# ENGINEERING TUTORIALS & COURSES

For students and professionals who want to master engineering analysis and design

## Where to start?

What do you want to learn? Pick a specific course, or work through a crafted learning pathway. Work at your own pace with dedicated Q&A support if and when you need it.

## Analytical Modelling of Plate and Shell Structures: Part 1 - Plates

### A practical guide to the analysis of circular and rectangular plates under load, from first principles.

After completing this course…

• You will have developed a deep first principles’ understanding of plate-bending behaviour – critical for the safe application of finite element solutions.
• You will be comfortable using Python’s SymPy library to work with symbolic math and turn symbolic expressions into graphical representations of plate deflection.
• You will have developed tools and techniques for solving the governing differential equations and unlocking the flexural behaviour of the rectangular and circular plates.
• You will understand how to apply Navier’s solution to approximate the solution to the governing differential equation for rectangular plate bending. in your own analyses.

## ALL ACCESS MEMBERSHIP

Learn, revise or refresh your knowledge and master engineering analysis and design with access to every DegreeTutors course
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## PRACTICAL PYTHON FOR ENGINEERS

Leverage the power of scripting and learn how to use Python to speed up your engineering workflows. Python beginner? No problem, learn by doing and start here
Get started with a free bitesize Python project

## Simulating crowd vibrations using the Duhamel Integral

In this Python mini-project, you’ll learn about the Duhamel Integral and how it can be used to simulate the dynamic response of a single degree of freedom system. We’ll discuss how to solve the integral and then write some Python code to implement our solution for any arbitrary loading. In the second half of this project, we’re going to use our Duhamel Integral solver to build a crowd loading simulation. This will allow us to simulate the vibration response of a footbridge to pedestrian traffic.

## Building a Beam Deflection Calculator in Python

In this project, we’ll build a beam deflection calculator that can generate beam deflections by directly integrating the bending moment diagram. The technique we’ll use for calculating deflection in this project is not limited to statically determinate structures, although you will need a complete bending moment diagram to integrate. This project builds on our previous Shear Force and Bending Moment Calculator project. So at the end of this project, the final result will be a complete beam analysis code that calculates beam reactions, shear forces, bending moments and deflections.

## Building a Shear Force and Bending Moment Diagram Calculator in Python

In this project we’re going to build a Shear Force and Bending Moment Diagram calculator using Python in the Jupyter Notebook development environment. Generating the shear force and bending moment diagram for a simple beam with anything other than basic loading can be a tedious and time-consuming process. Once you finish this project, you’ll have a calculator that can produce shear force and bending moment diagrams at the push of a button.

## Analytical Modelling of Plate and Shell Structures: Part 1 - Plates

### A practical guide to the analysis of circular and rectangular plates under load, from first principles.

After completing this course…

• You will have developed a deep first principles’ understanding of plate-bending behaviour – critical for the safe application of finite element solutions.
• You will be comfortable using Python’s SymPy library to work with symbolic math and turn symbolic expressions into graphical representations of plate deflection.
• You will have developed tools and techniques for solving the governing differential equations and unlocking the flexural behaviour of the rectangular and circular plates.
• You will understand how to apply Navier’s solution to approximate the solution to the governing differential equation for rectangular plate bending. in your own analyses.

## Fundamentals of Reinforced Concrete Design to Eurocode 2

### An introduction to ultimate limit state design for bending and shear

Play Video about Fundamentals-of-Reinforced-Concrete-Design-to-Eurocode-2_600 | DegreeTutors.com

After completing this course…

• You will be able to determine design actions using the Eurocodes Basis of Structural Design (EC0) and Actions on Structures (EC1).
• You will understand balanced section design and how to analyse and safely design singly and doubly reinforced concrete sections.
• You will understand how to apply the Variable Strut Inclination Method for shear reinforcement design.
• You will have developed your own reinforced concrete design codes in Python (the Python pathway is optional in this course).

## Modelling and Analysis of Non-linear Cablenet Structures using Python and Blender

### Learn how to combine parametric modelling, exploratory form-finding and iterative analysis techniques to simulate the behaviour of tensile structures.

Play Video about Modelling-and-analysis-of-non-linear-3D-cablenet-tensile-structures-in-Python_600 | DegreeTutors.com
After completing this course…
• You will understand how the behaviour of lightweight tensile structures leads to geometric non-linearity.
• You will be able to apply an iterative Newton-Raphson technique to solve for the non-linear behaviour of 3D cablenet structures.
• You will be able to apply parametric modelling and simulation-based form finding techniques to generate cablenet geometry.
• You will have developed a complete modelling, analysis and visualisation workflow for exploring these elegant yet complex structures.

## Non-linear finite element analysis of 2D catenary & cable structures using Python

### Build an iterative solution toolbox to analyse structures that exhibit geometric non-linearity due to large deflections.

After completing this course…
• You will understand the concept of geometric non-linearity and when it should be considered.
• You will understand how to modify the axially loaded element stiffness matrix to account for large deflections and changes in geometry.
• You will have implemented a Newton-Raphson iterative solution algorithm that seeks to converge on the deformed state of the structure.
• You will have a workflow that leverages open-source modelling tools in Blender to quickly generate the initial structural geometry.

## Multi-Degree of Freedom Dynamics, Modal Analysis and Seismic Response Simulation in Python

### Build the knowledge and tools to decode the dynamic response of real-world structures to real-world loads.

After completing this course…

• You will have a deep understanding of the solution strategies employed for linear and non-linear MDoF analysis.
• You will be able to model the influence of earthquake-induced ground motion and other dynamic loads on multi-storey structures.
• You will develop numerical tools to solve the coupled equations of motion.
• You will understand the role of modal decomposition in uncoupling the equations of motion and identifying the underlying dynamic characteristics of multi-degree of freedom systems.
Checkout the full course library here

Hi, I’m Seán, the founder and lead tutor at DegreeTutors.com. Before turning all my attention to DegreeTutors, I spent 10 years teaching students about engineering analysis and design at the University of Exeter, Warwick University and The University of Nottingham. I’m a Chartered Engineer and Fellow of the Higher Education Academy.

DegreeTutors is designed to support students and construction industry professionals to enhance their engineering analysis and design skills. Whether you want to sharpen up on the basics of constructing shear and moment diagrams or want to better understand how to analyse complex, indeterminate structures (with or without a computer), by taking courses with me on DegreeTutors, you’ll build the knowledge and skills you need.

If you’re interested in leveraging the power of Python programming to supercharge your analysis and design, then this is also the place for you…whether you’re brand new to programming or already proficient.

Dr Seán Carroll B.Eng (Hons), M.Sc, Ph.D, CEng MIEI, FHEA
Founder of DegreeTutors.com

# Analytical Modelling of Plate and Shell Structures: Part 1 - Plates

## A practical guide to the analysis of circular and rectangular plates under load, from first principles.

Play Video about Analytical-Modelling-of-Plate-and-Shell-Structures-Plates | DegreeTutors.com
After completing this course you will understand how to model 2D plate behaviour from first principles and be able to turn this understanding into a Plate Deflection Calculator using Python

Plate structures are found all around the built environment. They are as fundamental to how we build modern structures as beams and columns. Yet, generally speaking, they are less well understood than linear elements.

This course will help you rectify this! If you want to deploy FE with confidence, you should have a solid understanding of the fundamental behaviour first.

By the end of this course, you should have a good understanding of how to analyse both circular and rectangular plates using purely analytical means – so no finite elements or numerical methods – just fundamental closed-form solutions.

Although our analytical methods can only be practically deployed on idealised or simplified structures, they give us a foundation of knowledge that means we can use more sophisticated tools with greater confidence.

In addition to learning about the specifics of plate behaviour, you should also walk away with a better understanding of how to develop analytical models in the form of governing differential equations. You’ll also have a few new tools and techniques that you can use to unlock tricky math problems using Python.

The course is divided into 4 sections:

• Course Introduction
• An Introduction to Plate and Shell Structures
• Analysis of Circular Plates
• Analysis of Rectangular Plates

In the final section, we’ll spend quite a lot of time exploring Navier’s solution for simply supported rectangular plates subject to various loading conditions.

Our goal at the end of this section is to have a ‘Python Plate Calculator’ that parameterises and automates our plate analysis.

No prior experience with Python is required to complete this course.

# Fundamentals of Reinforced Concrete Design to Eurocode 2

## An introduction to ultimate limit state design for bending and shear with optional calculation automation using Python.

Play Video about Fundamentals-of-Reinforced-Concrete-Design-to-Eurocode-2_1000 | DegreeTutors.com
After completing this course you’ll be able to design flexural and shear reinforcement in accordance with Eurocode 2 and know how to implement your design calculations in Python.

One of the most widely used and versatile construction materials at our disposal is concrete and, more specifically, steel reinforced concrete. It’s arguably the most important and certainly the most ubiquitous material in the construction industry globally.

Reinforced concrete has many benefits over other materials; it’s strong, durable, naturally corrosion resistant, has fantastic fire resistance, has excellent inherent damping characteristics and when designed correctly, results in incredibly safe and robust structures.

So, one of the core skill sets an engineer needs is the ability to design reinforced concrete. This can only come after establishing a solid understanding of the fundamental behaviour of reinforced concrete and the composite action developed between the concrete and embedded reinforcing steel. We’ll focus on this foundational and fundamental knowledge in this course.

The course is divided into 5 sections:

• Overview and course breakdown
• Actions and limit state design
• Bending of Reinforced Concrete
• Shear Resistance of Reinforced Concrete
• Automating section analysis in Python

The final section covers how to take manual calculations and implement them in a Python coding environment. The final section is optional – it will focus on Python implementation and will not develop any new concrete design theory.

No prior experience with Python is required to complete this course.

# Modelling and Analysis of Non-linear Cablenet Structures using Python and Blender

## Learn how to combine parametric modelling, exploratory form-finding and iterative analysis techniques to simulate the behaviour of tensile structures.

Play Video about Modelling-and-analysis-of-non-linear-3D-cablenet-tensile-structures-in-Python_1000 | DegreeTutors.com
After completing this course you’ll have developed a complete workflow for the modelling and analysis of non-linear 3D cablenet structures.

In this course, we’ll expand beyond what we covered in our study of 2D non-linear cables by adapting the tools we built previously, for the analysis of non-linear 3D cablenet structures.

However, instead of just modifying our existing code, we’ll spend time fleshing out a complete workflow that takes you from initial form-finding of cablenet geometry, right through to iterative stiffness method simulation to identify the cablenet deflections and tension profile.

If you’re intrigued by these elegant and efficient structures and want to understand how to analyse their behaviour, this course is for you. Keep in mind that the tools developed in this course are not meant to be a replacement for commercial non-linear solvers. Our objective is to build your understanding of the behaviour of cablenet structures and geometric non-linearity more generally. The best way to do this is to roll up your sleeves and build your own solver.

After taking this course, you’ll be able to use commercial software which much greater confidence now that you understand what’s happening behind the scenes. The code developed within each section of the course is also provided for download as a reference.

This course is divided into 8 sections:

• Introduction, Course Breakdown & Prerequisites
• Developing the 3D non-linear stiffness matrix
• Extending our Blender Utility Scripts
• Extending our solver toolbox from 2D to 3D
• Cable-stayed antenna tower…in 3D
• Parametric modelling and form-finding in Blender
• Cablenet Pavilion – Hyperbolic Paraboloid
• Frei Otto’s Dancing Fountain in Cablenet form

The final code will be capable of handling structures like the one pictured above that consist of a mixture of axially loaded cable (tension only) and bar (tension and compression) elements. Our solver implements an iterative algorithm, so a solution that converges is not always guaranteed! We’ll be leaving the relative comfort and certainty of linear analysis behind!

This course picks up where Non-linear finite element analysis of 2D catenary & cable structures using Python. Make sure to cover that course first, before starting this course.

# Non-linear finite element analysis of 2D catenary & cable structures using Python

## Build an iterative solution toolbox to analyse structures that exhibit geometric non-linearity due to large deflections

Play Video about Nonlinear-finite-element-analysis-of-2D-catenary-&-cable-structures-in-Python | DegreeTutors.com
After completing this course, you’ll have built an iterative numerical solver for cable and truss structures that exhibit geometric non-linearity due to large deformations.

This course focuses on building the understanding and tooling necessary to analyse structures that undergo large deformations when loaded. These large changes to the geometry of a structure can alter the internal stress distribution within the structure. This is known as geometric non-linearity and requires a more sophisticated solution strategy.

This course will build on the understanding developed in previous DegreeTutors courses and in particular our linear 2D analysis course, The Direct Stiffness Method for Truss Analysis with Python. It is strongly recommended that you complete this course first before tackling non-linear analysis.

We’ll place particular emphasis on cable and catenary structures as these are classic examples of structures whose deformation under load can lead to geometric non-linearity. However, the code developed can be equally deployed to flexible truss structures.

The tools developed in this course are not meant as a replacement for commercial non-linear solvers (we’re not going to be rebuilding SAP2000! :) – the objective here is to build your understanding of the behaviour and the best way to do this is by implementing what you learn by building your own solver.

This course is divided into 9 sections:

• Introduction and course overview
• ‘Heavy’ cables – the linear solution
• Getting comfortable with non-linearity
• The non-linear stiffness matrix
• Building our 2D solver toolbox
• Visualising the results
• ‘Heavy’ cables – the non-linear solution
• Modelling initial geometry in Blender
• Mixing cables and bars in the same model

The final code will be capable of handling structures like the one pictured above that consist of a mixture of axially loaded cable (tension only) and bar (tension and compression) elements. Our solver implements an iterative algorithm, so a solution that converges is not always guaranteed! We’ll be leaving the relative comfort and certainty of linear analysis behind!

You DO NOT need to be a Python programming guru to take this course. If you’ve taken the prerequisite course – or even if you’re just familiar with basic programming ideas like functions, loops and variables that will be plenty to get you started.

# Multi-Degree of Freedom Dynamics, Modal Analysis and Seismic Response Simulation in Python

## Build the knowledge and tools to decode the dynamic response of real-world structures to real-world loads.

Play Video about Multi-Degree-of-Freedom-Dynamics,-Modal-Analysis-and-Seismic-Response-Simulation | DegreeTutors.com

By the time you complete this course, you’ll have a toolbox full of dynamic analysis tools and the knowledge and confidence to apply them to your own projects.

This course is for anyone who wants to understand multi-degree of freedom (MDoF) structural dynamics. The course is built around the theme of seismic analysis and determining the response of structures to earthquake-induced ground motion.

In reality, that’s just one form of excitation; when you complete the course you’ll be able to handle ground motion as well as any kind of directly applied dynamic loads such as wind loading or blast pressure waves for example.

This course is divided into 6 sections:

• Welcome and preliminaries
• Introduction to ground motion modelling
• Modelling Multi-DoF Dynamic Systems
• Modal Analysis and Decoupling the Equations of Motion
• Damping Orthogonality
• Bringing it all together: N-storey response to earthquake ground motion

The course culminates in you developing a code for analysing the response of multi-story structures to realistic ground motion. The final code will be capable of handling anything from a 2 to 200 storey shear building. More important than the code itself, is the fact that you’ll understand how and why every line of it works – meaning you’ll have no problem adapting it or further developing or customising it for your own use beyond this course.

You DO NOT need to be a Python programming guru to take this course. If you’ve taken any of the prerequisite courses – or even if you’re just familiar with basic programming ideas like functions, loops and variables that will be plenty to get you started.