624.011

wood, bending element, stress-strain state, tangential stresses, optimized wood deformation diagram.

The basis for the calculation of reinforced bending wooden elements, taking into account the nonlinearity of wood deformation, has been developed. For the proposed calculation, optimized diagrams of wood deformation (polynomial of the 4th degree) were used. A method of determining the tangential stresses of bending reinforced wooden elements, taking into account the nonlinearity of the deformation of the material, has been developed.

1. Gomon P. S. Metodyka pobudovy diahramy deformuvannya “ ” dlya derevyny na osnovi eksperymentalʹnykh doslidzhenʹ z·hynalʹnykh elementiv. Resursoekonomni materialy, konstruktsiyi, budivli i sporudy. Rivne: NUVHP, 2014. Vypusk 29. Р. 102–107. [In Ukrainian].
2. Homon S. S., Gomon P. S. Pobudova diysnykh diahram mekhanichnoho stanu derevyny «s-u» sutsilʹnoho pererizu yalyny ta berezy za zhorstkoho rezhymu vyprobuvanʹ. Resursoekonomni materialy, konstruktsiyi, budivli ta sporudy. Rivne, 2020. Vyp. 38. Р. 321–330. [In Ukrainian].
3. Gomon S. S., Homon S. S., Sasovsʹkyy T. A. Diahramy mekhanichnoho stanu derevyny sosny za odnorazovoho korotkochasnoho deformuvannya do povnoyi vtraty mitsnosti materialu. Resursoekonomni materialy, konstruktsiyi, budivli ta sporudy. Rivne. 2012. Vyp. 23. Р. 166–171. [In Ukrainian].
4. Yasniy P., Gomon S., Gomon P. On approximation of mechanical condition diagrams of coniferous and deciduous wood species on compression along the fibers. Scientific Journal of Ternopil National Technical University. Ternopil: TNTU. 2020. Vol. 97. No 1. P. 57–64.
5. Yasniy P., Gomon S. Timber with improved strength and deformable properties. Scientific Journal of Ternopil National Technical University. Ternopil: TNTU, 2020. Vol. 99. No 3. P. 17–27.
6. Yasniy P., Homon S., Iasnii V., Gomon S. S., Gomon P., Savitskiy V. Strength properties of chemically modified solid woods. Procedia Structural Integrity. 2022. 36. P. 211–216.
7. Da Silva A., Kyrіakides S. Compressive response and failure of  balsa wood. International Journal of Solids and Structures. 2007. Volume 44. Issues 25–26. P. 8685–8717.
8. Zhou A., Bian Y., Shen Y., Huang  D., Zhou M. Inelastic bending performances of laminated bamboo beams: experimental investigation and analytical study. Bio Resources, 2018. 13 (1). P. 131–146.
9. Gomon P. S. Aproksymatsiya diahramy «moment-kryvyna» derevʺyanykh armovanykh ta nearmovanykh balok pryamokutnoho pererizu. Mistobuduvannya ta terytorialʹne planuvannya. Kyyiv: KNUBA, 2021. №78. S. 157-165. [in Ukrainian].
10. Gomon P.S. Osoblyvosti pobudovy diahramy «moment-kryvyna» pidsylenykh balok z derevyny pryamokutnoho pererizu. Visnyk Natsionalʹnoho universytetu vodnoho hospodarstva ta pryrodokorystuvannya. Seriya «Tekhnichni nauky». Rivne: NUVHP, 2021. Vypusk 3(95). S. 128-138. [in Ukrainian].
11. Gomon P.S.  Napruzheno-deformovanyy stan balok iz derevyny z kombinovanym armuvannyam na riznykh rivnyakh zavantazhenʹ. Suchasni tekhnolohiyi ta metody rozrakhunkiv u budivnytstvi. Lutsʹk: LNTUЮ 2022. Vypusk 17. Р. 23–30. [In Ukrainian].
12. Gomon P. S. Sumisnistʹ roboty armatury ta derevyny v balkakh, yaki pratsyuyutʹ za poperechnoho z·hynu. Suchasni problemy arkhitektury ta mistobuduvannya. Kyiv: KNUBA. 2022. Vypusk 63. Р. 327–335.
13. Homon P. S. Modelyuvannya roboty derevʺyanoyi balky z poslidovnym zavantazhennyam. Mistobuduvannya ta terytorialʹne planuvannya. Kyiv: KNUBA. 2022. No. 80. Р. 159–165. [In Ukrainian].
14. De la Rosa García P., Cobo Escamilla A., Nieves González Garcia M. Bending Reinforcement of Timber Beams with Composite Carbon Fiber and Basalt Fiber Materials. Compos. Part B Eng. 2013. 55. P. 528–536.
15. Wdowiak A., Brol J. Effectiveness of reinforcing bent non-uniform pre-stressed glulam beams with basalt fibre reinforced polymers rods. Materials 2019. 12. Р. 31–41.
16. De Luca V., Marano C. Prestressed glulam timbers reinforced with steel bars. Constr. Build. Mater., 30 (2012). P. 206–217.
17. Usman A., Sugiri S. Analysis of the Strength of Timber and Glulam Timber Beams with Steel Reinforcement. Materials Science, 2015.
18. Negrão J. H. Preliminary study on wire prestressing methods for timber pieces reinforcement. Constr. Build. Mater., 102. 2016. Р. 1093–1100.
19. Donadon B. F., Mascia N. T., Vilela R., Trautwein L. M. Experimental investigation of glued-laminated timber beams with vectran-frp reinforcement. Eng. Struct. 2020. 202.109818.
20. Jasieńko J., Nowak T. P. Solid timber beams strengthened with steel plates – experimental studies. Constr. Build. Mater., 63. 2014. Р. 81–88.
21. Gomon P. S., Oleksin I. O. Vyznachennya dotychnykh napruzhenʹ v derevʺyanykh balkakh z vrakhuvannyam neliniynosti deformuvannya materialu. Resursoekonomni materialy, konstruktsiyi, budivli ta sporudy. Rivne: NUVHP. 2022. Vyp. 41. Р. 126–134. [In Ukrainian].
22. Babich V. YE., Gomon P. S., Prashchur O. Shlyakhy pidvyshchennya zhorstkosti elementiv z tsilʹnoyi ta kleyenoyi derevyny za poperechnoho z·hynu. Resursoekonomni materialy, konstruktsiyi, budivli ta sporudy. Rivne: NUVHP, 2021. Vyp. 40. Р. 97–104. [In Ukrainian].
23. Gomon P. S., Polishchuk M. V. Prohyny pidsylenykh ta nepidsylenykh balok pryamokutnoho pererizu z kleyenoyi derevyny. Suchasni budivelʹni konstruktsiyi z metalu ta derevyny. Odesa: ODABA, 2022. Vypusk 26. Р. 88–96. [In Ukrainian].

1. Gomon P. S. Metodyka pobudovy diahramy deformuvannya “ ” dlya derevyny na osnovi eksperymentalʹnykh doslidzhenʹ z·hynalʹnykh elementiv. Resursoekonomni materialy, konstruktsiyi, budivli i sporudy. Rivne: NUVHP, 2014. Vypusk 29. Р. 102–107. [In Ukrainian].
2. Homon S. S., Gomon P. S. Pobudova diysnykh diahram mekhanichnoho stanu derevyny «s-u» sutsilʹnoho pererizu yalyny ta berezy za zhorstkoho rezhymu vyprobuvanʹ. Resursoekonomni materialy, konstruktsiyi, budivli ta sporudy. Rivne, 2020. Vyp. 38. Р. 321–330. [In Ukrainian].
3. Gomon S. S., Homon S. S., Sasovsʹkyy T. A. Diahramy mekhanichnoho stanu derevyny sosny za odnorazovoho korotkochasnoho deformuvannya do povnoyi vtraty mitsnosti materialu. Resursoekonomni materialy, konstruktsiyi, budivli ta sporudy. Rivne. 2012. Vyp. 23. Р. 166–171. [In Ukrainian].
4. Yasniy P., Gomon S., Gomon P. On approximation of mechanical condition diagrams of coniferous and deciduous wood species on compression along the fibers. Scientific Journal of Ternopil National Technical University. Ternopil: TNTU. 2020. Vol. 97. No 1. P. 57–64.
5. Yasniy P., Gomon S. Timber with improved strength and deformable properties. Scientific Journal of Ternopil National Technical University. Ternopil: TNTU, 2020. Vol. 99. No 3. P. 17–27.
6. Yasniy P., Homon S., Iasnii V., Gomon S. S., Gomon P., Savitskiy V. Strength properties of chemically modified solid woods. Procedia Structural Integrity. 2022. 36. P. 211–216.
7. Da Silva A., Kyrіakides S. Compressive response and failure of  balsa wood. International Journal of Solids and Structures. 2007. Volume 44. Issues 25–26. P. 8685–8717.
8. Zhou A., Bian Y., Shen Y., Huang  D., Zhou M. Inelastic bending performances of laminated bamboo beams: experimental investigation and analytical study. Bio Resources, 2018. 13 (1). P. 131–146.
9. Gomon P. S. Aproksymatsiya diahramy «moment-kryvyna» derevʺyanykh armovanykh ta nearmovanykh balok pryamokutnoho pererizu. Mistobuduvannya ta terytorialʹne planuvannya. Kyyiv: KNUBA, 2021. №78. S. 157-165. [in Ukrainian].
10. Gomon P.S. Osoblyvosti pobudovy diahramy «moment-kryvyna» pidsylenykh balok z derevyny pryamokutnoho pererizu. Visnyk Natsionalʹnoho universytetu vodnoho hospodarstva ta pryrodokorystuvannya. Seriya «Tekhnichni nauky». Rivne: NUVHP, 2021. Vypusk 3(95). S. 128-138. [in Ukrainian].
11. Gomon P.S.  Napruzheno-deformovanyy stan balok iz derevyny z kombinovanym armuvannyam na riznykh rivnyakh zavantazhenʹ. Suchasni tekhnolohiyi ta metody rozrakhunkiv u budivnytstvi. Lutsʹk: LNTUЮ 2022. Vypusk 17. Р. 23–30. [In Ukrainian].
12. Gomon P. S. Sumisnistʹ roboty armatury ta derevyny v balkakh, yaki pratsyuyutʹ za poperechnoho z·hynu. Suchasni problemy arkhitektury ta mistobuduvannya. Kyiv: KNUBA. 2022. Vypusk 63. Р. 327–335.
13. Homon P. S. Modelyuvannya roboty derevʺyanoyi balky z poslidovnym zavantazhennyam. Mistobuduvannya ta terytorialʹne planuvannya. Kyiv: KNUBA. 2022. No. 80. Р. 159–165. [In Ukrainian].
14. De la Rosa García P., Cobo Escamilla A., Nieves González Garcia M. Bending Reinforcement of Timber Beams with Composite Carbon Fiber and Basalt Fiber Materials. Compos. Part B Eng. 2013. 55. P. 528–536.
15. Wdowiak A., Brol J. Effectiveness of reinforcing bent non-uniform pre-stressed glulam beams with basalt fibre reinforced polymers rods. Materials 2019. 12. Р. 31–41.
16. De Luca V., Marano C. Prestressed glulam timbers reinforced with steel bars. Constr. Build. Mater., 30 (2012). P. 206–217.
17. Usman A., Sugiri S. Analysis of the Strength of Timber and Glulam Timber Beams with Steel Reinforcement. Materials Science, 2015.
18. Negrão J. H. Preliminary study on wire prestressing methods for timber pieces reinforcement. Constr. Build. Mater., 102. 2016. Р. 1093–1100.
19. Donadon B. F., Mascia N. T., Vilela R., Trautwein L. M. Experimental investigation of glued-laminated timber beams with vectran-frp reinforcement. Eng. Struct. 2020. 202.109818.
20. Jasieńko J., Nowak T. P. Solid timber beams strengthened with steel plates – experimental studies. Constr. Build. Mater., 63. 2014. Р. 81–88.
21. Gomon P. S., Oleksin I. O. Vyznachennya dotychnykh napruzhenʹ v derevʺyanykh balkakh z vrakhuvannyam neliniynosti deformuvannya materialu. Resursoekonomni materialy, konstruktsiyi, budivli ta sporudy. Rivne: NUVHP. 2022. Vyp. 41. Р. 126–134. [In Ukrainian].
22. Babich V. YE., Gomon P. S., Prashchur O. Shlyakhy pidvyshchennya zhorstkosti elementiv z tsilʹnoyi ta kleyenoyi derevyny za poperechnoho z·hynu. Resursoekonomni materialy, konstruktsiyi, budivli ta sporudy. Rivne: NUVHP, 2021. Vyp. 40. Р. 97–104. [In Ukrainian].
23. Gomon P. S., Polishchuk M. V. Prohyny pidsylenykh ta nepidsylenykh balok pryamokutnoho pererizu z kleyenoyi derevyny. Suchasni budivelʹni konstruktsiyi z metalu ta derevyny. Odesa: ODABA, 2022. Vypusk 26. Р. 88–96. [In Ukrainian].