Optimum limit design of continuous prestressed concrete beams

Earlier studies on the design of reinforced concrete structures by equilibrium-serviceability methods (that simultaneously satisfy collapse and service criteria) are extended to continuous prestressed and partially prestressed concrete structures. The objectives of the paper are to present a practical design approach to nonlinear design for prestressed concrete structures and to identify its potential benefits. The paper also demonstrates the conflict between desirable plastic redistribution (at ultimate limit state) and zero or limited cracking (at serviceability limit state) for fully prestressed concrete structures. Optimization results suggest that partially prestressed concrete structures represent the most economical compromise between these conflicting criteria, and the optimal prestressing degree strikes a good balance between adequate service conditions (stresses, cracking, and deflection) and economy. Optimization of prestressed concrete beams is cast as a nonlinear programming problem and is solved by the projected Lagrangian algorithm. Examples of (three-span and two-span) continuous-beam optimizations illustrate the method and its features, as well as resulting differences between full and partial prestressing design solutions.