6. Reciprocal relation

Try these first

1. 1.

   What is an influence coefficient?

   Hint

   Think about how forces relate to displacements.

2. 2.

   State the reciprocal relation formula.

   Hint

   Recall the principle of symmetry in responses.

3. 3.

   What does an influence coefficient indicate?

   • A measure of stress
   • Relationship between force and displacement
   • Energy stored in a material

   Hint

   Focus on the concept of forces causing movements.

4. 4.

   True or False: The reciprocal relation states that k_ij = k_ji.

   • True
   • False

   Hint

   Recall the symmetry principle in mechanics.

5. 5.

   Consider a loaded beam at two points. If the first load is twice the second, derive the relationship between their influence coefficients using energy considerations.

   Hint

   Focus on energy storage and how it changes with different loads.

6. 6.

   In a structural analysis program, explain how the reciprocal relation could reduce computation time during the finite element analysis.

   Hint

   Think about leveraging existing data for new configurations.