Julián Alcalá

Design of reinforced concrete bridge frames by heuristic optimization

This paper deals with the economic optimization of reinforced concrete box frames used in road construction. It shows the efficiency of four heuristic algorithms applied to a problem of 50 design variables. Heuristic methods used are the random walk and the descent local search. The metaheuristic methods are the threshold accepting and the simulated annealing. The four methods have been applied to the same frame of 13 m of horizontal span. The comparison of the four heuristic algorithms leads to the conclusion that the proposed threshold accepting is more efficient, since it improves cost results of the random walk and descent local search by 7.5% and 1.4%, respectively, while improving deviation of random results of the simulated annealing. Finally, the inclusion of the deflections and fatigue limit states appears to be crucial, since their ignorance leads to 3.9% more economic but unsafe results.

Optimization of concrete I-beams using a new hybrid glowworm swarm algorithm

In this paper a new hybrid glowworm swarm algorithm (SAGSO) for solving structural optimization problems is presented. The structure proposed to be optimized here is a simply-supported concrete I-beam defined by 20 variables. Eight different concrete mixtures are studied, varying the compressive strength grade and compacting system. The solutions are evaluated following the Spanish Code for structural concrete. The algorithm is applied to two objective functions, namely the embedded CO2 emissions and the economic cost of the structure. The ability of glowworm swarm optimization (GSO) to search in the entire solution space is combined with the local search by Simulated Annealing (SA) to obtain better results than using the GSO and SA independently. Finally, the hybrid algorithm can solve structural optimization problems applied to discrete variables. The study showed that large sections with a highly exposed surface area and the use of conventional vibrated concrete (CVC) with the lower strength grade minimize the CO2 emissions.

Simulated Annealing Optimization Of Walls,Portal And Box Reinforced ConcreteRoad Structures

This paper deals with the economic optimization of reinforced concrete walls, portal and box frame structures typically used in road construction. It shows the efficiency of heuristic optimization by the simulated annealing algorithm. The evaluation of solutions follows the Spanish Code for structural concrete. Stress resultants and envelopes of framed structures are computed by an external finite element program. Design loads are in accordance with the national IAP Code for road bridges. The algorithm is first applied to RC retaining walls with 26 continuous design variables of geometry, materials and reinforcement. Results on this topic show the importance of limiting the deflection of walls. No restriction leads to slender solutions with deflections of up to 1/40 the height of the wall. Such elements are unfeasible and, hence, a limitation of 1/150 of the height is adopted for the design of these structures. The second structure analysed is a 10 m horizontal span RC portal frame. This example has 28 discrete variables, 5 geometrical, 3 types of concrete and 20 types of reinforcement bars of fixed length. The evaluation module includes the limit states that are commonly checked in design: flexure, shear, deflections, etc. Results of this research are again quite slender, i.e. a slab of 0.375 m (1/26.67 slab/span ratio), not complying with the rarely checked fatigue of concrete. The last type of structure analysed is a 13 m horizontal span RC box road frame. This example has 44 discrete variables, 2 geometrical, 2 types of concrete and 40 reinforcement bars and bar lengths. The evaluation module includes fatigue plus other limit states. Results are now reasonably slender, i.e. a slab of 0.65 m (1/20 slab/span ratio). Finally, run times indicate that heuristic optimization is a forthcoming option for the design of real RC structures.

Optimization of Reinforced Concrete Structures by Simulated Annealing

Early attempts of optimised structural designs go back to the 1600s, when Leonardo da Vinci and Galileo conducted tests of models and full-scale structures [1]. A 1994`s review of structural optimization can be found in the study by Cohn and Dinovitzer [2], who pointed out that there was a gap between theoretical studies and the practical application in practice. They also noted the short number of studies that concentrated on concrete structures. A review of structural concrete optimization can be found in the 1998`s study by Sarma and Adeli [3]. The methods of structural optimization may be classified into two broad groups: exact methods and heuristic methods. The exact methods are the traditional approach. They are based on the calculation of optimal solutions following iterative techniques of linear programming [4,5]. The second main group comprises the heuristic methods, whose recent development is linked to the evolution of artificial intelligence procedures. This group includes a broad number of search algorithms [6-9], such as genetic algorithms, simulated annealing, threshold accepting, tabu search, ant colonies, etc. These methods have been successful in areas different to structural engineering [10]. They consist of simple algorithms, but require a great computational effort, since they include a large number of iterations in which the objective function is evaluated and the structural restrictions are checked. Among the first studies of heuristic optimization applied to structures, the contributions of Jenkins [11] and of Rajeev and Krishnamoorthy [12] in the early 1990s are to be mentioned. Both authors applied genetic algorithms to the optimization of the weight of steel structures. As regards RC structures, early applications in 1997 include the work of Coello et al [13], who applied genetic algorithms to the economic optimization of RC beams. Recently, there has been a number of RC applications [14-16], which optimize RC beams and building frames by genetic algorithms. Also recently, our research group has applied simulated annealing and threshold acceptance to the optimization of walls, frame bridges and building frames [17-20]. However, despite advances on structural concrete optimization, present design-office practice of concrete structures is much conditioned by the experience of structural engineers. Most procedures are based on the adoption of cross-section dimensions and material grades based on sanctioned common practice. Once the structure is defined, it follows the analysis of stress resultants and the computation of passive and active O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

Sustainable design using multiobjective optimization of high-strength concrete I-beams

Sustainable designs require long-term environmental vision. To this end, this study proposes a methodology to design reinforced concrete I-beams based on multiobjective optimization techniques. The objective functions are the economic cost, the CO2 emissions, the service life, and the overall safety coefficient. The procedure was applied to a simply supported concrete I-beam including several high-strength concrete mix compositions. The solution of this 15 m beam was defined by a total of 20 variables. Results indicate that highstrength concrete is used for long-term solutions. Further, the economic feasibility of low-carbon structures remaining in service for long periods and ensuring safety is proven. This methodology is widely applicable to different structure designs and therefore, gives engineers a worthy guide to enhance the sustainability of their designs.

Computer-support tool to optimize bridges automatically

In bridge design, many variables like material grades, cross-sectional dimensions, passive and prestressing steel need to be modeled to evaluate structural performance. Efficiency gains are intended while satisfying the serviceability and ultimate limit states imposed by the structural code. In this paper, a computer-support tool is presented to analyze continuous post-tensioned concrete (PSC) box-girder road bridges, to minimize the cost as well as to provide optimum design variables. The program encompasses six modules to perform the optimization process, the finite-element analysis, and the limit states verification. The methodology is defined and applied to a case study. A harmony search (HS) algorithm optimizes 33 variables that define a three-span PSC box-girder bridge located in a coastal region. However, the same procedure could be implemented to optimize any structure. This tool enables one to define the fixed parameters and the variables that are optimized by the heuristic algorithm. Moreover, the output provides useful rules to guide engineers in designing PSC box-girder road bridges.

Heuristic Design Of A Precast-prestressed Concrete U-beam And Post-tensioned Cast-in-place Concrete Slab Road Bridges

This paper proposes simulated annealing and threshold accepting procedures for the automatic design of two different bridge types. Both cases are prestressed concrete road bridge decks typically used in public road construction. Simulated annealing is first applied to a precast beam of 30–30 meters of longitudinal spans and 12.00 m of width. The beam has a double U-shape cross-section and a beam spacing of 6 m. This problem involves 59 discrete design variables for the geometry of the beam and the slab, concrete grade, reinforcing steel and prestressing steel. The simulated annealing method indicates savings of about 5% with respect to a traditional design. The second bridge case is a 20–36–20 m posttensioned cast-in-place concrete slab road bridge deck. This example needs 33 discrete variables to define the complete structure. The threshold accepting method is used for the optimization. Our findings indicate savings of about 7.5% with respect to the design based on experience. Finally, the results show that heuristic optimization provides other options to reduce the design costs of real prestressed bridge decks.

Heuristic Optimization Of Prestressed ConcretePrecast Pedestrian Bridges

This paper deals with the economic optimization of prestressed concrete precast pedestrian bridges typically used in public works construction. These bridges are made of a precast concrete beam that integrates an upper reinforced concrete slab for the pedestrian traffic. The beam has a U-shape cross-section. Typical span lengths range from 20 to 40 m and the width ranges from 3.00 to 6.00 m. The study shows the efficiency of heuristic optimization by the simulated annealing (SA) and the threshold accepting (TA) algorithms. The evaluation of solutions follows the Spanish Code for structural concrete. Stress resultants and envelopes of these structures are computed by direct calculation. Design loads are in accordance with the national IAP Code for road bridges. The algorithms are applied to a typical pedestrian bridge of 40 m of span length and 6.00 m of width. This example has 59 discrete design variables for the geometry of the beam and the slab, materials in the two elements and active and passive reinforcement. The evaluation module includes the limit states that are commonly checked in design: flexure, shear, deflections, etc. The application of the SA and TA algorithms requires the calibration of the initial temperature and threshold, the number of variables modified in each iteration, the length of the Markov chains and the reducing coefficient. Each heuristic is run nine times so as to obtain statistical information about the minimum, average and deviation of the results. The best result has a cost of 27,586 euros for the SA algorithm and 27,570 euros for the TA algorithm. Finally, solutions and run times indicate that heuristic optimization is a forthcoming option for the design of real prestressed structures.