3. Verification of reciprocal relation

Try these first

1. 1.

   What does Castigliano’s theorem state?

   Hint

   Look for the definitions provided in the lecture.

2. 2.

   Explain the concept of the reciprocal relation in your own words.

   Hint

   Think about how one effect leads to another in structural mechanics.

3. 3.

   What does the reciprocal relation describe?

   • The relation between two loads on a beam at different points.
   • The correlation between moment and rotation at a single point.
   • How one beam load influences the rotation at a different point.

   Hint

   Consider what happens when forces are applied.

4. 4.

   True or False: Castigliano’s theorem can be applied to nonlinear materials.

   • True
   • False

   Hint

   Think about the assumptions made in elastic analysis.

5. 5.

   Consider a beam with a known force applied at one end. Calculate the rotation at the opposite end using the reciprocal relation and verify it against a direct calculation method.

   Hint

   Check your results against the influence coefficients.

6. 6.

   Demonstrate the reciprocal relation by calculating the impact of a moment applied at the free end of a clamped beam and compare it to the effect of a force applied elsewhere.

   Hint

   Use the previously derived moments and forces as reference points.