Optimization of Continuous Post-Tensioned Concrete Bridge Girders of Non-Uniform Depth

Post-tensioned single-cell concrete box girders of variable depth are used in continuous bridges to achieve both economy and aesthetics. In this paper, the minimum prestressing for a given two- or three-span continuous bridge deck profile is achieved through a constrained optimization procedure using linear programming in conjunction with gradient method of optimization. The constrained nonlinear problem is solved by transforming it to a linear one by introducing a new design variable which proportions long (full length) and short tendons. A gradient search technique is used to solve iteratively the optimization problem. The design variables include interior to exterior span ratio (for three-span), the depth profile of the cross-section, tendon profile, and prestressing force. The total cost of the member is taken as the cost of structural materials (concrete and prestressing steel), excluding the cost of formwork. The design constraints are the prescribed limits on the allowable stresses, ultimate strength, and serviceability requirements as per ACI 343R-95. A purpose-built computer program has been developed to readily determine the optimum prestressing for a given bridge deck profile. From solutions of a number of hypothetical bridge girders using AASHTO H20 bridge loading, several useful results related to design are obtained. Results show that for a symmetrical three-span and two-span continuous bridge girder, the optimum prestressing consists of an optimum arrangement of both long and short tendons, and for a three-span girder of prescribed length, the optimum design is attained at an optimum ratio of interior to exterior span with 1.35 to 1.45.