Solid Mechanics | 10. Mohr’s Circle Recap by Abraham | Learn Smarter
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10. Mohr’s Circle Recap

The chapter delves into Mohr's circle, discussing its application in determining principal stresses and shear stress in various planes. It also covers stress invariants, octahedral stress components, and the decomposition of the stress tensor into hydrostatic and deviatoric parts. Key examples illustrate the graphical methods of analysis and the limitations associated with Mohr's circle.

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Sections

  • 1

    Mohr’s Circle Recap

    This section recaps the concepts surrounding Mohr’s Circle, its significance in stress analysis, and key equations used to determine principal stresses.

    Learning Practice

  • 1.1

    Planes Of Principal Stresses In Mohr’s Circle

    This section discusses how to determine the orientation of principal stress planes and their associated stresses using Mohr's Circle.

    Learning Practice

  • 1.2

    An Example

    This section explores an example using Mohr's circle to determine principal stress and shear stress components from a given stress matrix.

    Learning Practice

  • 2

    Mohr’s Stress Plane

    This section discusses Mohr's stress plane, defining the concept and illustrating it with the behavior of stress tensors in various conditions.

    Learning Practice

  • 2.1

    Special Case I

    This section discusses special cases of the Mohr’s stress plane when principal stress components become equal, leading to simplified stress analysis.

    Learning Practice

  • 2.2

    Special Case Ii

    Special Case II discusses scenarios where all principal stress components are equal, leading to a hydrostatic state of stress.

    Learning Practice

  • 3

    Stress Invariants

    This section delves into stress invariants, demonstrating how certain stress quantities remain unchanged under coordinate transformations.

    Learning Practice

  • 4

    Octahedral Stress Components

    This section introduces octahedral stress components, detailing their definitions, calculations, and significance in stress analysis.

    Learning Practice

  • 5

    Hydrostatic And Deviatoric Parts In Stress Tensor

    This section explains how to decompose the stress tensor into hydrostatic and deviatoric components, detailing the significance and properties of each part.

    Learning Practice

References

ch10.pdf

Class Notes

Memorization

What we have learnt

  • Mohr's circle is a graphica...
  • Stress invariants are quant...
  • The stress tensor can be de...

Final Test

Revision Tests