## 7 Conclusions and Recommendations  
A detailed numerical investigation of the behavior of skew composite bridges with high-performance steel girders under truck loads was conducted for this study. The numerical approach applied included an extensive study of continuous bridges to determine the effect of various key parameters of bridges on the live load distribution factors for both shear and bending moment. Empirical expressions for the shear and bending moment distribution factors were derived that are suitable for use with current bridge design codes. The proposed expressions are a function of the skewness, girder spacing, number of lanes loaded, and span length of bridges. Based on the results obtained from the sensitivity investigation, the following conclusions can be drawn:  
* A good agreement in the structural responses was achieved between the 3-dimensional modeling of the prototype bridges and the results obtained experimentally, confirming that numerical models can reliably predict the responses of slab-on-girder bridges. * The discrepancy between the finite element results and those calculated using the codified AASHTO LRFD equations revealed that the current LRFD specifications are not suitable for predicting the live load distribution factors for both the bending moment and the shear force for skewed composite bridge with HPS girders. It was therefore necessary to develop a new set of _LDF_ equations for both shear and moment. * Based on the results of the parametric study on prototype bridges, the span length, girder spacing, number of lane loaded, and skew angle were identified as the key parameters affecting the _LDF_s of skewed composite bridges. The _LDF_s for both shear force and bending moment decreased with increasing span length and number of lanes, and increased with increased girder spacing. Increasing the skew angle of the bridge superstructures increased the _LDF_s for shear force but decreased those for bending moment. * Based on the statistical analysis, conducted for this study, a set of simplified expressions were developed for the _LDF_s for both shear force and bending moment. The slightly greater than \begin{table}
\begin{tabular}{c c c c c} \hline _LDF_ & **Girder Type** & **AVG.** & **SD.** & _COV._ \\ \hline _MDF\({}_{ex}\)_ & External & 1.065 & 0.076 & 0.071 \\ _MDF\({}_{in}\)_ & Internal & 1.045 & 0.069 & 0.067 \\ _CDF\({}_{ex}\)_ & External & 1.072 & 0.082 & 0.076 \\ _CDF\({}_{in}\)_ & Internal & 1.059 & 0.094 & 0.085 \\ \hline \end{tabular}
\end{table} 
Table 3: Comparative Statistics of _LDF_s for prototype bridges. Figure 9: Proposed _LDF_ equations and American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD)equations vs. Rigorous _LDF_. (**a**) bending moment of external girder; (**b**) bending moment of internal girder; (**c**) shear force of external girder; (**d**) shear force of internal girder. unity average and low standard deviation and coefficient of variation for each of the proposed expressions indicate high reliabilities for these proposed expressions in estimating the _LDF_s for shear force and bending moment of skewed composite bridge with HPS girders. * More studies can be carried to assess the dynamic interaction of these type of bridge and moving load due to traffic conditions. The simplified equations can be derived to determine dynamic impact factor of bridges with HPS steel. * Analytical and computational approaches to study the seismic response characteristics of bridges are the most economically feasible methods. It is particularly important to investigate the performance of skewed bridges with HPS steel due to vertical ground motions. The study, therefore, would provide comprehensive results through including all the parameters interacting for a wide range of skew angles. J.K. designed and coordinated the study. I.M. performed the theoretical and numerical study under the supervision of [PERSON]. Y.K.C.