Single objective reliability-based optimization of prestressed concrete beams

A general approach to the single objective reliability-based optimum (SORBO) design of prestressed concrete beams (PCB) is presented in this paper. The proposed approach incorporates all behavior and side constraints specified by the American Concrete Institute (ACI) code for prestressed concrete. Loading, material properties, prestressing force and the models used to predict structural performance at various stages––initial, final and ultimate stages––are all treated as random variables. Several limit states are considered, including permissible tensile and compressive stresses at both initial and final stages, prestressing losses, ultimate shear strength, ultimate flexural strength, cracking moment, crack width, and the immediate deflection and the final long term deflection. A general SORBO methodology is developed and solved by integrating PCB design and reliability analysis computer programs with an automated design optimization package using the feasible direction method. The single objective function represented by the overall cost of the PCB in terms of concrete, prestressing steel, mild steel, and formwork––is minimized subjected to 11 reliability constraints and four geometrical constraints. The design variables consist of six geometrical dimensions that shape the PCB cross section and one that represents the amount of prestressing steel. Numerical examples are presented to illustrate the application of the proposed approach to the SORBO of PCB. The results consist of, but not limited to, the initial and final prestressing forces, prestressing losses, immediate and final deflections, and upper and lower bounds on the parabolic tendon profile.