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

85f(g)βσ gFailure RegionArea = p fFigure 2.17: Combined PDFs that represents the safety margin and reliability index (Adaptedafter Paikowsky et al. 2004)Two statistical methods are commonly used in the resistance and load factorscalibration, and they are First-Order Second-Moment (FOSM) and First-Order ReliabilityMethod (FORM). Existing AASHTO specifications are based on the FOSM analysis. Acomparison in calculating resistance factors using both methods has been studied byPaikowsky et al. (2004). They concluded that FORM provides higher resistance factors thanthe FOSM by approximate 10%. Kim (2002) described that the load (Q) and resistance (R)are lognormally distributed, mutually independent, and ln(Q) and ln(R) are normallydistributed. Thus, the mean value of limit state function g(Q,R) can be expressed by Eq.(2.42) and its standard of deviation (ζ g ) can be expressed by Eq. (2.43). By definition, thereliability index (β) is the ratio of ̅ over ζ g given by Eq. (2.44). Replacing R with Eq. (2.41)and rearranging Eq. (2.44), the resistance factor (φ) is given by Eq. (2.45). Paikowsky et al.(2004) described that the probabilistic characteristics of the random variables for dead load(Q D ) and live load (Q L ) are based on the assumption used by current AASHTO and loadcombination for strength I as listed in Table 2.14, which are different from the initial factorsproposed by Barker et al. (1991).0 g = ln(R/Q) g = ln(R/Q)