Welcome to section 3. In this section, we’re going to introduce the First Order Second Moment Method for evaluating the safety index. This is the first of the two methods we’ll cover in this course.

Focusing initially on the First Order Second Moment Method will allow us to get a good understanding of the core building blocks of safety index calculation. This will be the foundation we need before tackling the First Order Reliability Method in the next section.

Both methods for calculating the safety index are built upon the Taylor Series Expansion. This is a technique that we can use to approximate a function with a polynomial series. Most of us have covered this mathematical technique at some point in the past. However, since it’s central to our reliability index calculations, we’ll start section 3 by reviewing the fundamentals.

From here, we’ll derive the core equations used to calculate the safety index and then bring the First Order Second Moment calculation procedure to life with some worked examples.

We’ll finish this section by highlighting one of the big limitations of the first order second moment - the lack of invariance problem. The lack of invariance problem presents itself when we have a non-linear limit state function. As such, it’s a significant limitation to our analysis capabilities at this stage in the course! Overcoming this is the motivation for the First Order Reliability Method that we’ll cover in the fourth and final section of the course.