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

This course is a comprehensive guide to the effects of forces on rigid bodies, a critical topic in engineering mechanics. It moves beyond particles to analyse systems where the point of application of a force is crucial, introducing the concepts of moments and couples. The material covers the calculation of moments in two and three dimensions, the properties of couples, and the methods for reducing complex force systems into simpler, statically equivalent systems. Understanding moments is fundamental to all structural and mechanical analysis. These principles are used to calculate the bending and twisting stresses in beams, shafts, and machine components, and to ensure the rotational stability of structures and vehicles. A command of this subject is non-negotiable for designing any object intended to withstand real-world loads without failing or rotating unintentionally. By the end of this course, you will be able to calculate the moment of a force about any point or axis using both scalar and vector methods. You will also be able to determine the moment of a couple, and reduce any complex system of forces and couples acting on a rigid body to its simplest equivalent form, such as a single resultant force and couple moment at a specified point. This course is for undergraduate students in any engineering discipline who have already completed a course on the statics of particles. It is the direct prerequisite for the study of the equilibrium of rigid bodies, and is a necessary foundation for advanced courses in dynamics, mechanics of materials, and structural analysis.

36

50 hrs

Payment required for enrolment
Enrolment valid for 12 months
This course is also part of the following learning track. You may join the track to gain comprehensive knowledge across related courses.
[University] Engineering Mechanics - Statics
[University] Engineering Mechanics - Statics
Master the science of structural stability. This programme provides a complete education in engineering statics, covering the analysis of forces, moments, and equilibrium in rigid bodies. It delivers the non-negotiable principles required to design safe and reliable structures. This learning track is for first or second-year undergraduate students in Civil, Mechanical, Aerospace, and Structural Engineering. It is the foundational mechanics course upon which all subsequent design and analysis subjects are built. Analyse the forces within any static structure, from simple trusses to complex machines. You will master free-body diagrams, equilibrium equations, and structural analysis methods. This programme equips you with the core analytical skills for a career in structural, mechanical, or civil design.

Master the science of structural stability. This programme provides a complete education in engineering statics, covering the analysis of forces, moments, and equilibrium in rigid bodies. It delivers the non-negotiable principles required to design safe and reliable structures. This learning track is for first or second-year undergraduate students in Civil, Mechanical, Aerospace, and Structural Engineering. It is the foundational mechanics course upon which all subsequent design and analysis subjects are built. Analyse the forces within any static structure, from simple trusses to complex machines. You will master free-body diagrams, equilibrium equations, and structural analysis methods. This programme equips you with the core analytical skills for a career in structural, mechanical, or civil design.

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.

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.

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.

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.