Analysis of the prestressed composite beams using flexibility-stiffness method and optimization of design variables

The use of prestressed concrete, has begun progress today and on this basis, both experimental and theoretical has strong backing, but this technique is less concerned with steel, and especially when the combination of concrete and steel is used, the lack of instructions becomes more apparent. In this paper, by presenting the proposed increase in load method, the first results of the plastic analysis of a single-span beam were compared with the strain increase method and the experiment and then, the method of analysis of a continuous double beam with combine of stiffness and flexible method, such as a bridge, has been investigated and finally, the variables of cable length, eccentricity of the cable, and the thickness of the slab in terms of performance optimization, are illustrated by the diagram. It has been found that in the combinatorial method analysis , the inversion of smaller matrices is required compared to the stiffness method, and  the results in the optimization section are shown, adding cables will increase the final load bearing in this sample, and a larger eccentricity will cause a larger internal resistance in the beam. Also, although the thickness of the concrete slab strength, increases the final capacity in these specimens, it does not affect the elastic capacity in pre-tension before concrete.