Structural Engineering and Mechanics

  • 제85권6호
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  • Pages.825-835
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  • 2023
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

A new method for determining the effective length factor of columns in partially braced frames on elastic supports

  • Adel Slimani (Built Environment Research Laboratory, Faculty of Civil Engineering, University of Science and Technology Houari Boumediene (USTHB)) ;
  • Toufik Belaid (Built Environment Research Laboratory, Faculty of Civil Engineering, University of Science and Technology Houari Boumediene (USTHB)) ;
  • Messaoud Saidani (Institute for Clean Growth and Future Mobility, Coventry University) ;
  • Fatiha Ammari (Built Environment Research Laboratory, Faculty of Civil Engineering, University of Science and Technology Houari Boumediene (USTHB)) ;
  • Redouane Adman (Built Environment Research Laboratory, Faculty of Civil Engineering, University of Science and Technology Houari Boumediene (USTHB))
  • 투고 : 2022.02.08
  • 심사 : 2023.02.27
  • 발행 : 2023.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

The effective buckling length factor is an important parameter in the elastic buckling analysis of steel structures. The present article aims at developing a new method that allows the determination of the buckling factor values for frames. The novelty of the method is that it considers the interaction between the bracing and the elastic supports for asymmetrical frames in particular. The approach consists in isolating a critical column within the frame and evaluating the rotational and translational stiffness of its restraints to obtain the critical buckling load. This can be achieved by introducing, through a dimensionless parameter 𝜙i, the effects of coupling between the axial loading and bending stiffness of the columns, on the classical stability functions. Subsequently, comparative, and parametric studies conducted on several frames are presented for assessing the influence of geometry, loading, bracing, and support conditions of the frame columns on the value of the effective buckling length factor K. The results show that the formulas recommended by different approaches can give rather inaccurate values of K, especially in the case of asymmetric frames. The expressions used refer solely to local stiffness distributions, and not to the overall behavior of the structure.

키워드

과제정보

The authors are grateful to both the Faculty of Civil Engineering of the USTHB (Algeria) and the Faculty of Engineering, Environment and Computing at Coventry University (UK) for proving their research facilities for the completion of this research. The authors declare that they have no conflicting interest or known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

참고문헌

  1. Adman, R. and Saidani, M. (2013), "Elastic buckling of columns with end restraint effects", J. Constr. Steel Res., 87, 1-5. https://doi.org/10.1016/j.jcsr.2013.03.022.
  2. American Institute of Steel Construction (2010), Specification for Structural Steel Buildings, ANSI/AISC 360-10, American Institute of Steel Construction, Chicago, Illinois.
  3. Aristizabal-Ochoa, J.D. (1994), "Stability of columns under uniform axial load with semirigid connections", J. Struct. Eng., 120, 3212-3222. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:11(3212).
  4. Aristizabal-Ochoa, J.D. (1994a), "K-factor for columns in any type of construction: nonparadoxical approach", J. Struct. Eng., 120, 1272-1290. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:4(1272).
  5. Aristizabal-Ochoa, J.D. (1994b), "Slenderness K factor for leaning columns", J. Struct. Eng., 120, 2977-2991. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:10(2977).
  6. Aristizabal-Ochoa, J.D. (1996), "Braced, partially braced and unbraced columns: complete set of classical stability equations", Struct. Eng. Mech., 4(4), 365-381. https://doi.org/10.12989/sem.1996.4.4.365.
  7. Autodesk (2013), Robot Structural Analysis Professional, San Rafael, CA.
  8. Bridge, R.Q. and Fraser, D.J. (1987), "Improved G-factor method for evaluating effective lengths of columns", J. Struct. Eng., 113(6), 1341-1356. https://doi.org/10.1061/(ASCE)0733-9445(1987)113:6(1341).
  9. Cheong-Siat-Moy, F. (1986), "K-factor paradox", J. Struct. Eng., 112, 1747-1760. https://doi.org/10.1061/(ASCE)0733-9445(1986)112:8(1747).
  10. Cheong-Siat-Moy, F. (1999), "An improved K-factor formula", J. Struct. Eng., 125, 169-174. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:2(169).
  11. Corsi, M., Bagassi, S, Moruzzi, M. and Weigand F. (2020), Additively manufactured negative stiffness structures for shock absorber applications", Mech. Adv. Mater. Struct., 29(7), 999-1010. https://doi.org/10.1080/15376494.2020.1801917.
  12. EN 1993-1-1: Eurocode 3 (2005), Design of Steel Structures, Part 1-1: General Rules and Rules for Buildings, Comite Europeo de Normalizacion.
  13. Farajian, M., Sharafi, P. and Kildashti, K. (2021), "The influence of inter-module connections on the effective length of columns in multi-story modular steel frames", J. Constr. Steel Res., 177, 1-26. https://doi.org/10.1016/j.jcsr.2020.106450.
  14. Gantes, C.J. and Mageirou, G.E. (2005), "Improved stiffness distribution factors for evaluation of effective buckling lengths in multi-story sway frames", Eng. Struct., 27, 1113-1124. https://doi.org/ 10.1016/j.engstruct.2005.02.009.
  15. Girgin K., Ozmen, G. and Orakdogen, E. (2006), "Buckling lengths of irregular frame columns", J. Constr. Steel Res., 62(6), 605-613. https://doi.org/10.1016/j.jcsr.2005.09.006.
  16. Gunaydin, A. and Aydin, R. (2019), "A simplified method for instability and second-order load effects of framed structures: Story-based approach", Struct. Des. Tall Spec. Build., 28(13), 1-23. https://doi.org/10.1002/tal.1655.
  17. Ihaddoudene, A., Saidani, M. and Jaspart, J. (2017), "Mechanical model for determining the critical load of plane frames with semi-rigid joints subjected to static loads", Eng. Struct., 145, 109-117. https://doi.org/10.1016/j.engstruct.2017.05.005.
  18. Kalochairetis, K.E. and Gantes, C.J. (2012), "Elastic buckling load of multi-story frames consisting of Timoshenko members", J. Constr. Steel Res., 71, 231-244. https://doi.org/10.1016/j.jcsr.2011.11.007.
  19. Konstantakopoulos, T.G., Raftoyiannis, I.G. and Michaltsos, G.T. (2012), "Stability of steel columns with non-uniform cross-sections", Open Constr. Build Technol., 6, 1-7. https://doi.org/10.2174/1874836801206010001.
  20. Krzysztof, M. and Alexandre de Macedo, W. (2021), "Stability, stress and strain analysis of very slender pinned thin-walled box columns according to FEM, Euler and TSTh", Am. J. Eng. Appl. Sci., 14(2), 214-254. https://doi.org/10.3844/ajeassp.2021.214.257.
  21. LeMessurier, W.J. (1977), "A practical method of second order analysis, Part 2-Rigid Frames", Eng. J., 14, 49-67. https://doi.org/10.62913/engj.v14i2.292
  22. Li, Q., Zou, A. and Zhang, H. (2016), "A simplified method for stability analysis of multi-story frames considering vertical interactions between stories", Adv. Struct. Eng., 19, 599-610. https://doi.org/10.1177/1369433216630191.
  23. Livesley, R.K. and Chandler, D.B. (1956), Stability Functions for Structural Frameworks, Manchester University Press.
  24. Lui, E.M. (1994), "A novel approach for K factor determination", Eng. J., 4, 150-9.
  25. Ma., T and Xu, L. (2020), "Story-based stability of multistory steel semibraced and unbraced frames with semirigid connections", J. Struct. Eng., 147(1), 1-15. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002874.
  26. Mageirou, G.E. and Gantes, C.J. (2006), "Buckling strength of multi-story sway, non-sway and partially-sway frames with semi-rigid connections", J. Constr. Steel Res., 62(9), 893-905. https://doi.org/10.1016/j.jcsr.2005.11.019.
  27. Mahini, M.R. (2022), "An efficient K-factor formula for stability evaluation of steel frames with web-tapered members", Iran. J. Sci. Technol., Trans. Civil Eng., 1-15. https://doi.org/10.1007/s40996-022-01022-5.
  28. Raftoyiannis, I.G. (2005), "The effect of semi-rigid joints and an elastic bracing system on the buckling load of simple rectangular steel frames", J. Constr. Steel Res., 61(9), 1205-1225. https://doi.org/10.1016/j.jcsr.2005.01.005.
  29. Rezaiee-Pajand, M., Shahabian, F. and Bambaeechee, M. (2016), "Stability of non-prismatic frames with flexible connections and elastic supports", KSCE J. Civil Eng., 20(2), 832-846. https://doi.org/ 10.1007/s12205-015-0765-6.
  30. Ruiz A., Cho, D., Cabrera, A. and Bustamante, Y. (1999), Load and Resistance Factor Design (LRFD) specification for structural steel buildings, American Institute of Steel Construction Inc., Chicago, Illinois, USA.
  31. Slimani, A., Ammari, F. and Adman, R. (2018), "The effective length factor of columns in unsymmetrical frames asymmetrically loaded", Asian J. Civil Eng., 19, 1-13. https://doi.org/ 10.1007/s42107-018-0038-z.
  32. Smyrell, A.G. (1994), "Approximate formulas for effective length of steel columns", J. Struct. Eng., 120(9), 2793-2801. https://ascelibrary.org/doi/10.1061/(ASCE)0733-9445(1994)120:9(2793).
  33. Sun, Y., Guo, Y., Chen, H. and Cao, K. (2020), "Stability of large-size and high-strength steel angle sections affected by support constraint", Int. J. Steel Struct., 21(1), 85-99. https://doi.org/10.1007/s13296-020-00419-0.
  34. Teh, L.H. and Gilbert, B.P. (2016), "A buckling model for the stability design of steel columns with intermediate gravity loads", J. Constr. Steel Res., 117, 43-54. https://doi.org/10.1016/j.jcsr.2015.10.019.
  35. Tian, W., Hao, J. and Zhong, W. (2020), "Buckling of stepped columns considering the interaction effect among columns", J. Constr. Steel Res., 177, 1-16. https://doi.org/10.1016/j.jcsr.2020.106416.
  36. Tian, W., Sun, J. and Hao, J. (2021), "Effective length factors of three-and two-segment stepped columns", J. Constr. Steel Res., 181, 1-28. https://doi.org/10.1016/j.jcsr.2021.106585.
  37. Tian, W., Wu, Y. and Zhou, X. (2016), "Stability of sway-inhibited prismatic columns subjected to internal axial loads", Pract. Period. Struct. Des. Constr., 22(1), 04016019. https://doi.org/10.1061/(ASCE)SC.1943-5576.0000303.
  38. Tian, W., Zhou, X. and Fan, C. (2017), "Effect of internal axial loads on the stability of sway-permitted prismatic columns", J. Constr. Steel Res., 133, 300-309. https://doi.org/10.1016/J.JCSR.2017.02.018.
  39. Tong, G. and Wang, J. (2006), "Column effective lengths considering inter-story and inter-column interactions in sway-permitted frames", J. Constr. Steel Res., 62, 413-423. https://doi.org/10.1260/1369433042863279.
  40. Webber, A., Orr, J., Shepherd, P. and Crothers, K., (2015), "The effective length of columns in multi-storey frames", Eng. Struct., 102, 132-143. https://doi.org/10.1016/j.engstruct.2015.07.039.
  41. Zheng, L., Qu, X., Gao, Y. and Guo, H. (2021), "The in-plane effective length factor of web members of the steel truss", Int. J. Steel Struct., 21, 800-819. https://doi.org/10.1007/s13296-021-00474-1.