7. Stress Transformations

Introduction

What is the stress state at a given point? It turns out that this question is not as straightforward as you imagine. The stress components that we have been calculating all throughout this course have been dependent on the coordinate system we defined. So what would happen if we changed the coordinate system? Enter the world of stress transformations. Luckily for us, there is a simple graphical method that we can employ to represent this complexity in the stress state at a given point. In this unit, we will learn about these transformations, the graphical method to determine them. Finally, we will see how these stress transformations become helpful in evaluating failure in a given material.

Learning Objectives

By the end of this unit, students should be able to…

• Explain the reasoning for why stress at a point depend on orientation
• Recall and apply the procedure to construct the Mohr Circle and determine stress states at differing orientations
• Explain the term principal stress and determine these values using the Mohr’s Circle
• Apply the Tresca failure criterion to a point with a known stress state