# Structural Reliability Analysis and Limit State Functions

The available reliability methods are presented in several publications (e. g. Nowak and Collins 2000) and, therefore, the details are not discussed in this paper. The methods vary with regard to accuracy, required input data, and computational effort. Most of the available procedures are suitable for a reliability analysis for individual components rather than structural systems. System reliability methods are more complex but they offer considerable advantages, and therefore they are the subject of the present paper.

In case of the component reliability, it is almost always possible to define a performance function g(X) of the basic random variables X such that g > 0 corresponds to a satisfactory performance and g < 0 corresponds to failure of a structure. On the other hand, the formulation of limit state function for the entire bridge is much more complex and requires a special approach. This is because of, among other things, the possible statistical dependence among the random variables, load redistribution after some members’ failure, redundancy of the structure that is causing a load sharing.

So far, a number of approaches have been proposed that allow to define a limit state function, and consequently failure, for entire bridge. Zhou (1987) proposed that system failure occurs when two adjacent girders fail. Tabs and Nowak (1991) considered several girders must reach their ultimate capacity before the structure collapses. Ghosn and Moses (1998) defined the bridge resistance as the maximum gross vehicle load that is causing the formation of a collapse mechanism. Enright and Frangopol (1999) studied a number of system models for a five girder bridge. Estes and Frangopol (1999) assumed that failure occurs when three adjacent girders out of five fail. Liu and Moses (2001) considered a damaged steel girder bridge. It was assumed that damage can be caused by corrosion, collision, etc.

In this paper, however, it is assumed that the failure of a bridge is defined as a maximum load that the bridge can carry, or as 0.0075 of the span length deflection in any of the main members of the bridge, whichever governs. The deflection is calculated only due to live load, including static and dynamic components.