PSI - Issue 81

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

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Comparison of the deflections of the analyzed fixed-end perforated beams without haunches shows that the horizontal beam experiences the largest deflection. Compared to the horizontal beam, the double-pitched perforated beam exhibits a 58.3% smaller deflection, whereas the arched beam shows a 63.5% reduction. For beams with haunches, the installation of haunches reduced deflection by 35.2% for the horizontal beam, 34.6% for the double-pitched beam, and 21.5% for the arched beam. It should be noted that, on average, the addition of haunches at the eaves and apex joints increased the total beam weight by 17.8%. It was also found that among the beams without haunches, the arched beam exhibited the smallest deflection, whereas among the beams with haunches, the double-pitched beam demonstrated the best stiffness performance. Thus, the addition of haunches in the arched beam with a circular profile and rise corresponding to a 5° pitch was found to be the least effective, despite the noticeable increase in material volume. For horizontal and double-pitched perforated beams, however, the use of haunches significantly improves structural efficiency and can be considered beneficial. A comparative analysis of deflections indicates that the type of support has the most significant effect on their values. For instance, the deflection of a simply supported horizontal perforated beam is 276.03 mm, which is 3.43 times greater than that of the corresponding fixed-end beam. It should be noted that the deflection of the simply supported beam with a 24 m span exceeds the allowable limit of 96 mm (EN 1993-1-13:2024, Eurocode 3, 2024). Clearly, if a simply supported beam were used, its cross section would need to be substantially increased. 3.2. Stress Analysis The analysis of stresses arising in the beams is of critical importance, as the design of perforated beams exhibiting lower stress levels (together with reduced deflections) is a primary objective in optimizing lightweight structural systems. For all beam configurations, the equivalent (von Mises) stresses were evaluated for the bottom and top flanges, as well as around the perforation openings, which act as stress concentrators. For the flanges, the equivalent stress distributions along the entire beam length were obtained (Fig. 7, Table 2). The stress state of perforated beams exhibits specific features. Due to the presence of perforations, the stiffness of perforated beams varies along their length; consequently, the stress distribution demonstrates a sinusoidal pattern (Fares et al., 2016). In beams with single-row perforation, the highest stresses in the flanges do not occur in the sections weakened by the openings, as might be expected, but rather in the sections passing through the web posts. Therefore, to ensure an accurate representation of stress results, the number of measurement points should correspond to the number of perforation openings (Fig. 7). Among the investigated types of perforated beams, the smoothest stress variation profile is observed in the arched beam, both without haunches and with strengthening elements such as haunches. Local stress extrema are associated with the specific distribution of internal forces induced by fixed supports (see Fig. 1). It should be noted that rigid fixity has a beneficial effect on the stress – strain state of all the investigated structural systems, which is well known (Strømmen, 2020). Stress analysis of a horizontally oriented simply supported beam showed that the maximum stress level of 236.91 MPa is 1.4 times higher compared to a horizontally fixed beam, 1.43 times higher compared to a fixed double-pitched beam, and 1.34 times higher compared to a fixed arched beam. The installation of haunches leads to an additional reduction in maximum stresses: by a factor of 1.24 in the horizontal beam, 1.43 in the double-pitched beam, and 1.67 in the arched beam. As can be observed, the use of haunches results in a substantial reduction in stresses; however, the structural weight simultaneously increases by 17.8%. Based on the analysis of the maximum equivalent stresses obtained along the contours of the perforation openings, the following conclusions can be made: The highest equivalent stresses around perforations were observed in the horizontal beams, both with and without haunches. Overall, the addition of haunches in perforated beams significantly reduces equivalent stresses around the perforation closest to the support and central perforation by up to 75.5% in horizontal beams, 80.8% in double-pitched beams, and 80.0% in arched beams.

Table 2. Equivalent stress values for beams without and with haunches.

Horizontal

Double-pitched

Arched

Without haunch 1459.3 167,00 169,98 695.59 437.87 124.76

With haunch Without haunch

With haunch Without haunch

With haunch

Parameters

Weight, kg

1776.1 137,40 118,72 170.34 447.08 148.03

1471.8 166,00

1787.4 116,49

1472.5 177,00

1793.2 106,13

Max. stress, bottom flange, MPa Max. stress, top flange, MPa Max. stress around end opening, MPa

86,62

69,72 95.78

86,27

78,67 48.83

498.51 181.20 192.51

244.23 154.14 153.34

Max. stress around quarter-span opening, MPa Max. stress around central opening, MPa

217.29 114.46

209.31 137.14