NUMERICAL-ANALYTICAL TECHNIQUE FOR DETERMINING INTERNAL FORCES IN CROSS-SECTIONS OF BUILDING STRUCTURES

This paper presents a numerical-analytical technique for determining internal forces in cross-sections of building structures that are modeled using finite element methods (FEM). The study focuses on structural components that, despite being represented by a set of finite elements of different dimensions (beam, plate, and volumetric elements), exhibit behavior similar to bar-like structures: pilons, short piers, lintels, deep beams, prefabricated floor slabs, wall panels, diaphragms, core walls.The methodology is based on summing nodal reactions from selected finite elements over a defined cross-section and transforming these forces into a chosen coordinate system. The proposed approach allows for determining internal forces in sections composed of multiple nodes and adjacent finite elements, ensuring consistency with engineering analysis and design principles. The results obtained through this approach can be used as standalone data for evaluating structural behavior or as input for further design calculations, including load-bearing capacity assessments, serviceability limit state verification, reinforcement calculation, and cross-section parameter determination.The implementation of this method in the LIRA-SAPR software system is discussed in detail. It is integrated into two subsystems: "Stone and Reinforced Masonry Structures" and "Bar Analogues". To validate the accuracy and applicability of the method, several verification problems are presented. These include structural models analyzed using beam elements, shell elements, and solid finite elements, with the computed internal forces being compared against theoretical values derived from classical mechanics of materials. The study demonstrates that the numerical-analytical approach produces results that are highly consistent with traditional beam theory calculations, confirming its validity for practical engineering applications.One of the key advantages of this approach is its ability to keep the structural integrity of the original finite element model while allowing engineers to obtain results in a format that aligns with standard design practices. Unlike traditional stress integration methods, which can be affected by local stress concentrations and numerical inaccuracies, the use of nodal reactions provides a more robust and reliable means of extracting internal forces from FEM models. Despite its advantages, the method requires careful selection of finite elements and nodal regions to ensure accurate force summation. The automation of this process within the LIRA-SAPR software significantly simplifies the task, providing engineers with an efficient tool for evaluating internal forces in complex structures.In conclusion, this numerical-analytical technique offers a powerful tool for engineers and researchers involved in structural analysis using finite element methods. Its integration into commercial structural engineering software ensures practical usability and efficiency, making it an essential advancement for modern engineering practice.