10.6. Numerical Evaluation of Duhamel Integral

Try these first

1. 1.

   What is the purpose of numerical methods in evaluating Duhamel's Integral?

   Hint

   Think about the nature of dynamic loads like those from earthquakes.

2. 2.

   Name one numerical technique used for evaluating integrals.

   Hint

   Consider how you could approximate areas under a curve.

3. 3.

   What is the primary reason for using numerical methods in evaluating Duhamel's Integral?

   • To simplify the equations
   • To approximate the integral
   • To provide exact solutions

   Hint

   Think about how real-world data impacts calculations.

4. 4.

   True or False: Simpson's Rule is less accurate than the Trapezoidal Rule in estimating areas under a curve.

   • True
   • False

   Hint

   Consider the shapes used in both rules when forming your answer.

5. 5.

   Given a sample digital ground motion signal, evaluate the displacement response using Newmark's method. Outline your calculation steps.

   Hint

   Remember to consider how each time step contributes cumulatively.

6. 6.

   You have been provided with ground motion data before an earthquake event; compute the integral using Simpson's Rule to find how far a building will sway.

   Hint

   Reflect on how intervals affect your approximation!