PSI - Issue 81

Mykola Pidgurskyi et al. / Procedia Structural Integrity 81 (2026) 539–546

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As can be observed, under rigid fixity with horizontal restraint, bending moments along the structural members are reduced, while in inclined beams axial forces arise, which affect the stress – strain state (SSS) of the structure. It should be noted that high-strength bolts are used to form rigid joints (Bishay-Girges, 2020); however, for structural considerations, haunches are often provided at the eaves and apex joints of the beams. Haunches increase the support region of the beam, reduce stresses in the adjacent areas, and allow the installation of additional bolts. The influence of haunches at the eaves and apex joints is significant, as they alter the stress-strain state of the structure while slightly increasing its weight. In the study by Pidgurskyi I., et al. (2023), the stress-strain state of beams without haunches was analyzed, revealing improved stiffness parameters but increased stresses. Therefore, the influence of haunches on the stress-strain state of perforated beams within frame structures requires more detailed investigation. It should be noted that і n this study, the height of the perforated beams allowed for rigid connections to the columns without the use of haunches. However, for structural considerations and to study stress redistribution in perforated beams, analyses were also performed for configurations with haunches. Thus, the aim of this study is a comprehensive investigation of the influence of the inclination of perforated beams and arched beams under conditions of fixed support and the use of haunches on their stress – strain state. 2. Research Methodology The stress-strain state of steel perforated beams in a pitched position was investigated using the finite element method (FEM). The structural modeling was performed using the ANSYS software suite, specifically the ANSYS Mechanical Structure module, designed for static and nonlinear structural analysis. Finite element modeling followed by an analysis of the stress – strain state (SSS) of the structure was performed in accordance with international standards (EN 1993-1-5, 2006; EN 1993-1-14, 2025). This methodology is consistent with previous studies on the stress-strain state of perforated beams (Pidgurskyi et al., 2021; Liu and Chung, 2003; Dutt, 2015). In particular, in the study by Pidgurskyi, et al., (2021) a comparison of deflections and stresses in the flanges of perforated beams obtained by analytical methods and by the finite element method using the ANSYS software package is presented. In study by Pidgurskyi, M., et al., (2023), a comparative analysis of the stress – strain state of perforated beams with circular openings was carried out using the LIRA-SAPR, SolidWorks, and ANSYS software packages. The influence of finite element mesh size was investigated. It was established that for large-scale structures, a finite element mesh with an element size of 20 mm is acceptable. The discrepancies in the evaluated parameters obtained using the three software packages did not exceed 4.45% (Pidgurskyi, M., et al., 2023). The modeling involved constructing a three-dimensional model of the beam, taking into account the geometry of the perforated web as well as the actual support and loading conditions. Structural steel of grade S345 was adopted for the material, in accordance with regulatory requirements. The average size of the finite element was 20 mm (Fig. 2).

Fig. 2. Finite element mesh at the apex joint: a) double-pitched beam; b) arched beam.

The investigation of the stress-strain state included the assessment of normal, shear, and equivalent stresses, which were determined according to the von Mises yield criterion. Deformation characteristics of the beams were evaluated based on vertical displacements (deflections) monitored along the bottom flange. Stresses were analyzed along the lower and upper flanges, and, to mitigate the influence of stress concentrators, mean stress values were also considered. Additionally, stress distributions around the perforation openings were examined, specifically around the end, central, and quarter-span openings, where, according to the internal force diagrams (see Fig. 1), the extreme values occur. The modelling was carried out under the assumption of linear elastic material behaviour. To model the beam as a rigidly fixed element with thrust, all translational (X, Y, Z) and rotational (UX, UY, UZ) degrees of freedom were restricted at both ends of the beam (Fig. 3).