# TUTORIALS

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

## 3D Truss Calculator – Quick Start Guide

Welcome to this quick start guide on how to use the 3D truss analysis toolbox. In this tutorial, weโll work through the solution of a sample 3D space frame (pin-jointed) structure. Weโll determine reaction forces, axial forces and nodal displacements. By the end of this tutorial, you’ll be comfortable using the toolbox to analyse your own structures. In the video accompanying this tutorial, weโll also use the Blender modelling template file provided to model and analyse a structure from scratch. Like the 2D toolbox, students in particular, should find it helpful as a quick and easy tool for generating structural response data.

## 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 loading. Our starting point will be to explore the concept of strain as it applies to circular bars and to derive an equation that relates the strain to the angle of twist in the bar. Next, weโll tie shear stress into the story and see how it relates to applied torque and torsional deformation. Finally, weโll bring everything together with some numerical examples to demonstrate how to deploy the equations weโve developed.

## 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 structures. In this tutorial, we’ll focus on applying the moment distribution method to beams. We’ll start by getting a clear understanding of the steps in the procedure before applying what we’ve learned to a more challenging worked example at the end.

## 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 underpins many elegant and versatile analysis procedures. We’ll focus here on how it can be applied to trusses. This tutorial will initially develop the underlying theory, starting with the concept of strain energy. This will make the jump to virtual work much easier to understand. We’ll bring it all together with a thorough worked example at the end.

## 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 an object are shown. Free body diagrams are a simple tool to help us identify all of the forces that influence an object or structure. Typically, one of the first steps in analysing a structure is to sketch out its free body diagram, identifying all of the forces that must be considered in the analysis.

## 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 called Macauley’s Method which greatly speeds up the calculation process. We’ll work our way through a couple of numerical examples before discussing how we can use the principle of superposition and tabulated formulae to speed up the process even further.

## 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, weโll start from the very beginning and discuss forces, moments or torques generated by forces and how to evaluate systems of forces and moments. Once you complete this tutorial and all of the worked examples, youโll be well prepared for the analysis of simple structures in later tutorials in the series.

## 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 the analysis and design of structures, a firm grounding in fundamental structural behaviour is essential. In this post, I want to provide a complete structural analysis guide – a roadmap for learning structural analysis from the beginning; what to study, in what order and why.

## 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 through the process of analysing a simple truss structure. By the end, you’ll be comfortable using the truss calculator to quickly analyse your own truss structures. Students, in particular, should find it helpful as a quick and easy tool to test manual solutions against.

## 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 additional or secondary moment is generated in a column due to the combination of axial load (P) and lateral sway, (Delta), of the column. This leads to non-linear structural behaviour and can result in lateral deflections far in excess of those arising from lateral loading alone. We’ll explore the phenomenon and write some code to help visualise the behaviour.

## 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 briefly considering what exactly a truss is – but we’ll very quickly move on to truss analysis and demonstrate the joint resolution method and method of sections with some worked examples.

## 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 finite element models models. Weโll apply this iterative approach by starting with a simple beam model and incrementally working towards a full 3D finite element model. Throughout this post weโll make use of finite element analysis codes developed in DegreeTutors courses.

## 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 the method works, how to implement it for truss analysis and you should understand the power and scalability of the technique. Once understood, the direct stiffness method opens the door to structural analysis of large scale complex structures.

## 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, dynamic loads occur with sufficient frequency that we need to understand how to assess their influence on a structure. Typical forms of dynamic loading can include loading due to earthquakes, wind, vehicle or pedestrian traffic or wave loading on coastal or offshore structures.

## 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 itโs probably the one structural analysis skill most students struggle with most. So in this post weโll give you a thorough introduction to shear forces, bending moments and how to draw shear and moment diagrams. By the end of this post youโll know a lot more about shear forces and moment moments then when you started.

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

In this tutorial, weโre going to work out exactly how to determine the plastic moment capacity of a cross-section. Weโll also explore the concept of moment redistribution with an illustrative example. By the end of this post youโll be able to calculate the plastic moment capacity of any cross-section and understand in detail how moment redistribution occurs in a structure and ultimately how collapse can occur as a result of hinge formation.

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

So why is plastic behaviour so important to understand? Itโs probably fair to say that most of our engineering analysis assumes linearly elastic behaviour. But in reality, if we limit our designs to purely elastic behaviour, weโre leaving a lot of structural capacity untapped. Structures very often have more load carrying capacity than a linearly elastic analysis suggests. In this post weโll explore this reserve capacity.

## Structural Analysis and Stability – Asymmetrically Propped Structures (2/2)

In part two of this tutorial series weโll consider how to analyse the lateral stability of a multi-storey structure with an asymmetrical arrangement of stabilising elements. Asymmetrically propped structures undergo twisting or rotation about the centre of stiffness in addition to direct lateral translation. We will consider how to determine the additional forces induced by this twisting. Finally weโll compare our hand analysis results to a simple finite element analysis model.

## Structural Analysis and Stability – Symmetrical Structures (1/2)

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 forces due to groundwater (acting against basement walls for example) or inertia forces due to ground motion (earthquakes). In this, the first of a two-part series on structural stability, we will introduce common lateral stability schemes before diving into some numerical examples in this and the next post.

## Column Buckling: Realistic Buckling Behaviour (3/3)

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 to eccentric axial load and columns with an initial deformation, i.e. columns that don’t start out straight.ย It’s important to recognise that for a column with these characteristics, we do not observe the strict mathematical behaviour predicted for perfectly loaded perfectly straight columns