28.4.3.3. Numerical Analysis

Try these first

1. 1.

   What is a reliability index?

   Hint

   Think about safety ratings and how they gauge structural performance.

2. 2.

   Name one method for evaluating reliability indices.

   Hint

   It involves running random scenarios to see potential outcomes.

3. 3.

   What is the primary purpose of the reliability index?

   • To quantify risk
   • To measure utility
   • To indicate structural performance

   Hint

   Consider what the term 'reliability' implies in terms of safety.

4. 4.

   True or False: Monte Carlo simulations require an analytic expression for the performance function.

   • True
   • False

   Hint

   Think about the flexibility of simulation methods.

5. 5.

   A bridge has a mean capacity of 200 tons and a standard deviation of 30 tons. If the mean demand is 190 tons with a standard deviation of 20 tons, determine the reliability index using Taylor's series.

   Hint

   Remember to calculate the variances using the provided standard deviations.

6. 6.

   In a Monte Carlo simulation of a support beam with random variables related to its materials and loads, how would you assess the failure probability after 1,000 trials showing 50 failures?

   Hint

   Think of how the ratio of failures to total scenarios represents the risk.