Reinforced concrete is an essential material in the modern world, and the use of genetic algorithms that aim at the optimization of the structures of this material is an increasingly widespread tool. The objective of the present work was to propose a method by means of a Genetic Algorithm to find the optimized geometry of a rectangular reinforced concrete column based on its cost. The two main parts of the work were developed as: a geometry verification algorithm that received height, base, layers in x and y directions, diameters of transverse and longitudinal steel rebar as the main parameters of the proposed sections, and a genetic algorithm that generated 240 random populations and selected them, crossed among them and then generated new 100 generations of individuals, followed by selection of optimized ones by its penalized cost. The generations had more and more favorable individuals and it was possible to determine an optimized geometry for the proposed example. It is, therefore, concluded that genetic algorithms are useful tools for optimizing reinforced concrete parts with multiple parameters. The proposed algorithm methodology really checks and selects the best individuals for the sections proposed by engineers, and larger initial populations are essential to find a minimum global cost among the different options.
This paper aims to evaluate the hypothesis regarding the homogeneity of wood batches, as provided in the Brazilian standard for wooden structures ABNT NBR 7190 through an experimental study simulating the condition of a sawmill where the control of the harvest region, location of the sample in the trunk, edaphoclimatic condition, relief, and vegetation are variables that cannot be controlled. An experimental study was performed on 15 properties (3 physical and 12 mechanical) of Ipe (Tabebuia sp.) wood. Batches from three harvesting regions (Mucajaí [RR-A], Bonfim [RR-B], and Cláudia [MT]) were used to verify the existence of significant differences between the properties of the three areas. The properties were obtained following the test methods established in ABNT NBR 7190-3, with 540 specimens being manufactured and characterized, prior to being submitted to a statistical analysis, where ANOVA was applied with the Anderson–Darling normality test, the homogeneity of variance of multiple comparisons, and the Tukey test. Statistical analysis indicated that the wood harvesting regions showed significant differences in six (40%) and non-significant differences in nine (60%) of the fifteen properties evaluated. Among the properties evaluated, the compressive strength parallel to the grain (fc0) showed significant differences. This property is used to classify the wood strength class according to the Brazilian standard ABNT NBR 7190-1. The batches from the harvesting regions RR-A, RR-B, and MT were classified using the strength classes D60, D50, and D50, respectively. These results directly impact the consideration of the homogeneity of the batches, considering that the sawmills receive samples from different regions. For future research, a numerical method can be applied to consider the influence of the wood harvesting area.
This study aimed to compare the mechanical performance of two truss typologies, the modified Fan and Howe trusses, using five different wood species: Cambará-rosa, Cupiúba, Angelim-pedra, Garapa, and Jatobá. The spans considered were 6, 9, 12, and 15 m, and the optimization algorithm used was a swarm intelligence algorithm to minimize the structure weight. The study found that wood is a sustainable and viable option for truss constructions, with different wood species having distinct mechanical properties that must be considered when designing the structure. The Howe truss typology presented lower results for the objective function in comparison with the modified Fan truss. The distribution of normal forces in the truss correlated with the characteristic strength in compression and tensile of the species. The Howe truss typology presented a larger amplitude in relation to the modified Fan truss typology in most of the conditions adopted for the Ultimate Limit State constraints. Constraints associated with deflection in the immediate condition were observed to limit the optimization process. The study used the matrix analysis method to evaluate internal efforts and nodal displacements in the trusses. In summary, this study demonstrates the importance of considering all constraints when dimensioning timber structures and the benefits of using different wood species for sustainable construction.
Wood, due to its complex anatomy, requires meticulous characterization that imposes several tests to be carried out to evaluate its properties. Normative codes adopt different specimens to this aim. Geometric specificities proposed by NBR 7190-3:2022 and ASTM D143-22 to specimens used for estimating wood strength in tensile perpendicular to grain (ft90) make them difficult to carry out. Thus it is advisable to consider relating ft90 with another mechanical property, for example, the shear strength parallel to the grain (fv0). This paper aims to establish a coefficient relating the characteristic values of ft90 and fv0, for strength classes D40 and D60 (frequently used for structural purposes) of Brazilian Code 7190:3-2022. A further aim, if possible, is to determine a single representative coefficient for both classes. Tests made it possible to obtain those properties for four species from each class, following NBR 7190-3:2022 guidelines. The optimal coefficient was determined using the least squares method (MMQ). Ratios ft90,k/fv0,k were 0.22 and 0.19, for classes D40 and D60, respectively. As these ratios don’t present a significant difference, it is viable to adopt a single relationship for both classes, thus simplifying characterization procedures.