Optimum integer number and position of several groups of prestressing tendons for given concrete dimensions

Abstract The following design problem is solved: Given are the concrete dimensions and the loadings (e.g. dead load plus traffic loading). The engineer can choose the number of groups of tendons he wishes to use. For each group the following data are given: the location of the cross-sections at which the tendons are anchored, the prestressing force of one tendon, which can also be variable along the length of the beam to take friction losses approximately into consideration, the maximum and minimum number of tendons, the lower and upper bounds of the zone permissible for guaranteeing sufficient concrete coverage (these bounds can also vary along the length of the beam), the smallest permissible radius of curvature, as well as a relative price. Several load combinations, under service conditions with specified allowable maximum and minimum concrete stresses are selected by the engineer. A reduction factor for creep and shrinkage is also included in the input. Determined are (a) the overall most favorable integer number of tendons in each group, and (b) the position along the length of the beams, such that the stress margin that results in every section and under the stress conditions formulated under the most unfavorable load positions shall be a maximum. The optimization algorithm employs in part a linear program. Methods to eliminate redundant constraints on the level of the cross-sections and the elements are discussed. The procedure is illustrated with a highway bridge (deck on raking legs), using three groups of tendons.