CARACTERIZACIÓN DE LOS OPERARIOS DE LAS EMPRESAS PETROQUÍMICA

8.7.1

Increase in Allowable Axle Load

In this short subsection the effect of raising the allowable axle load has been isolated and studied. Figure 8.16 shows the effect of raising the allowable axle load to 25, 27.5 and 30 tonnes for the case of a ten metre concrete span bridge using the assumption of the GPD load model. The studied standard in this case is the 1940 standard. As can be seen from the figure the increase causes a parallel displacement of the curves in the vertical direction, an increase in axle load decreasing the safety index.

8.7.2

Assumption of the Model Uncertainty

In this section the assumption behind the resistance model uncertainty is changed to see its impact on the reliability analysis. All the previous calculations have assumed

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 4.6 4.8 5 5.2 5.4 5.6 5.8 6 25 t 27.5 t 30 t β ν

Figure 8.16: The figure shows the effect of increasing the allowable axle load using the GPD model. Shown are the results for 1940, a span of 10 m, a concrete material and for the three cases of 25, 27.5 and 30 tonnes. The increase causes an almost parallel displacement in the vertical axis, representing a decrease in safety.

that the engineering models used to describe the resistance of a section have been chosen conservatively and represents the 5 % quantile, see section 4.8. Another alternative is that the resistance model represents the mean value, in which case the assumed mean value of resistance will be lower by approximately 20 % in the case of the concrete, compare (4.55) and (4.57). In Figure 8.17 a comparison is made between the results of the reliability analysis under these two assumptions. The figure shows how the change of assumptions causes a significant drop in the resulting safety index. This is a reasonably obvious result, however, it should be borne in mind when comparing models from older design codes which may have been lacking in some areas or where known problems of design have subsequently been discovered.

Figure 8.18 shows the same comparison but for the case of a 13 m steel bridge with an allowable axle load of 30 tonnes. The change in mean value of resistance from the one assumption to the other represents a 14 % lower value. This change of assumption produces a lower safety index, with the respective curves undergoing a parallel displacement in the vertical plane. This relatively small change in the assumed value of the mean of the resistance produces considerably lower safety indices.

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 4 4.5 5 5.5 6 6.5 7 1980 1960 1940 β ν

Figure 8.17: The figure shows the effect of changing the underlying assumption of the resistance model. The case of the resistance model used in design representing the mean and the 5 % quantile are detailed. Shown are the results for a concrete span bridge of 8 m and for the cases of 27.5 tonnes axle load under the assumption of a GPD model. The mean value as- sumption yields a lower assumed mean value of resistance of the section and hence a lower safety index.

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 4 5 6 7 8 9 10 11 1980 1960 1940 1901 β ν

Figure 8.18: The figure shows the effect of changing the underlying assumption of the resistance model. The case of the resistance model used in design representing the mean and the 5 % quantile are detailed. Shown are the results for a 13 m steel bridge and for the cases of 30 tonnes axle load under the assumption of a GPD model. The mean value assumption yields a lower assumed mean value of resistance of the section and hence a lower safety index.

Discussions and Conclusions

9.1

General

The work in this thesis presented methods by which field data, such as measured axle loads, axle spacings, train configurations and speeds, may be analysed to create a model of the traffic load effects on railway bridges.

The traffic load effect considered in this thesis was the mid-span moment of simply supported bridges. Only short to medium span bridges have been studied in the thesis with spans ranging from 4–30 metres.

The model used to simulate the load effect from the collected field data was the so-called moving force model. In this model, the bridge was portrayed as a two dimensional beam of constant cross-section and bending stiffness. Each train was idealised as a succession of point loads travelling at constant speed. Accordingly, only the dynamic effect of trains travelling across a bridge with a geometrically perfect track can be simulated in this model. The effects of track defects was allowed for afterwards by multiplying the dynamic moment history by a factor, which was dependent on the train speed and the bridge span. Also the forces were modelled as having direct contact with the bridge, therefore neglecting the distribution of axle loads via rail, sleepers and possible ballast.

The model used to describe the traffic load effects from the results of the moving force model was based on Extreme Value Theory and adopts the use of the family of distributions known collectively as the Generalised Extreme Value (GEV) or alternatively the Generalised Pareto Distribution (GPD). This model allows for the extrapolation past the available data. While the extrapolation past the existing data can not be justified mathematically the extreme value theory provides the only consistent model for this extrapolation. The uncertainties involved in the parameter estimates were incorporated and, at least to some degree, allowed for in the method. Since this model builds on the theory of extreme values it is only suitable for use in the ultimate limit state analysis.

making it possible to investigate upgrading of existing railway bridges to greater permissible axle loads. Only the ultimate limit state was considered in this analysis. In order to perform a reliability analysis, information was gathered concerning the codes to which the existing bridges were designed. Only a limited number of material codes and a limited number of code traffic load models have been considered. In some cases quite coarse assumptions were made, especially as regards the inferred safety factors of the code formats using permissible stresses. Also due to lack of information, the material codes of one period are used in conjunction with load models from another period, which is obviously incorrect but at least provides an indication as to the safety of the structures.

To the knowledge of the author, no previous work has adopted the use of measured axle loads and train configurations when attempting to describe a model for the traffic load effects. The majority of the earlier work appears to assume deterministic axle loads and in the majority of the cases even deterministic train configurations.