Practice Deriving expression for energy stored in a beam in terms of internal contact force and moment which acts in the beam’s cross-section - 2 | 30. Castigliano’s First Theorem | Solid Mechanics
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Knowledge

2 - Deriving expression for energy stored in a beam in terms of internal contact force and moment which acts in the beam’s cross-section

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is Castigliano's theorem?

💡 Hint: Think about what happens to energy when forces are applied.

Question 2

Easy

Define bending moment.

💡 Hint: Consider what forces cause a beam to curve.

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 theorem relate to?

  • A. Stress Distribution
  • B. Energy and Displacement
  • C. Load Capacity

💡 Hint: Think about how energy changes when applying forces.

Question 2

True or False: The energy stored in a beam can be computed without knowing the exact deformation modes.

  • True
  • False

💡 Hint: Recall the types of deformation we discussed.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

A beam of length 10m is subjected to a uniformly distributed load resulting in a maximum deflection. Derive the expression for total energy stored considering axial, bending, and shear energy.

💡 Hint: Separate each type of energy and apply the appropriate formulas before summing up.

Question 2

Explain how the stored energy would differ if the beam were made of a more elastic material versus a more rigid material under the same load conditions.

💡 Hint: Consider the relationship between stress, strain, and material properties in your explanation.

Challenge and get performance evaluation