Stress and Strain Tensor — Lesson 1

This lesson covers the concept of stress calculation in components. It delves into the calculation of stresses in components like slides, bars, and shafts subjected to actual, bending, and torsional loading. The lesson further explains the quantification of internal forces and strains at a point on the body. It introduces the concept of stress or traction vector and explains how to calculate the intensity of these forces. The lesson also discusses the concept of a 3D stress tensor and its components. It provides an illustrative example of how to show stresses on an element around a given point.

Video Highlights

01:59 - Discussion on quantifying stresses and strain at a point
05:11 - Understanding the concept of splitting a body into two parts
12:15 - Explanation of how forces act on different parts of a body
23:29 - Understanding the concept of 2D stress tensor
40:51 - Explanation of the sign convention for stresses
49:07 - Understanding the concept of positive shear deformation

Key Takeaways

- Stress calculation in three dimensions involves quantifying internal forces and strains at a point on a body.
- A stress tensor in three dimensions is symmetric, meaning the shear stresses on two perpendicular planes are equal.
- Positive shear deformation results in a reduction in the original angle between two planes.