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.
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.
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!
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.
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.