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The main aim of the present study is to achieve optimum design of reinforced concrete (RC) plane moment frames using bat algorithm (BA) which is a newly developed meta-heuristic optimization algorithm based on the echolocation behaviour of bats. The objective function is the total cost of the frame and the design constraints are checked during the optimization process based on ACI 318-08 code. Design variables are the cross-sectional assignments of the structural members and are selected from a data set containing a finite number of sectional properties of beams and columns in a practical range. Three design examples including four, eight and twelve story RC frames are presented and the results are compared with those of other algorithms. The numerical results demonstrate the superiority of the BA to the other meta-heuristic algorithms in terms of the frame optimal cost and the convergence rate.

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A new meta-heuristic algorithm is proposed for optimal design of reinforced concrete (RC) frame structures subject to combinations of gravity and lateral static loads based on ACI 318-08 design code. In the present work, artificial bee colony algorithm (ABCA) is focused and an improved ABCA (IABCA) is proposed to achieve the optimization task. The total cost of the RC frames is minimized during the optimization process subject to constraints on demand capacity ratios (DCRs) of structural members. Three benchmark design examples are tested using ABCA and IABCA and the results are compared with those of presented in the literature. The numerical results indicate that the proposed IABCA is an efficient computational tool for discrete optimization of RC frames.

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One of the main tasks of engineers is to design structural systems light and economic as possible, yet resistant enough to withstand all possible loads arising during their service life and to absorb the induced seismic energy in a controlled and predictable fashion. The traditional trial-and-error design approach is not capable to determine an economical design satisfying also the code requirements. Structural design optimization, on the other hand, provides a numerical procedure that can replace the traditional design approach with an automated one. The objective of this work is to propose a performance-based seismic design procedure, formulated as a structural design optimization problem, for designing steel and steel-concrete composite buildings subject to interstorey drift limitations. In particular a straightforward design procedure is proposed where the influence on both record and incident angle is considered. For this purpose six test examples are considered, in particular three steel and three steel-concrete composite buildings are optimally designed for minimum initial cost.

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Structural  design  optimization  usually  deals  with  multiple  conflicting  objectives  to  obtain the minimum construction cost, minimum weight, and maximum safety of the final design. Therefore, finding the optimum design is hard and time-consuming for  such problems.  In this paper, we borrow the basic concept of multi-criterion decision-making and combine it with  Particle  Swarm  Optimization  (PSO)  to  develop  an  algorithm  for  accelerating convergence  toward  the  optimum  solution  in  structural  multi-objective  optimization scenarios.  The effectiveness of the proposed algorithm was illustrated in some benchmark reinforced concrete (RC) optimization problems. The main goal was to minimize the cost or weight of structures while satisfying all design requirements imposed by design codes.  The results confirm the ability of the proposed algorithm to efficiently find optimal solutions for structural optimization problems.

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Due to several uncertainties  which  affect structural responses of Reinforced concrete (RC) frames,  it is sensibly required  to  apply  a vulnerability analysis tool such as fragility curve. To  construct an analytical fragility curve, the incremental dynamic analysis (IDA) method has been extensively used as an applicable seismic analysis tool. To employ the IDA method for constructing fragility curves of RC frames,  it is important  to know  how many records will  be  adequate  to  assess  seismic  risk  analysis  properly?  Another  issue  is  to  know  how many IDA steps  are  required for developing an accurate fitted fragility function? For this purpose,  two 3D RC frames  called  3STRCF and 5STRCF have been nonlinearly modeled and 200 2-componets actual records have been considered for  the  IDA. The results  reveal that at least 15 IDA steps  are  required  to  reduce  fragility function error to less than 5% and 10  IDA  steps  are  required  to  yield  less  than  10%  error.  In  addition,  it  is  revealed  that  a selection of 100 records is completely adequate to be certain   to have  an accurate fragility curve. It is concluded that at least 25 records are required to decrease fragility curve error to less than 5% and 15 records to  have  less than 10%. The closeness of fragility curve error variation for two models and in all limit states show that these results can be generalized to other RC frames.

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This paper deals with the effect of fiber aspect ratio of steel fibers on shear strength of steel fiber reinforced concrete deep beams loaded with shear span to depth ratio less than two using the artificial neural network technique. The network model predicts reasonably good results when compared with the equation proposed by previous researchers. The parametric study involves deep beams of M55 grade concrete with fiber volume fraction 0.5% to 2% of fiber aspect ratio ranging from 50 to 100 and longitudinal steel percentage varying from 0% to 2.5%. The analysis reveals that the fiber aspect ratio also affects the shear strength and needs to be combined with fiber volume fraction.
 

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This paper presents a Cuckoo Optimization Algorithm (COA) model for the cost optimization of the one-way and two-way reinforced concrete (RC) slabs according to ACI code. The objective function is the total cost of the slabs including the cost of the concrete and that of the reinforcing steel. In this paper, One-way and two-way slabs with various end conditions are formulated as ACI code. The two-way slabs are modelled and analyzed using direct design method. The problems are formulated as mixed-discrete variables such as: thickness of slab, steel bar diameter, and bar spacing. The presented model can be applied in design offices to reduce the cost of the projects. It is also the first application of the Cuckoo Optimization Algorithm to the optimization of RC slabs. In order to demonstrate the superiority of the presented method in convergence and leading to better solutions, the results of the proposed model are compared with the other optimization algorithms.

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Reinforced concrete (RC) slabs exhibit complexities in their structural behavior under load due to the composite nature of the material and the multitude and variety of factors that affect such behavior. Current methods for determining the load-deflection behavior of reinforced concrete slabs are limited in scope and are mostly dependable on the results of experimental tests. In this study, an alternative approach using Artificial Neural Network (ANN) model is produced to predict the load-deflection behavior of a two-way RC slab. In the study, 30 sets of RC slab specimens of sizes 700mm x 600mm x 75mm were cast, cured for 28days using the sprinkling method of curing and tested for deflection experimentally by applying loads ranging from 10kN to 155kN at intervals of 5kN. ANN model was then developed using the neural network toolbox of ANN in MATLAB version R2015a using back propagation algorithm. About 54% of the RC specimens were used for the training of the network while 23% of the sets were used for validation leaving the remaining 23 % for testing the network. The experimental test results show that the higher the applied load on the slab, the higher the deflection. The result of the ANN model shows a good correlation between the experimental test and the predicted results with training, validation and test correlation coefficients of 0.99692, 0.98921 and 0.99611 respectively. It was also found that ANN model is quite efficient in determining the deflection of 2-way RC slab. The predicted accuracy of performance value for the load-deflection set falls at 96.67% of the experimental load-deflection with a 0.31% minimum error using the Microsoft spreadsheet model. As such the comprehensive spreadsheet tool created to incorporate the optimum neural network. The spreadsheet model uses the Microsoft version 2013 excel tool software and can be used by structural engineers for instantaneous access to the prediction if any aspect of a concrete slab behavior given minimal data to describe the slab and the loading condition.

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The constitutive relationships presented for concrete modeling are often associated with unknown material constants. These constants are in fact the connectors of mathematical models to experimental results. Experimental determination of these constants is always associated with some difficulties. Their values are usually determined through trial and error procedure, with regard to experimental results. In this study, in order to determine the material constants of an elastic-damage-plastic model proposed for concrete, the results of 44 uniaxial compression and tension experiments collected from literature were used. These constants were determined by investigating the consistency of experimental and modeling results using a genetic algorithm optimization tool for all the samples; then, the precision of resulted constants were investigated by simulating cyclic and biaxial loading experiments. The simulation results were compared to those of the corresponding experimental data. The results observed in comparisons indicated the accuracy of obtained material constants in concrete modeling.

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Several researchers have proved that the constitutive models of concrete based on combination of continuum damage and plasticity theories are able to reproduce the major aspects of concrete behavior. A problem of such damage-plasticity models is associated with the material constants which are needed to be determined before using the model. These constants are in fact the connectors of constitutive models to the experimental results. Experimental determination of these constants is always associated with some problems, which restricts the applicability of such models despite their accuracy and capabilities. In the present paper, the values of material constants for a damage-plasticity model determined in part I of this work were used as a database. Genetic programming was employed to discover equations which directly relate the material constants to the concrete primary variables whose values could be simply inferred from the results of uniaxial tension and compressive tests. The simulations of uniaxial tension and compressive tests performed by using the constants extracted from the proposed equations, exhibited a reasonable level of precision.  The validity of suggested equations were also assessed via simulating experiments which were not involved in the procedure of equation discovery. The comparisons revealed the satisfactory accuracy of proposed equations.

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In this study, the complex behavior of steel encased reinforced concrete (SRC) composite beam–columns in biaxial bending is predicted by multilayer perceptron neural network. For this purpose, the previously proposed nonlinear analysis model, mixed beam-column formulation, is verified with biaxial bending test results. Then a large set of benchmark frames is provided and P-M_x-M_y triaxial interaction curve is obtained for them. The specifications of these frames and their analytical results are defined as inputs and targets of artificial neural network and a relatively accurate estimation model of the nonlinear behavior of these beam-columns is presented. In the end, the results of neural network are compared to some analytical examples of biaxial bending to determine the accuracy of the model.

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In structural design, either the experience of designer is used or a uniform grouping is usually utilized to group the elements. This type of grouping affects the fundamental cost of the buildings, including the cost of concrete, steel and formwork, as well as secondary costs such as laboratory, checking, fabrication and etc. However, the secondary costs are not usually considered in the cost function. Strategies can also be used to automate the grouping of members in structural design. In this strategy beams and columns are automatically grouped into a limited number of groups to achieve the lowest cost. In this study, enhanced colliding bodies optimization algorithm is used to automatically group the beams and columns of the reinforced concrete structures and also to optimize their cost. The proposed procedure applied to three reinforced concrete frames with four, eight and twelve stories and the influence of automatic grouping of the members in optimal cost is investigated. Using this method, the beams and columns are automatically grouped and the results show that the optimal cost obtained from the automatic grouping is less than the manual grouping of the members.

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Reducing waste material plays an essential role for engineers in the current world. Nowadays, recycled materials are going to be used in order to manufacture concrete beams. Previous studies concluded that the currently proposed formulas to predict the flexural and shear behavior of the reinforced concrete beams were not appropriate for those manufactured by recycled materials. This study aims to employ the Particle Swarm Optimization Algorithm to suggest the flexural and shear performance of recycled material reinforced concrete beams. For this purpose, the previous experimental outcomes are utilized, and new equations are established to anticipate both flexural and shear behavior of the recycled material concrete beams. Consequently, all findings are compared with those achieved experimentally. The attained significances of this study show that the proposed formulas have high accuracy for the experimental data.

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The main object in optimizing reinforced concrete frames based on the performance is decreasing the initial cost or life cycle cost or total cost. The optimization performed here is with the requirement of satisfying story drifts and rotation of plastic hinges. However, this optimization may decrease seismic strength of the structure. Newton Meta-Heuristic Algorithm (NMA) was used to optimize three-, six-, and twelve-story reinforced concrete frames based on the performance and utilizing the cost objective function. The seismic parameters of the optimized frames were calculated. The results showed that the inter-story drifts at the performance level of LS controls the design. According to the results, the objective function for construction cost is not useful for the optimization of the reinforced concrete frames. Because the amounts of the over strength, the absorbed plastic energy, and the ductility factor for the optimized frames are low using the objective function for the construction cost.

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In this paper, a new robust metaheuristic optimization algorithm called improved time evolutionary optimization (ITEO) is applied to design reinforced concrete one-way ribbed slabs. Geometric and strength characteristics of concrete slabs are considered as design variables. The optimal design is such that in addition to achieving the minimum cost, all design constraints are satisfied under American Concrete Institute’s ACI 318-05 Standard. So, the numerical examples considered in this study have a large number of design variables and design constraints that make it complicated to converge the global optimal design. The ITEO has an excellent balance between the two phases of exploration and extraction and it has a high ability to find the optimal point of such problems. The comparison results between the ITEO and some other metaheuristic algorithms show the proposed method is competitive compared to others, and in some cases, superior to some other available metaheuristic techniques in terms of the faster convergence rate, performance, robustness of finding an optimal design solution, and needs a smaller number of function evaluations for designing considered constrained engineering problems.
 

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In this article, the optimum design of a reinforced concrete solid slab is presented via an efficient hybrid metaheuristic algorithm that is recently developed. This algorithm utilizes the mouth-brooding fish (MBF) algorithm as the main engine and uses the favorable properties of the colliding bodies optimization (CBO) algorithm. The efficiency of this algorithm is compared with mouth-brooding fish (MBF), Neural Dynamic (ND), Cuckoo Search Optimization (COA) and Particle Swarm Optimization (PSO). The cost of the solid slab is considered to be the objective function, and the design is based on the ACI code. The numerical results indicate that this hybrid metaheuristic algorithm can to construct very promising results and has merits in solving challenging optimization problems.
 

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The main objective of this study is to optimize reinforced concrete (RC) frames in the framework of performance-based design using metaheuristics. Three improved and efficient metaheuristics are employed in this work, namely, improved multi-verse (IMV), improved black hole (IBH) and modified newton metaheuristic algorithm (MNMA). These metaheuristic algorithms are applied for performance-based design optimization of 6- and 12-story planar RC frames. The seismic response of the structures is evaluated using pushover analysis during the optimization process. The obtained results show that the IBH outperforms the other algorithms.
 

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In this paper an enhanced ant colony optimization algorithm with a direct constraints handling strategy is proposed for the optimization of reinforced concrete frames. The construction cost of reinforced concrete frames is considered as the objective function, which should be minimized subject to geometrical and behavioral strength constraints. For this purpose, a new probabilistic function is added to the ant colony optimization algorithm to directly satisfy the geometrical constraints. Furthermore, the position of an ant in each iteration is updated if a better solution is found in terms of objective value and behavioral strength constraints satisfaction. Five benchmark design examples of planar reinforced concrete frames are presented to illustrate the efficiency of the proposed algorithm.  
 

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This study uses an elitist Genetic Algorithm (GA) to optimize material costs in one-way reinforced concrete slabs, adhering to ACI 318-19. A sensitivity analysis demonstrated the critical role of elitism in GA performance. Without elitism, the GA consistently failed to reach the target objective, with success rates often nearing zero across various crossover fractions. Incorporating elitism dramatically increased success rates, highlighting the importance of preserving high-performing individuals. With an optimal configuration of 0.3 crossover fraction and 0.45 elite percentage, a 92% success rate was achieved, finding a cost of 24.91 in 46 of 50 runs for a simply supported slab. This optimized design, compared to designs based on ACI 318-99 and ACI 318-08, yielded material cost savings of between 5.8% to 8.6% for simply supported, one-end continuous, both-ends continuous, and cantilevered slabs. The influence of slab dimensions on cost was evaluated across 64 scenarios, varying slab lengths from 5 to 20 feet for each support condition. Resulting cost versus slab length diagrams illustrate the economic benefits of GA optimization.