2 Reliability-Based Design and Analysis

Structural design has been moving toward a more rational and probability-based design procedure referred to as limit states design. Such a design procedure takes into account more information than deterministic methods in the design of structural components. This information includes uncertainties in the strength of various structural elements, in loads, and modeling errors in analysis procedures. Reliability-based design formats are more flexible and rational than working stress formats because they provide consistent levels of safety over various types of structures.

The development of a methodology for reliability-based design for piping requires the consideration of the following three components (Ang and Tang 1990, Ang 1984, Ellingwood 1980, Mansour et al. 1996, Ayyub and McCuen 2003): (1) loads, (2) structural strength, and (3) methods of reliability analysis. There are two primary approaches for reliability-based design: (1) direct reliability-based design and (2) load and resistance factor design (LRFD). The two approaches are shown in Figure 2-1. The three components of the methodology are also shown in this figure in the form of several blocks for each. In addition, the figure shows their logical sequence and interaction. The direct reliability-based design approach can include both Level 2 and∕or Level 3 reliability methods. Level 2 reliability methods are based on the moments (mean and variance) of random variables, whereas, Level 3 reliability methods use the complete probabilistic characteristics of the random variables. In some cases, Level 3 reliability analysis is not possible because of lack of complete information on the full probabilistic characteristics of the random variables. Also, computational difficulty in Level 3 methods sometimes discourages their uses. The LRFD approach is called a Level 1 reliability method. Level 1 reliability methods utilize partial safety factors (PSF) that are reliability based; but the methods do not require explicit use of the probabilistic description of the variables.

The two reliability-based design approaches start with the definition of a structural system or element. Then, the general dimensions and arrangements, structural member sizes, and details need to be assumed. The weight of the structure can then be estimated to ensure its conformance to a specified limit. Using assumed load effects, the two methods can then be used to design or analyze the structural system or element under question. The two approaches, beyond this stage, proceed in two different directions.