Simulations for Other Spans and Influence Lines

The analytical S-N curves for loading histories applicable to other influence lines and bridge spans were generated by conducting a number of simulations. A similar methodology was successfully used in [11] to study the adequacy of the current design provisions for the fatigue design of aluminum structures. Twenty (20) VA load histories were considered consisting of influence lines for five locations of four bridge spans of 15, 25, 40, and 60 m. These locations included midspan moment for 1- and 2-span girders, intermediate support moment for 2-span girders, and support reactions for 1- and 2-span girders.

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The selected influence lines and spans were intended to cover a broad range of VA load history

characteristics that are possible in bridge structures. Each in-service VA load history was generated by taking random samples of 1,000 trucks from the larger Ontario database [11]. As described in Chapter 2 and 3, the Ontario survey data included the axle weight and spacing data for 10,198 trucks measured in Ontario in 1995 [12]. Figure 5.10 shows the gross truck weight histogram based on this survey data. A similar histogram was used to generate realistic in-service loading histories in a number of previous studies, e.g. in [1, 11]. It should be noted that the static weights are used for the truck weights in this figure. Thus, to approximate the corresponding dynamic load effects, each axle load should be multiplied by an impact factor of 1.25, in accordance with CAN/CSA-S6 [13].

Figure 5.10: Truck weight histogram based on 1995 Ontario survey [1, 12]

The analysis results are presented in Figure 5.11 to Figure 5.13. In these figures, the results are plotted as envelopes in terms of the equivalent stress range, ΔSeq, assuming m=5. The proposed design S-N curves for the as-welded and treated specimens, derived in Chapter 3, are also plotted in these figures for comparison purposes.

In Figure 5.11, the analysis results for the treated Type-X specimens are presented. The results show that both of the FAT-135* and FAT-182* design curves, for the nominal and structural stresses, respectively, lie below the VA loading envelopes for the most part. Based on the results, a significant fatigue life improvement cannot be claimed due to the HFMI treatment for N < 106 _{cycles. The VA loading}

envelopes exhibit a change of slope at around 200 million load cycles which may suggest approaching a fatigue threshold.

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Figure 5.11: Results of the analysis of other spans and influence lines for Type-X: (a) nominal stress; (b) structural stress

The analysis results for the treated Type-L specimens are presented in Figure 5.12. The FAT-41 and 82 curves for the nominal stress approach (FAT-76 and 151 for the structural stress approach) represent design curves for the as-welded weld toe and as-welded weld root, respectively. Two other curves with m = 5 are also plotted in this figure including FAT-77* and FAT-143* which represent the treated weld toe. These curves were obtained based on the effective notch stress FAT-339* curve by considering the structural and effective notch stress coefficients (1.85 and 4.38, respectively).

Figure 5.12: Results of analyses of other spans and influence lines for Type-L: (a) nominal stress; (b) structural stress

The results show that both of the nominal stress FAT-77* and structural stress FAT-143* design curves lie below the VA loading envelopes for the most part and provide a good design basis for the studied

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load carrying weld toes. By comparing the VA loading envelopes and the design curves for root failures (FAT-82 and 151), it can be concluded that the failure mode changes from the failure at the treated toe for N < 105 cycles to the secondary mode of failure for N > 106. Consequently, a significant fatigue life improvement can be claimed due to the HFMI treatment for N > 106 cycles. The VA loading envelopes exhibit a change of slope at around 100 million load cycles. This change in the slope, that is not as significant as the change observed for Type-X specimens, may suggest approaching a fatigue threshold. The analysis results for the treated weld toes for both types of specimens are presented in Figure 5.13 in terms of the effective notch stress range. Considering the width of the VA envelopes, the suggested FAT-339* design curve provides a good basis for the fatigue design of treated weld toes. Similar to the previous conclusions, significant fatigue life improvements can be expected due to HFMI treatment for N > 106.

Figure 5.13: Results of analyses of other spans and influence lines for Type-X and L: effective notch stress

By considering the VA loading envelopes in Figure 5.11 to Figure 5.13, it can be concluded that the in- service VA loading characteristics have a significant influence on the analytical VA loading S-N curve. The shapes of the curves, however, followed a general S-shaped trend with two flatter parts in the low and high cycle domains with a steeper transitioning part in the middle. The flatter design S-N curve in the low cycle domain was found to have resulted from the severe overloads that were present in the VA load history, while the flatter portion in the high cycle domain is due to approaching a fatigue threshold. Overall, the S-N design curves with m = 5 were found to be the reasonably accurate design tools in all cases.

100 1000

1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09

E ff ec ti v e No tc h S tr es s R an ge , Δ S eq (M P a) Number of Cycles, N FAT-339* (m=5) FAT-175 Type-X Type-L

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