# A Study on Cost Optimised Structural Design of Reinforced Concrete Beams - CivilEngineeringBible.com (Download FREE!)

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Cement Concrete is basically a mixture of all Binding Materials such as Cement, Fine Aggregate, Coarse Aggregate, Water and Admixture in a proper proportion in order to achieve a Concrete comprises of Desired properties at it’s Both the State – Fresh as well as Hardened. As Concrete is a Heterogeneous Material comprises of Brittle Failure and Thus, we need Any Material which can take Tension and that basically termed as a Reinforcement. Now, both of them Combined together will give us Reinforced Cement Concrete. Here, Basically, Steel is most acceptable because it gives very High Strength, Most Economical among all the metals and most importantly, Coefficient of Thermal Expansion is comparable that of Concrete.

Basically this Research Paper talks about the Design as well as Analysis Portion of the Reinforced Cement Concrete Beam. The Analysis Portion is related to Equilibrium, Compatibility and Energy related factors which each and every Structure must ensure before making any Design. Design related to whether it’s Steel, Reinforced Cement Concrete, Prestressed Concrete – Here the factors which mainly influenced are-

1) __Safety__ – Each and Every Structure must be safe enough by providing a certain Factor of safety for each load which may acts on it during it’s expected life.

2) __Serviceability__ – Each and Every Structure should provide service for which it has to be constructed.

3) __Durability __- Each and Every Structure should be capable enough to sustain the loading for which it was designed and it should perform well with respect to its Safety as well as Serviceability during it’s intended life. Serviceability plays a vital role in Durability. Basically, Durability without Serviceability with providing certain kind of Less Margin of safety has no meaning at all.

4) __Economy__ – Design and Construction of any Structure like Residential, Commercial, Industrial, Institutional, Bridges, Dams, Culverts etc. should be economical without affecting the first three parameters such as Safety, serviceability and Durability.

5) __Aesthetic__ – Aesthetic plays a vital role when huge investment is involved in a particular project.

Here, In this Paper, Genetic Algorithm is used to Initialize the Population and then Based upon Fitness Value, will Select Best Few among it and then by Process of Cross-Over and Mutation, Will Generate Next Population and will again Evaluate it and this Cycle will keep on Going. The Same thing has been followed by Nature too. As we move from Generations to Generations, Function improve upon the fitness through a process of Cross over and Mutation. The similar thing is also adapted in case of optimization problems. Here, basically we create the Population of Feasible Solutions and as we all know that fitness function is equivalent to the objective function and solutions which are more fit than others have more chance of getting selected. And out of them, we have a Cross over and a Mutation process through which we create the new Population for the next Generation and finally we create a set of feasible solutions with higher average fitness values. Best one will be closer to Optimal Solution and the entire process is called Genetic Algorithm.

The program in the MATLAB was executed for different values of Imposed loads (Live Loads) and Spans. The Spans chosen for optimizing the Total Cost of RCC Beam was 2, 3 4, 6 and 8 meters respectively. The Imposed loads were varied as 10, 25, 50 and 100 kN. The Design Variables were observed to be found increasing with increase in Imposed load and Span.

The Cost of Concrete here increases from M15 to M30 as mentioned earlier in Decision Variables. This may be because rich mixes require additional ingredients like admixtures, more specific procedures and testing. Here, Grade of Concrete vs Cost is as given earlier in Table as M15, M20, M25 and M30 were found to be 6570.00, 7074.30, 8634.05 and 8710.55 rupees respectively. Optimum cost of Concrete will be achieved if lower grades of concrete are used.

To meet the Strength Constraints, the Sectional Properties should be accordingly increased. Fig. 10 shows the variation of Grade of Concrete with Span. As shown in Figure, The results shows that the program tried to maximize the use of M15 grade for shorter spans. For Bigger Spans, the Bending Moments will be higher and hence it requires higher grades to resist the same.

The Cost of Reinforcing Steel is found to be around 20 times of that of cost of Concrete. Therefore, the main focus of Reinforced Concrete Beam optimisation should be on the minimization of quantity of steel. The program has tried to keep the Area of Steel closer to the lower bound value as far as possible. The Area of Steel obtained was very less even for higher spans. But as indicating in the Figure, at a heavy load of 100 kN/m^{2}, the Ast values were found higher.

For Smaller spans, the Ast values are nearer to the lower bound value. Also the grade of concrete were lesser ones. The limiting moment has a second degree variation with respect to effective depth. That is only one of the reason for the selection of Higher Depths even for Smaller Spans. The Spacing of Stirrups *Sv *values were chosen closer to the upper bound value 300 mm for almost all the spans. However for heavy loading, the spacing has gone down.

In Practical Problems, there may be additional site specific constraints like Architectural Limits for Beam Dimensions, Available size of form work, Available grade of concrete and steel etc. The program has been conveniently modified to suit the local requirements.

This, The Optimisation of RCC beam was carried out by the Minimisation of Cost of the Beam considering the Design Constraints into accountant. The problem was solved using Genetic Algorithm Optimisation Technique. MATLAB R2014a was used for the Programming of the Optimisation Problem. The Genetic Algorithm based Optimisation gave reasonable results satisfying the Design Constraints. The results show a good trade - off between the grade of concrete and the sectional properties. The program can be suitably modified to meet the practical requirements of a given problem. The results obtained from the program can be used as an aid for design of RCC members.

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