Pergamon Compurrrs & Srrucrures Vol. 64, No. 14, pp. 729-735, 1997 0 1997 Civil-Comp Lfd and Elsevier Science Ltd. All rights rexrved Printed in Great Britain PII: SO0457949(96)00429-4 0045-7949/97 $17.00 + 0.00 INTEGRATING SYSTEM RELIABILITY AND OPTIMIZATION IN PRESTRESSED CONCRETE DESIGN A. S. Al-Harthy* and D. M. Frangopolt *Department of Civil Engineering, Sultan Qaboos University, P.O. Box 33, Al-Khoudh 123, Oman TDepartment of Civil, Environmental, and Architectural Engineering, University of Colorado at Boulder, Boulder, Colorado 80309-0428, U.S.A. Abstract-In this paper, second moment reliability method for components and systems are integrated with optimi.zation tools in the design of prestressed concrete (PC) beams. Loading, material properties, prestressing force levels, as well as the models used to predict flexural behavior are all treated as random variables. The performance functions considered are related to the stresses at initial and final stages as well as the flexural strength of the beam. System reliability methods are used to compute the probabilities of unsatisfactory performance of PC beams at these limit states. Reliability-based design examples of double-tee PC beams commonly used in the construction industry are presented in design-chart formats. 0 1997 Civil-Comp Ltd and Elsevier Science Ltd. 1.. INTRODUCTION Various design codes ensure proper performance of structures by using traditional safety factors in their provisions. In the working stress design format, the structural member is designed such that the elastic stresses caused by the specified loadings do not exceed permissible (allowable) stresses. These per- missible stresses are defined in the design codes and are derived from material strength but lowered through a factor of safety. In the load and resistance factor design format, the code-specified loads are multiplied by appropriate load factors and the nominal strengths are reduced by strength reduction factors. Safety is assured if the factored resistance is at least equal to the factored load. These load and resistance modifie:r factors, which are intended to cover uncertainties, are derived on the basis of experience and/or engineering judgements. Properly, these ought to ibe developed also on the basis of satisfying specified reliability requirements. The current AC1 practice [l] in prestressed concrete (PC) design invol.ves the consideration of all load stages that may be significant including the transfer load stage, the service load stage, and the factored load stage. Recognizing th.e existence of uncertainties and the random nature of the variable involved in the design process, some codes like the zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFED Ontario Highway Bridge Design C,ode, [2] the Load and Resistance Factor Design h4anual of Steel Construction [3], and the Common Unified Rules for Concrete Struc- tures [4], have been developed by using reliability- based methods. As shown in Al-Harthy and Frangopol [5, 61 deterministic methods could be replaced by reliability methods where the uncertain nature of the variables is considered in a rational manner if agreement could be obtained on the following issues: l selection of basic random variables for each specific problem, their distribution types and relative statistical parameters; l form of the various limit state equations; l choice of models and target reliability levels to be adopted in different design situations. In this paper, which integrates and further develops previous results obtained by the authors [5,6], the design of PC beams is carried out satisfying reliability requirements directly rather than through the traditional safety factors or the more recent modifiers factors. The design procedure integrates system reliability and optimization methods in the solution process. Using reliability levels implied in the current AC1 Code [l] for PC beams as target values, the design of PC beams that simultaneously satisfy stresses at initial, final, and ultimate limit states is demonstrated. The search algorithm of the feasible directions method is used as the optimization tool in the design process. Various PC beams that are commonly used in the U.S. construction industry for offices and retail buildings are given as examples to demonstrate the proposed reliability-based design approach. 2. RELIABILITY INDEX AND LIMIT STATES Over the last two decades, second-moment methods where only the first two moments of each 729