Модели и методы исследования судовых балок с изломом стенки и пояска
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Опубликован:
сен 1, 2020
Ключевые слова:
тонкостенная балка, балка с изломом оси, балка с изломом стенки и пояска, непризматическая балка, I- , H- , T- сечения, двутавр, депланация
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Аннотация
В работе представлено обоснование выбора методов расчета исследуемой типовой судновой балки с изломом стенки и пояска путем анализа различных моделей, которые применяются для расчета тонкостенных конструкций. Проанализированы теории расчета тонкостенных стержней с целью возможности их применения к исследуемой балке и показана невозможность применения этих теорий по причине сложной депланации пояска в местах его излома и на наклонной части судновой балки. Доказано необходимость применения по крайней мере оболочечных, а лучше объемных моделей теории упругости. Рассмотрена проблема эффективной ширины свободного пояска вызванной сдвиговой задержкой и местной потерей устойчивости. Показана необходимость учета депланации пояска при определении эффективной ширины. Произведен обзор публикаций посвященных сдвиговой задержке и эффективной ширине и выявлены основные тенденции в этом направлении. Коротко осмотрены основные методы расчета устойчивости. Охвачены проблемы сварного шва и оптимального проектирования тонкостенных сварных балок касательно исследуемой балки.
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Как цитировать
Соков, В., & Коростылев, Л. (2020). Модели и методы исследования судовых балок с изломом стенки и пояска. Весник Одеского национального морского университета, (63), 76-105. https://doi.org/10.47049/2226-1893-2020-3-76-105
Раздел
Теория и проектирование судов
Литература
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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.
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