7. Maxwell-Betti-Rayleigh reciprocal theorem

Try these first

1. 1.

   What does the Maxwell-Betti-Rayleigh theorem state?

   Hint

   Think about the relationship between work and forces.

2. 2.

   Define influence coefficient.

   Hint

   It helps explain how much displacement results from a force.

3. 3.

   What does the Maxwell-Betti theorem state?

   • Forces relate without displacement
   • Work done in one situation equals another
   • Displacements can never relate

   Hint

   Think about how forces affect displacements in different scenarios.

4. 4.

   True or False: The influence coefficient only applies to forces and not to moments.

   • True
   • False

   Hint

   Consider how moments would interact in mechanics.

5. 5.

   Use the Maxwell-Betti theorem to find the displacement on a beam subjected to two different loads in sequential order. Define each step in the calculation.

   Hint

   Think through how each load affects the beam and compare the displacements.

6. 6.

   Analyze a rotating disk subjected to moments at different points and apply the reciprocal theorem to show its effect on angle rotated.

   Hint

   Utilize your understanding of generalized forces in this context.