PSI - Issue 81

Mykola Pidgurskyi et al. / Procedia Structural Integrity 81 (2026) 439–446

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Equivalent stress values were obtained for each opening within half of the beam span. Due to the symmetric support and loading conditions, the stress distribution in the opposite half of the span is also symmetric. Based on the obtained results, a diagram of maximum equivalent stresses around the openings was constructed (Fig. 9).

Fig. 9. Variation of maximum equivalent stresses around openings of perforation along the beam

It should be noted that for all beam types, the highest equivalent stresses occur around the end perforation openings. The greatest maximum stress among all beams is observed around the second opening of the horizontal beam without haunches, reaching 755.28 MPa. Compared to the horizontal beam, the maximum stresses around the 1st opening of the double-pitched beam (498.51 MPa) are 1.52 times lower, while in the arched beam the highest stresses occur around the 2nd opening (264.29 MPa), being 2.86 times lower. For both horizontal and double-pitched beams, the installation of haunches in the eaves and apex joints reduces the maximum equivalent stresses around perforation openings by a factor of 1.27 for the horizontal beam and 1.37 for the double-pitched beam. At the same time, the total mass of all beams increased on average by a factor of 1.22. For the arched beam, the stresses around the end perforation openings decrease with the use of haunches, but after the haunch ends, the stresses increase around the subsequent openings. For example, the maximum stresses around the 6th opening in the arched beam with haunches are 1.03 times higher than the maximum stresses around the 2nd opening of the same beam without haunches. Thus, for this particular arched beam, the use of haunches does not provide the desired reduction in stresses around the openings (while increasing the mass of the arch). It is important to note that the stresses around the perforation openings of the arched beam, both with and without haunches, do not exceed the yield strength. Therefore, haunches should be considered primarily as structural elements for connecting the beam to the column or for joining two beam segments in long spans. The effect of reinforcement with stiffening rings was then analyzed for the horizontal and double-pitched beams for two configurations: beams without haunches and beams with haunches. For the horizontal beam, reinforcement using stiffening rings was applied as follows: for beams without haunches openings 1 through 13; for beams with haunches openings 4 through 13. For the double-pitched beam, stiffening rings were added as follows: for beams without haunches openings 1 through 6; for beams with haunches openings 6 and 7. For beams reinforced with stiffening rings around the openings, the results of equivalent stresses around the openings with maximum values were obtained (Fig. 10), and diagrams of the variation of maximum equivalent stresses along the beam length were constructed (Fig. 11). For comparison, the diagram for the arched beam without haunches and without reinforcement is also provided. The masses of the reinforced beams were as follows: horizontal beam without haunches – 1555.7 kg, with haunches – 1850.2 kg; double-pitched beam without haunches – 1516.3 kg, with haunches – 1802.2 kg. Compared to similar beams without haunches and without reinforcement: horizontal beams without haunches reinforced with stiffening rings are 6.2% heavier, and beams with haunches are 21.1% heavier; double-pitched beams without haunches reinforced with stiffening rings are 2.9% heavier, and beams with haunches are 18.3% heavier.