S - Kam Ng PhD Dissertation Final.pdf - Digital Repository of CCEE ...

F (R), f (Q)84Figure 2.16 shows probability density functions (PDFs) for load (Q) and resistance(R). In principle, failure happens when the load exceeds the resistance, and the probabilityof failure (p f ) is related to the extent to which the two probability density functions overlap.By combining both the probability density functions, the margin of safety or the reliabilityindex (β) can be expressed as shown in Figure 2.17. The reliability index (β) is defined asthe number of standard deviations of the derived PDFs separating the mean safety marginand the nominal failure value of zero (Paikowsky et al., 2004), or simply the distancemeasured in standard deviations between the mean safety margin and the failure limit (Allen,2005).QFS = R / QQ nLoad Effect(Q)R QR sRResistance (R)R, QFigure 2.16: Probability density functions for load and resistance (Adapted after Paikowskyet al. 2004)