Lecture 17: The lack of invariance problem | 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?

17. The lack of invariance problem

The First Order Second Moment 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

18. Section overview - first order reliability method