32.3.2. Forced Vibration Under Ground Motion

Try these first

1. 1.

   Define Duhamel's integral in your own words.

   Hint

   Think about how it relates to the system's response.

2. 2.

   What are initial conditions?

   Hint

   Consider what happens at the first moment of an event.

3. 3.

   What is the main purpose of Duhamel's integral in earthquake engineering?

   • To calculate static loads
   • To evaluate dynamic responses
   • To determine material strength

   Hint

   Think about its application in response calculations.

4. 4.

   True or False: Initial conditions do not significantly affect the analysis of structures under seismic loads.

   • True
   • False

   Hint

   Consider their fundamental role in system behavior.

5. 5.

   How would you use Duhamel's integral to analyze a structure subjected to a non-uniform earthquake load over time? Provide a step-by-step approach.

   Hint

   Break down each step based on structural response components.

6. 6.

   Discuss a real-life scenario where poor initial conditions led to structural failure during an earthquake, outlining the lessons learned.

   Hint

   Think about historical examples and lessons from engineering.