OPTIMUM DESIGN OF FIXED RC BEAM USING A META-HEURISTIC TECHNIQUE by Vijay Kumar
Abstract
In the present era of infrastructural and economic development, civil engineering structures play a very important role. Since the construction cost has sky rocketed in recent years, it becomes imperative for builders and clients to look for economical design that fulfils all safety parameters. To survive the competition, construction companies try to reduce the cost of structures as much as possible for which they need to reduce the cost of every structural element. This can be done by finding a possibility, among thousands of cases, that leads to minimum cost keeping the strength and other parameters satisfied. So, optimization becomes an essential requirement. There are various optimization techniques based on different criterion, which are being used by researchers. Each of these has certain advantages and limitations. There is no technique that can be considered an all-weather technique, because these techniques have been developed by the researchers considering a particular problem. The motivation behind present work was to check the suitability of one of the latest optimization techniques namely ‘Ray Optimization’ for the design of fixed reinforced concrete (RC) beam. This technique is based on ‘refraction phenomena’ of light. Since the phenomena under consideration is a physical one, it becomes easy to understand and use the technique. Exploration capabilities of this technique have also been found to be good. The law of refraction, known as Snell’s Law plays its role in defining the algorithm. The convergence of the process is dependent on the value ‘refractive index ratio’ that can be defined by the user as an input, and this parameter defines the rate of convergence to the global optimum solution. Other factors that affects the convergence are size of search space, number of local minima etc. In this research, a fixed RC beam is optimized using Ray Optimization for different cases of loadings and spans. Two algorithms, one for design of fixed RC beam and second for Ray Optimization have been written in MATLAB editor as functions. Both these programs are combined to work as a single entity for optimum beam design. Two variables namely effective depth of beam and width of beam are considered as variables for the optimization problem. Other parameters like grade of concrete, grade of steel, width of support, span and loading are taken as inputs from user, hence during the optimization process they are considered as constants. A number of designs considering different spans, grade of steel and concrete are generated using the algorithm to check their effect on overall cost of the beam. A number of optimum designs are studied and variation of cost is compared with the grades of concrete and steel, which indicates that higher grade of steel leads to reduced overall cost of the member. Percentage optimization also increased from 8 percent to 15 percent as span of the beam was increasing and
the results of the program was best when the refractive index ratio was kept between 0.4 to 0.7.
