Stress Transformations: Further Reading and Problems

Course subject(s) 7. Stress Transformations

Summary of Key Equations

Stress transformations are a result of simple equilibrium; however, they can be represented with the equation of a circle known as Mohr’s circle. This is given by the equation:

\[(\sigma_{x'}-\sigma_{ave})^2 + \tau_{x'y'}^2=R^2 \]

Where the stresses in the x’-y’ directions represent the rotated coordinate frame, sigma_ave is the average normal stress in the original x-y coordinate frame. R is determined through triginometry using the two points on the Mohr Circle defined by the known stress state in the x-y coordinate frame.

One of the main applications of stress transformations relates to the application of failure criteria. Althoug numerous failure criteria exist, for this course we will focus only on one: Tresca’s Yield Criterion, which is given by

\[\tau_{max}=\frac{\sigma_{yield}}{2} \]

Further Reading and Problems

7.1 What is a Stress Transformation
Relevant textbook reading: Ch. 9.1

7.2 Mohr’s Circle
Relevant textbook reading: Ch. 9.4
Practice problems: 9.44-9.46, 9.67, 9.71, 9.73

7.3 Failure Criteria
Relevant textbook reading: Ch. 10.7
Practice problems: 10.71, 10.85

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