# STRESS ANALYSIS

## Tools and techniques for modelling and understanding the underlying state of stress in structures ## Fundamentals of 2D Stress Analysis and Mohr’s Circle

### Perform 2D stress analysis and use Mohr’s Circle to visualise the complete stress field. After completing this course…

• You will understand the concepts of plane stress, the 2D stress field and how to use transformation equations to explore the state of stress at a point.
• You will be able to determine principal planes, principal stresses and maximum positive an negative shear stresses.
• You will be able use Mohr’s Circle of Stress to visualise the complete stress field at a point using Python and hand sketches.

## Finite Element Analysis of Continuum Structures in Python

### Use the Isoparametric Finite Element Method to build an analysis tool for 2D structures in Python. After completing this course…

• You will have the tools to analyse continuum structures using your own Isoparameteric Finite element Python code, developed from the ground up.
• You will understand how the plane stress and plane strain approximations allow us to analyse 3D structures accurately with 2D planar models.
• You will be able to use open source tools to generate structural models and mesh data that can be analysed with your FE code.

## TUTORIALS ### 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, we’ll tie shear stress into the story and see how it relates to applied torque and torsional deformation. Finally, we’ll bring everything together with some numerical examples to demonstrate how to deploy the equations we’ve developed. ### 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 fundamental topics that lead up to Mohr’s circle of stress. You will learn about how we use the 2D stress element to represent the state of stress at a point, the purpose of stress transformation equations, principal stresses and principal planes planes and of course Mohr’s circle! ### 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. By the end of this post you’ll 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? 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 purely elastic behaviour, we’re leaving a lot of structural capacity untapped. Structures very often have more load carrying capacity than a linearly elastic analysis suggests. In this post we’ll explore this reserve capacity.

# Finite Element Analysis of Continuum Structures in Python

## Use the Isoparametric Finite Element Method to build an analysis tool for 2D structures in Python.

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In this course we’re going to build a full Isoparametric Finite Element solver. This unlocks our ability to model and analyse any 2D structural form.

When we combine our finite element analysis solver with knowledge of the theory of plane stress and plane strain, this course will equip you with the ability to model 3D structures using 2D finite element models. When you complete this course you will have built your own 2D Finite Element solver, but more importantly, you’ll understand exactly how it works and what every single line of code does!

Once complete, you can use your solver to show:

• deflected shapes
• normal stress and strain fields
• shear stresses and strains fields
• principal stress magnitudes fields
• principal plane orientations
• von Mises stress fields

We’ll build in the ability to simulate the influence of point load forces, distributed forces and body or self-weight forces. Once you complete this course you’ll have the knowledge, experience and confidence to extend your solver and add the new features that matter to you.

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. 