Fundamentals of Virtual Work for Civil Engineers

Fundamentals of Virtual Work for Civil Engineers

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

⏰ 3 h 18 min | 30 lessons
Published: August 2018
After completing this course...
You will have a complete understanding of how basic concepts such as work, energy and elasticity combine to give us the Principle of Virtual Work.
You will have robust solution strategies to apply Virtual Work in the analysis of pin-jointed truss structures.
You will be able to use Virtual Work to calculate unknown nodal displacements in pin-jointed truss structures.
You will be able to use Virtual Work to calculate internal forces in pin-jointed truss structures.

In this course you’ll be introduced to an immensely powerful method of civil engineering analysis. A fundamental requirement of any civil 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 engineering student – the aim for this course is to help you hit that milestone!

Each video lecture is structured and delivered to ensure you get the most out of your time investment. If you take this course, don’t expect to sit back and let the videos wash over you – you’ll need to actively work your way through the course, constantly comparing your developing understanding with what you learn in each lecture.

You’re strongly encouraged to develop your own notes as we move through the course…we’ll be avoiding ‘death by PowerPoint’ at all costs. The mode of presentation is predominantly through hand-drawn notes and sketches; a method universally favoured by every engineering student I’ve ever had!

Course Breakdown

Section 1: Welcome and Introduction

In the first short section I’ll set out the plan for the course, discussing what we’ll cover and why I’ve structured the course the way I have. This is followed by a short video where I offer you some advice on maximising value from the course. Anyone familiar with my style of teaching will know what to expect here 🙂

Section 2: Quick Review of Trusses (optional)

In this section, we’ll cover some of the essential background knowledge required to proceed through the course. Basically, you need to be able to analyse statically determinate trusses to determine their internal member forces. To bring everyone up to speed, we’ll make sure you can do this by the end of this section.

Section 3: Strain Energy

In section 3, we’ll start thinking about structures as energy storage devices and how this allows us to tie together the concepts of work, energy and elastic deformation. What we’re doing in this section is laying the groundwork required to develop a solid understanding of virtual work in the next section. By the end of this section you’ll understand what we mean by strain energy and you’ll have conquered your first energy-based analysis technique.

Section 4: Virtual Work

Here we’ll introduce the Principle of Virtual Work. This should be much easier to digest after completing the previous section on strain energy. In this section, we’re simply focusing on the principle of virtual work and the building blocks required to use it in our structural analyses. For many students that struggle with virtual work, this is the missing link!

Section 5: Pin-Jointed Structures / Trusses

Now that you understand the Principle of Virtual Work and how it evolves out of some pretty simple ideas, we need to take it and turn it into a structural analysis technique. In this section we’ll develop the analysis strategies that you can routinely apply to pin-jointed truss structures. Understanding the material in this section is going to be key to you being able to use virtual work as an analysis technique out in the wild beyond this course.

Section 6: Practice Questions

At this point you’ve covered all of the groundwork and should have a good understanding of the theory that underpins the principle of virtual work and how it applies to structural analysis. Now it’s about practice. In this section there are five practice questions to get you started and help you confirm for yourself that you’ve understood everything we’ve worked on in this course. After successfully completing this final section, you’ll be confident in determining how one of the most common forms of civil engineering structure (trusses!) deform under load.

Who this course is for

  • Engineering students who want to move beyond basic analysis techniques and determine displacements in structures under load
  • Engineering students who want to get a good understanding of how to harness the Principle of Virtual Work for structural analysis
  • Engineering students who have come across Virtual Work but are confused about how and why it works
  • More advanced engineering students or practitioners who have covered Virtual Work methods but want a concise refresher in the underlying theory and its application
Section 1
Welcome and Introduction
1. Welcome to the course
03:26 (Preview)
2. Syllabus walkthrough
01:47 (Preview)
3. Maximise course value
Section 2
Quick Review of Trusses
4. Section 2 overview
5. Key features of a truss
6. The joint resolution method 📂
7. The method of sections
8. Worked example
Section 3
Strain Energy
9. Section 3 overview
01:13 (Preview)
10. What is strain energy?
16:45 (Preview)
11. Energy stored in a structure
12. Energy storage and trusses
13. Let’s try that again
14. What are the limitations of strain energy?
Section 4
Virtual Work
15. Section 4 overview
01:12 (Preview)
16. The basic idea
13:23 (Preview)
17. Equilibrium force system
18. Compatible displacement system
19. The Principle of Virtual Work
Section 5
Pin-Jointed Structures / Trusses
20. Section 5 overview
01:01 (Preview)
21. A strategy for analysing trusses
22. Finding unknown displacements
23. Finding unknown forces
Section 6
Practice Questions
24. Section 6 moverview
00:58 (Preview)
25. Practice Question 1
26. Practice Question 2
27. Practice Question 3
28. Practice Question 4
29. Practice Question 5
Section 7
Course wrap up and debrief
30. Closing comments and advice
Completion certificate
Completion certificate
  • Download your personalised Certificate of Completion once you’ve finished all course lectures.

  • Applying for jobs? Use your Certificate of Completion to show prospective employers what you’ve been doing to improve your capabilities.

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Ready to get started?
Very good course. Highly recommended
Lekai Nalei Sakaio
Dr Seán Carroll
BEng (Hons), MSc, PhD, CEng MIEI, FHEA
Hi, I’m Seán, the founder of (formerly I hope you found this tutorial helpful. After spending 10 years as a university lecturer in structural engineering, I started this site to help more people understand engineering and get as much enjoyment from studying it as I do. Feel free to get in touch or follow me on any of the social accounts.

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