PSI - Issue 81

Volodymyr Romaniuk et al. / Procedia Structural Integrity 81 (2026) 276–281

279

The stress state analysis of the perforated compression-flexural arch chord was carried out by comparing theoretical and experimental stresses in 14 of its cross sections (7 for each half-arch) near the support nodes, spacer attachment nodes, ridge node, and points of application of concentrated forces (see Fig. 1, b). Theoretical stresses were calculated using the design code methodology DBN V.2.6 198 (2014), which uses bending theory that assumes the determination of stresses as in a conventional beam weakened by an opening. To measure the experimental stresses, strain gauges were used, which were bonded along the height of the cross-sections of the half-arch chords. The actual values of mechanical characteristics of steel for individual elements of the experimental structure were determined on standard specimens cut from these elements. In particular, for the I-beam of the upper chord, the yield strength was f y = 244 MPa, which corresponds to steel grade S235. The half-chords of the arch were fabricated from perforated I-beams, in the upper and lower flanges of which, depending on the location of the design cross-section, stresses of compression (with sign "-") and tension (with sign "+") occurred

Fig. 2. Hinged support that allows changing the position of the tie (nodes B and C ).

respectively under the action of external loading. The results of theoretical calculations and experimental measurements are given in the Table 1 and Fig. 3, 4. The comparison of stresses in characteristic cross-sections was carried out with the following tie rod positions: at the zero position, i.e., without displacement from the design position; at the raised position by 50 mm compared to the design position; and at the lowered position by 50, 100, and 150 mm compared to the design position. The obtained data show that the most stressed element at zero tie rod position is the lower flange of the I-beam in cross-section 5-5, at the spacer attachment node, which is a kind of intermediate support for the continuous chord of the half-arch. The theoretical stress here is σ T = -190.3 MPa. This ensures local stability of the flanges and the profile web without the use of additional structural elements, for example, transverse stiffeners or elements that reinforce the web in the areas where the holes are located. Shifting the tie rod downwards reduces the stresses in section 5-5 but increases the stresses in the support section 1-1. The optimal tie rod displacement can be determined from the condition that the stresses in the lower flange in sections 1-1 and 5-5 of the half-arch chord will be equal.

Table 1. Stress in the upper and lower flanges of the half-arch chord.

Tie rod shifting e 0 (mm)

Cross-sections

Stress (МPа)

Flange

1-1

2-2

3-3

4-4

5-5

6-6

7-7

-50

Upper

-111.12 -108.63 -36.82 -34.12 -83.86 -89.36 -57.90 -55.76 -36.82 -36.04 -110.00 -101.10 15.61 18.02 -162.9 -139.30

-186.38 -177.50 83.17 78.13 -151.1 -143.4 66.01 64.09 -136.70 -139.4 37.97 32.98 -125.8 -125.70 11.59 10.20 -94.30 -88.40 -10.55

-145.17 -146.32 39.01 34.24 -141.7 -144.9 35.42 29.92 -140.70 -137.70 30.04 25.09 -139.5 -132.0 23.28 18.70 -132.80 -130.70

-24.21 -26.23 -121.23 -111.54 -31.47 -36.75 -104.2 -88.48 -40.72 -38.20 -89.92 -74.88 -47.77 -39.61 -78.41 -68.34 -58.75 -71.06 -62.99 -50.12

138.19 124.33 -208.14 -192.39 113.9 97.52 -190.3 -175.1 94.36 93.42 -180.60 -161.30

101.26

-53.14 -52.07 61.27 53.72 -47.54 -49.64 50.40 41.96 -40.51 -33.26 38.75 32.10 -34.61 -13.60 28.98 24.65 -27.48

σ T σ E σ T σ E σ T σ E σ T σ E σ T σ E σ T σ E σ T σ E σ T σ E σ T σ E σ T σ E

92.17

Lower

-111.51 -102.18 94.26 81.26 -99.46 -84.80 77.06 65.96 -86.88 -77.18 62.62 61.88 -76.31 -66.13 45.14 60.52 -63.52 -56.21

0

Upper

Lower

50

Upper

Lower

100

Upper

78.81 62.90

Lower

-174.70 -152.80

150

Upper

63.45 53.66

59.04 53.72

8.50

Lower

-186.83 -180.50

20.96 77.06

-158.10 -144.08

17.16 20.74

-8.84