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

Try these first

1. 1.

   What is Castigliano's theorem?

   Hint

   Think about what happens to energy when forces are applied.

2. 2.

   Define bending moment.

   Hint

   Consider what forces cause a beam to curve.

3. 3.

   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.

4. 4.

   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.

5. 5.

   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.

6. 6.

   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.