Моделі та методи дослідження суднових балок зі зламом стінки та пояску
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Опубліковано:
вер 1, 2020
Ключові слова:
тонкостінна балка, балка зі зламом осі, балка зі зламом стінки і пояску, непризматична балка, I- , H- , T- переріз, двотавр, депланація
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Анотація
У роботі представлено обґрунтування вибору методів розрахунку досліджуваної типової суднової балки зі зламом стінки та пояску шляхом аналізу різних моделей, що застосовуються для розрахунку тонкостінних конструкцій. Проаналізовано теорії розрахунку тонкостінних стержнів з метою можливості їх застосування до досліджуваної балки та показана неможливість застосування цих теорій по причині складної депланації пояску в місцях його зламу та на похилій частині суднової балки. Доведено необхідність застосування по крайній мірі оболонкових, а краще об’ємних моделей теорії пружності. Розглянута проблема ефективної ширини вільного пояску викликаної зсувною затримкою та місцевою втратою стійкості. Показано необхідність врахування депланації пояску при визначенні ефективної ширини. Зроблено огляд публікацій присвячених зсувній затримці і ефективній ширині та виявлені основні тенденції в цьому напрямі. Коротко оглянуті основні методи розрахунку стійкості. Захоплені проблеми зварного шва і оптимального проекту-вання тонкостінних зварних балок стосовно досліджуваної балки.
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Як цитувати
Соков, В., & Коростильов, Л. (2020). Моделі та методи дослідження суднових балок зі зламом стінки та пояску. Вісник Одеського національного морського університету, (63), 76-105. https://doi.org/10.47049/2226-1893-2020-3-76-105
Розділ
Теорія і проектування суден
Посилання
1. Det Norske Veritas and Germanischer Lloyd. (2019). Rules for classification: Ships. Part 3. Hull. Oslo: DNV GL AS.
2. Lloyd's Register. (2019). Rules and Regulations for the Classification of Ships. London: Lloyd’s Register Group Limited.
3. Russian maritime register of shipping. (2020). Rules for the classification and construction of sea-going ships. Part II. Hull. ND No. 2-020101-124-E. Saint-Petersburg: RMRS.
4. American Bureau of Shipping. (2020). Rules for building and classing marine vessels. Part 3. Hull construction and equipment. 1701 City Plaza Drive Spring, TX 77389 USA: ABS.
5. Yefremov, N.A. (2019). Rossiyskiy rechnoy Registr. Pravila klassifikatsii i postroyki sudov (PKPS). [Russian river register. Rules of classification and building of ships]. Moscow: RRR. (in Russian).
6. DBN V.2.6-198:2014. (2014). Derzhavni budivelni normy Ukrainy. Stalevi konstruktsii. Normy proektuvannia. [Ukrainian national structural rules. Steel constructions. Design rules]. Kyiv: Minrehion Ukrainy. (in Ukrainian).
7. TKP YeN 1993-1-1-2009 (02250). (2009). Yevrokod 3. Proyektirovaniye stalnykh konstruktsiy. Chast 1-1. Obshchiye pravila i pravila dlya zdaniy (EN 1993-1-1:2005, IDT). [Eurocode 3. Design of steel constructions. Part 1-1. General rules and rules for buildings]. Minsk: Minstroyarkhitektury. (in Russian).
8. TKP EN 1993-1-5–2009* (02250). (2014). Yevrokod 3. Proyektirovaniye stalnykh konstruktsiy. Chast 1-5. Plastinchatyye elementy konstruktsiy (EN 1993-1-5:2006, EN 1993-1-5:2006/AS:2009, IDT). [Eurocode 3. Design of steel constructions. Part 1-5. Plate elements of constructions]. Minsk: Minstroyarkhitektury. (in Russian).
9. SP 294. 1325800.2017. (2017). Konstruktsii stalnyye. Pravila proyektirovaniya. [Steel constructions. Design rules]. Moscow: Minstroy Rossii. (in Russian).
10. ANSI/AISC 360-16. (2016). American Institute of Steel Construction (AISC). Specification for structural steel buildings. USA, Chicago, IL: AISC.
11. Arya, C. (2009). Design of structural elements: concrete, steelwork, masonry and timber designs to British standards and Eurocodes (3-rd ed.). CRC Press.
12. Bogdanovich, A.U. (2008). Tonkostennyye sterzhni peremennogo secheniya: monografiya. [Thin-walled rods of variable crosssection: monography]. Kazan: Kazan State University of Architecture and Engineering. (in Russian).
13. Suslov, V.P., Balandin, A.A. (1972). O reduktsionnom koeffitsiyente poyaska balki, imeyushchey izlom osi. [About reduction factor of a girdle of a beam having a break of an axis]. Proceedings of Vsesoyuz. nauch.-tekhn. konf. po problemam prochnosti i konstruirovaniya krupnotonnazhnykh sudov. Leningrad: Sudostro-yeniye, vol. 182, pp. 123-129. (in Russian).
14. Suslov V.P., Balandin A.A. (1972). Reduktsionnyy koeffitsiyent poyaska v rayone yego izloma. [Reduction factor of a girdle in the regions of its break]. Proceedings of Konferentsii po povrezhdeniyam i ekspluatatsionnoy nadezhnosti sudovykh konstruktsiy. Vladivostok: DVPI, 0.4 p.s. (in Russian).
15. Suslov V.P., Balandin A.A. (1973). Priblizhennoye teoreticheskoye resheniye zadachi o napryazhennom sostoyanii balok, imeyushchikh izlomy poyaskov. [Approximate theoretical solution of the problem of stress state of beams with breaks of girdles]. Sudostroyeniye i morskiye sooruzheniya, vol. 20, 0.5 p.s. (in Russian).
16. Ascione L., Berardi V., Feo L., Fraternali F., Tralli A. M. (2017). Non-prismatic thin-walled beams: critical issues and effective modeling. Proceedings of AIMETA 2017 XXIII Conference, (Salerno, Italy, 4–7 September 2017). Salerno, pp. 301–308.
17. Korostilov L.І., Sokov V. M. (2008). Otsenka kontsentratsii napryazheniy v tipovykh ochagakh konstruktivnykh uzlov korpusa sudna. [Estimation of the stress concentration in the typical hotbeds of structural assemblies of ship hull]. Zbirnyk naukovykh prats NUK, no. 5 (422), pp. 11-17. (in Russian).
18. Sokov, V.M., Korostilov, L.І. (2010). Kontsentratsiya napryazheniy v tipovom ochage tonkostennykh konstruktsiy. [Stress concentration in the typical hotbed of thin-walled constructions]. Zbirnyk naukovykh prats NUK, no. 1 (430), pp. 10-16. (in Russian).
19. Sokov, V.M., Korostilov, L.І. (2010). Proyektirovaniye konstruktivnogo uzla korpusa sudna s uchetom tekhnologicheskikh faktorov. [Design of the structural assembly of ship hull considering technology factors]. Zbirnyk naukovykh prats NUK, no. 5 (434), pp. 3-10. (in Russian).
20. Rybakov, V.A., Gamayunova, O.S. (2013). Napryazhenno-deformirovannoye sostoyaniye elementov karkasnykh sooruzheniy iz tonkostennykh sterzhney. [Stress-strain state of elements of wireframe structures fabricated of thin-walled rods]. Internetzhurnal «Stroitelstvo unikalnykh zdaniy i sooruzheniy», no. 7 (12), pp. 79-123. (in Russian).
21. Vlasov, V.Z. (1959). Tonkostennyye uprugiye sterzhni. [Thinwalled elastic rods]. Moscow: Gos. izd-vo fiziko-matematicheskoy lit-ry. (in Russian).
22. American Iron and Steel Institute. (2006). Direct strength method design guide. Washington, DC, USA: AISI.
23. Cheung, Y.K. (1976). Finite strip method in structural analysis. Oxford: Pergamon.
24. Schardt, R. (1989). Verallgemeinerte Technische Biegetheorie: Lineare Probleme. Berlin: Springer-Verlag. (in German).
25. Umanskiy, A.A. (1939). Izgib i krucheniye tonkostennykh aviatsionnykh konstruktsiy. [Bending and torsion of thin-walled aviation constructions]. Moscow: Oboronizdat. (in Russian). 26. Schafer, B. W. (2006). Designing cold-formed steel using the direct strength method. Proceedings of 18th International Specialty Conference on Cold-Formed Steel Structures (October 26-27, 2006, Orlando, Florida). Orlando, Florida. pp. 475-489.
27. Li, Z., Schafer, B.W. (2010). Application of the finite strip method in cold-formed steel member design. Journal of Constructional Steel Research, vol. 66, iss. 8-9, pp. 971-980.
28. Henriques, D., Gonçalves, R., Camotim, D. (2015). A physically non-linear GBT-based finite element for steel and steel-concrete beams including shear lag effects. Thin-Walled Structures, vol. 90, pp. 202-215.
29. Slivker, V.I. (2005). Stroitelnaya mekhanika. Variatsionnyye osnovy. Uchebnoye posobiye. [Structural mechanics. Variational basics. Textbook]. Moscow: ASV. (in Russian).
30. Rybakov, V.A. (2012). Primeneniye polusdvigovoy teorii V.I. Slivkera dlya analiza napryazhenno-deformirovanogo sostoyaniya sistem tonkostennykh sterzhney. [Application of the semishear theory of V.I. Slivker for analyzing of stress-strain state of thin-walled rod systems]. (PhD thesis), Saint-Petersburg: Peter the Great St-Petersburg Polytechnic University. (in Russian).
31. Sovetnikov, D.O., Azarov, A.A., Ivanov, S.S., Rybakov, V.A. (2018). Metody rascheta tonkostennykh sterzhney: statika, dinamika, ustoychivost. [Methods of calculation of thin-walled rods: statics, dynamics, stability]. Alfabuild, no. 2(4), pp. 7-33. (in Russian).
32. Dyakov, S.F. (2013). Sravnitelnyy analiz zadachi krucheniya tonkostennogo sterzhnya po modelyam Vlasova i Slivkera. [Comparative analysis of the problem of torsion of thin-walled rod using models of Vlasov and Slivker]. Stroitelnaya mekhanika inzhe-nernykh konstruktsiy i sooruzheniy, no. 1, pp. 24-31. (in Russian).
33. El-Mahdy, G.M., El-Saadawy, M.M. (2015). Ultimate strength of singly symmetrical I-section steel beams with variable flange ratio. Thin-Walled Structures, vol. 87, pp. 149-157.
34. Asgarian, B., Soltani, M., Mohri, F. (2013). Lateral-torsional buckling of tapered thin-walled beams with arbitrary crosssections. Thin-walled structures, vol. 62, pp. 96-108.
35. Suslov, V.P., Kochanov, Yu.P., Spikhtarenko, V.N. (1972). Stroitelnaya mekhanika korablya i osnovy teorii uprugosti. [Structural mechanics of ship and basis of theory of elasticity]. Leningrad: Sudostroyeniye. (in Russian).
36. Trubina, D.A., Kononova, L.A., Kaurov, A.A., Pichugin, Ye.D., Abdulayev, D.A. (2014). Mestnaya poterya ustoychivosti stalnykh kholodnognutykh profiley v usloviyakh poperechnogo izgiba. [Local buckling of steel cold-formed profiles in conditions of lateral bending]. Stroitelstvo unikalnykh zdaniy i sooruzheniy, no. 4(19), pp. 109-127. (in Russian).
37. Bassam, Adib Burgan. (1987). Special problems in wide and narrow stiffened compression flanges. (PhD thesis). London: University of London.
38. Hughes, O.F., Ma, M. (1996). Inelastic analysis of panel collapse by stiffener buckling. Computers & structures, vol. 61, no. 1, pp. 107-117.
39. Schardt, R. (1994). Generalized beam theory – an adequate method for coupled stability problems. Thin-walled structures, vol. 19, iss. 2-4, pp. 161-180.
40. Skliarov, I.O. (2014). Eksperymentalno-teoretychna metodyka rozrakhunku stalevykh ram zi zvarnykh dvotavriv zminnoho pererizu z hnuchkoiu stinkoiu. [Experimental-theoretical methodology of calculation of steel frames made of welded joists of variable cross section with a flexible web]. Mistobuduvannia ta terytorialne planuvannia, no. 52, pp. 381-386. (in Ukrainian). 41. Timoshenko, S.P., Goodier, J.N. (1970). Theory of Elasticity: 3-rd ed. New York: McGraw-Hill Book Company.
42. Nadolskiy, V.V., Dergachev, M.G. (2017). Uchet sdvigovogo zapazdyvaniya soglasno trebovaniyam TKP EN 1993-1-5. [Consideration of shear lag due to demands of TKP EN 1993-1-5]. Proceedings of «Innovatsionnaya podgotovka inzhenernykh kadrov na osnove yevropeyskikh standartov (Evrokodov)», (Minsk, 30 may, 2017). Minsk: BNTU, pp. 109-117. (in Russian).
43. Kraus, M. (2017). Numerical approach for bending stress ascertainment in beam theory considering effects of elastic shear lag. Engineering Structures and Technologies, vol. 9, iss. 1, pp. 1- 8.
44. Zhang, Y.H., Lin, L.X. (2014). Shear lag analysis of thin-walled box girders based on a new generalized displacement. Engineering Structures, vol. 61, pp. 73-83.
45. Mazinani, I., Jumaat, M.Z., Ismail, Z., Chao, O.Z. (2014). Comparison of shear lag in structural steel building with framed tube and braced tube. Structural Engineering and Mechanics, vol. 49, no. 3, pp. 297-309.
46. Zhou, W.B., Jiang, L.Z., Liu, Z.J., Liu, X.J. (2012).Closed-form solution to thin-walled box girders considering effects of shear deformation and shear lag. Journal of Central South University, no. 19, pp. 2650-2655.
47. Zhang, Y.H. (2011). Improved finite-segment method for analyzing shear lag effect in thin-walled box girders. Journal of Structural Engineering, vol. 138, iss. 10, pp. 1279-1284.
48. Zhou, S.J. (2010).Finite beam element considering shear-lag effect in box girder. Journal of Engineering Mechanics, vol. 136, iss. 9, pp. 1115-1122.
49. Tahan, N., Pavlovic, M.N., Kotsovos, M.D. (1997). Shear-lag revisited: The use of single Fourier series for determining the effective breadth in plated structures. Computers & structures, vol. 63, iss. 4, pp. 759-767.
50. Sedlacek, G., Bild, S. (1993). A simplified method for the determination of the effective width due to shear lag effects. Journal of Constructional Steel Research, vol. 24, iss. 3, pp. 155- 182.
51. Kristek, V., Studnicka, J. (1991). Negative shear lag in flanges of plated structures. Journal of structural engineering, vol. 117, iss. 12, pp. 3553-3569.
52. Shushkewich, K.W. Negative shear lag explained. (1991). Journal of structural engineering, vol. 117, iss. 11, pp. 3543-3546.
2. Lloyd's Register. (2019). Rules and Regulations for the Classification of Ships. London: Lloyd’s Register Group Limited.
3. Russian maritime register of shipping. (2020). Rules for the classification and construction of sea-going ships. Part II. Hull. ND No. 2-020101-124-E. Saint-Petersburg: RMRS.
4. American Bureau of Shipping. (2020). Rules for building and classing marine vessels. Part 3. Hull construction and equipment. 1701 City Plaza Drive Spring, TX 77389 USA: ABS.
5. Yefremov, N.A. (2019). Rossiyskiy rechnoy Registr. Pravila klassifikatsii i postroyki sudov (PKPS). [Russian river register. Rules of classification and building of ships]. Moscow: RRR. (in Russian).
6. DBN V.2.6-198:2014. (2014). Derzhavni budivelni normy Ukrainy. Stalevi konstruktsii. Normy proektuvannia. [Ukrainian national structural rules. Steel constructions. Design rules]. Kyiv: Minrehion Ukrainy. (in Ukrainian).
7. TKP YeN 1993-1-1-2009 (02250). (2009). Yevrokod 3. Proyektirovaniye stalnykh konstruktsiy. Chast 1-1. Obshchiye pravila i pravila dlya zdaniy (EN 1993-1-1:2005, IDT). [Eurocode 3. Design of steel constructions. Part 1-1. General rules and rules for buildings]. Minsk: Minstroyarkhitektury. (in Russian).
8. TKP EN 1993-1-5–2009* (02250). (2014). Yevrokod 3. Proyektirovaniye stalnykh konstruktsiy. Chast 1-5. Plastinchatyye elementy konstruktsiy (EN 1993-1-5:2006, EN 1993-1-5:2006/AS:2009, IDT). [Eurocode 3. Design of steel constructions. Part 1-5. Plate elements of constructions]. Minsk: Minstroyarkhitektury. (in Russian).
9. SP 294. 1325800.2017. (2017). Konstruktsii stalnyye. Pravila proyektirovaniya. [Steel constructions. Design rules]. Moscow: Minstroy Rossii. (in Russian).
10. ANSI/AISC 360-16. (2016). American Institute of Steel Construction (AISC). Specification for structural steel buildings. USA, Chicago, IL: AISC.
11. Arya, C. (2009). Design of structural elements: concrete, steelwork, masonry and timber designs to British standards and Eurocodes (3-rd ed.). CRC Press.
12. Bogdanovich, A.U. (2008). Tonkostennyye sterzhni peremennogo secheniya: monografiya. [Thin-walled rods of variable crosssection: monography]. Kazan: Kazan State University of Architecture and Engineering. (in Russian).
13. Suslov, V.P., Balandin, A.A. (1972). O reduktsionnom koeffitsiyente poyaska balki, imeyushchey izlom osi. [About reduction factor of a girdle of a beam having a break of an axis]. Proceedings of Vsesoyuz. nauch.-tekhn. konf. po problemam prochnosti i konstruirovaniya krupnotonnazhnykh sudov. Leningrad: Sudostro-yeniye, vol. 182, pp. 123-129. (in Russian).
14. Suslov V.P., Balandin A.A. (1972). Reduktsionnyy koeffitsiyent poyaska v rayone yego izloma. [Reduction factor of a girdle in the regions of its break]. Proceedings of Konferentsii po povrezhdeniyam i ekspluatatsionnoy nadezhnosti sudovykh konstruktsiy. Vladivostok: DVPI, 0.4 p.s. (in Russian).
15. Suslov V.P., Balandin A.A. (1973). Priblizhennoye teoreticheskoye resheniye zadachi o napryazhennom sostoyanii balok, imeyushchikh izlomy poyaskov. [Approximate theoretical solution of the problem of stress state of beams with breaks of girdles]. Sudostroyeniye i morskiye sooruzheniya, vol. 20, 0.5 p.s. (in Russian).
16. Ascione L., Berardi V., Feo L., Fraternali F., Tralli A. M. (2017). Non-prismatic thin-walled beams: critical issues and effective modeling. Proceedings of AIMETA 2017 XXIII Conference, (Salerno, Italy, 4–7 September 2017). Salerno, pp. 301–308.
17. Korostilov L.І., Sokov V. M. (2008). Otsenka kontsentratsii napryazheniy v tipovykh ochagakh konstruktivnykh uzlov korpusa sudna. [Estimation of the stress concentration in the typical hotbeds of structural assemblies of ship hull]. Zbirnyk naukovykh prats NUK, no. 5 (422), pp. 11-17. (in Russian).
18. Sokov, V.M., Korostilov, L.І. (2010). Kontsentratsiya napryazheniy v tipovom ochage tonkostennykh konstruktsiy. [Stress concentration in the typical hotbed of thin-walled constructions]. Zbirnyk naukovykh prats NUK, no. 1 (430), pp. 10-16. (in Russian).
19. Sokov, V.M., Korostilov, L.І. (2010). Proyektirovaniye konstruktivnogo uzla korpusa sudna s uchetom tekhnologicheskikh faktorov. [Design of the structural assembly of ship hull considering technology factors]. Zbirnyk naukovykh prats NUK, no. 5 (434), pp. 3-10. (in Russian).
20. Rybakov, V.A., Gamayunova, O.S. (2013). Napryazhenno-deformirovannoye sostoyaniye elementov karkasnykh sooruzheniy iz tonkostennykh sterzhney. [Stress-strain state of elements of wireframe structures fabricated of thin-walled rods]. Internetzhurnal «Stroitelstvo unikalnykh zdaniy i sooruzheniy», no. 7 (12), pp. 79-123. (in Russian).
21. Vlasov, V.Z. (1959). Tonkostennyye uprugiye sterzhni. [Thinwalled elastic rods]. Moscow: Gos. izd-vo fiziko-matematicheskoy lit-ry. (in Russian).
22. American Iron and Steel Institute. (2006). Direct strength method design guide. Washington, DC, USA: AISI.
23. Cheung, Y.K. (1976). Finite strip method in structural analysis. Oxford: Pergamon.
24. Schardt, R. (1989). Verallgemeinerte Technische Biegetheorie: Lineare Probleme. Berlin: Springer-Verlag. (in German).
25. Umanskiy, A.A. (1939). Izgib i krucheniye tonkostennykh aviatsionnykh konstruktsiy. [Bending and torsion of thin-walled aviation constructions]. Moscow: Oboronizdat. (in Russian). 26. Schafer, B. W. (2006). Designing cold-formed steel using the direct strength method. Proceedings of 18th International Specialty Conference on Cold-Formed Steel Structures (October 26-27, 2006, Orlando, Florida). Orlando, Florida. pp. 475-489.
27. Li, Z., Schafer, B.W. (2010). Application of the finite strip method in cold-formed steel member design. Journal of Constructional Steel Research, vol. 66, iss. 8-9, pp. 971-980.
28. Henriques, D., Gonçalves, R., Camotim, D. (2015). A physically non-linear GBT-based finite element for steel and steel-concrete beams including shear lag effects. Thin-Walled Structures, vol. 90, pp. 202-215.
29. Slivker, V.I. (2005). Stroitelnaya mekhanika. Variatsionnyye osnovy. Uchebnoye posobiye. [Structural mechanics. Variational basics. Textbook]. Moscow: ASV. (in Russian).
30. Rybakov, V.A. (2012). Primeneniye polusdvigovoy teorii V.I. Slivkera dlya analiza napryazhenno-deformirovanogo sostoyaniya sistem tonkostennykh sterzhney. [Application of the semishear theory of V.I. Slivker for analyzing of stress-strain state of thin-walled rod systems]. (PhD thesis), Saint-Petersburg: Peter the Great St-Petersburg Polytechnic University. (in Russian).
31. Sovetnikov, D.O., Azarov, A.A., Ivanov, S.S., Rybakov, V.A. (2018). Metody rascheta tonkostennykh sterzhney: statika, dinamika, ustoychivost. [Methods of calculation of thin-walled rods: statics, dynamics, stability]. Alfabuild, no. 2(4), pp. 7-33. (in Russian).
32. Dyakov, S.F. (2013). Sravnitelnyy analiz zadachi krucheniya tonkostennogo sterzhnya po modelyam Vlasova i Slivkera. [Comparative analysis of the problem of torsion of thin-walled rod using models of Vlasov and Slivker]. Stroitelnaya mekhanika inzhe-nernykh konstruktsiy i sooruzheniy, no. 1, pp. 24-31. (in Russian).
33. El-Mahdy, G.M., El-Saadawy, M.M. (2015). Ultimate strength of singly symmetrical I-section steel beams with variable flange ratio. Thin-Walled Structures, vol. 87, pp. 149-157.
34. Asgarian, B., Soltani, M., Mohri, F. (2013). Lateral-torsional buckling of tapered thin-walled beams with arbitrary crosssections. Thin-walled structures, vol. 62, pp. 96-108.
35. Suslov, V.P., Kochanov, Yu.P., Spikhtarenko, V.N. (1972). Stroitelnaya mekhanika korablya i osnovy teorii uprugosti. [Structural mechanics of ship and basis of theory of elasticity]. Leningrad: Sudostroyeniye. (in Russian).
36. Trubina, D.A., Kononova, L.A., Kaurov, A.A., Pichugin, Ye.D., Abdulayev, D.A. (2014). Mestnaya poterya ustoychivosti stalnykh kholodnognutykh profiley v usloviyakh poperechnogo izgiba. [Local buckling of steel cold-formed profiles in conditions of lateral bending]. Stroitelstvo unikalnykh zdaniy i sooruzheniy, no. 4(19), pp. 109-127. (in Russian).
37. Bassam, Adib Burgan. (1987). Special problems in wide and narrow stiffened compression flanges. (PhD thesis). London: University of London.
38. Hughes, O.F., Ma, M. (1996). Inelastic analysis of panel collapse by stiffener buckling. Computers & structures, vol. 61, no. 1, pp. 107-117.
39. Schardt, R. (1994). Generalized beam theory – an adequate method for coupled stability problems. Thin-walled structures, vol. 19, iss. 2-4, pp. 161-180.
40. Skliarov, I.O. (2014). Eksperymentalno-teoretychna metodyka rozrakhunku stalevykh ram zi zvarnykh dvotavriv zminnoho pererizu z hnuchkoiu stinkoiu. [Experimental-theoretical methodology of calculation of steel frames made of welded joists of variable cross section with a flexible web]. Mistobuduvannia ta terytorialne planuvannia, no. 52, pp. 381-386. (in Ukrainian). 41. Timoshenko, S.P., Goodier, J.N. (1970). Theory of Elasticity: 3-rd ed. New York: McGraw-Hill Book Company.
42. Nadolskiy, V.V., Dergachev, M.G. (2017). Uchet sdvigovogo zapazdyvaniya soglasno trebovaniyam TKP EN 1993-1-5. [Consideration of shear lag due to demands of TKP EN 1993-1-5]. Proceedings of «Innovatsionnaya podgotovka inzhenernykh kadrov na osnove yevropeyskikh standartov (Evrokodov)», (Minsk, 30 may, 2017). Minsk: BNTU, pp. 109-117. (in Russian).
43. Kraus, M. (2017). Numerical approach for bending stress ascertainment in beam theory considering effects of elastic shear lag. Engineering Structures and Technologies, vol. 9, iss. 1, pp. 1- 8.
44. Zhang, Y.H., Lin, L.X. (2014). Shear lag analysis of thin-walled box girders based on a new generalized displacement. Engineering Structures, vol. 61, pp. 73-83.
45. Mazinani, I., Jumaat, M.Z., Ismail, Z., Chao, O.Z. (2014). Comparison of shear lag in structural steel building with framed tube and braced tube. Structural Engineering and Mechanics, vol. 49, no. 3, pp. 297-309.
46. Zhou, W.B., Jiang, L.Z., Liu, Z.J., Liu, X.J. (2012).Closed-form solution to thin-walled box girders considering effects of shear deformation and shear lag. Journal of Central South University, no. 19, pp. 2650-2655.
47. Zhang, Y.H. (2011). Improved finite-segment method for analyzing shear lag effect in thin-walled box girders. Journal of Structural Engineering, vol. 138, iss. 10, pp. 1279-1284.
48. Zhou, S.J. (2010).Finite beam element considering shear-lag effect in box girder. Journal of Engineering Mechanics, vol. 136, iss. 9, pp. 1115-1122.
49. Tahan, N., Pavlovic, M.N., Kotsovos, M.D. (1997). Shear-lag revisited: The use of single Fourier series for determining the effective breadth in plated structures. Computers & structures, vol. 63, iss. 4, pp. 759-767.
50. Sedlacek, G., Bild, S. (1993). A simplified method for the determination of the effective width due to shear lag effects. Journal of Constructional Steel Research, vol. 24, iss. 3, pp. 155- 182.
51. Kristek, V., Studnicka, J. (1991). Negative shear lag in flanges of plated structures. Journal of structural engineering, vol. 117, iss. 12, pp. 3553-3569.
52. Shushkewich, K.W. Negative shear lag explained. (1991). Journal of structural engineering, vol. 117, iss. 11, pp. 3543-3546.