21.20.2 - Case 2: Soil Mechanics
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Practice Questions
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What is a stress tensor?
💡 Hint: Think about how forces are distributed at a point.
Define principal stresses.
💡 Hint: These are critical for structural safety.
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Interactive Quizzes
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What does a stress tensor represent?
💡 Hint: Focus on what happens inside the soil.
True or False: Principal stresses are always positive.
💡 Hint: Consider the nature of stresses in soil.
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Challenge Problems
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Given a stress tensor as \(\sigma = \begin{bmatrix} 10 & 5 \ 5 & 15 \end{bmatrix}\), find the principal stresses and directions.
💡 Hint: Don't forget to set up the determinant for the characteristic polynomial!
Consider a soil mass subjected to varying loads resulting in a stress tensor of \(\sigma = \begin{bmatrix} 20 & -10 \ -10 & 30 \end{bmatrix}\). Analyze how the principal stresses affect the design of an embankment.
💡 Hint: Think about what happens if stress surpasses soil yield levels!
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