Buckling and free vibration analysis of non-prismatic columns using optimized shape functions and Rayleigh method

In this paper, optimized shape functions have been used in Rayleigh method to determine the critical buckling load and the fundamental natural frequency of non-prismatic steel-reinforced slender concrete columns. A range of admissible shape functions describing the mode shape in buckling as well as for the fundamental natural frequency of the column are considered and then an optimization strategy is developed to arrive at the optimum shape function. The results obtained from the present method based on the implementation of Rayleigh method through the concept of generalized coordinates are verified and validated by the finite element method. The application of the theory is demonstrated by two illustrative examples, both of which are steel-reinforced concrete towers that are representative of practical structures. Of particular significance is the duality between the free vibration and buckling problems which is captured and fruitfully exploited in the analysis. The effect of an additional mass located at the top of the tower is included in the investigation. Additionally, the impact of the creep behavior of the towers on results due to continuing lapse of time is critically examined and assessed. Finally, significant conclusions are drawn following the discussion of results.