3. Castigliano’s Theorems

Try these first

1. 1.

   What is the relationship described by Castigliano's First Theorem?

   Hint

   Think about how energy changes when forces are applied.

2. 2.

   Define strain energy in your own words.

   Hint

   Consider what happens when a material is stretched or compressed.

3. 3.

   What does Castigliano’s First Theorem calculate?

   • Deflection
   • Strain Energy
   • Bending Moment

   Hint

   Focus on what the theorem is specifically concerned with.

4. 4.

   True or False: Fictitious forces are used to make calculations simpler in redundant structures.

   • True
   • False

   Hint

   Remember how these forces aid in simplifying the analysis.

5. 5.

   Using Castigliano's First Theorem, calculate deflection for a cantilever beam with a point load at its free end. Assume L = 5 m, E = 200 GPa, I = 5 x 10⁻⁶ m⁴.

   Hint

   Ensure to convert units appropriately when substituting.

6. 6.

   Consider a complex truss with multiple members subjected to external loads. Apply Castigliano's Second Theorem and outline the steps to compute deflections without solving directly using basic equilibrium.

   Hint

   Breaking the problem into smaller parts will make it easier.