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## Tutorials

Tutorials to guide you through engineering analysis and design from the ground up

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Machine Learning in Civil Engineering - Advanced Surrogate Models with Graph Neural Networks

In this tutorial, we delve deeper into the world of machine learning and use graph neural networks to analyse the behaviour of 2D frame structures. Our goal is to build a machine learning pipeline to ...more

Ehsan Es'haghi

Machine Learning in Civil Engineering - Surrogate Models

In this tutorial, we continue to acquaint ourselves with the basics of machine learning by learning how to design specific function approximators called surrogate models. Traditional numerical analysi...more

Ehsan Es'haghi

Machine Learning in Civil Engineering - Sensitivity Analysis

In this tutorial, we'll dive into the world of machine learning and structural optimisation by focusing on sensitivity analysis as our first topic. We'll start by learning how to define a simple optim...more

Ehsan Es'haghi

Gridshell form finding and analysis with Blender and OpenSeesPy

In part 2 of our gridshell analysis series, we'll build a workflow that allows us to digitally re-create the classic hanging chain form finding models used to identify the optimal shapes of gridshell ...more

Dr Seán Carroll

A Structural Modelling and Analysis Addon for Blender?

Have you ever thought that a structural modelling and analysis addon for Blender would be a good idea? Yeah...me too! Blender is a fantastic all round 3D modelling tool. Although mainly used by 3D art...more

Dr Seán Carroll

An overview of the CFD simulation process in OpenFOAM

In this tutorial, we'll be taking a practical look at the CFD simulation process in OpenFOAM. We'll be using a simple case study to demonstrate the key steps involved in a typical CFD simulation. The ...more

Dr Sumit Verma

Fundamentals of Computational Fluid Dynamics

Computational Fluid Dynamics (CFD) is a branch of fluid mechanics, which primarily deals with solving the governing partial differential equations of fluid flow using numerical techniques. In civil a...more

Dr Sumit Verma

Plate Girder Design to Eurocode 3

In this tutorial, we cover the design of steel plate girders to Eurocode 3. We’ll review exactly what a plate girder is, how it differs from a hot rolled I-section and under what circumstances you mig...more

Callum Wilson

Using VIKTOR to Build a Shareable Truss Calculator App - Project Overview

In this article, we’ll discuss how you can build a user-friendly and shareable, truss analysis app that can be easily shared and used in the browser. This means the end user doesn’t need to download o...more

Dr Seán Carroll

Parametric Graphic Statics with GeoGebra

We're back with more Graphic Statics - except this time, we're taking our analysis in the digital world! In this tutorial, we introduce a free online programme called GeoGebra. With GeoGebra, we have ...more

Prof Edmond Saliklis

A primer on the form and behaviour of gridshell structures

In this article, we’ll begin our exploration of gridshell structures. Our overall aim is to build up step-by-step, an appreciation for these elegant structures and their contribution to the built envi...more

Dr Seán Carroll

Steel Truss Design to Eurocode 3

This is the third part of our steel design tutorial series. This time, we’re focussing on the design of steel trusses - one of the most ubiquitous structural forms in the built environment. Our steel ...more

Callum Wilson

Getting Started with Graphic Statics

Graphical structural analysis or graphic statics is a powerful tool for understanding the load flow in a structure. This tutorial will introduce you to the basic concepts and techniques of graphical s...more

Prof Edmond Saliklis

Steel Column Design using Eurocode 3 - A Complete Guide

This is the second tutorial in our series focusing on structural steel design to Eurocode 3. This time, we'll be learning about steel column design. Just like part 1, this is a long and detailed tutor...more

Callum Wilson

Build a Parametric Continuous Beam Calculator using OpenSeesPy

In this short tutorial, we’ll build a continuous beam analysis script using OpenSessPy. Multi-span continuous beams are so common, that it makes sense to have a script in our toolbox to very quickly g...more

Dr Seán Carroll

Steel Beam Design - A Step-by-Step Guide using Eurocode 3

This is the first in a series of tutorials covering the design of structural steel elements to Eurocode 3. In this first tutorial, we will focus on steel beam design. This is a long and in-depth tutor...more

Callum Wilson

The Road to Becoming a Graduate Structural Engineer

This is a short recap of some of the twists and turns on my journey to becoming a Graduate Structural Engineer - if you’re somewhere along your own journey, hopefully, my story will give you some enco...more

Thomas Thompson

A Python Programming Roadmap for Structural Engineers

EngineeringSkills.com has grown over the years and now has a huge number of resources for engineers interested in Python. This tutorial provides a convenient entry point and roadmap to these resources...more

Dr Seán Carroll

Building a Parametric Frame Analysis Pipeline with OpenSeesPy and OpsVis

In this second tutorial in our series focusing on OpenSeesPy, we’ll build a pipeline for the elastic analysis of a 2D portal frame structure using OpenSeesPy. Along the way, we’ll parameterise our cod...more

Dr Seán Carroll

An Introduction to OpenSees and OpenSeesPy for 2D Truss Analysis

In this tutorial, we’ll take a first look at OpenSeesPy, a Python library for performing finite element analysis based on the OpenSees framework. By the end of this tutorial, you’ll be able to perform...more

Dr Seán Carroll

DegreeTutors is now EngineeringSkills

This is the new version of DegreeTutors.com and combines that site, the DegreeTutors Podia site and Labs, all into one platform. I've fully custom-coded and developed this platform to be the best plac...more

Dr Seán Carroll

Arch Analysis – How to Analyse Determinate and Indeterminate Arches

Arches are one of the most efficient and elegant structural forms. Their efficiency has seen them selected throughout history as the go-to form for spanning large distances. In this tutorial, we’ll ex...more

Callum Wilson

Influence Lines - A Complete Introduction for Civil and Structural Engineers

In this tutorial on influence lines, we will explore influence lines and the techniques that can be used to construct influence line diagrams for determinate and indeterminate beam structures. By the ...more

Callum Wilson

Plastic Analysis of Frames – A Complete Guide – Part 2

In the second part of this series on plastic collapse analysis, we explore how what we learned in part one can be applied the frames. Plastic analysis methods are particularly useful in the analysis o...more

Callum Wilson

Plastic Analysis and Plastic Collapse – A Complete Guide – Part 1

Often in structural analysis, linear-elastic analysis is used, predicting failure when structural members reach their yield stress. This method, while effective, ignores the plasticity that some struc...more

Callum Wilson

Calculating and Interpreting the Second Moment of Area

This tutorial focussed on the second moment of area, also known as the moment of inertia. By the end of this tutorial, you should be comfortable explaining what the second moment of area is, why it's ...more

Callum Wilson

How moment redistribution leads to more efficient designs

In this tutorial, we’ll discuss moment redistribution in reinforced concrete and how we can use it to our advantage to achieve more efficient designs. When designing any structural element, our first ...more

Dr Seán Carroll

Reinforced Concrete Fundamentals - Analysis and Design of Steel Reinforcement

In this tutorial, we’ll introduce the role of steel reinforcement in reinforced concrete design. We’ll see that steel plays a critical role in developing an internal moment of resistance and compensat...more

Dr Seán Carroll

How I Coded an Analytical Beam Calculator

In this post, guest author Vittorio Lora talks us through how he developed the idea for and ultimately built Beamsolver.com. A structural engineer by training, Vittorio has pivoted in his career to fo...more

Vittorio Lora

An Introduction to Concrete and its Strengths and Weaknesses

Concrete is one of the most important and ubiquitous materials in the construction industry globally. Twice as much concrete is used (by weight) as steel, wood, plastics and aluminium combined. Its gl...more

Dr Seán Carroll

3D Truss Calculator – Quick Start Guide

Welcome to this quick start guide on how to use the 3D truss analysis toolbox. In this tutorial, we’ll work through the solution of a sample 3D space frame (pin-jointed) structure. We’ll determine rea...more

Dr Seán Carroll

An Introduction to Uniform Torsion in Cylindrical Shafts

In this tutorial, we introduce torsion. This is simply a bending moment applied about the longitudinal axis. Torsion will cause twisting about the longitudinal axis and is a very common form of loadin...more

Dr Seán Carroll

How to Analyse Indeterminate Beams using the Moment Distribution Method

In this tutorial we'll explore the moment distribution method. This is an excellent technique for quickly determining the shear force and bending moment diagrams for indeterminate beam and frame struc...more

Dr Seán Carroll

How to Apply the Virtual Work Method to Trusses

In this tutorial, you'll learn how to use the virtual work method to analyse trusses and calculate truss deflections. The virtual work method is based upon the Principle of Virtual Work which underpin...more

Dr Seán Carroll

How to Calculate Reactions using Free Body Diagrams

In this tutorial, we'll cover free body diagrams and how to use them to evaluate the forces acting on a structure in equilibrium. A free body diagram is a diagram in which only the forces imposed on a...more

Dr Seán Carroll

How to Calculate Beam Deflection

In this tutorial, you'll learn how to calculate beam deflection from first principles using the differential equation of the deflection curve. We'll cover several calculation techniques, including one...more

Dr Seán Carroll

Forces, Moment of a Force and Force Systems

Welcome to the Fundamental Engineering Mechanics tutorial series. This is part one in a multi-part series aimed at anyone just starting out in the study of engineering. In this tutorial, we’ll start f...more

Dr Seán Carroll

A Complete Guide to Learning Structural Analysis

Learning how to use mathematics and mechanics to analyse structural behaviour is among the most challenging topics student engineers struggle with. Yet, for an engineer, particularly one involved in t...more

Dr Seán Carroll

Free Truss Calculator – Quick Start Guide

This is a quick start guide for our free online truss calculator. Follow this short text tutorial or watch the Getting Started video to quickly orientate yourself with this handy free tool. We'll walk...more

Dr Seán Carroll

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 integr...more

Dr Seán Carroll

P-Delta Analysis and Geometric Non-linearity

In this tutorial, we'll explore the P-Delta effect; a form of non-linear behaviour that can lead to large magnitude sway deflections in columns. Put simply, P-Delta describes the phenomenon whereby an...more

Dr Seán Carroll

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 t...more

Dr Seán Carroll

Shear and Moment Diagrams – An Ultimate Guide

Shear force and bending moment diagrams tell us about the underlying state of stress in the structure. Determining shear and moment diagrams is an essential skill for any engineer. Unfortunately it’s ...more

Dr Seán Carroll

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 dia...more

Dr Seán Carroll

Building a Mohr’s Circle Calculator for Stress Analysis in Python

In this Python project we're going to build a Mohr's Circle calculator. By the end of this project, you will have built your own stress analysis Python code. Along the way we'll cover all of the funda...more

Dr Seán Carroll

Truss Analysis using the Method of Joints and Method of Sections

In this tutorial we're going to focus on trusses, also known as pin-jointed structures. We'll briefly discuss their key features and methods of analysis. We're going to start at the very beginning by ...more

Dr Seán Carroll

Finite Element Analysis and Structural Behaviour Modelling Case Study

In this post we will use the Tintagel footbridge as a case study to explore structural behaviour and show how we can build up an understanding of the structure through analysis of increasingly refined...more

Dr Seán Carroll

Truss Analysis using the Direct Stiffness Method

In this tutorial we examine the Direct Stiffness Method and work our way through a detailed truss analysis. By the end of this complete introduction, you should understand the basic ideas behind why t...more

Dr Seán Carroll

Understanding Structural Dynamics and Inertia

By the end of this post you'll understand when and why a dynamic analysis is performed instead of a (usually more straightforward) static analysis. Although we typically encounter static loading, dyna...more

Dr Seán Carroll

The Stress-Strain Curve & Plastic Hinges in Beams (1/2)

So why is plastic behaviour so important to understand? It’s probably fair to say that most of our engineering analysis assumes linearly elastic behaviour. But in reality, if we limit our designs to p...more

Dr Seán Carroll

Yielding, Plastic Deformation and Moment Redistribution in Beams (2/2)

In this tutorial, we’re going to work out exactly how to determine the plastic moment capacity of a cross-section. We’ll also explore the concept of moment redistribution with an illustrative example....more

Dr Seán Carroll

Structural Analysis and Stability – Asymmetrically Propped Structures

In part two of this tutorial series we’ll consider how to analyse the lateral stability of a multi-storey structure with an asymmetrical arrangement of stabilising elements. Asymmetrically propped str...more

Dr Seán Carroll

Structural Analysis and Stability – Symmetrical Structures

All structures typically experience some form of lateral loading during their design life. Typical sources of lateral loading include forces due to wind blowing against the structure, hydrostatic forc...more

Dr Seán Carroll

Column Buckling - Realistic Buckling Behaviour

In this final post in this series on Column Buckling, we'll look at more realistic buckling behaviour you're likely to observe in reality. In particular we'll explore the behaviour of columns subject ...more

Dr Seán Carroll

Column Buckling Equations

In this post we'll start to consider more realistic column structures. In particular we'll determine an expression for the critical load for an axially loaded column with pinned ends. Then we'll explo...more

Dr Seán Carroll

Column Buckling and Stability

Long slender structural elements under the action of an axial load may fail due to buckling rather than direct compression. Buckling failure occurs when axial load induces a lateral deflection leading...more

Dr Seán Carroll

Structural Analysis Case Study

Structural analysis is the process of using mathematical and mechanical principles to determine the magnitude of internal forces in a structure. One of the main roles of a civil or structural engineer...more

Dr Seán Carroll

What is a Truss?

A truss is a structure that consists of a collection of elements connected at pin joints or nodes. In theory, the pin joints provide no rotational resistance and behave as hinges. In practice this is ...more

Dr Seán Carroll