Abstract
Several solutions in the form of curve families, simplified closed form equations and numerical approaches have been proposed by researchers for evaluating the stability of individual web-tapered compression members, while frame instability is rarely addressed and accounted for. In this paper, using structural mechanics concepts and curve fitting, the lateral stiffness for a constrained web-tapered column is approximated in a simple parabolic form. Utilizing the simplified stiffness function and following the story sway concept, an elastic effective length factor (K-factor) formula is presented to be used for sway frames that are composed of web tapered columns. A proper length modification factor formula for partially tapered restraining girders is proposed to facilitate stiffness ratio calculations at the columns’ ends. Moreover, a closed form equation for individual column K-factor evaluation is introduced which can be considered as a sound alternative to the available approaches which function under the basis of curve families. The proposed method improves the K-factors resulted from a member instability (p-δ) study by considering the inter-story interaction of columns known as frame instability (P-Δ) effects. This method is capable of considering the contribution of any leaning column in the story stability assessment. Some examples are considered to illustrate the proposed method’s efficiency and verify its accuracy. Based on the studied frames and by comparing the results and solution procedure with available methods, it is shown that the proposed method removes difficulties of using curve families or solving eigenvalue problems by employing single valued closed form formulas. Also, the solution algorithm is not restricted to columns with ideal base fixities and it can deal with any restraining base condition with satisfactory accuracy. Furthermore, the effects of frame asymmetry and existence of any leaning column are simply accounted for by following the proposed formula without any need for first-order analysis.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
AISC (2016) Specification for Structural Steel Buildings, ANSI/AISC 360-16. Am Inst Steel Constr 676
Amirikian A (1952) Wedge-beam framing. Trans Am Soc Civ Eng 117(1):596–631. https://doi.org/10.1061/taceat.0006615
Aristizabal-Ochoa JD (1994) K-factor for columns in any type of construction: nonparadoxical approach. J Struct Eng 120(4):1272–1290. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:4(1272)
Bai R, Liu SW, Chan SL, Yu F (2019) Flexural buckling strength of tapered-I-section steel columns based on ANSI/AISC-360-16. Int J Struct Stab Dyn. https://doi.org/10.1142/S0219455419501347
Bazeos N, Karabalis DL (2006) Efficient computation of buckling loads for plane steel frames with tapered members. Eng Struct 28(5):771–775. https://doi.org/10.1016/j.engstruct.2005.10.004
Cary CW, Murray TM, Holzer SM (1997) Effective lengths of web-tapered columns in rigid metal building frames, April, 160
Chan SL (1990) Buckling analysis of structures composed of tapered members. J Struct Eng 116(7):1893–1906. https://doi.org/10.1061/(asce)0733-9445(1990)116:7(1893)
Chen W-F, Lui EM (1987) Structural stability: theory and implementation, vol 490
Chen YY, Chuan GH (2015) Modified approaches for calculation of effective length factor of frames. Adv Steel Constr 11(1):39–53
Chiorean CG, Marchis IV (2017) A second-order flexibility-based model for steel frames of tapered members. J Constr Steel Res 132(May):43–71. https://doi.org/10.1016/j.jcsr.2017.01.002
Duan L, Chen W-F (1999) Effective length factors of compression members. In: Structural engineering handbook. CRC Press LLC, Boca Raton
Duan L, King WS, Chen WF (1993) K-factor equation to alignment charts for column design. ACI Struct J 90(3):242–248. https://doi.org/10.14359/4232
Eröz M, White DW, DesRoches R (2008) Direct analysis and design of steel frames accounting for partially restrained column base conditions. J Struct Eng 134(9):1508–1517. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:9(1508)
Gallagher RH, Lee C-H-H (1970) Matrix dynamic and instability analysis with non-uniform elements. Int J Numer Methods Eng 2(2):265–275. https://doi.org/10.1002/nme.1620020212
Gere J, Carter WO (1962) Critical buckling loads for tapered columns. J Struct Div 88(1):1–12
Giaquinta M, Hildebrandt S (2004) Calculus of variations I. Grundlehren Math Wiss. https://doi.org/10.1007/978-3-662-03278-7
Ibrahim SM (2021) Effective buckling length of frames with tapered columns and partially tapered beams. J Constr Steel Res 187(December):106993. https://doi.org/10.1016/J.JCSR.2021.106993
Karabalis DL, Beskos DE (1983) Static, dynamic and stability analysis of structures composed of tapered beams. Comput Struct 16(6):731–748. https://doi.org/10.1016/0045-7949(83)90064-0
Karamanlidis D, Jasti R (1987) Geometrically nonlinear finite element analysis of tapered beams. Comput Struct 25(6):825–830. https://doi.org/10.1016/0045-7949(87)90198-2
Kishi N, Chen WF, Goto Y (1997) Effective length factor of columns in semirigid and unbraced frames. J Struct Eng 123(3):313–320. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:3(313)
Kohnke P (ed) (1994) ANSYS theory reference. ANSYS Inc., Canosburg
Kucukler M, Gardner L (2018) Design of laterally restrained web-tapered steel structures through a stiffness reduction method. J Constr Steel Res 141(February):63–76. https://doi.org/10.1016/j.jcsr.2017.11.014
Lee GC, Morrell ML (1975) Application of AISC design provisions for tapered members. Eng J 12(1 First Q):1–13
Lee GC, Morrell ML, Ketter RL (1972) Design of tapered members. Weld Res Counc Bull 173. https://forengineers.org/bulletin/wrc-173
Lee GC, Ketter RL, Hsu TL (1981) The design of single story rigid frames. Metal Building Manufacturers Association, Cleveland
LeMessurier WJ (1977) A practical method of second order analysis part 2; rigid frames |. Am Inst Steel Constr 14:49–67
Lui EM (1992) A novel approach for K factor determination. Eng J Am Inst Steel Constr 29:150–159
Mahini MR, Seyyedian H (2006) Effective length factor for columns in braced frames considering axial forces on restraining members. Struct Eng Mech 22(6):685–700. https://doi.org/10.12989/sem.2006.22.6.685
Newmark NM (1943) Numerical procedure for computing deflections, moments, and buckling loads. Trans Am Soc Civ Eng 108(1):1161–1188. https://doi.org/10.1061/taceat.0005640
Quan C, Kucukler M, Gardner L (2020) Design of web-tapered steel I-section members by second-order inelastic analysis with strain limits. Eng Struct 224(December):111242. https://doi.org/10.1016/J.ENGSTRUCT.2020.111242
Saffari H, Rahgozar R, Jahanshahi R (2008) An efficient method for computation of effective length factor of columns in a steel gabled frame with tapered members. J Constr Steel Res 64(4):400–406. https://doi.org/10.1016/j.jcsr.2007.09.001
Salama MI (2014) New Simple Equations for Effective Length Factors. HBRC J 10(2):156–159. https://doi.org/10.1016/j.hbrcj.2013.10.003
Salvadori MG (1951) Numerical computation of buckling loads by finite differences. Trans Am Soc Civ Eng 116(1):590–624. https://doi.org/10.1061/taceat.0006570
Serna MA, Ibáñez JR, López A (2011) Elastic flexural buckling of non-uniform members: closed-form expression and equivalent load approach. J Constr Steel Res 67(7):1078–1085. https://doi.org/10.1016/J.JCSR.2011.01.003
Slimani A, Ammari F, Adman R (2018) The effective length factor of columns in unsymmetrical frames asymmetrically loaded. Asian J Civ Eng 19(4):487–499. https://doi.org/10.1007/S42107-018-0038-Z
Tankova T, Martins JP, da Silva LS, Simões R, Craveiro HD (2018) Experimental buckling behaviour of web tapered I-section steel columns. J Constr Steel Res 147(August):293–312. https://doi.org/10.1016/j.jcsr.2018.04.015
Timoshenko S, Gere JG, Gere JM (1961) Theory of elastic stability, 2nd edn. McGraw-Hill, Auckland
Utku S, Norris CH, Wilbur JB (1991) Elementary structural analysis, vol 829
Funding
The author declares that no funds, grants, or other support were received during the preparation of this manuscript.
Author information
Authors and Affiliations
Contributions
All material preparation, data collection, analysis, and drafting the manuscript are solely done by the author.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Data Availability
Some or all data, models, or code that support the findings of this study are available upon reasonable request.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Mahini, M.R. An Efficient K-Factor Formula for Stability Evaluation of Steel Frames with Web-Tapered Members. Iran J Sci Technol Trans Civ Eng 47, 1673–1687 (2023). https://doi.org/10.1007/s40996-022-01022-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40996-022-01022-5