Practice Castigliano’s First Theorem - 1 | 30. Castigliano’s First Theorem | Solid Mechanics
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Knowledge

1 - Castigliano’s First Theorem

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define Castigliano's First Theorem.

💡 Hint: Think about how displacement connects to energy.

Question 2

Easy

What types of energies are associated with deformation in beams?

💡 Hint: Recall the acronym ABTS.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What does Castigliano's First Theorem relate?

  • Stress to strain
  • Energy to displacement
  • Force to load

💡 Hint: Think about the connection between energy and motion.

Question 2

True or False: The reciprocal relation states that displacement at one point determines the force at another.

  • True
  • False

💡 Hint: Focus on the concept of interconnected responses.

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Challenge Problems

Push your limits with challenges.

Question 1

A cantilever beam with a length L is subjected to a point load W at its free end. Derive the expression for the deflection at the free end using Castigliano's theorem.

💡 Hint: Start with the basic equations of bending and consider the contribution along the beam.

Question 2

Consider a composite beam with varying cross-sections. Use Castigliano’s theorem to find the displacement at a specific segment by first calculating energies in different sections.

💡 Hint: Breakdown helps understand how each section contributes to overall behavior.

Challenge and get performance evaluation