Minimum cost design of multispan partially prestressed concrete beams using DCOC

An earlier study on the application of discretized continuum-type optimality criteria (DCOC) to the optimum design of simple partially prestressed concrete (PPC) beams is extended to multispan beams. The cost of construction which includes the costs of concrete, prestressing steel, non-prestressing steel and formwork is minimized. The design constraints include limits on the maximum deflection, flexural and shear strengths, in addition to ductility requirements, and upper and lower bounds on design variables as stipulated by the Australian Code AS 3600. Based on Kuhn-Tucker necessary conditions, the optimality criteria are explicitly derived in terms of the design variables-effective depth, eccentricity of prestressing steel and non-prestressing steel ratio. The prestressing profile is prescribed by parabolic functions. The self-weight of the structure is included in the equilibrium equation of the real system, as is the secondary effect resulting from the prestressing force. An iterative procedure for updating the design variables is outlined. Two numerical examples of multispan PPC beams with rectangular cross-section are solved to show the applicability and efficiency of the DCOC-based technique.