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The work presented here shows the SSM is useful for predicting lateral load distribution for bridges with integral girder-to-cap connections. The SSM can provide a simple approach for determining more realistic lateral load distribution than the current design recommendations. Based on the SSM results presented previously, a suitable approach is to use the SSM prediction for all girders along with an appropriate variability margin. If α is introduced as a variability factor, and DFSSM is defined as the girder

distribution factors determined from Eqs. 5.11 and 5.12 as appropriate, the recommended distribution factor, DFrecom, can be defined as:

DFrecom = α DFSSM (Eq. 5.13)

The variability factor, α, is introduced to provide a safety margin since the simple model is not intended to be an exact representation of all the complexities of the real structure. Trial-and-error reveals that a value of 1.2 provides good results for the four structures in this study; similar studies could be used to further refine this variability factor. Using α = 1.2 and the interior fractional distribution values from Table 5.2 for each test unit, the recommended distributions for the interior girders in this study are 0.37, 0.44, 0.42, and 0.29, respectively, for the PBT, SPC1, SPC2, and ITB test units. The ratios of these recommended distributions to the measured experimental distributions range from 1.10 for the PTB test unit to 1.34 for the SPC1 test unit. The recommended distributions are shown graphically in Figure 5.10 (“Proposed”) along with the current AASHTO/Caltrans approach (“Current”) and compared with the experimental, GMA, and SSM predictions. Examining the data from the interior girders in the PBT test unit, the ratio of the current recommendation to the experimental distribution is 1.50. However, the ratio of the proposed recommendation to the experimental distribution is 1.10. Thus, when compared with current design recommendations, the SSM prediction for the PBT structure compares 40% more favorably with the experimental results. The improvements of the SSM model in distribution prediction for the SPC1, SPC2, and ITB structures are 17%, 22%, and 19%, respectively.

Figure 5.10. Distribution comparison for interior girder latera

This study focused on the development of simple stiffness models (SSMs) to predict seismic load distribution between girders in integral bridge superstructures. The conclusions drawn from this study are presented below:

1. Current practice and recommendations related to vertical distribution of dead load and vehicle live load are appropriate. Under high seismic horizontal displacements, the experimental girder strain values due to vertical load increase, but the vertical load distribution be

remains relatively constant. Vertical load distributions determined using techniques such as the vertical simple stiffness model (SSM) and grillage model analysis (GMA) are shown to match well with current recommendations and experimental res

2. Current practice and recommendations limit the distribution of column seismic overstrength moment—expected under horizontal seismic action longitudinally along the bridge

girders in the superstructure immediately adjacent to the column.

from large-scale tests confirm the girders that are not adjacent to the column consistently resist a significant amount of the column moment.

. Distribution comparison for interior girder lateral load

5.9. Conclusions

This study focused on the development of simple stiffness models (SSMs) to predict seismic load distribution between girders in integral bridge superstructures. The conclusions drawn from this study

and recommendations related to vertical distribution of dead load and vehicle live load are appropriate. Under high seismic horizontal displacements, the experimental girder strain values due to vertical load increase, but the vertical load distribution between girders remains relatively constant. Vertical load distributions determined using techniques such as the vertical simple stiffness model (SSM) and grillage model analysis (GMA) are shown to match well with current recommendations and experimental results.

Current practice and recommendations limit the distribution of column seismic overstrength expected under horizontal seismic action longitudinally along the bridge

girders in the superstructure immediately adjacent to the column. Observed load distributions scale tests confirm the girders that are not adjacent to the column consistently resist a significant amount of the column moment.

l load

This study focused on the development of simple stiffness models (SSMs) to predict seismic load distribution between girders in integral bridge superstructures. The conclusions drawn from this study

and recommendations related to vertical distribution of dead load and vehicle live load are appropriate. Under high seismic horizontal displacements, the experimental girder

tween girders remains relatively constant. Vertical load distributions determined using techniques such as the vertical simple stiffness model (SSM) and grillage model analysis (GMA) are shown to match well

Current practice and recommendations limit the distribution of column seismic overstrength expected under horizontal seismic action longitudinally along the bridge—to the

Observed load distributions scale tests confirm the girders that are not adjacent to the column consistently resist

3. Load predictions determined using the lateral load SSM compare favorably with more complex GMA techniques. The ratios of GMA interior girder distribution to SSM interior girder

distribution are 1.10, 0.98, 0.99, and 0.89, for the PBT, SPC 1, SPC 2, and ITB structures,

respectively. The largest difference between GMA and SSM predictions is for the ITB structure (a difference of 11.3%), and in this instance the SSM prediction matches the experimental

distribution almost exactly while the more complex GMA technique provides a poorer prediction.

4. The analytical predictions of lateral load distribution to the interior girders based on the SSM model average a difference of 5.0% from the experimental distribution values, with a maximum difference of 9.8%. The average percentage difference of the GMA predictions from the

experimental values is 5.9%, with a maximum difference of 12.7%.

5. At very low levels of lateral load (as low as 0.25 Fy, with Fy representing column yield due to

lateral load), the test units consistently show at least 15% of the lateral load being distributed to the exterior girders. This distribution remains almost constant all the way to the maximum displacement ductility levels (as high as µD = 10.0) experienced by each test unit.

6. Current design recommendations overestimate the lateral load distribution to the girders adjacent to the column by as much as 60%. As described in Conclusion 4, the SSM approach provides significant improvement in the distribution predictions without implementing a more complex analytical approach. When using the SSM approach, a multiplier of 1.2 is recommended over the calculated distribution factor, based on the results from the four structures in this study. The design girder moment determined using the SSM approach is then expected to be 10% to 20% higher than the measured moment, a marked improvement over current

recommendations. Improved distribution predictions will likely lead to shallower girders due to reduced demand in the connection region.