In this chapter, an optimization methodology for design of post-tensioned axially symmetric cylindrical reinforced concrete (RC) walls is presented. The objective of optimization is the minimization of total material cost of the wall including concrete, reinforced bars, post-tensioned cables, and form work required for wall and application of the post-tensioning. The optimized values are wall thickness, compressive strength of the concrete, locations and intensities of the post-tensioned loads, the diameter of the reinforcement bars (rebars), and distance between rebars. The optimization process employs the superposition method (SPM) for the analyses of the wall, and the design constraints are defined according to ACI-318: Building code requirements for structural concrete.
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For the storage of liquids, water tanks are formed by using analyzing and designing axially symmetric cylindrical walls. Since the storage is a liquid that can lead easily, serviceability requirements including the limitation of cracking under applied loads must be critically considered in addition to strength factors. All serviceability and structural state limits (stress factors) are formulated and ruled in design regulations such as ACI 318: Building code requirements for structural concrete. To provide all serviceability and stress conditions, unphysical solutions with very large wall thickness, big diameter and dense spacing of rebars may be needed. In this situation, water tank may not be economic. To decrease costs and provide better serviceability, the application of post-tension systems via cables can be considered. An optimized post-tensioning forces combination can reduce the magnitude of the internal forces, and due to that, slender container wall designs, decrease in the amount of rebars and reduction in the number and size of cracks can be provided.
The optimum design of RC liquid tanks has been investigated by only considering the optimum design of RC design without post-tensioning (Adidam & Subramanyam 1982; Saxena, Sharma, & Mohan, 1987; Thevendran & Thambiratnam 1988; Tan, Thevendran, & Gupta 1993; Barakat & Altoubat 2009; El Ansary, El Damatty, & Nassef, 2011; Bekdaş, 2014). The optimum design of reinforced concrete (RC) cylindrical walls with post-tensioning forces was also optimized by using harmony search (HS) (Bekdaş, 2015) and other algorithms such as Harmony Search (HS), Flower Pollination Algorithm (FPA), Teaching Learning Based Optimization (TLBO), Jaya Algorithm (JA) including hybrid ones (Bekdaş, 2018, 2019). In this chapter, the methodology developed by Bekdaş (2015) is presented.