Due to age, original design that is deficient by modern standards, inadequate maintenance, environmental conditions, and increasing loads, large numbers of bridges in United States and elsewhere are classified as deficient and in need of rehabilitation or replacement. According to a national bridge inventory established by the Federal Highway Administration, about a third of the bridges in the United States are substandard or deficient. Many deficient bridges are posted or closed to traffic, and repair or replacement decisions for these bridges involves both economical and safety considerations. To avoid the high costs of unnecessary replacement or repair, better analytical and statistical methods should be used to reveal load carrying capacity of bridge superstructures, these methods should be adopted by the current code and specifications, and they should be calibrated by using historically successful field performances. A statistical model for combined shear-moment resistance of conventionally reinforced concrete bridge girders with common vintage design details and properties was presented in Chapter 2. New statistical data on stirrup spacing variability were developed from field measurements on in-service deck-girder bridges and these were combined with available data in literature to model resistance uncertainty. The model produced bias factor and coefficient of variation for combined moment and shear capacity using Modified Compression Field Theory. Both AASHTO-LRFD and ACI-318 were utilized to calculate capacity of the selected sections and strength reduction factors in AASHTO-LRFD and ACI-318 were compared using the obtained statistical parameters. Twenty-six in-service decks were evaluated by using historically successful field performances in Chapter 3. The deck designs were compared with the current AASHTO-LRFD design moments (for strength and fatigue) as well as deflection criteria, the previous AASHTO-LRFD (1994) design moments, and with AASHTO-LRFD concrete slab deck design tables. Design demands, fatigue stress ranges, and deflection limits were compared for each of the deck considered. Three decks were used for further detailed finite element analysis. Based on the results, design recommendations were provided. Moment and deflection equations for infinitely wide and simply supported orthotropic plates subjected to arbitrary patch loading were developed in Chapter 4. Convergence rates of the equations were determined and compared with finite element analysis results considering both symmetrical and asymmetrical patch loading on the plate. Using the provided equations, influence of torsional rigidity was investigated.