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At present, several methods are available for optimization of structures. The application of such methods to real structural problems, however, has not been as intense as the development of the techniques themselves. One of the main reasons is that the great majority of the methods, based on mathematical programming, consider a continuous search space. This paper presents an application of the Simulated Annealing method to the optimization of trusses considering the cross sections of the members as discrete variables. The constraints imposed to the analysis were the allowable stresses and the displacements on nodes. Some examples are presented in order to demonstrate the effectiveness of the method when compared with other methods found in literature

Owing to the elevated cost of bridges, especially when compared to the cost of roads, their rational design and material selection are fundamental properties to consider when aiming to reduce the environmental impacts and lengthen the lifespan of the bridge. Especially in developing countries, the construction of new bridges (mainly short spanned) is still a necessity, and it is important that these new structures are designed according to all the sustainability parameters, instead of being based only on the construction cost. Thus, the present work aims to study short-span bridges by integrating environmental assessments into the decision-making process. To achieve this goal, three short-span bridge designs, proposed by public organizations in Brazil, are evaluated: Precast concrete bridge, mixed concrete/steel bridge, and timber bridge. In order to allow comparison, the same location and span are considered. The structures are evaluated considering the following quantitative aspects: Cost of construction, assembly and material transportation, lifespan, and environmental impact (measured by the global warming potential, GWP). In addition, some more subjective factors are considered, such as the architecture (layout and appearance) and the user’s sensation of security. The selection is made by the adoption of two multi-criteria decision-making methods (analytic hierarchy process or AHP and Vikor). The results obtained with both methods indicate the mixed concrete/steel bridge as the most adequate alternative. Some additional analysis is performed in order to evaluate the influence of the qualitative aspects, as well as to study the importance of the variations in the costs on the results.

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In structural design, it is common practice to adopt the same cross-section dimensions for a group of elements. This procedure is mainly for practical and aesthetic reasons, as well as to reduce labour costs, but it also has a positive effect of reducing the number of variables, which simplifies the usual trial and error design process. On the other hand, the total materials cost obtained is closely related to this grouping. Based on this, the present work aims to minimize the cost of reinforced concrete plane frames considering the automated grouping of columns. To achieve this objective, an optimization software was developed by the association of matrix structural analysis, dimensioning and optimization. The sections dimensions, the area of steel and the concrete strength of beams and columns were taken as design variables. For a given maximum number of groups, the optimum grouping and the corresponding values to design variables are obtained. The strategy proposed in this paper to obtain the grouping reduces significantly the number of infeasible candidate solutions during the search process and avoid the proposition of unrealistic designs. For the optimization, a variant of the Harmony Search method was adopted. Some structures were analyzed in order to validate the application of the proposed formulation, as well as to verify the influence of the grouping of elements on the final results. In these structures, it was possible to observe a significant additional reduction in the total cost when automated grouping is performed regarding a uniform grouping, even when a small number of groups is considered. For the 20floor building frame analyzed, the cost reduction from uniform to automated grouping varied from 5.53 to 7.35%. The influence of the concrete strength on optimal results was also investigated, indicating a cost reduction of 9.74% from best (40 MPa) to worst case (20 MPa). In general, it can be concluded that, when applied in conjunction with the usual design variables, the proposed procedure can enable a significant additional economy, without affecting the structural safety.

Resumo O concreto é um dos materiais mais usados na construção civil no Brasil, e seu uso difundido advém da grande facilidade de execução e adaptação às mais diversas formas. Reduzir o consumo dos materiais envolvidos na produção do concreto é uma das maneiras de buscar uma maior sustentabilidade da construção civil. Estas reduções de consumo de materiais, se avaliadas levando-se em conta também os impactos que a produção e o transporte dos mesmos geram no meio ambiente, podem vir a aprimorar ou redirecionar as conclusões ou decisões a serem tomadas em relação à busca de uma maior sustentabilidade ambiental. Dentro deste enfoque foram levantadas e avaliadas as emissões de dióxido de carbono (CO2), impactos ambientais gerados quando da extração/produção e transporte até o local de utilização das matérias primas do concreto. Juntamente foram levantadas e avaliadas as emissões na produção e transporte do concreto até a obra. Dentre as conclusões do estudo constatou-se que menores resistências características do concreto produzirão menores emissões de CO2, e que a influência do transporte nas emissões é significativa devido às longas distâncias percorridas pela maior parte das matérias primas.