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

1 - Castigliano’s First Theorem

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Learning

Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

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Reference links

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