Systems of Forces on Rigid Bodies - Engineering Mechanics (Undergraduate Advanced)

Systems of Forces on Rigid Bodies - Engineering Mechanics (Undergraduate Advanced)

Analysis of systems of forces on rigid bodies in two and three dimensions - moments of forces about a point or axis, couples and equivalent systems of forces.

34

50 hrs

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This course is also part of the following learning track. You may join the track to gain comprehensive knowledge across related courses.

[OAU, Ife] MEE 205: Engineering Mechanics I - Statics

Comprehensive treatise of static equilibrium of particles and rigid bodies, with focus on the stability of machines and structures. Curated for second-year students of engineering and at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Comprehensive treatise of static equilibrium of particles and rigid bodies, with focus on the stability of machines and structures. Curated for second-year students of engineering and at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Course Chapters

1. Introduction

9

Welcome to the course and review of fundamental concepts - meaning of rigid bodies, principle of transmissibility of forces, vector products, etc.

Chapter lessons

1-1. Welcome

12:08

Welcome to the course, overview of course.

1-2. Mechanics

12:10

Review of the meaning of mechanics, engineering mechanics, mechanics of rigid bodies, etc.

1-3. Rigid bodies

7:06

Meaning of rigid bodies as used in engineering mechanics, in contrast to particles.

1-4. Principle of transmissibility of forces

7:55

Statement, meaning and implications of the principle of transmissibility of forces on rigid bodies.

1-5. Scalar products

13:31

Meaning and calculation of the scalar product of two vectors.

1-6. Vector products (1)

14:20

Review of the vector or cross product of vectors - magnitude and direction of vector products.

1-7. Vector products (2)

16:54

Review of the vector or cross product of vectors - rectangular components of vector products.

1-8. Scalar triple products

6:19

Meaning and calculation of the scalar or mixed triple products of vectors.

1-9. Properties

13:22

Some properties of vector products and scalar triple products of vectors, implied from some properties of matrix determinants.

2. Moment of a Force

8

Meaning, scalar and vector forms of the moment of a force about a point and its relation to the moment about an axis; Varignon's theorem.

Chapter lessons

2-1. Introduction

21:03

What exactly is the moment (or torque) of a force about a point or axis, where and how is it relevant?

2-2. Zero moment

8:51

Making sense of when and how the moment of a force about a given point or axis is zero.

2-3. Elementary calculation

8:44

Calculating moments using force times perpendicular distance.

2-4. A sign convention

12:06

How to determine and specify directions (clockwise or counterclockwise) for moments about an axis perpendicular to a given plane.

2-5. Vector formulation

16:39

Calculating moments using a vector product.

2-6. The r vector

9:38

A closer look at the r vector for calculating the moments of a force about a given point or axis.

2-7. Varignon's theorem

8:22

How the moment of a force about a point or axis obtains from those of its components.

2-8. Overview

6:13

An overview of methods for calculating the moment of a force about a point or axis in two and three dimensions.

3. Moment About a Point in Two Dimensions

1

12

Meaning and calculation of the moment of a force about a point in two dimensions.

Chapter lessons

3-1. Procedure

8:30

Review of the methods of calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases.

Ex. 3-1. Worked examples (1)

32:22

Worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases.

Ex. 3-2. Worked examples (2)

18:28

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases.

Ex. 3-3. Worked examples (3)

12:19

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases.

Ex. 3-4. Worked examples (4)

14:08

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases.

Ex. 3-5. Worked examples (5)

23:29

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases.

Ex. 3-6. Worked examples (6)

52:46

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases.

Ex. 3-7. Worked examples (7)

35:09

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases.

Ex. 3-8. Worked examples (8)

34:31

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases.

Ex. 3-9. Worked examples (9)

6:35

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases.

Ex. 3-10. Worked examples (10)

38:24

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases.

Ex. 3-11. Worked examples (11)

23:41

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases.

Ex. 3-12. Worked examples (12)

21:01

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases.

4. Moment About a Point in Three Dimensions

1

12

Meaning and calculation of moment of a force about a point in three dimensions.

Chapter lessons

4-1. Procedure

13:15

Review of the methods for calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases.

Ex. 4-1. Worked examples (1)

14:46

Worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases.

Ex. 4-2. Worked examples (2)

11:11

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases.

Ex. 4-3. Worked examples (3)

14:52

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases.

Ex. 4-4. Worked examples (4)

22:19

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases.

Ex. 4-5. Worked examples (5)

22:50

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases.

Ex. 4-6. Worked examples (6)

19:26

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases.

Ex. 4-7. Worked examples (7)

12:03

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases.

Ex. 4-8. Worked examples (8)

33:48

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases.

Ex. 4-9. Worked examples (9)

16:09

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases.

Ex. 4-10. Worked examples (10)

36:11

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases.

Ex. 4-11. Worked examples (11)

15:17

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases.

Ex. 4-12. Worked examples (12)

26:25

More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases.

5. Moment About an Axis

2

10

Meaning and calculation of the moment of a force about an arbitrary axis.

Chapter lessons

5-1. Introduction

44:35

What is the moment of a force about an axis? How is it calculated, and how is the direction determined?

5-2. Procedure

23:07

Procedure for calculating the moment of a force about an arbitrary axis - using both scalar and vector approaches.

6. Couples

6

16

Meaning and analysis of couples, moments of couples, and couple vectors.

Chapter lessons

6-1. Couple

14:19

Meaning of a couple (of forces) and their impact on the stability of a rigid body.

6-2. Moment of a couple

31:00

Calculation and some properties of the moment of a couple.

6-3. Equivalent force systems

28:40

Meaning of equivalent force systems, and overview of operations for simplifying a given force system to an equivalent one.

6-4. Equivalent couples

46:05

Proof of equivalence of couples with equal moments - in the same or parallel planes.

6-5. Addition of couples

10:56

How the moment of two couples derives from the sum of their individual moments.

6-6. Couple vectors

8:43

Representing moments of couples as vectors.

7. Force-Couple Systems

3

10

Analysis of simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force.

Chapter lessons

7-1. Introduction

9:34

Introduction to force-couple systems and the necessity for an interplay of forces and couples.

7-2. Force to force-couple resolution

18:45

How to resolve a single force into an equivalent force-couple system.

7-3. Force-couple to force resultant

15:15

How to obtain the resultant (equivalent) single force from a force-couple system, where feasible.

Ex. 7-1. Worked examples (1)

9:53

Worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force.

Ex. 7-2. Worked examples (2)

14:36

More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force.

Ex. 7-3. Worked examples (3)

30:34

More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force.

Ex. 7-4. Worked examples (4)

32:36

More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force.

Ex. 7-5. Worked examples (5)

25:24

More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force.

Ex. 7-6. Worked examples (6)

16:36

More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force.

Ex. 7-7. Worked examples (7)

30:37

More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force.

Ex. 7-8. Worked examples (8)

20:29

More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force.

Ex. 7-9. Worked examples (9)

23:57

More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force.

Ex. 7-10. Worked examples (10)

28:49

More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force.

8. General Systems of Forces

4

8

Simplifying general systems of forces and couples on rigid bodies.

Chapter lessons

8-1. Reduction to force-couple system

24:06

How to reduce a system of forces on a rigid body to an equivalent force-couple system.

8-2. Equivalence and equipollence

25:57

Meaning of equivalent and equipollent force-couple systems, and how they are related for a system of forces on a rigid body.

8-3. Reduction to a single force or couple

22:35

How and under what conditions does a system of forces on a rigid body reduce to a single force or couple?

8-4. Reduction to a wrench

24:18

How and under what conditions does a system of forces on a rigid body reduce to a wrench?

9. Distributed Loads

3

6

Simplifying systems of forces on rigid bodies involving distributed loads.

Chapter lessons

9-1. Introduction

17:57

Meaning and use of distributed loads.

9-2. Magnitude

19:45

Determining the magnitude of the resultant of distributed loads on a rigid body.

9-3. Location

31:18

Determining the location of the resultant of distributed loads on a rigid body.