Headnote
ABSTRACT
Objective: The objective of this study is to develop a computational interface to optimize the cross-section of ribbed slabs in normal and fire situations, with the aim of achieving maximum functionality and safety at minimum cost, following normative prescriptions.
Theoretical Framework: Structural optimization techniques stand out as innovative tools that promote the rational use of materials, enabling the reduction of consumption of resources such as concrete and steel, which, in turn, results in a lower environmental impact and cost reduction.
Method: The methodology adopted for this research was to implement a slab optimization program in MATLAB, using the Genetic Algorithms (GA) method. Comparing the consumption of concrete and steel in the design.
Results and Discussion: The results obtained revealed [synthesize the main results of the research]. In the discussion section, these results are contextualized in light of the theoretical framework, highlighting the implications and relationships identified. Possible discrepancies and limitations of the study are also considered in this section.
Research Implications: Genetic algorithm-based structural optimization is establishing itself as an innovation that promotes sustainability in structural engineering under fire conditions. The adopted approach contributes to the advancement of structural modeling aimed at reducing environmental impacts in civil construction.
Originality/Value: The research stands out for integrating evolutionary methods into the design of structural elements with fire resistance requirements, promoting the achievement of more efficient solutions from a mechanical, economic and environmental point of view.
Keywords: Optimization, Slabs, Fire Situation, Genetic Algorithm.
RESUMO
Objetivo: O objetivo deste estudo é desenvolver uma interface computacional para otimizar a seção transversal de lajes nervuradas em situação normal e em situação de incêndio, com o intuito de atende à máxima funcionalidade e segurança com o mínimo custo, seguindo as prescrições normativas.
Referencial Teórico: As técnicas de otimização estrutural destacam-se como ferramentas inovadoras que promovem o uso racional dos materiais, possibilitando a redução do consumo de recursos como concreto e aço, o que, por sua vez, resulta em menor impacto ambiental e redução de custos.
Método: A metodologia adotada para esta pesquisa foi implementar no MATLAB um programa de otimização de lajes, utilizando o método dos Algoritmos Genéticos (AG). Comparando do consumo de concreto e aço no dimensionamento.
Resultados e Discussão: Os resultados obtidos evidenciam que essa metodologia, além de apresentar facilidade de implementação e robustez, contribui para a obtenção de soluções otimizadas, economicamente viáveis e ambientalmente sustentáveis. Demonstra-se que o método tabular, não é econômico, portanto, indicada a utilização de métodos mais precisos.
Implicações da Pesquisa: A otimização estrutural baseada em algoritmos genéticos consolida-se como uma inovação a serviço da sustentabilidade na engenharia de estruturas em situação de incêndio. A abordagem adotada contribui para o avanço da modelagem estrutural orientada a redução de impactos ambientais na construção civil.
Originalidade/Valor: A pesquisa se destaca por integrar métodos evolutivos ao projeto de elementos estruturais com exigências de resistência ao fogo, promovendo a obtenção de soluções mais eficientes sob o ponto de vista mecânico, econômico e ambiental.
Palavras-chave: Otimização, Lajes, Situação de Incêndio, Algoritmo Genético.
RESUMEN
Objetivo: El objetivo de este estudio es desarrollar una interfaz computacional para optimizar la sección transversal de losas nervadas en situaciones normales y de incendio, con el fin de conseguir la máxima funcionalidad y seguridad al mínimo coste, siguiendo prescripciones normativas.
Marco Teórico: Las técnicas de optimización estructural se destacan como herramientas innovadoras que promueven el uso racional de los materiales, permitiendo la reducción del consumo de recursos como el concreto y el acero, lo que, a su vez, se traduce en un menor impacto ambiental y reducción de costos.
Método: La metodología adoptada para esta investigación consistió en implementar un programa de optimización de losas en MATLAB, utilizando el método de Algoritmos Genéticos (AG). Se comparó el consumo de hormigón y acero en el diseño.
Resultados y Discusión: The results show that this methodology, in addition to being easy to implement and robust, contributes to obtaining optimized, economically viable, and environmentally sustainable solutions. The tabular method is shown to be uneconomical, and therefore, the use of more precise methods is recommended.
Implicaciones de la investigación: La optimización estructural basada en algoritmos genéticos se consolida como una innovación que promueve la sostenibilidad en la ingeniería estructural ante incendios. El enfoque adoptado contribuye al avance del modelado estructural, orientado a reducir el impacto ambiental en la construcción civil.
Originalidad/Valor: La investigación destaca por integrar métodos evolutivos en el diseño de elementos estructurales con requerimientos de resistencia al fuego, promoviendo la consecución de soluciones más eficientes desde el punto de vista mecánico, económico y ambiental.
Palabras clave: Optimización, Losas, Situación de Incendio, Algoritmo Genético.
1 INTRODUCTION
Abstract: The significant advance of computational technologies and numerical methods has significantly boosted the area of Computational Mechanics, allowing a more accurate and efficient analysis of high complexity structures. In this context, structural optimisation techniques emerge as robust tools for the rationalisation of projects, aiming at reducing material consumption and increasing structural efficiency, with a direct impact on the cost and sustainability of buildings (MA et al., 2023; MENEZES et al., 2022).
Among the various existing optimisation methods, Genetic Algorithms (GAs), introduced by Holland (1975), have gained prominence for their ability to explore complex solution spaces and treat continuous or discrete variables with multiple simultaneous constraints. Such methods, inspired by the mechanisms of natural selection, are efficient in the search for global optimal solutions in extensive solution spaces (Maulana et al., 2022; Castilho; Debs; Nicoletti, 2007).
In civil engineering, these algorithms have been successfully applied in the optimal design of structural elements, especially in reinforced concrete systems, showing satisfactory results regarding material economy and structural efficiency, even in scenarios with little predictability of the solution behaviour.
Reinforced concrete, although widely used due to its versatility and resistance, presents significant sensitivity to thermal actions. The temperature rise in a fire situation compromises the resistant capacity of the constituent materials, alters their physical-mechanical properties and directly affects the overall stability of the structure. Such conditions impose the need for specific design, according to the guidelines of ABNT NBR 15200:2012, which establishes criteria for the design of concrete structures in fire situation, in accordance with the requirements of NBR 6118:2023 and NBR 14432:2001, regarding the minimum fire resistance of structural elements.
In Brazil, the use of ribbed slabs cast in loco is widespread, especially in residential and commercial buildings of medium size, due to its economy of material, ease of construction and relative lightness. Recent studies have shown that, even in fire conditions, it is possible to obtain optimised solutions that meet regulatory requirements and promote concrete and steel economy, contributing to the sustainability of the sector (Alibeigibeni et al., 2025; Freitas, 2014).
Economic projects, when designed based on technical criteria and optimisation tools, become essential tools for promoting sustainability in construction. The minimisation of the consumption of natural resources, combined with the reduction of waste and carbon emissions, gives the optimised projects a central role in mitigating the environmental impacts of the sector. In addition, the rationalisation of the use of materials contributes to the economic viability of buildings, without compromising the safety and structural performance required by current standards (Buildings, 2025).
The importance of the optimal design of ribbed slabs in fire situation lies in the need to ensure adequate structural safety with minimal resource consumption. The adoption of optimised approaches makes it possible to achieve more efficient solutions in the face of severe thermal requirements, ensuring the integrity of the structure during exposure to fire. Considering the critical nature of this type of request, the use of advanced computational methods, such as Genetic Algorithms, allows exploring different geometric and reinforcement configurations, seeking the best performance with less environmental and economic impact (Ma et al., 2023; Menezes et al., 2022).
In this context, this work proposes the development of a computational interface based on Genetic Algorithms for the optimised design of waffle slabs moulded in loco considering the design constraints under normal conditions and in a fire situation, simultaneously meeting the normative requirements of NBR 6118: 2023 and NBR 15200: 2012. The research contemplates the comparison between the conventional design (without thermal action) and in fire condition, with the objective of quantifying the increase in the consumption of materials and to evidence the viability of the use of optimisation techniques as a tool to support the structural project with a focus on performance, economy and sustainability.
2 THEORETICAL FRAMEWORK
2.1 RIBBED SLABS IN FIRE SITUATION
Ribbed slabs, characterised by the combination of longitudinal ribs and upper table, are widely used in multi-storey buildings due to their high structural efficiency and material savings. Its mechanical performance, especially in bending, allows larger spans with smaller volumes of concrete and reinforcement. However, in a fire situation, this type of structural element presents specific challenges, given the complexity of heat transfer in the reduced sections of the ribs and the direct exposure of parts of the reinforcement to heat (Cavaleri et al., 2016).
The thermal behaviour of ribbed slabs is highly dependent on the type of concrete, the thickness of the table, the geometry of the ribs and the arrangement of the reinforcement. Studies have shown that, to meet the normative criteria of fire resistance, significant reinforcements are often required, which can compromise the economic efficiency of the system. In this scenario, the application of optimisation algorithms, especially evolutionary ones, has shown great potential to find solutions that reconcile structural safety, resource savings and sustainability (Wahba et al., 2018; Gaffin et al., 2010).
The tabular method, as provided by ABNT NBR 15200:2021, is a simplified and widely used approach for the design of ribbed slabs in a fire situation. This method is based on the verification of the fire resistance by comparing with minimum values prescribed in normative tables, which consider parameters such as structural type, required resistance time (FRT), reinforcement cover, section geometry and concrete class. In the case of ribbed slabs, the standard recommends the analysis of ribs as isolated beams subjected to bending, requiring compliance with minimum thicknesses of the concrete table and additional coverings depending on the adopted TRRF. Although the tabular method presents advantages in terms of its simplicity and speed of application in the project, it tends to lead to conservative and often oversized solutions, resulting in greater material consumption. This limitation has driven the use of more sophisticated approaches, such as numerical methods and computational optimisation techniques, which allow to achieve a more efficient balance between fire safety, structural performance and sustainability.
2.2 STRUCTURAL OPTIMISATION AS A TOOL FOR SUSTAINABLE ENGINEERING
Structural optimisation consists of a mathematical and computational approach focused on the search for design solutions that simultaneously meet criteria of performance, safety and economy, subject to a set of technical and regulatory constraints. In civil engineering, this practice has been consolidated as an indispensable tool in the development of more efficient structural solutions, especially in contexts that require the rational use of materials and the reduction of environmental impacts associated with production and construction (Bendsøe & Sigmund, 2003; Arora, 2012).
Among the various optimisation methods, Genetic Algorithms (GAs) have been highlighted for their ability to explore large search spaces in a robust and effective way. It is a technique based on the principles of biological evolution, such as natural selection, crossing and mutation, whose main advantage is the ability to treat nonlinear problems with multiple interdependent variables and complex constraints - common characteristics in the design of structural elements (Goldberg, 1989; Holland, 1992).
In structural engineering, GAs have been used in topology, shape and structural design problems, enabling solutions that minimise weight, cost or maximum displacements, while meeting the normative requirements of safety and service. The flexibility of the method allows multiple objectives to be considered simultaneously, including, for example, the reduction of environmental impact through the more efficient use of structural materials such as steel and concrete (Silva et al., 2021; Souza & Lima, 2023).
The use of optimisation techniques, such as Genetic Algorithms, in the design of ribbed slabs in fire situation represents a convergence between technological innovation and socio-environmental responsibility. By allowing the definition of more efficient geometries and reinforcement rates, such methods contribute not only to the reduction of costs, but also to the more rational use of materials and the minimisation of environmental impacts resulting from construction. In addition, by automating the decision-making process, evolutionary methods expand the structural engineer's ability to explore alternative solutions with higher technical quality, integrating structural and thermal performance criteria with sustainable objectives (Silva et al., 2021; ABNT, 2024a).
3 MATERIALS AND METHODS
In this work, MATLAB implemented an optimisation programme for reinforced concrete slabs moulded on site in fire using the Genetic Algorithm (GA) method. In order to develop a programme to assist the design of ribbed slabs, in accordance with the regulatory restrictions imposed by ABNT NBR 6118: 2014 and NBR 15200: 2012, aiming to minimise the cost of materials (concrete and steel), the objective was to compare the consumption of concrete and steel in the design of ribbed slabs when used only the first standard or the two together.
In the MATLAB programming environment, there are already routines implemented to solve optimisation problems using GA, in the toolbox called toolboxes. To validate the implemented programme, two numerical examples were used to evaluate the efficiency and calibration of the programme. To validate the implemented implementations for the design of one-way ribbed slabs, the numerical example 1.1 of Carvalho and Pinheiro (2009) was used. The example used to validate the implementations for the design of bidirectional ribbed slabs was obtained from Bocchi and Giongo (2007).
The first implementations are associated with the entry of the data necessary for the execution of the programme. In the second part of the implementations, the design variables used in the optimisation (bw, hf, h, Asx and Asy) are defined, as well as the objective function and restriction function calls. With the objective function implemented in this algorithm, the linear cost of two ribbed slabs is minimised. In the process of minimising the cost function, the set of restrictions imposed on the problem according to NBR 6118: 2014 and NBR 15200: 2012 for the design of reinforced concrete ribbed slabs must be respected.
... (1)
... (2)
... (3)
Where:
fObjective function (linear cost);
Cc: Price of concrete per cubic metre (R$/cm3);
Cs50 Price: CA 50 steel per kilo (R$/kg);
lef: value of the effective length of the slab;
γs : specific weight of steel (kg/cm3);
As: total cross-sectional area of steel bars;
bw: thickness of the cross section of the slab rib;
bf: width of ribbed slab cross-section table;
hfHeight: Height of ribbed slab cross-section table;
hw: Height of ribbed slab cross section;
Finally, after the implementation of all the points mentioned above, the programme is implemented and the results are analysed.
3.1 GENETIC ALGORITHMS
AG's methods are analogous to Charles Darwin's theory of evolution, in which the least likely to survive and the fittest survive and produce offspring.
Briefly, the operation of the GA method can be given by the following steps: each individual represents a possible solution to a problem. A group of individuals forms a population. Each individual is assigned an aptitude value that corresponds to their degree of proximity to the optimal solution. Individuals who have higher fitness value, that is, are closer to the optimal solution (more adapted), are more likely to reproduce when compared to individuals with lower fitness value. To select the individuals that will reproduce, the algorithm uses methods that privilege the best adapted individuals. After selection, a genetic recombination is performed, in which the parents of the individuals will combine to give rise to a new generation, theoretically better adapted than the previous generation. The algorithm follows an iterative process until some stopping criterion is satisfied.
4 RESULTS AND DISCUSSIONS
For the purpose of validating the computer programme developed in this research, the comparison with consecrated examples available in the technical literature was adopted, in order to ensure its functionality and the reliability of the results obtained. The validation process is a fundamental step to ensure the consistency of the input parameters and the robustness of the implemented algorithms. In the modelling of ribbed slabs, the perforated ceramic brick with dimensions of 9 × 19 × 19 cm was used as filling material, as usual practice in multi-storey buildings. The other parameters adopted in the simulation are systematised in Table 1.
Based on the parameters presented, the thermal and structural analysis of the ribbed slab in a fire situation was performed. The computational model allowed to simulate the behaviour of the structure during the period of exposure to fire, considering the degradation of the properties of the materials and the associated thermal effects.
4.1 VALIDATION OF ONE-WAY SLAB
This example (Figure 2) was extracted from the book by Carvalho and Pinheiro (2009). As the ratio between spans is greater than two, this ribbed slab was dimensioned as reinforced in one direction.
Table 2 and Figure 3 present the results obtained by the programme implemented in this research for the design in normal situation and in fire situation of a unidirectional slab.
Based on the data presented in Table 2, it is verified that the computer programme developed in this research resulted in an optimised geometry of the T-type cross section for the ribbed slab in a fire situation. This new configuration presented a reduction in the total height (h) of the section, an increase in the width of the rib and an increase in the thickness of the upper table, which implied an increase in the total area of concrete.
In quantitative terms, there was an increase of approximately 7.82% in the cost relative to the volume of concrete, when compared to the design of the slab in a normal situation (without considering fire). This variation is mainly due to the increase in the width of the rib and the thickness of the table, parameters that have a significant influence on the consumption of concrete. This adaptation aims to meet the normative criteria of fire resistance, which demand greater physical protection of the reinforcement and increase the thermal capacity of the section. On the other hand, the reduction of the total height of the section has shown to have little expressive impact on the cost of the concrete, since the redistribution of the dimensions partially compensated the expected volumetric decrease.
As for the steel consumption, it was identified an increase of 13.12% in the total cost of the material, when compared to the slab designed for normal situation. This increase is attributed to the reduction of the resistant contribution of concrete subjected to high temperatures, which makes it necessary to increase the amount of reinforcement to guarantee structural performance. Even with the increase of the concrete section area, the loss of strength at high temperatures requires a structural compensation by the addition of steel, directly reflecting the total cost of the solution.
As a combined consequence of these factors, the total cost of the ribbed slab designed for a fire situation presented an increase of 9.25% compared to the design designed for normal conditions. This difference highlights the economic impact associated with the adequacy of the structures to the requirements of fire safety. It is also noteworthy that this impact can be mitigated through the application of structural optimisation techniques, which allow exploring geometric and detailing alternatives capable of balancing safety, thermal performance and economic viability of the project.
4.2 TWO-WAY SLAB VALIDATION
This example (Figure 4) was extracted from Bocchi and Giongo (2007). As the ratio between the spans is less than two, this ribbed slab was dimensioned as reinforced in two directions.
Table 3 presents the results obtained by the programme implemented in this research for the design in normal situation and in fire situation of a bidirectional slab
Based on the data presented in Table 3, it is verified that the results obtained by the programme developed in this research, for the case of the bidirectional slab in fire situation, reproduce the same structural behaviour previously identified in the analysis of the unidirectional slab. The optimised geometry of the resulting cross section presents a T-shaped configuration with lower total height (h), however with an increase in the width of the rib and in the height of the compressed table, resulting in an expansion of the area of the concrete section. This geometric adaptation aims to meet the normative requirements of fire resistance, increasing the protection of the reinforcement and the thermal inertia of the structural element.
As a direct consequence of these modifications, there was an increase of approximately 16.32% in the total cost of concrete and steel, compared to conventional design in a normal situation. This result shows that, even under different loading conditions and direction of the stress distribution, the structural optimisation behaviour under the thermal action maintains a similar pattern, demonstrating the consistency of the methodology adopted. It is also noteworthy that such variations in geometric parameters and associated costs did not present significant sensitivity to the variation of the total dimensions of the slab, which reinforces the robustness of the proposed model for different structural configurations.
5 CONCLUSION
Through the results, it can be stated that the implemented programme was able to fulfil its objectives. The results obtained showed consistency with the reference values present in the literature, both in relation to the temperature distribution and the loss of resistant capacity over time. The variation of material consumption between scenarios with and without fire consideration revealed a significant increase in the need for reinforcement and thickness of the upper table, in order to meet the normative requirements of fire resistance.
The parameter that increased the most was the width of the rib, which was already expected, since in NBR 15200: 2012 the structural function is guaranteed by the minimum width of the rib. In this case, it is demonstrated that the tabular method for calculating structures subjected to the action of temperature variation, although practical, is not economical, and therefore the use of more accurate methods is indicated.
In addition, it was verified that the application of the genetic algorithm made it possible to identify more efficient geometries and reinforcement rates, even in the face of the additional requirements imposed by the fire situation, highlighting the potential of the method as a decision support tool in sustainable structural design.
The Genetic Algorithm method presented a good performance in the optimisation and can be highlighted as positive points: the ease of implementation and the flexibility in dealing with problems with several constraints, functioning as a tool that assists the engineer in his decision making.
References
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