.10. Example Question 3: Two Cables7 min
3.6.1. Example Question 1: Cables and Weights3.6.2. Example Question 2: Weights and Two Cables3.6.3. Example Question 3: Cables3.6.4. Particle Equilibrium - Practice Questions (2D Problems - Part 1)3.6.5. Particle Equilibrium - Practice Questions (2D Problems - Part 2)8 min3.6.6. Particle Equilibrium - Practice Questions (3D Problems - Part 1)9 min3.6.7. Particle Equilibrium - Practice Questions (3D Problems - Part 2)13 min3.6.8. Quiz: Practice Questions - Particle Equilibrium (Part 1)1 Qn3.6.9. Quiz: Practice Questions - Particle Equilibrium (Part 2)2 Qns
4. Moments
6hr4.3.1. Moments About a Point - Scalar Formulation (for 2D)12 min4.3.2. Example 1 - Part 1 (M= r x F): Moment About a Point (2D)11 min4.3.3. Example 1 - Part 2 (M= Fd): Moment About a Point (2D)7 min4.3.4. Example 2: Moment About a Point (2D) - M = Fd 11 min4.3.5. Example: Computing Moments About a Point 4.3.6. Example: Computing Moments About a Point Example6 min4.3.7. Example: Computing Moments About a Point11 min4.3.8. Practice: Moments About a Point (2D) 7 min4.3.9. Practice: Moments About a Point (2D)13 min4.3.10. Moments About a Point - Practice Questions (2D)4.3.11. Quiz: Moments About a Point - Practice Questions (2D)4 Qns4.3.12. Moments About a Point - Vector formulation (for 3D)4.3.13. Example 1: Moment About a Point (3D) 12 min4.3.14. Practice: Moments About a Point (3D) 10 min4.3.15. Practice: Moments About a Point (3D)6 min4.3.16. Moments About a Point - Practice Questions (3D)4.3.17. Quiz: Moments About a Point - Practice Questions (3D)2 Qns
4.4.1. Computing Moments About an Axis2 min4.4.2. Example: Computing Moments About An Axis6 min4.4.3. Practice: Moments About an Axis (Part 1)7 min4.4.4. Moments About an Axis - Practice Questions (Part 1)4.4.5. Moments About an Axis - Practice Questions (Part 2)4.4.6. Quiz: Computing Moments About on Axis1 Qn
4.5.1. Couple Moments - The Basics9 min4.5.2. Couple Moments4 min4.5.3. Couple Moments (with Example)6 min4.5.4. Example 1: Couple Moments (2D)3 min4.5.5. Example 2: Couple Moments (2D)6 min4.5.6. Practice: Couple Moments (2D)5 min4.5.7. Couple Moments Practice - 2D (New)2 min4.5.8. Quiz: Couple Moments - Quiz Practice Questions (2D)2 Qns4.5.9. Example 3: Couple Moments (3D)17 min4.5.10. Practice: Couple Moments (3D)8 min4.5.11. Couple Moments Practice - 3D (New)6 min4.5.12. Quiz: Couple Moments - 3D Quiz1 Qn
4.6.1. Reduction of System of Forces & Moments (Equivalency)9 min4.6.2. Example: Force-Moment Systems4.6.3. Example 1: Equivalency (2D) - Part 112 min4.6.4. Example 1: Equivalency (2D) - Part 27 min4.6.5. Force Moment Systems - Practice Questions4.6.6. Force Moment Systems - Practice Questions (Shifting Wrench)4.6.7. Force Moment Systems - Practice Questions (3D)4.6.8. Practice 3: Equivalency - Force-Couple (3D)14 min4.6.9. Quiz: Force-Moment Systems2 Qns
4.7.1. Distributed Loads (Common Geometric Shapes & Integration)15 min4.7.2. Distributed Loads (Integration (more))6 min4.7.3. Example: Distributed Loads (Geometric Example)4.7.4. Example: Distributed Loads - Geometric2 min4.7.5. Distributed Loads - Practice Questions (Geometric Shapes)4.7.6. Quiz: Distributed Loads - Quiz Practice Questions (Geometric Shapes)4 Qns4.7.7. Quiz: Distributed Loads Practice - Geometric Shapes Quiz2 Qns4.7.8. Quiz: Distributed Loads - Quiz Practice Questions (Geometric Shapes)4 Qns4.7.9. Example 1: Distributed Loads9 min4.7.10. Example 2: Distributed Loads11 min4.7.11. Practice 1: Distributed Loads10 min4.7.12. Practice 2: Distributed Loads10 min4.7.13. Distributed Loads - Practice Questions (Geometric Shapes)6 min4.7.14. Example: Distributed Loads (Integration Example)4.7.15. Example: Distributed Loads - Integration2 min4.7.16. Distributed Loads - Practice Questions (Integration)4.7.17. Distributed Loads - Practice Questions (Integration)4 min4.7.18. Distributed Loads Practice - Integration4 min4.7.19. Distributed Loads Practice - Integration4.7.20. Quiz: Distributed Loads Practice - Integration Quiz1 Qn4.7.21. Quiz: Distributed Loads Practice - Integration Quiz1 Qn
5. Rigid Body Equilibrium
7hr5.1.1. Rigid Body Equilibrium (2D)9 min5.1.2. 2D Rigid Body - Free Body Diagram (FBD) Practice 18 min5.1.3. Example 1: 2D Rigid Body Equilibrium (Warm Up!)11 min5.1.4. Example 1: 2D Rigid Body Equilibrium 11 min5.1.5. Example 2: 2D Rigid Body Equilibrium - Part 1 (IMPORTANT!)16 min5.1.6. Example 2: 2D Rigid Body Equilibrium - Part 2 (IMPORTANT!) 10 min5.1.7. Practice 2: 2D Rigid Body Equilibrium 25 min5.1.8. Practice 1: 2D Rigid Body Equilibrium (Try This - Check your work!)33 min5.1.9. Practice 3: Spring Practice Problem 21 min5.1.10. 2D Solution Method53 sec5.1.11. 2D Solution Method3 min5.1.12. Example: 2D Solution Method5.1.13. Example: 2D Solution Method6 min5.1.14. Rigid Body - Practice Questions (2D - Part 1)5.1.15. Practice: Rigid Body (2D - Part 1)10 min5.1.16. Quiz: 2D solution Method5 Qns
5.2.1. 2D Solution Method53 sec5.2.2. Example: 2D Solution Method Example4 min5.2.3. Practice: Rigid Body (2D - Part 1)6 min5.2.4. Practice: Rigid Body (2D - Part 2)2 min5.2.5. Quiz: 2D solution Method Quiz7 Qns5.2.6. Practice: Rigid Body Practice - 2D (Part 1)2 min5.2.7. Practice: Rigid Body 2D (Part 2)8 min5.2.8. Practice: Rigid Body 2D (Part 3)8 min5.2.9. Quiz: 2D Solution Method (New)5 Qns
5.3.1. 3D Rigid Body Equilibrium14 min5.3.2. 3D Rigid Body - Support Reactions and FBDs12 min5.3.3. Example 1: 3D Rigid Body Equilibrium (IMPORTANT!) - Part 114 min5.3.4. Example 1: 3D Rigid Body Equilibrium - Part 210 min5.3.5. Example 1: 3D Rigid Body Equilibrium - Part 317 min5.3.6. Example 2: 3D Rigid Body Equilibrium32 min5.3.7. Practice 1: 3D Rigid Body Equilibrium (IMPORTANT!)38 min5.3.8. Practice 2: 3D Rigid Body Equilibrium (IMPORTANT!)34 min
6. Dry Friction
2.3hr6.1.1. Friction11 min6.1.2. Friction Guidelines6 min6.1.3. Example: Friction4 min6.1.4. Practice 1: Friction (EXAM-LIKE!)22 min6.1.5. Practice 2: Friction (EXAM-LIKE!)23 min6.1.6. Practice 3: Friction (EXAM-LIKE!)21 min6.1.7. Practice: Friction - Multiple Bodies7 min6.1.8. Practice: Friction - Wedges12 min6.1.9. Quiz: Friction Practice Questions6 Qns
7. Moment and Product of Inertia
35min8. Structural Analysis of Trusses
5hr8.3.1. Method of Sections (MOS)10 min8.3.2. Example 1: Method of Sections 17 min8.3.3. Example 2 - Part 1: Combo of Method of Joints and Method of Sections12 min8.3.4. Example 2 - Part 2: Combo of Method of Joints and Method of Sections12 min8.3.5. Practice 1: Method of Sections22 min8.3.6. Practice 2: Method of Sections19 min8.3.7. Practice 3: Method of Sections 19 min8.3.8. Quiz: Method of Sections Practice5 Qns8.3.9. Quiz: Method of Sections Practice5 Qns
8.4.1. Frames and Machines13 min8.4.2. Example 1 - Part 1: Frames and Machines (IMPORTANT-EXAM LIKE!)11 min8.4.3. Example 1 - Part 2: Frames and Machines (IMPORTANT - EXAM LIKE!)8 min8.4.4. Example 2: Frames and Machines (IMPORTANT - EXAM LIKE!)20 min8.4.5. Example - Frames and Machines - Multiple Pulleys 8.4.6. Example - compound beam8.4.7. Practice 1: Frames and Machines (IMPORTANT - EXAM LIKE!)22 min8.4.8. Practice 2: Frames and Machines Practice (IMPORTANT - EXAM LIKE!)29 min8.4.9. Practice 2: Frames and Machines (IMPORTANT-EXAM LIKE!)16 min8.4.10. Practice 3: Frames and Machines Practice (OPTIONAL)14 min8.4.11. Quiz: Frames and Machines Quiz6 Qns
9. Structural Analysis of Beams
4hr9.1.1. Internal Forces10 min9.1.2. Example: Internal Force (at a point) Simple Beam9.1.3. Example: Internal Forces (at a point) bar with pulleys9.1.4. Example 1: Internal Forces at a Point (OPTIONAL) 17 min9.1.5. Example: Internal Forces6 min9.1.6. Practice: Internal Forces9 min9.1.7. Practice 1: Internal Forces at a Point (OPTIONAL) 8 min9.1.8. Practice 2: Internal Forces at a Point (OPTIONAL) 10 min
9.2.1. Method 1 - using Method of Sections7 min9.2.2. Example 1: Drawing Shear and Moment Diagrams (DO THIS!)12 min9.2.3. Example 2: Drawing Shear and Moment Diagrams20 min9.2.4. Practice 1: Drawing Shear and Moment Diagrams (DO THIS!)14 min9.2.5. Practice 2: Drawing Shear and Moment Diagrams (DO THIS!)16 min9.2.6. Example 2 - Part 1: ENGG 13015 min9.2.7. Example 2 - Part 2: ENGG 13015 min9.2.8. Method 2 - using Shortcuts11 min9.2.9. Practice 3 (IMPORTANT - EXAM LIKE!) : Drawing Shear and Moment Diagrams22 min9.2.10. Practice: Internal Forces (Graphical)11 min9.2.11. Practice 3: Internal Forces as a Function of x. (MUST KNOW!) 14 min9.2.12. Practice 4: Internal Forces as a Function of x. (MUST KNOW!) 10 min9.2.13. Practice 5: Internal Forces as a Function of x. (MUST KNOW!) 12 min
10. Introduction
55minCE 221 Overview
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Course Notes
Wizeprep's course notes with hundreds of easy-to-understand explanations, diagrams, and practice problems.