PSI - Issue 72

Andrii Ivaniuk et al. / Procedia Structural Integrity 72 (2025) 323–329

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Next, we will compare how much these values are greater relative to the values of beams without a defect of the same cross-section and span. I n this case, with a span of 6000 мм, when loaded with 5 forces with values of P 1 = 15.75 kN, P 2 =12.5 kN, P 3 =9.9 kN, the normal stresses σ x for a solid beam will be 8.15 М P а, 6.29 М P а, 5.12 М P а, respectively. For beams with cracks, they are 9.46 М P а, 7.59 М P а, 6.44 М P а, respectively. Analyzing the distribution of normal stresses x  acting along the edges of the crack (Fig. 4), it should be noted that, in the middle of the crack length at its upper face, the wood is in a stretched state, and in the lower face – in a compressed state. At the same time, at the crack tips, this picture changes to the opposite, with the normal stresses σ x at the crack tip being several times greater in their values than the stresses σ x at the middle of the crack length. This nature of the distribution of normal stresses σ x can be explained by their concentration at the crack tips, and the change in sign by the fact that the upper part of the beam tries to shift relative to the lower part. As a result of beam tests, it was established that they have the same type of destruction. The destruction of the beams began from the top of the crack, which was closer to the support. The magnitude of the destructive load t P was taken to be the force of the upper boundary of the elastic work region of the relative displacement of the crack edges, which was determined from the diagrams “Р – U ” ( Fig.5). So for beam B 1 it was P t 1 = 17.1 kN; for beam B 2 it was P t 2 = 14.1 kN and for beam B3 it was, P t 3 =11.7 kN. The loading time for a beam with a crack length of 3300 mm was t 1 = 14400 s, for a beam with a crack length of 3700 mm was t 2 = 13200 s and for a beam with a crack length of 4200 mmwas t 3 = 15600 s. Load-bearing capacity P II for the beam B 1 was P II 1 = 7.71 kN; for the beam B 2 was P II 2 =6.3 kN; for the beam B 3 was P II 3 = 5.23 kN. After analyzing the values П P , we can conclude that the load-bearing capacity of the beams is decreasing. While for a beam with a solid cross-section, the required load-bearing capacity is 23.296 kN.

Fig. 5. Diagrams of relative displacements of beam crack edges (a) and their increments (b)

Comparing the values of the bearing capacity of beams with cracks relative to the bearing capacity of solid beams, we note that the bearing capacity is respectively less by 67%; 72%; 77%, that is, when the length of the crack increases, the bearing capacity decreases. 4. Conclusions 1. The methodology and results of experimental studies of glued wooden beams with through cracks along the neutral axis are presented. 2. The distribution of tangential stresses along the height of beams in different cross-sections has been established.