The Serviceability-based Optimum Design Of Prestressed Concrete Beams

At present, the design of concrete in many countries has been in a gradual transit to the design based on performances, but in most cases, the designers specify the shape and the size of the component according to their experience, other conditions which they know, or the constrain of working conditions to, then determine the amount of steel bar and tendon on the basis of ultimate limit states and serviceability limit states. The importance of balancing between reliability and economy must be considered. It is an optimum design problem to make sure that the structure can complete its functions in its design working life by a most economy way in practice.The main factors which influence the performances of components include loadings and their effects, material strengths, the quality of construction, resistance forces and so on. The uncertainty of the loadings and their combinations which leads to the uncertainty of the load effects which is inverted by the loadings, adding to the uncertainty of material strengths, the uncertainty in experiment and statistics and the differences in samples and real materials determines the uncertainty of the material performances. So we should design based on reliability.Although the formulas in our codes concerning serviceability limit states are based on the theory of reliability, most of them are a little complex and nonlinear in high degree. It is too erroneous for practice to use JC method to deal with these formulas.The paper proceeds with the balance between reliability and economy. In serviceability limit states, with the size of the component and the amount of steel bar as design variables, material parameters as random variables, the reliability indexes which are no less than specified reliability indexes as constrain requirement, pre-stressed concrete beams are optimized by a combination of response surface method and complex method. As a result, the beams can not only satisfy the requirements in serviceability limit states, but also minimize the cost in order to save the budget.