Analysing Hybrid Indeterminate Civil Engineering Structures

Powerful techniques for analysing realistic civil engineering structures.

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What you'll learn

You will learn how to analysis complex and indeterminate structures using hand-analysis techniques
You will learn how to apply the Principle of Virtual Work to indeterminate structures
You will learn how to calculate deflections, member forces and bending moments in indeterminate structures
You will learn how the Principle of Superposition can be used to decipher and unlock the behaviour of complex structures


In this course we’ll apply the Principle of Virtual Work and the Principle of Superposition to analyse complex indeterminate civil engineering structures. Engineering students typically start learning structural analysis by focusing on simple trusses, then beams and frames.

In reality many civil engineering structures are complex hybrids of both axially loaded (truss) and bending (beam and frame) elements. Realistic civil engineering structures are also very often statically indeterminate, meaning direct application of simple statics alone won’t unlock their behaviour.

In this course it is these complex, indeterminate structures that we’ll focus on analysing. We’ll start by developing a solution strategy. You’ll develop a sound understanding of this strategy as we develop everything from simple first principles, namely, Virtual Work and Superposition.

The second half of the course focuses on implementation – you will work your way through a number of challenge questions, with my worked solutions as your back-up if you get stuck. By the end of this course you’ll be confidently analysing structures that leave most other students scratching their heads in confusion.

As a senior university lecturer in structural engineering, I have a lot of experience guiding students through these topics. 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!

Who this course is for

  • Engineering students who want to extend their ability to analyse more complex real world structures
  • Engineering students who can analyse basic truss or beam/frame structures but who have realised that real world structures are often a combination of both
  • Engineering students who have some familiar with the Principle of Virtual Work but want to learn how deploy its power more broadly
  • Engineering students who want the ability to analyse indeterminate structures without the need to resort to analysis software

Course Completion Certificate

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Course preview

Lecture #3: What are complex structures?

Lecture #4: How does superposition help us?

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Course content


Analysing Complex Indeterminate Structures | 1
Welcome to the course (Preview)
Analysing Complex Indeterminate Structures | 2
Course overview and tips for success (Preview)

Complex Structure Analysis Strategy

Analysing Complex Indeterminate Structures | 3
What are complex structures? (Preview)
Analysing Complex Indeterminate Structures | 4
How does superposition help us? (Preview)
Analysing Complex Indeterminate Structures | 5
Dealing with axial forces
Analysing Complex Indeterminate Structures | 6
Dealing with bending moments
Analysing Complex Indeterminate Structures | 7
Finding the scale factor, alpha
Analysing Complex Indeterminate Structures | 8
Analysis Walkthrough – Part 1
Analysing Complex Indeterminate Structures | 9
Analysis Walkthrough – Part 2

Challenge Questions

Analysing Complex Indeterminate Structures | 10
Challenge Question 1 – Part 1
Analysing Complex Indeterminate Structures | 11
Challenge Question 1 – Part 2
Analysing Complex Indeterminate Structures | 12
Challenge Question 2 – Part 1
Analysing Complex Indeterminate Structures | 13
Challenge Question 2 – Part 2
Analysing Complex Indeterminate Structures | 14
Challenge Question 3 – Part 1
Analysing Complex Indeterminate Structures | 15
Challenge Question 3 – Part 2
Analysing Complex Indeterminate Structures | 16
Challenge Question 4 – Part 1
Analysing Complex Indeterminate Structures | 17
Challenge Question 4 – Part 2
Analysing Complex Indeterminate Structures | 18
Challenge Question 5 – Part 1
Analysing Complex Indeterminate Structures | 19
Challenge Question 5 – Part 2

Course wrap up

Analysing Complex Indeterminate Structures | 20
Course wrap up and debrief


Consider this first...

This course is a first introduction to the principle of virtual work and covers the analysis of trusses. You will need to be comfortable with this before tackling the current course.

...and also this first...

This course covers how we apply virtual work to structures that resist bending. This is also going to be important to know before taking the current course.

📍 You're here

Try this next...

This course covers the moment distribution method which is suitable for analysing indeterminate structures. This is a good next step after completing the current course.

...or this next...

This course is a first introduction to the direct stiffness method. This is another method suitable for indeterminate structures and is much faster and more efficient than manual methods like virtual work.

Frequently Asked Questions

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