1.1 - Representation of gradient
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Practice Questions
Test your understanding with targeted questions
What is the formula for the gradient in cylindrical coordinates?
💡 Hint: Think of how each term corresponds to a direction.
Define radial strain.
💡 Hint: It's related to changes in distance from the center in a cylindrical structure.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the primary purpose of a gradient?
💡 Hint: Think about how the shape of a hill indicates steepness.
True or False: The displacement vector in cylindrical coordinates can have three unique components.
💡 Hint: Recall the terms used in cylindrical representation.
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Challenge Problems
Push your limits with advanced challenges
If a hollow cylinder experiences a radial displacement of 5 cm and a hoop displacement of 3 cm, calculate the strains ε_rr and ε_θθ assuming initial lengths were 50 cm.
💡 Hint: Use the formula for strain: ε = ΔL / L₀.
A cylindrical structure shows a non-uniform displacement due to varying internal pressure. Describe how this affects the overall strain calculations and what assumptions might need adjusting.
💡 Hint: Think about how pressure changes can result in different strain responses.
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