PSI - Issue 48

Petro Gomon et al. / Procedia Structural Integrity 48 (2023) 195–200 Homon Sviatoslav et al. / Structural Integrity Procedia 00 (2021) 000 – 000

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most often it is used as load-bearing bending elements in roofs and ceilings in the form of beams (Zhao et al. (2020), Rescalvo et al. (2020), Sobczak-Piastka et al. (2020), Betts et al. (2010)), truss rods, rafters. Such wood-based elements can easily compete with elements made of metal (Iasnii et al. (2023), Kovalchuk et al. (2018)), concrete (Dvorkin et al. (2021)) and reinforced concrete.

Nomenclature f lim

ultimate deflection of the element uniformly distributed load

q F

concentrated force

l , b, h

beam length, width and height, respectively

M F , M F K , M q , M q k maximum moments i 

rotation angle in the section of the bending wooden element

length on the i- th section of the beam turning radius on the i -th section of the beam

i l i r

curvature on i -th section rotation angle on n sections number of beam sections starting rotation angle

i 

n 

n

0  

rotation angle of the neutral line to the initial neutral line of the bending element dependence function of curvature along the length of beam in the section of the bending element

  l 

beam initial deflection

f o f i f o

deflection of the beam in the i -th section

beam deflection

Load-bearing wooden elements are subject to various types of loads (Kulman et al. (2019), Zakic (1974), Gomon et al. (2019)). These elements are reliable and durable if they are provided with normal operating conditions. However, to guarantee such conditions and predict the operation of such elements, it is necessary to determine the ultimate value of the load-bearing capacity and the possible ultimate deflection of the element that will ensure the reliability of the structure. In previous works, the stress-strain state of a wooden bending element with and without reinforcement was established (Gomon et al. (2022)), the peculiarities of plotting Moment-Curvature graphs (Gomon (2021)) were described, as well as their relevance in modeling the operation of structures using wood as the main material. In this paper, we will focus on a new method for the calculation of the deflections of wooden bending elements using the Moment-Curvature graphs, which take into account the nonlinearity of the deformation of wood as a material. This work aims the development of a new method for calculating deflections of wooden beams based on the Moment-Curvature graphs, taking into account the nonlinearity of the deformation of wood as a material. 2. Results and discussion To find the ultimate deflection of a beam, we use the standard value, namely the ratio of deflection to span (DBN B.2.6-161:2017, Eurocode 5:2010, NDS:2018) . To relate the value of the bending moment to the deflection of the beam, various loading options must be assumed (Pysarenko et al. (1988)) (Fig. 1a, Fig. 1b, Fig. 1c, Fig. 1d). The calculation of deflections is carried out in the following sequence: 1) The external diagram of the moments acting along the length of the beam (Fig. 1) using the basic principles of the strength of materials (Pysarenko et al. (1988)) depending on the maximum moments F M , к F M , q M , к q M shall be found. 300 , 250 , 150 lim l l l f 