5. Example 2

Try these first

1. 1.

   What theorem helps us calculate displacements in structures?

   Hint

   Think about energy methods.

2. 2.

   Define a transverse load.

   Hint

   Think of how the force orientation relates to the beam.

3. 3.

   What does Castigliano's theorem allow you to find?

   • Displacements
   • Forces
   • Both

   Hint

   Consider what information you gain from analyzing energy in a structure.

4. 4.

   True or False: A roller support can exert moments on a structure.

   • True
   • False

   Hint

   Think about how different support types interact with loads.

5. 5.

   A cantilever beam of length 4 m with a load of 1000 N applied at 2 m from the fixed end. Determine the reactions and the deflection at the free end using energy methods.

   Hint

   Break down the structure into sections and analyze each using equilibrium.

6. 6.

   Consider a beam subjected to varying loads along its length. How would you modify the approach of Castigliano’s theorem?

   Hint

   Think about how distributed loads change the energy calculation.