# Bridge (system) resistance

The design of bridges is based on consideration of individual components, therefore, the performance of the whole structure can be underestimated because it does not account for redundancy and ductility. Failure of a component does not necessarily mean failure of the entire bridge. Therefore, bridge safety can be determined using system reliability approach that includes multiple failure path, load sharing and load redistribution after member failure. Consequently, the system reliability can be considered as a more accurate measure of safety. However, the system reliability computations are more difficult than the reliability analysis of a component, because there are many additional parameters.

The need for the system reliability analysis of bridge structures has long been recognized. There are many different modes of system failure. In this paper, the system resistance is considered in terms of the deflection of the main girders caused by live load. It is assumed that the ultimate limit state is reached when the maximum deflection of any girder exceeds 0.0075 of the span length.

The system resistance is considered in terms of the gross vehicle weight (GVW) of two side-by-side trucks with axle configuration of the design truck (AASHTO 2004), as shown in Figure 2. The calculations are performed for various transverse positions of the vehicles (within the roadway width). The incremental loading method is used. For each transverse truck position, the GVW is gradually increased until the deflection of one of the girders exceeds 0.0075 of the span length. The system resistance is defined as the GVW corresponding to this critical deflection. It can be different depending on the position of trucks within the roadway width. Each transverse position is associated with a certain probability of occurrence. Therefore, the system resistance, Rsystem, is equal to the expected value of the GVW, calculated for different transverse positions:

Rsystem =EP> ■ GVW> (!)

i=1

where GVWi = gross vehicle weight of two trucks side-by-side, causing deflection equal to

0. 0075 of the span length corresponding to i-th transverse position of trucks, pi = probability of trucks occurring in the i-th position. Figure 4 shows a typical cross section of a 6-girder bridge and the truck positions considered in the system resistance analysis.

 * All dimensions in cm Figure 4 Truck Positions Considered in the System Resistance Analysis

An example of the deterministic load-deflection curve for a 30 m span composite steel girder bridge is shown in Figure 5.

 Figure 5 Deterministic Bridge Load-Deflection Relationships for Span Length of 30 m