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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Practice Questions
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What is Castigliano's theorem?
💡 Hint: Think about what happens to energy when forces are applied.
Define bending moment.
💡 Hint: Consider what forces cause a beam to curve.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does Castigliano’s theorem relate to?
💡 Hint: Think about how energy changes when applying forces.
True or False: The energy stored in a beam can be computed without knowing the exact deformation modes.
💡 Hint: Recall the types of deformation we discussed.
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Challenge Problems
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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.
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.
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