• Advances in Computational Design
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• 제8권4호
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• pp.295-307
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• 2023

This paper presents an optimization of the reinforced concrete ribbed slab in terms of minimum CO₂ emissions and an economic justification of the final optimal design. The design variables are six geometry variables including the slab thickness, the ribs spacing, the rib width at the lower and toper end, the depth of the rib and the bar diameter of the reinforcement, and the seventh variable defines the concrete strength. The objective function is considered to be the minimum amount of carbon dioxide gas (CO₂) emission and at the same time, the optimal design is economical. Seven significant design constraints of American Concrete Institute's Standard were considered. A robust metaheuristic optimization method called improved dolphin echolocation and ant colony optimization (IDEACO) has been used to obtain the best possible answer. At optimal design, the three most important sources of CO₂ emissions include concrete, steel reinforcement, and formwork that the contribution of them are 63.72, 32.17, and 4.11 percent respectively. Formwork, concrete, steel reinforcement, and CO₂ are the four most important sources of cost with contributions of 67.56, 19.49, 12.44, and 0.51 percent respectively. Results obtained by IDEACO show that cost and CO₂ emissions are closely related, so the presented method is a practical solution that was able to reduce the cost and CO₂ emissions simultaneously.

• Computers and Concrete
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• 제13권4호
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• pp.457-482
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• 2014

This paper summarizes available literature on the optimization of reinforced concrete (RC) beams. The objective of optimization (e.g. minimum cost or weight), the design variables and the constraints considered by different studies vary widely and therefore, different optimization methods have been employed to provide the optimal design of RC beams, whether as isolated structural components or as part of a structural frame. The review of literature suggests that nonlinear deterministic approaches can be efficiently employed to provide optimal design of RC beams, given the small number of variables. This paper also presents spreadsheet implementation of cost optimization of RC beams in the familiar MS Excel environment to illustrate the efficiency of the exhaustive enumeration method for such small discrete search spaces and to promote its use by engineers and researchers. Furthermore, a sensitivity analysis is performed on the contribution of various design parameters to the variability of the overall cost of RC beams.

• Steel and Composite Structures
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• 제29권2호
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• pp.243-256
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• 2018

This study conducts an optimization and sensitivity analysis on rectangular reinforced concrete (RC) beam using Lagrangian Multiplier Method (LMM) as programming optimization computer soft ware. The analysis is conducted to obtain the minimum design cost for both singly and doubly RC beams according to the specifications of three regulations of American concrete institute (ACI), British regulation (BS), and Iranian concrete regulation (ICS). Moreover, a sensitivity analysis on cost is performed with respect to the effective parameters such as length, width, and depth of beam, and area of reinforcement. Accordingly, various curves are developed to be feasibly utilized in design of RC beams. Numerical examples are also represented to better illustrate the design steps. The results indicate that instead of complex optimization relationships, the LMM can be used to minimize the cost of singly and doubly reinforced beams with different boundary conditions. The results of the sensitivity analysis on LMM indicate that each regulation can provide the most optimal values at specific situations. Therefore, using the graphs proposed for different design conditions can effectively help the designer (without necessity of primary optimization knowledge) choose the best regulation and values of design parameters.

• Structural Engineering and Mechanics
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• 제51권3호
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• pp.361-375
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• 2014

The main aim of this paper is to investigate the relationship between thickness and height of the axially symmetric cylindrical reinforced concrete (RC) walls by the help of a meta-heuristic optimization procedure. The material cost of the wall which includes concrete, reinforcement and formwork, was chosen as objective function of the optimization problem. The wall thickness, compressive strength of concrete and diameter of reinforcement bars were defined as design variables and tank volume, radius and height of the wall, loading condition and unit cost of material were defined as design constants. Numerical analyses of the wall were conducted by using superposition method (SPM) considering ACI 318-Building code requirements for structural concrete. The optimum wall thickness-height relationship was investigated under three main cases related with compressive strength of concrete and density of the stored liquid. According to the results, the proposed method is effective on finding the optimum design with minimum cost.

• Computers and Concrete
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• 제14권4호
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• pp.445-462
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• 2014

To solve structural optimization problems, it is necessary to integrate a structural analysis package and an optimization package. There have been many packages that can be employed to analyze reinforced concrete plane frames. However, because most structural analysis packages suffer from closeness of systems, it is very difficult to integrate them with optimization packages. To overcome the difficulty, we proposed a possible alternative, DAMDO, which integrates Design, Analysis, Modeling, Definition, and Optimization phases into an integration environment as follows. (1) Design: first generate many possible structural design alternatives. Each design alternative consists of many design variables X. (2) Analysis: employ the structural analysis software to analyze all structural design alternatives to obtain their internal forces and displacements. They are the response variables Y. (3) Modeling: employ artificial neural networks to build the models Y=f(X) to obtain the relationship functions between the design variables X and the response variables Y. (4) Definition: employ the design variables X and the response variables Y to define the objective function and constraint functions. (5) Optimization: employ the optimization software to solve the optimization problem consisting of the objective function and the constraint functions to produce the optimum design variables. The RC frame optimization problem was examined to evaluate the DAMDO approach, and the empirical results showed that it can be solved by the approach.

• Computers and Concrete
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• 제26권1호
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• pp.1-10
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• 2020

In this paper, a procedure for automated optimized design of reinforced concrete frames has been presented. The procedure consists of formulation and solution of the design problem in the form of an optimization problem. The minimization of total cost of R/C frame has been taken as the objective of optimization problem. In this research, consistent approximation method is applied to explicitly formulate constraints and objective function in terms of the design variables. In the presented method, the primary optimization problem is replaced with a sequence of explicit sub-problems. Each sub-problem is efficiently solved using the Sequential Quadratic Programming (SQP) method. The proposed method is demonstrated through a four-story frame and an eight-story frame, and the optimum results are compared with those in the available literature. It is shown that the proposed method can be easily applied to obtain rational, reliable, economical and practical designs for Reinforced Concrete Moment Resisting Frames (RCMRFs) while it is converged after a few analyses.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1999년도 가을 학술발표회 논문집
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• pp.127-134
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• 1999

An optimization algorithm based on Genetic Algorithm(GA) is developed for discrete optimization of reinforced concrete plane frame by constructing databases. Under multiple loading conditions, discrete optimum sets of reinforcements for both negative and positive moments in beams, their dimensions, column reinforcement, and their column dimensions are found. Construction practice is also implemented by linking columns and beams by group ‘Connectivity’between columns located in the same column line is also considered. It is shown that the developed genetic algorithm was able to reach optimum design for reinforced concrete plane frame construction practice.

• Computers and Concrete
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• 제3권5호
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• pp.313-334
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• 2006

A novel formulation aiming to achieve optimal design of reinforced concrete (RC) structures is presented here. Optimal sizing and reinforcing for beam and column members in multi-bay and multistory RC structures incorporates optimal stiffness correlation among all structural members and results in cost savings over typical-practice design solutions. A Nonlinear Programming algorithm searches for a minimum cost solution that satisfies ACI 2005 code requirements for axial and flexural loads. Material and labor costs for forming and placing concrete and steel are incorporated as a function of member size using RS Means 2005 cost data. Successful implementation demonstrates the abilities and performance of MATLAB's (The Mathworks, Inc.) Sequential Quadratic Programming algorithm for the design optimization of RC structures. A number of examples are presented that demonstrate the ability of this formulation to achieve optimal designs.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1998년도 봄 학술발표회논문집(II)
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• pp.541-546
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• 1998

The use of steel fibers in conventional reinforced concrete increases the strength and ductility under various loading conditions. In order to examine the possibility of the use of these combinations achieving required strength and ductility of a reinforced concrete beam, a refined optimization procedure based on nonlinear layered finite element method and nonlinear programming technique is developed in this study. Six design variables-beam width and depth, fiber volume fraction, amounts of tensile and compressive rebars, and stirrup, and stirrup spacing-are considered. The developed model can be used as a tool in determining the economical use of steel fibers in designing the reinforced steel fibrous concrete beam.

• KCI Concrete Journal
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• 제12권1호
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• pp.79-89
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• 2000

This research developed an accelerated curing processe for cellulose fiber reinforced cement composites using vigorous reaction between carbon dioxide and cement paste. A wet-processed cellulose fiber reinforced cement system was considered. Carbonation curing was used to complement conventional accelerated curing. The parametric study followed by optimization investigation indicated that the carbonation curing can enhance the productivity and energy efficiency of manufacturing cellulose fiber reinforced cement composites. This also adds environmental benefits to the technical and economical advantages of the technology.