5.7.3. Numerical Solution Techniques

Try these first

1. 1.

   Define what is meant by a Single Degree of Freedom (SDOF) system.

   Hint

   Think about how many coordinates define the motion.

2. 2.

   Name two time-stepping methods discussed in this section.

   Hint

   They're both key methods for incremental calculations.

3. 3.

   What are the two primary time-stepping methods used in SDOF analysis?

   • Euler and Leapfrog
   • Newmark-beta and Runge-Kutta
   • Trapezoidal and Simpson's

   Hint

   Recall the methods mentioned in the section.

4. 4.

   True or False: A Fourier Transform helps analyze only time-domain data.

   • True
   • False

   Hint

   Think about the data transformation context.

5. 5.

   Analyze the response of a cantilever beam with a mass at the top when subjected to a sinusoidal loading condition using the Newmark-beta method. Include initial conditions and parameter values.

   Hint

   Start with the beam's properties and define how the external sinusoidal force is applied.

6. 6.

   Compare the effectiveness of time-stepping methods versus frequency domain methods in predicting response during non-constant seismic events.

   Hint

   Consider situations where ground motion varies significantly over time.