In this course, we’ll apply the Principles of Virtual Work and Superposition to analyse complex, indeterminate structures. Many civil engineering structures are hybrids of axially loaded (truss) and bending (beam and frame) elements. Realistic structures are also very often statically indeterminate, meaning the direct application of simple statics alone won’t unlock their behaviour. We’ll start by developing a solution strategy. Then, we’ll work our way through a number of challenge questions. By the end of this course, you’ll be confidently analysing indeterminate hybrid structures.

Welcome to the course

Course overview and tips for success

What are complex structures?

How does superposition help us?

Dealing with axial forces

Dealing with bending moments

Finding the scale factor, alpha

Analysis Walkthrough – Part 1

Analysis Walkthrough – Part 2

Challenge Question 1 – Part 1

Challenge Question 1 – Part 2

Challenge Question 2 – Part 1

Challenge Question 2 – Part 2

Challenge Question 3 – Part 1

Challenge Question 3 – Part 2

Challenge Question 4 – Part 1

Challenge Question 4 – Part 2

Challenge Question 5 – Part 1

Challenge Question 5 – Part 2

Course wrap up and debrief

Powerful techniques for analysing realistic civil engineering structures.

Analysing Hybrid Indeterminate Civil Engineering Structures

In this course, you will develop analysis strategies that allow you to apply the Principle of Virtual Work to beam and frame structures. In order to fully leverage this powerful engineering principle, you need to be able to apply it to structures that experience bending. That’s the focus of this course. A fundamental engineering skill is being able to estimate how a structure will deflect and by how much! The Principle of Virtual work allows us to develop extremely efficient analysis techniques to accomplish this task using only hand calculation. By the end of this course, you will be confident in calculating unknown deflections for common civil engineering structures. 

Course Introduction

Syllabus walkthrough

Getting the most from your course

Section 2 overview

Relating bending moment to bending stress

Internal bending moment and equilibrium

Using cuts to reveal the internal bending moment

Worked Example 1

Worked Example 2

Worked Example 3

Section 3 overview

The basic idea

Equilibrium force system

Compatible displacement system

The Principle of Virtual Work

Section 4 overview

A strategy for bending

Virtual work equation for bending

Walkthrough – Part 1

Walkthrough – Part 2

Integral tables

Section 5 overview 

Practice Question 1 – Part A

Practice Question 1 – Part B

Practice Question 2 – Part A

Practice Question 2 – Part B

Practice Question 2 – Part C

Practice Question 3 – Part A

Practice Question 3 – Part B

Practice Question 4 – Part A

Practice Question 4 – Part B

Practice Question 5 – Part A

Practice Question 5 – Part B

Closing comments and advice

Analyse complex beam and frame structures using Virtual Work.

Mastering Virtual Work for Engineers

In this course, you’ll be introduced to an immensely powerful method of engineering analysis - the virtual work method. A fundamental requirement of any civil or structural engineer is an ability to estimate how a structure will deform and behave under load. The Principle of Virtual Work is an elegant and efficient tool that gives us that ability. Being able to look at a structure and estimate the magnitude of its deflection is a key milestone in the development of any student of engineering – the aim of this course is to help you hit that milestone.

Maximise course value

Key features of a truss

The joint resolution method

The method of sections

Worked example

What is strain energy?

Energy stored in a structure

Energy storage and trusses

Let’s try that again

What are the limitations of strain energy?

Section 5 overview

A strategy for analysing trusses

Finding unknown displacements

Finding unknown forces

Section 6 moverview

Practice Question 1

Practice Question 2

Practice Question 3

Practice Question 4

Practice Question 5

Enhance your structural analysis skillset with these powerful engineering analysis techniques.

Fundamentals of Virtual Work for Civil Engineers

Techniques for analysing determinate and indeterminate structures to determine axial forces, shear forces, bending moments and deflections

Virtual Work

In this tutorial we walk through arch analysis methods for determining shear forces, bending moments, axial forces and reactions.

Arch Analysis | Structural Analysis of Determinate & Indeterminate Arches | EngineeringSkills.com

Learn how to apply virtual work methods to unlock the behaviour of indeterminate arches

Arch Analysis – How to Analyse Determinate and Indeterminate Arches

In this tutorial on influence lines for civil and structural engineers, we will explore methods for constructing influence line diagrams.

Influence Lines - A Complete Introduction for Civil and Structural Engineers | EngineeringSkills.com

Learn how to construct influence lines for determinate and indeterminate structures

Influence Lines - A Complete Introduction for Civil and Structural Engineers

Apply the Principle of Virtual Work and learn how to use the virtual work method to analyse trusses and calculate truss deflections

How to Apply the Virtual Work Method to Trusses | EngineeringSkills.com

Apply the Principle of Virtual Work to determine truss deflections

How to Apply the Virtual Work Method to Trusses

HUB / VIRTUAL WORK

Techniques for analysing determinate and indeterminate structures to determine axial forces, shear forces, bending moments and deflections

Virtual Work Courses

Virtual Work Tutorials