Comparison of the predicted and the field data strain response

The verification of the developed FE models including the SH, M-S, and S-S models are also performed by comparing the field strain response collected during the load test, to the analytical strain results at the installed strain gages’ locations. Having a cluster of five strain rosettes in a single gusset-less connection provides the opportunity to compare the strain distribution (strain contours) of the developed models under the truck load to the field strain rosettes’ responses. The B-model is not included in this comparison as it does not capture the local strain response of the gusset-less connection. The differences between the field strain response and the predicted response by FE models can result from the modeling assumptions, including the material properties and the modeling simplifications, such as ignoring the weld geometry and the bolted connection in the model.

In Figure 4-11, the strain contours of the global M-S model are shown under the testing truck load at the second stop. It is observed that the M-S model can sufficiently provide the required information related to the local performance of the connections modeled with shell elements while providing the global behavior of the bridge modeled with beam and shell elements with an efficient reduction in the computational time shown in Table 4-2. In Figure 4-12, the time history for the principal strain response of the four strain rosettes installed at the bottom connection

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is shown. The graphs belong to the quasi-static load test with two stops at the northbound (toward the tower).

Figure 4-11Strain contour response of the multi-scale model under the truck load (LUSAS ®).

As shown in Figure 4-12, the specified part showing the truck stop is considered for model verification purposes. The time- history response data collection was started from zero for each load test. Therefore, the resulting structural responses are only due to the excitation of the test truck, as the impact of environmental demands was minimal over each ∼120-s test run. Shown in Figure 4-13 are the principal strain contours of the SH, S-M, and S-S models at the bottom gusset- less connection. In addition, the locations of the five strain rosettes installed at the bottom

Figure 4-12 The field strain time-history response during the load test for the strain rosettes at the bottom connection, locations shown in Figure 4-13

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connection are specified (A–E). For each model, the presence of the stress concentrations, strain response magnitude, and the agreement with the field data are evaluated. Comparing the strain distribution of the three models, it is illustrated that the SH-model, which is shown in Figure 4-13a, has the most uniform strain distribution with minimum concentrated strain. For the M-S model shown in Figure 4-13b, minor strain concentrations are observed at the location of the floor beam attachment. The S-S model also includes more strain concentrations as compared to the two other models shown in Figure 4-13c.

The concentrated stress areas for the M-S and S-S models are due to the application of the beam element for the floor beams, which indicates a single beam element might not appropriately represent the whole floor beam causing strain concentrations at the gusset-less connection. In the planar coupling conditions, this can be addressed by changing the interface point along the beam element. In the out-of- plane coupling conditions, the problem can be solved by considering a larger area of coupling. However, the strain concentration is less observed in the area where the skewed beam is coupled to the gusset-less connection, proving the efficiency of the out-of-plane constraint equations developed in this study.

In evaluating the magnitude of the strain response of the FE models, the SH-model has a higher strain value due to the flexible property of the shell element compared to the beam element. Therefore, the M-S model has lower strain response due to the higher stiffness of the model compared to the SH-model. The S-S model has the highest strain response values compared to the other models due to the applied loads that were determined from the global model. The comparison between the strain contours of the S-S and M-S models also demonstrates that application of the developed MPC equations in a single global model may result in a more accurate response compared to the sub-structuring method. Presence of the concentrated stress areas, as well as the

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higher strain response of the S-S model, can result in over-estimations for further damage assessments.

The focus of this study is to develop an efficient FE global model which provides the required information on the local as well as the global performance of the bridge. The concentrated regions observed in the strain contours of the M-S model do not warrant the modeling of the floor beam with shell elements. Including more shell elements in the M-S model will significantly increase the number of DOFs, and therefore, the time of analysis. However, this information provides the intuition about the causes of the difference between the developed FE models and the acquired field data in the model calibration and validation process.

Figure 4-13 The principal strain contours of the a) SH-model b) M-S model c) S-S model LUSAS ® under the truck load

A numerical comparison between the strain results of the FE models and the strain gages’ response is performed through some statistical efforts. The results are shown in the bars for all five-installed strain rosettes (A to E, shown in Figure 4-13) at the bottom and top gusset-less connection, shown in Figure 4-14(a) and Figure 4-14(b) respectively. It is demonstrated that at most of the strain gage’s locations, the S-S model has more difference to the field data. In the next section, the difference between the results are quantified.

82 Figure 4-14 The comparison between the strain response of the FE models and field data a) bottom connection, and b) top connection.