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The aim of this paper is to present the influence of the subgrade reaction coefficient modelling on the simple 3D frame. For simplicity, it was assumed that the construction was made on the square foundations on granular soil. The soil reaction coefficient is modelled by different expressions drawn by different authors. For this reason different values of the coefficient were obtained. In order to observe the behaviour of these coefficients for each author curve families are created. They give us the relationship between the dimension of the square foundations and the value of the reaction coefficient. The paper then follows the response of the characteristic structural framework to these impacts.

This paper provides an analysis of settlement of foundation plates using finite difference method, and is designed in the aim to prove how this method, implemented in our Matlab program code, will give results similar to those obtained with the finite element method, and to show that plate' settlements are less dependent on the change of modulus of soil reaction.

SažetakImplementacije mnogih metoda diskretne matematike, posebice teorije grafova i teorije kompleksnih mreža, te metode rudarstva podataka, imaju važnu ulogu u rješavanju NP -teških problema iz područja kombinatorne optimizacije. Dosadašnja istraživanja su pokazala kako značajnu ulogu o ovim problemima imaju istraživanja važnosti pojedinog vrha unutar grafa, te konstruiranje maksimalno balansirane particije u grafu. Takvi problemi u praksi nisu rijetki, ali nisu ni predmet istraživanja isključivo matematičara, već ih izučavaju i istraživači iz drugih područja znanosti, inženjerstva, ekonomije, obrazovanja. Ključne riječi: graf, maksimalno balansirana povezana particija u grafu, pohlepni algoritam, cluster analiza Structure of maximally balanced connected partition in graph AbstractThe implementation of various discrete mathematics methods, especially graphs, complex network theory, and the data mining methods, play an important role in solving NP-difficult problems in the field of combinatorial optimization. Previous research has shown that these issues are greatly influenced by study of the importance of a single vertex within the graph, and the design of maximally balanced connected partitions in graph. These problems are not rare in practice, and are not studied solely by mathematicians, but also by researches from other areas of science, engineering, economy, and education.

This paper is a continuation of the research on the influence of different modeling of the subgrade reaction coefficient on the selected static system. This paper analyzes the behavior of a two-story reinforced concrete frame for different foundation dimensions and different values of the subgrade reaction coefficient. It presents an overview of values of these coefficients, which represent the stiffness of Winkler springs with respect to the specific geometry of shallow foundations. The values are different depending on the author, and the average value was used as relevant for comparison. Results of the numerical analysis for an individual reinforced concrete two-story frame were obtained using the SE_Calc and Tower 8 programs. After obtaining the results for each individual frame, they were combined and analyzed.