Practice Verification of reciprocal relation - 3 | 30. Castigliano’s First Theorem | Solid Mechanics
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3 - Verification of reciprocal relation

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What does Castigliano’s theorem state?

💡 Hint: Look for the definitions provided in the lecture.

Question 2

Easy

Explain the concept of the reciprocal relation in your own words.

💡 Hint: Think about how one effect leads to another in structural mechanics.

Practice 1 more question and get performance evaluation

Interactive Quizzes

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

Question 1

What does the reciprocal relation describe?

  • The relation between two loads on a beam at different points.
  • The correlation between moment and rotation at a single point.
  • How one beam load influences the rotation at a different point.

💡 Hint: Consider what happens when forces are applied.

Question 2

True or False: Castigliano’s theorem can be applied to nonlinear materials.

  • True
  • False

💡 Hint: Think about the assumptions made in elastic analysis.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Consider a beam with a known force applied at one end. Calculate the rotation at the opposite end using the reciprocal relation and verify it against a direct calculation method.

💡 Hint: Check your results against the influence coefficients.

Question 2

Demonstrate the reciprocal relation by calculating the impact of a moment applied at the free end of a clamped beam and compare it to the effect of a force applied elsewhere.

💡 Hint: Use the previously derived moments and forces as reference points.

Challenge and get performance evaluation