PSI - Issue 72

Denys Mykhailovskyi et al. / Procedia Structural Integrity 72 (2025) 315–322

316

et al. (2022); Homon et al. (2024); Gong et al. (2019); Datsiuk et al. (2024)) and bending are curved. They have an ascending and descending branch (Homon et al. (2024)). That is, materials and elements work in the pre-critical and critical stages of operation (Homon et al. (2023); Datsiuk et al. (2024)).

Nomenclature x N

forces acting along the bending element

uniformly distributed load

z M

internal forces acting in the compressed and stretched zone of wood

wc wt N N , , ,

external bending moment acting on the cross section

i M i N

external force acting along the neutral line

beam height beam width

h b

internal moments acting in the compressed and stretched zone of wood height of the compressed and stretched zone of wood in the cross section extreme deformations occurring at the edges of the cross-section of a wooden beam wood deformation functions (dependence of stresses on deformations)

wc wt M M , , ,

c y y ,

t

wc wt u u , , ,

( ) ), u f u wc ( , wt t ,

f

, wc

forces arising in a compressed reinforcing bar moment perceived by a compressed reinforcement bar forces arising in a tensile carbon tape moment perceived by a tensile carbon tape cross-sectional area of compressed reinforcement cross-sectional area of tensile carbon tape function of deformation of compressed reinforcement function of deformation of tensile carbon tape

s c N , s c M , cs t N , cs t M , s c A , cs t A ,

  с s c s f u , ,   t сs t сs f u , ,

distance from the neutral line to the center of the compressed reinforcement distance from the neutral line to the center of tensile carbon tape

s c y , t сs y ,

To increase the rigidity of wooden elements, they are reinforced by used steel reinforcement and tapes with a high modulus of elasticity. (Gomon et al. (2022); Sobczak-Piastka et al. (2019); Komar et al. (2024); Gomon et al. (2023); Mykhaylovsky et al. (2022)). The calculation of such elements and constructions can be carried out according to the current normative documents (DBN B.2.6-161: 2017, Eurocode 5: 2004) or by deformation method (Gomon et al. (2023); Pavluk et al. (2024); Gomon et al. (2024)). It is also very important to study the work of wooden elements and structures under complex types of stress-strain conditions. These include curved bending elements and structures. The main purpose is to develop a mathematical model of compressed-bent and compressed-stretched wooden elements and constructures work and to determine the stages of the stressed-deformed state. 2. Methods of theoretical research Fig. 1 and Fig. 2 shows the tension and compression strain diagrams for wood and stress-deformed state of a typical straight wood beam. The high flexibility of wooden elements is associated with a small modulus of elasticity (MOE) of wood, as well as rheological properties (creep and relaxation). To reduce the influence of rheological properties on the wooden element, as well as to reduce the flexibility of wooden structures, it is possible to use reinforcement of structures with high stiffness characteristics.