Lecture 20: Converting to standard normal space | Uncertainty, Risk and Reliability Part 1 - Probabilistic Modelling of Structural Failure | EngineeringSkills.com

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Section 1

Course Introduction

1. Welcome and course overview

03:36 (Preview)

2. The evolution of engineered construction and our understanding of it

Section 2

Safety and Reliability Fundamentals

3. Section overview - safety and reliability fundamentals

01:18 (Preview)

4. Modes of failure

5. Sources of uncertainty

6. How safe is safe enough?

7. Safety factors and partial safety factors - a semi-probabilistic approach

8. A probabilistic approach - the basic idea

9. Evaluating and visualising probability of failure in Python

Section 3

The First Order Second Moment Method

10. Section overview - first order second moment method

01:25 (Preview)

11. Understanding the Taylor Series expansion

12. Taylor Series - expanding to more variables

13. The first order second moment method

14. Deriving the safety index

15. Example 1 - FOSM

16. Example 2 - FOSM

17. The lack of invariance problem

Section 4

The First Order Reliability Method

18. Section overview - first order reliability method

01:40 (Preview)

19. A strategy for non-linear limit state functions

20. Converting to standard normal space

21. Iterative algorithm to estimate the reliability index

22. Example 3 - FORM

23. Targeting a specific safety index

24. Example 4 - FORM

25. Dealing with non-normally distributed variables

26. Implementing the Normal Tail Approximation

27. Example 5 - FORM

28. FORM code refactor

29. Example 6 - FORM for reinforced concrete beam

30. Challenges estimating strength and loading variables

31. Intermission - part 1 recap and what next?

20. Converting to standard normal space

The First Order Reliability Method

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Uncertainty, Risk and Reliability Part 1 - Probabilistic Modelling of Structural Failure

Uncover the role uncertainty plays in structural behaviour with the First Order Reliability Method

After completing this course...

You will understand how the partial factor methodology captures uncertainty and the limitations inherent in this approach.
You will understand how limit state functions can be developed to calculate the safety or reliability index.
You will understand how to apply both the First Order Second Moment method and the First Order Reliability method of reliability analysis.
You will have developed tools to efficiently apply these analysis techniques using Python.

Next Lesson

21. Iterative algorithm to estimate the reliability index