Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Imperfections in thin-walled steel profiles with modified cross-sectional shapes - Current state of knowledge and preliminary studies

  • Aleksandra M. Pawlak (Division of Strength of Materials and Structures, Poznan University of Technology) ;
  • Tomasz A. Gorny (Division of Strength of Materials and Structures, Poznan University of Technology) ;
  • Michal Plust (Division of Strength of Materials and Structures, Poznan University of Technology) ;
  • Piotr Paczos (Division of Strength of Materials and Structures, Poznan University of Technology) ;
  • Jakub Kasprzak (Division of Strength of Materials and Structures, Poznan University of Technology)
  • Received : 2024.03.14
  • Accepted : 2024.07.04
  • Published : 2024.08.10
⟨ Previous Next ⟩

Abstract

This paper is the first in a series of articles dealing with the study and analysis of imperfections in thin-walled, cold-formed steel sections with modified cross-sectional shapes. A study was conducted, using 3D scanning techniques, to determine the most vulnerable geometric imperfections in the profiles. Based on a review of the literature, it has been determined that few researchers are studying thin-walled sections with modified cross-sectional shapes. Each additional bend in the section potentially generates geometric imperfections. Geometric imperfections significantly affect the resistance to loss of stability, which is crucial when analyzing thin-walled structures. In addition, the most critical locations along the length where these imperfections occur were determined. Based on the study, it was found that geometric imperfections cause a reduction in critical load. It should be noted that the tests performed are preliminary studies, based on which a program of further research will be developed. In addition, the article presents the current state of knowledge in the authors' field of interest. The future objective is to ascertain if these imperfections could potentially contribute positively to structural integrity. This enhanced understanding may pave the way for novel methodologies in structural engineering, wherein imperfections are viewed not solely as flaws but also as elements that could enhance the end product.

Keywords

Acknowledgement

The project was funded by the National Science Centre, Poland, and allocated on the basis of the decision No. DEC-2021/43/B/ST8/00845 of 2022-05-23 - Contract No. UMO-2021/43/B/ST8/00845.

References

  1. Aktepe, R. and Erkal, B.G. (2023), „State-of-the-art review on measurement techniques and numerical modeling of geometric imperfections in cold-formed steel members", J. Construct. Steel Res., 207, 107942. https://doi.org/10.1016/j.jcsr.2023.107942.
  2. Aktepe, R. and Erkal, B.G. (2023a), "Experimental and numerical study on flexural behaviour of cold-formed steel hat-shaped beams with geometrical imperfections", J. Construct. Steel Res., 202, 107774. https://doi.org/10.1016/j.jcsr.2023.107774.
  3. Ali, M.A., Tomko, M., Demjan, I. and Kvocak, V. (2012), "Thin-walled cold-formed compressed steel members and the problem of initial imperfections", Procedia Eng., 40, 8-13. https://doi.org/10.1016/j.proeng.2012.07.047.
  4. Arrayago, I., Rasmussen, K.J. and Real, E. (2020), "Statistical analysis of the material, geometrical and imperfection characteristics of structural stainless steels and members", J. Construct. Steel Res., 175, 106378. https://doi.org/10.1016/j.jcsr.2020.106378.
  5. Bernard, E., Coleman, R. and Bridge, R. (1999), "Measurement and assessment of geometric imperfections in thin-walled panels", Thin-Wall. Struct., 33(2), 103-126. https://doi.org/10.1016/s0263-8231(98)00043-3.
  6. Bologna, F., Tannous, M., Romano, D. and Stefanini, C. (2022), "Automatic welding imperfections detection in a smart factory via 2-D laser scanner", J. Manufact. Processes, 73, 948-960. https://doi.org/10.1016/j.jmapro.2021.10.046.
  7. Calladine, C. (1995), "Understanding imperfection-sensitivity in the buckling of thin-walled shells", Thin-Wall. Struct., 23(1-4), 215-235. https://doi.org/10.1016/0263-8231(95)00013-4.
  8. Chen, B., Wang, Y., Xu, D., Yuan, H. and Yan, L. (2023), "Finite element analysis and proposed design rules for 304D high-strength stainless steel I-shaped members in shear", J. Construct. Steel Res., 204, 107861. https://doi.org/10.1016/j.jcsr.2023.107861.
  9. Chen, B., Wang, Y., Xu, D., Yuan, H. and Yan, L. (2023), "Finite element analysis and proposed design rules for 304D high-strength stainless steel I-shaped members in shear", J. Construct. Steel Res., 204, 107861. https://doi.org/10.1016/j.jcsr.2023.107861.
  10. Chen, Y., Chen, W., Hao, H. and Xia, Y. (2022), "Damage evaluation of a welded beam-column joint with surface imperfections subjected to impact loads", Eng. Struct. Eng. Struct., 261, 114276. https://doi.org/10.1016/j.engstruct.2022.114276.
  11. Chen, Y., Chen, W., Hao, H. and Zhou, X. (2022), "Impact behavior of beam-column joint with geometric imperfections at weld root", Eng. Struct. Eng. Struct., 266, 114611. https://doi.org/10.1016/j.engstruct.2022.114611.
  12. Combescure, A. (1997), "Influence of initial imperfections on the collapse of thin walled structures", Studies Appl. Mech., 385-394. https://doi.org/10.1016/s0922-5382(97)80040-2.
  13. Couto, C. and Real, P.V. (2019), "Numerical investigation on the influence of imperfections in the local buckling of thin-walled I-shaped sections", Thin-Wall. Struct., 135, 89-108. https://doi.org/10.1016/j.tws.2018.10.039.
  14. Couto, C. and Real, P.V. (2021), "The influence of imperfections in the critical temperature of I-section steel members", J. Construct. Steel Res., 179, 106540. https://doi.org/10.1016/j.jcsr.2021.106540.
  15. Dar, M.A., Fayaz, S.J., Rather, S., Dar, A. and Hajirasouliha, I. (2023), "Incremental stiffening approach for CFS built-up-beams with large imperfections: Tests and flexural-behaviour", Structures, 53, 1318-1340. https://doi.org/10.1016/j.istruc.2023.05.003.
  16. Dubina, D. and Ungureanu, V. (2023), "Local/distortional and overall interactive buckling of thin-walled cold-formed steel columns with open cross-section", Thin-Wall. Struct., 182, 110172. https://doi.org/10.1016/j.tws.2022.110172.
  17. EN 1993-1-3 (2008), Eurocode 3, Design of Steel Structures. Part 1-3 General Rules. Supplementary Rules for Structures Made of Sections and Cold-Formed Plates, PKN, Warsaw 2008.
  18. Farzanian, S., Louhghalam, A., Schafer, B. and Tootkaboni, M. (2023), "Geometric imperfections in CFS structural members: Part I: A review of the basics and some modeling strategies", Thin-Wall. Struct., 186, 110619. https://doi.org/10.1016/j.tws.2023.110619.
  19. Farzanian, S., Louhghalam, A., Schafer, B. and Tootkaboni, M. (2023a), "Geometric imperfections in CFS structural members, Part II: Data-driven modeling and probabilistic validation", Thin-Wall. Struct., 185, 110620. https://doi.org/10.1016/j.tws.2023.110620.
  20. Fasoulakis, Z., Vamvatsikos, D. and Papadopoulos, V. (2021), "Stability of single-bolted thin-walled steel angle members with stochastic imperfections", J. Struct. Eng., 147(8). https://doi.org/10.1061/(asce)st.1943-541x.0003061.
  21. Feng, S., Duan, Y., Yao, C., Yang, H., Liu, H., Wang, B. and Hao, P. (2022), "A Gaussian process-driven worst realistic imperfection method for cylindrical shells by limited data", Thin-Wall. Struct., 181, 110130. https://doi.org/10.1016/j.tws.2022.110130.
  22. Garifullin, M. and Nackenhorst, U. (2015), "Computational analysis of cold-formed steel columns with initial imperfections", Procedia Eng., 117, 1073-1079. https://doi.org/10.1016/j.proeng.2015.08.239.
  23. Garstecki, A., Kakol, W. and Rzeszut, K. (2002), "Classification of local-sectional geometric imperfections of steel thin-walled cold-formed sigma members", Found. Civil Enviro. Eng., 87-96.
  24. Godoy, L.A. (1996), "Thin-walled structures with structural imperfections, analysis and behavior", Pergamon, 978-0-08-042266-4.
  25. Godoy, L.A. (1998), "Stresses and pressures in thin-walled structures with damage and imperfections", Thin-Wall. Struct., 32(1-3), 181-206. https://doi.org/10.1016/s0263-8231(98)00032-9.
  26. Grenda, M. and Paczos, P. (2019), "Experimental and numerical study of local stability of non-standard thin-walled channel beams", J. Theoretic. Appl. Mech. Mechanika Teoretyczna I Stosowana, 57(3), 549-562. https://doi.org/10.15632/jtampl/109601.
  27. Halabi, Y. and Alhaddad, W. (2020), "Manufacturing, applications, analysis and design of cold-formed steel in engineering structures: A review", Int. J. Adv. Eng. Res. Sci., 7(2), 11-34. https://doi.org/10.22161/ijaers.72.3.
  28. Hemmatnezhad, M., Iarriccio, G., Zippo, A. and Pellicano, F. (2022), "Modal localization in vibrations of circular cylindrical shells with geometric imperfections", Thin-Wall. Struct., 181, 110079. https://doi.org/10.1016/j.tws.2022.110079.
  29. Huang, L., Yang, W., Shi, T. and Qu, J. (2020), "Local and distortional interaction buckling of cold-formed thin-walled high strength lipped channel columns", Int. J. Steel Struct. Int. J. Steel Struct., 21(1), 244-259. https://doi.org/10.1007/s13296-020-00436-z.
  30. Hubner, S.T., Simmen, K., Breitbarth, A.M.M. and Notni, G. (2021), "Standard-compliant detection of fillet weld surface imperfections for MAG-welding using a 3D-line scanner", Dimensional Optical Metrology Inspection Practical Applications X, 117320A. https://doi.org/10.1117/12.2588536
  31. Ismail Mahmud, J. and Jailani, A. (2023), "Buckling of an imperfect spherical shell subjected to external pressure", Ocean Eng., 275, 114118. https://doi.org/10.1016/j.oceaneng.2023.114118.
  32. Jasion, P., Pawlak, A. and Paczos, P. (2021), "Buckling and post-buckling behaviour of selected cold-formed C-beams with atypical flanges", Eng. Struct. Eng. Struct., 244, 112693. https://doi.org/10.1016/j.engstruct.2021.112693.
  33. Jinwu, X. (2004), "3D detection technique for surface defects of steel plates based on linear laser", J. Univ. Sci. Technol., Beijing.
  34. Jun, S., Hongbin, Y., Dihong, Z., Bin, Z. and Xiande., L. (2019), "Three-dimensional laser scanning-based high-precision steel structure quality detection device".
  35. Jurdeczka, U. (2020), "Model-based analysis of constructional steel structures exemplified by dimensional checking on railway car shells using 3D scanning", J. Sensors Sensor Syst., 9(1), 109-116. https://doi.org/10.5194/jsss-9-109-2020.
  36. Kolakowski, Z., Kubiak, T., Zaczynska, M. and Kazmierczyk, F. (2020), "Global-distortional buckling mode influence on post-buckling behaviour of lip-channel beams", Int. J. Mech. Sci., 184, 105723. https://doi.org/10.1016/j.ijmecsci.2020.105723.
  37. Korsun, N. and Prostakishina, D. (2019), "Bearing capacity of steel thin-walled profiles in reliability assessment", E3S Web of Conferences, 97, 04049. https://doi.org/10.1051/e3sconf/20199704049.
  38. Laim, L., Rodrigues, J.P.C. and Craveiro, H.D. (2015), "Flexural behaviour of beams made of cold-formed steel sigma-shaped sections at ambient and fire conditions", Thin-Wall. Struct., 87, 53-65. https://doi.org/10.1016/j.tws.2014.11.004.
  39. Li, B., Wang, Y., Zhang, Y., Meng, X., Yuan, H. and Zhi, X. (2022), "Flexural buckling of extruded high-strength aluminium alloy SHS columns", Thin-Wall. Struct., 179, 109717. https://doi.org/10.1016/j.tws.2022.109717.
  40. Li, S. and Zhao, O. (2022), "Local-flexural interactive buckling behaviour and resistance of press-braked stainless steel slender channel section columns", Eng. Struct. Eng. Struct., 270, 114871. https://doi.org/10.1016/j.engstruct.2022.114871.
  41. Luo, Y. and Zhan, J. (2020), "Linear buckling topology optimization of reinforced thin-walled structures considering uncertain geometrical imperfections", Struct. Multidiscipl. Optimiz., 62(6), 3367-3382. https://doi.org/10.1007/s00158-020-02738-6.
  42. Maali, M., Aydin, A.C., Showkati, H., Fatemi, S.M. and Sagiroglu, M. (2018), "Longitudinal imperfections on thin walled cylindrical shells", J. Civil Environ. Eng., 08(02). https://doi.org/10.4172/2165-784x.1000309.
  43. Machavolu, S.S.P.K., Michael, T.C., Jebaseelan, D.D., Karthik, B. and Panneerselvam, D. (2023), "Risk assessment of strain hardened pipe bends with shape imperfections under in-plane closing bending moment", Mater. Today: Proceedings. https://doi.org/10.1016/j.matpr.2023.03.214.
  44. Mageirou, G. and Lemonis, M. (2021), "Influence of imperfections on the progressive collapse of steel moment resisting frames", J. Construct. Steel Res., 183, 106744. https://doi.org/10.1016/j.jcsr.2021.106744.
  45. Mahidan, F. and Ifayefunmi, O. (2021), "The imperfection sensitivity of axially compressed steel conical shells - Lower bound curve", Thin-Wall. Struct., 159, 107323. https://doi.org/10.1016/j.tws.2020.107323.
  46. Martins, A., Dinis, P., Camotim, D. and Providencia, P. (2015), "On the relevance of local-distortional interaction effects in the behaviour and design of cold-formed steel columns", Comput. Struct., 160, 57-89. https://doi.org/10.1016/j.compstruc.2015.08.003.
  47. Martins, A.D., Camotim, D., Goncalves, R. and Dinis, P.B. (2018), "On the mechanics of local-distortional interaction in thin-walled lipped channel columns", Thin-Wall. Struct., 125, 187-202. https://doi.org/10.1016/j.tws.2017.12.029.
  48. Matsubara, G.Y., De M Batista, E. and Salles, G.C. (2019), "Lipped channel cold-formed steel columns under local-distortional buckling mode interaction", Thin-Wall. Struct., 137, 251-270. https://doi.org/10.1016/j.tws.2018.12.041.
  49. Mehretehran, A.M. and Maleki, S. (2022), „Axial buckling of imperfect cylindrical steel silos with isotropic walls under stored solids loads: FE analyses versus Eurocode provisions", Eng. Fail. Anal., 137, 106282. https://doi.org/10.1016/j.engfailanal.2022.106282.
  50. Mykhailo, L. and Isaak, I. (2011), "Influence of initial imperfections upon the operation of beams with a corrugated wall".
  51. Nemer, S. and Papp, F. (2021), "Influence of imperfections in the buckling resistance of steel beam-columns under fire", Pollack Periodica, 16(2), 1-6. https://doi.org/10.1556/606.2021.00303.
  52. Obst, M., Rodak, M. and Paczos, P.R. (2016), "Limit load of cold formed thin-walled nonstandard channel beams", J. Theoretic. Appl. Mechanics/Mechanika Teoretyczna I Stosowana, 1369. https://doi.org/10.15632/jtam-pl.54.4.1369
  53. Paczos, P. and Pawlak, A.M. (2021), "Experimental optical testing and numerical verification by CuFSM of compression columns with modified Channel Sections", Materials, 14(5), 1271. https://doi.org/10.3390/ma14051271.
  54. Pastor, M., Casafont, M., Bonada, J. and Roure, F. (2014), "Imperfection amplitudes for nonlinear analysis of open thin-walled steel cross-sections used in rack column uprights", ThinWall. Struct., 76, 28-41. https://doi.org/10.1016/j.tws.2013.10.025.
  55. Pham, N.H. (2023), "Impacts of geometric imperfections on global buckling behaviors of cold-rolled aluminium alloy channel beams", Mater. Today: Proceedings, 85, 14-18. https://doi.org/10.1016/j.matpr.2023.05.246.
  56. Pircher, M., Berry, P., Ding, X. and Bridge, R. (2001), "The shape of circumferential weld-induced imperfections in thin-walled steel silos and tanks", Thin-Wall. Struct., 39(12), 999-1014. https://doi.org/10.1016/s0263-8231(01)00047-7.
  57. Rodrigues, L., Silva, F.M. and Goncalves, P.B. (2020), "Influence of initial geometric imperfections on the 1:1:1:1 internal resonances and nonlinear vibrations of thin-walled cylindrical shells", Thin-Wall. Struct., 151, 106730. https://doi.org/10.1016/j.tws.2020.106730.
  58. Roy, K., Chen, B., Fang, Z., Uzzaman, A., Chen, X. and Lim, J.B. (2021), "Local and distortional buckling behaviour of back-to-back built-up aluminium alloy channel section columns", Thin-Wall. Struct., 163, 107713. https://doi.org/10.1016/j.tws.2021.107713.
  59. Rzeszut, K. (2022), "Post-buckling behaviour of steel structures with different types of imperfections", Appl. Sci., 12(18), 9018. https://doi.org/10.3390/app12189018.
  60. Rzeszut, K. and Garstecki, A. (2016), "Stability of steel structures with clearances and imperfection", https://doi.org/10.7712/100016.2147.11151
  61. Saad-Eldeen, S., Garbatov, Y. and Soares, C.G. (2016), "Experimental strength analysis of steel plates with a large circular opening accounting for corrosion degradation and cracks subjected to compressive load along the short edges", Marine Struct., 48, 52-67. https://doi.org/10.1016/j.marstruc.2016.05.001.
  62. Santos, E.S.D., Batista, E.M. and Camotim, D. (2012), "Experimental investigation concerning lipped channel columns undergoing local-distortional-global buckling mode interaction", Thin-Wall. Struct., 54, 19-34. https://doi.org/10.1016/j.tws.2012.02.004.
  63. Santos, W.S., Landesmann, A. and Camotim, D. (2020), "Distortional strength of end-bolted CFS lipped channel columns: Experimental investigation, numerical simulations and DSM design", Thin-Wall. Struct., 148, 106469. https://doi.org/10.1016/j.tws.2019.106469.
  64. Sapalas, A., Sauciuvenas, G., Rasiulis, K., Griskevicius, M. and Gecys, T. (2019), "Behaviour of vertical cylindrical tank with local wall imperfections", J. Civil Eng. Manage., 25(3), 287-296. https://doi.org/10.3846/jcem.2019.9629.
  65. Schafer, B. and Pekoz, T. (1998), "Computational modeling of cold-formed steel: characterizing geometric imperfections and residual stresses", J. Construct. Steel Res., 47(3), 193-210. https://doi.org/10.1016/s0143-974x(98)00007-8.
  66. Schafer, B., Li, Z. and Moen, C. (2010), "Computational modeling of cold-formed steel", Thin-Wall. Struct., 48(10-11), 752-762. https://doi.org/10.1016/j.tws.2010.04.008.
  67. Schneider, W., Timmel, I. and Hohn, K. (2005), "The conception of quasi-collapse-affine imperfections: A new approach to unfavourable imperfections of thin-walled shell structures", Thin-Wall. Struct., 43(8), 1202-1224. https://doi.org/10.1016/j.tws.2005.03.003.
  68. Selvaraj, S. and Madhavan, M. (2018), "Geometric imperfection measurements and validations on cold-formed steel channels using 3D noncontact laser scanner", J. Struct. Eng., 144(3). https://doi.org/10.1061/(asce)st.1943-541x.0001993.
  69. Somodi, B., Barnkopf, E. and Kovesdi, B. (2023), "Applicable equivalent bow imperfections in GMNIA for Eurocode buckling curves - SHS, RHS and welded box sections", J. Construct. Steel Res., 204, 107860. https://doi.org/10.1016/j.jcsr.2023.107860.
  70. Somogyi, J.R., Lovas, T., Szabo-Leone, K. and Feher, A. (2022), "Steels specimens' inspection with structured light scanner", Periodica Polytechnica. Civil Engineering/Periodica Polytechnica. Civil Engineering. https://doi.org/10.3311/ppci.20081.
  71. Su, A. and Zhao, O. (2022), "Experimental and numerical investigations of S960 ultra-high strength steel slender welded I-section columns failing by local-flexural interactive buckling", Thin-Wall. Struct., 180, 109898. https://doi.org/10.1016/j.tws.2022.109898.
  72. Sun, Y., Tian, K., Li, R. and Wang, B. (2020), "Accelerated Koiter method for post-buckling analysis of thin-walled shells under axial compression", Thin-Wall. Struct., 155, 106962. https://doi.org/10.1016/j.tws.2020.106962.
  73. Ungureanu, V. and Dubina, D. (2005), "Erosion effect of geometrical and material imperfections on the buckling strength of thin-walled cold-formed steel members", In Elsevier eBooks 497-504. https://doi.org/10.1016/b978-008044637-0/50072-x.
  74. Wagner, H., Huhne, C. and Janssen, M. (2020), "Buckling of cylindrical shells under axial compression with loading imperfections: An experimental and numerical campaign on low knockdown factors", Thin-Wall. Struct., 151, 106764. https://doi.org/10.1016/j.tws.2020.106764.
  75. Wang, H., Guilleminot, J., Schafer, B.W. and Tootkaboni, M. (2022), "Stochastic analysis of geometrically imperfect thin cylindrical shells using topology-aware uncertainty models", Comput. Meth. Appl. Mechanics and Engineering, 393, 114780. https://doi.org/10.1016/j.cma.2022.114780.
  76. Wheeler, A. and Pircher, M. (2003), "Measured imperfections in six thin-walled steel tubes", J. Construct. Steel Res., 59(11), 1385-1395. https://doi.org/10.1016/s0143-974x(03)00089-0.
  77. Xu, D., Wang, Y., Liu, X., Chen, B. and Bu, Y. (2023), "A novel method and modelling technique for determining the initial geometric imperfection of steel members using 3D scanning", Structures, 49, 855-874. https://doi.org/10.1016/j.istruc.2023.01.136.
  78. Xu, Y., Wu, B. and Zheng, B. (2023), "Full-field geometric imperfection and effect on cross-section capacity of circular steel tubes", J. Construct. Steel Res., 201, 107749. https://doi.org/10.1016/j.jcsr.2022.107749.
  79. Yang, L., Yin, F., Wang, J., Bilal, A., Ahmed, A.H. and Lin, M. (2022), "Local buckling resistances of cold-formed high-strength steel SHS and RHS with varying corner radius", Thin-Wall. Struct., 172, 108909. https://doi.org/10.1016/j.tws.2022.108909.
  80. Yu, C. and Schafer, B.W. (2006), "Finite element modeling of cold-formed steel beams validation and application", International Specialty Conference on ColdFormed Steel Structures (2006) - 18th International Specialty Conference on Cold-Formed Steel Structures.
  81. Zeinoddini, V. and Schafer, B. (2012), "Simulation of geometric imperfections in cold-formed steel members using spectral representation approach", Thin-Wall. Struct., 60, 105-117. https://doi.org/10.1016/j.tws.2012.07.001.
  82. Zeinoddini, V. and Schafer, B. (2012a), "Simulation of geometric imperfections in cold-formed steel members using spectral representation approach", Thin-Wall. Struct., 60, 105-117. https://doi.org/10.1016/j.tws.2012.07.001.
  83. Zhang, P. and Alam, M.S. (2022), "Compression tests of thin-walled cold-formed steel columns with Σ-shaped sections and patterned perforations distributed along the length", Thin-Wall. Struct., 174, 109082. https://doi.org/10.1016/j.tws.2022.109082.
  84. Zhang, P., and Alam, M. S. (2020). "Elastic buckling behaviour of Σ-shaped rack columns under uniaxial compression". Engineering Structures/Engineering Structures (Online), 212, 110469. https://doi.org/10.1016/j.engstruct.2020.110469
  85. Zheng, J., Li, K., Liu, S., Ge, H., Zhang, Z., Gu, C., Qian, H. and Hua, Z. (2018), "Effect of shape imperfection on the buckling of large-scale thin-walled ellipsoidal head in steel nuclear containment", Thin-Wall. Struct., 124, 514-522. https://doi.org/10.1016/j.tws.2018.01.001.
  86. Zhou, F., Huang, L. and Li, H.T. (2022), "Cold-formed stainless steel SHS and RHS columns subjected to local-flexural interactive buckling", J. Construct. Steel Res., 188, 106999. https://doi.org/10.1016/j.jcsr.2021.106999.
  87. Zidlicky, B. and Jandera, M. (2023), "An interaction formula proposed for stainless steel SHS and RHS beam-columns", Thin-Wall. Struct., 185, 110573. https://doi.org/10.1016/j.tws.2023.110573.