5. Degrees of Freedom and SDOF

Try these first

1. 1.

   Define Degrees of Freedom in structural engineering.

   Hint

   Consider how many different ways a structure can move.

2. 2.

   What is a Single-Degree-of-Freedom (SDOF) system?

   Hint

   Think about how we can summarize complex movements.

3. 3.

   What does DOF stand for?

   • Degrees of Freedom
   • Degree of Function
   • Dynamic Operating Factor

   Hint

   Think about the movement possibilities in structural analysis.

4. 4.

   True or False: All structures can be accurately modeled as SDOF systems.

   • True
   • False

   Hint

   Consider the limitations of simplifications.

5. 5.

   Given a cantilever beam with a mass at the free end, derive the equation of motion considering both damping and ground acceleration.

   Hint

   Focus on identifying each term’s physical meaning.

6. 6.

   Analyze a multi-story frame with 10 floors to determine feasible moments of inertia to justify SDOF vs. MDOF models.

   Hint

   Think about the implications of inter-story drift and higher mode coupling.