Issue 45

D. Peng et alii, Frattura ed Integrità Strutturale, 45 (2018) 33-44; DOI: 10.3221/IGF-ESIS.45.03 39 N UMERICAL EXAMPLES AND RESULTS ANALYSIS n analysis of cracking in Bridge 62 with an assumed corrosion rate of 0.024 mm/yr was chosen to illustrate this approach. (This corrosion rate corresponds to the fastest rate measured at the three sites examined in Section 2.) In these initial analyses the initiating (inherent) crack was taken from [4], which tested a section from a condemned and badly corroded steel bridge, to be a 0.05 mm deep semi-circular initial crack. The sub-structure of this bridge was subjected to significant moisture and resulting corrosion during the wet seasons. The bridge has two rail tracks, each of which is supported by four girders with 4.87 m length. The dimensions of the girders are given in Tab. 2. Depth 381mm Web thickness 12mm Flange width 152mm Flange thickness 22mm (average) Table 2: Dimensions of the Bridge 62 girders. The yield stress for this steel was conveyed by V/Line staff to be approximately 240 MPa. This implies that retirement resulting from corrosion from an as-new state is approximately 244 years. As mentioned in [28], the deflection requirement of deflection limits of a railway bridge for serviceability limit state under live load plus dynamic load allowance shall be not greater than 1/640 of the span. It is obvious that deflection in this analysis is not a safety issue. The next stage of this study used the finite element model to compute crack growth. For simplicity the loading applied to model was based on the worse case when an ore train (i.e. one G Class locomotive and 20 fully loaded wagons) transited the bridge. The G Class locomotive has the following specifications: Total weight =128 tons, axle loading = 21.3 tons, wheel base = 3810 mm, axle spacing = 1905 mm and leading wheel leading bogie to leading wheel trailing bogie = 12622 mm. Due to symmetry considerations only a quarter of the wheel was modelled. The resultant mesh, which was created using the software program FEMAP [29], had 18,146 twenty-one-noded elements and 91,590 nodes (with a total of 274,770 degrees of freedom). The stresses at critical region were in reasonably good agreement with the results obtained from the field strain gauges measurement presented in Section 3 and discussed in more detail in [30]. In the coupled “corrosion-fatigue” analysis, if the crack growth in a year is less than 0.024 mm, it was assumed that the crack has been “eaten” by corrosion and its length reset to its initial size of 0.05 mm. In this coupled analysis the section thickness continually reduces with time, i.e. as the loss of metal increases, and the stresses increase accordingly. This coupled analysis yielded a life to failure of approximately 81 years. As such there is a difference of ~18 % in the computed fatigue life between the no corrosion and the coupled “corrosion-fatigue” analyses. Figure 5: The resultant computed crack growth histories ( a i = c i = 1 mm). 0 2 4 6 8 10 12 14 16 18 20 0 10 20 30 40 50 Crack Depth (mm) Number of Years Initial Crack Size: a = C = 1 mm With Corrosion A