PSI - Issue 59

Andrii Pavluk et al. / Procedia Structural Integrity 59 (2024) 566–574 Andrii Pavluk et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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Today, in modern construction conditions, resource conservation in the construction of various objects plays a significant role (Donadon et al. (2020)). Wood, as a building material, is considered an economically viable option in the construction industry due to its low weight, considerable strength, ease of processing, and thermal characteristics (Janiak et al. (2023); Green and Kretschmann (1992); Homon et al. (2023)) compared to analogues made of concrete (Dvorkin et al. (2021)). Calculations of wooden structural elements require further development, taking into account the material's actual behaviour under different load levels (Homon et al. (2023); Madsen (1975); Gomon et al. (2023)). This is because modern design standards incorporate a significant safety margin in the calculations for wooden elements. During bending and oblique bending, compressive and tensile forces are generated in the outermost fibers of the beams (Gomon et al. (2019); Soriano et al. (2016); Pavluk et al. (2023)). The existing design standards (DBN B.2.6 161:2017; Eurocode 5) do not fully account for the behaviour of wood in these zones, leading to underestimated load-carrying capacity in calculations.

Nomenclature σ m,z,d

calculated bending stress about the z-z axis calculated bending stress about the y-y axis calculated bending strength values about the z-z axis calculated bending strength values about the y-y axis

σ m,y,d f m,z,d f m,y,d

coefficient accounting for stress redistribution and material non-uniformity in the cross-section

k m

compressive stress

σ с,d σ t,d

tensile stress

modulus of elasticity for wood in compression modulus of elasticity for wood in tension relative compression deformations of wood relative tensile deformations of wood

E c E t

u c,d u t,d

stress in the compressed zone stress in the tensile zone

f 1 (u) f 2 (u)

bending curvature

1/ρ

total compression deformations of wood along the fibers

u c,fin,d f c,0,d k 1 , k 2

ultimate strength

coefficients of polynomials

distance from the neutral axis to any point in the compressed and tensile zones

z b

width of the beam cross-section

total bending moment from external loading

M

bending moment in the compressed zone from external loading bending moment in the tensile zone from external loading resultant internal forces in the compressed zone

M с M t N с N t

resultant internal forces in the tensile zone N с1 , N с2 compression forces in the element at different cross-section segments N t1 , N t2 tensile forces in the element at different cross-section segments M с1 , M с2 bending moments in the compressed zone at different cross-section segments M t1 , M t2 bending moments in the tensile zone at different cross-section segments

Bending is one of the most common stress states in building structures, including wooden ones (Zhou et al. (2018); Gomon et al. (2019); Sobczak-Piastka et.al (2020), Gomon et al. (2022)). Oblique bending is a type of bending (Sobczak-Piastka et.al (2023)). Current standards (DBN B.2.6-161:2017) propose calculating the strength of obliquely bent elements using the following formulas: