This dissertation presents a new method for predicting fractional transport rates of bedmaterial load in sand-bed channels. The proposed method is developed based on the concept of the transport capacity fraction (TCF) approach. The bed-material concentration for a given size fraction is obtained by weighting the bed-material concentration, C1, with a transport capacity distribution function, Pci. The procedure and a detailed example problem showing the use of the proposed method are provided. Two transport capacity distribution functions are developed. The first function is in terms of relative fall velocity. This function is derived from the unit stream power theory and the concepts of the TCF approach and the bed material fraction (BMF) approach. The second function is in terms of relative diameter. It is derived from the Engelund and Hansen's transport relations and the concepts of the TCF approach and the BMF approach. The sheltering and exposure effects are considered in both functions. The coefficients in both functions were calibrated using 118 sets of flume and field data (891 data points) falling in sand sizes. The formulations using relative diameter is suggested for practical applications because of its simplicity (no need for relative fall velocity computations). For the computation of bed-material concentrations, the effect of size gradations on the transport of sediment mixtures is investigated in detail. First, a new relationship is proposed for predicting the median diameter, D50t, of bed-material load. This equation is developed based on the 118 sets of data used for the development of transport capacity distribution functions plus 280 sets of CSU flume data. Then, the effect of size gradation on the transport of sediment mixtures is demonstrated by the use of Engelund and Hansen's transport function and Yang's unit stream power function. To account for size gradation effects, the newly developed expression for the median diameter, D50t, is proposed for use as the representative size in bed-material load computations. For the existing bed-material load equations, an equivalent diameter, De, is proposed. This equivalent diameter, which is related to D50t, is incorporated into the Engelund and Hansen, Ackers and White, and Yang formulas for the computation of bed-material concentrations. The proposed method is compared with various existing fractional transport methods using 118 sets of measurements (891 data points) and verified using 48 sets of independent data (327 data points). Comparison and verification indicate that the proposed method provides better predictions for fractional bed-material concentrations and size fractions of sediment in transport.