Modification of the Euler Load for the Stiffened Compressive Members and Determination of the Optimal Stiffening for the Maximum Buckling Load

Document Type : Regular Paper


Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran


The potential of buckling in compressive members has been considered as a disadvantage when using steel members in the construction industry. In spite of the progress made in this regard, buckling is still considered as a challenge in the analysis and design of compressive steel structural members. Such a challenging phenomenon can be controlled by strengthening of compressive members. Stiffened compressive members can control the weakness of steel members in the global buckling. In this paper, elastic buckling behavior of three-segment symmetric steel members with pinned ends is investigated. The differential stability equation for non-prismatic three-segment members is solved numerically. Critical load parameter for stiffened members is calculated considering different stiffened length and moment of inertia ratios. Based on a wide range of the calculated data, the buckling load could be accounted as a safe measure to be used in the design formulas. Evaluation of the effects of various parameters on the buckling load shows that the desired buckling load value can be achieved by a partially stiffened member. By constant increase of a member’s weight, the shorter the length of the variation in the cross-section, the higher moment of inertia is essential in the stiffened segment; and the maximum critical load parameter is achieved by a stiffened length ratio between 0.4 and 0.6.


Main Subjects

[1] Timoshenko SP, Gere JM (1961) Theory of elastic stability. New York: McGraw-Hill, 1961.
[2] Arbabi F, Li F (1991) Buckling of variable cross-section columns: integral-equation approach. Journal of Structural Engineering 117 (8):2426-2441
[3] MATHEMATICA Computational Program.
[4] Li QS (2000) Buckling of elastically restrained non-uniform columns. Engineering structures 22 (10):1231-1243
[5] Al-Sadder SZ (2004) Exact expressions for stability functions of a general non-prismatic beam–column member. Journal of Constructional Steel Research 60 (11):1561-1584
[6] Rahai AR, Kazemi S (2008) Buckling analysis of non-prismatic columns based on modified vibration modes. Communications in Nonlinear Science and Numerical Simulation 13 (8):1721-1735
[7] Coşkun SB, Atay MT (2009) Determination of critical buckling load for elastic columns of constant and variable cross-sections using variational iteration method. Computers & Mathematics with Applications 58 (11-12):2260-2266
[8] Darbandi SM, Firouz-Abadi RD, Haddadpour H (2010) Buckling of variable section columns under axial loading. Journal of Engineering Mechanics 136 (4):472-476
[9] Huang Y, Li XF (2012) An analytic approach for exactly determining critical loads of buckling of nonuniform columns. International Journal of Structural Stability and Dynamics 12 (04):1250027
[10] Marques L, Taras A, da Silva LS, Greiner R, Rebelo C (2012) Development of a consistent buckling design procedure for tapered columns. Journal of Constructional Steel Research 72:61-74
[11] Konstantakopoulos TG, Raftoyiannis IG, Michaltsos GT (2012) Stability of steel columns with non-uniform cross-sections. Open Constr ion and Building Technology Journal 6:1-7
[12] Avraam TP, Fasoulakis ZC (2013) Nonlinear postbuckling analysis of frames with varying cross-section columns. Engineering Structures 56:1-7
[13] Cristutiu IM, Nunes DL, Dogariu AI (2013) Steel Members with Variable I Cross Sections under Bending and Compression with Lateral Restraints–Behavior by Experimental Test. In: Design, Fabrication and Economy of Metal Structures. Springer, pp 193-198
[14] Saljooghi R, Ahmadian MT, Farrahi GH (2014) Vibration and buckling analysis of functionally graded beams using reproducing kernel particle method. Scientia Iranica Transaction B, Mechanical Engineering 21 (6):1896-1906
[15] Hadianfard MA, Khakzad AR, Vaghefi M (2015) Analysis of the effect of stiffener on the buckling capacity and non-elastic behavior of bracing gusset plates. Scientia Iranica Transaction A, Civil Engineering 22 (4):1449
[16] Andreev VI, Tsybin NY (2015) On the stability of rod with variable cross-section. Procedia Engineering 111:42-48
[17] Chen Y, Shu G, Zheng B, Lu R (2019) Local buckling behavior of welded π-shaped compression stub columns. Journal of Constructional Steel Research 154:224-234
[18] Couto C, Real PV (2019) Numerical investigation on the influence of imperfections in the local buckling of thin-walled I-shaped sections. Thin-Walled Structures 135:89-108
[19] Dhurvey P (2017) Buckling analysis of composite laminated skew plate of variable thickness. Materials Today: Proceedings 4 (9):9732-9736
[20] He B, Liu D, Long J, Ma L, Ma P (2019) A high order finite strip transfer matrix method for buckling analysis of single-branched cross-section thin-walled members. Thin-Walled Structures 135:1-11
[21] Jiao P, Borchani W, Hasni H, Alavi AH, Lajnef N (2016) Post-buckling response of non-uniform cross-section bilaterally constrained beams. Mechanics Research Communications 78:42-50
[22] Jobbágy D, Ádány S (2017) Local buckling behaviour of thin-walled members with curved cross-section parts. Thin-Walled Structures 115:264-276
[23] Khaniki HB, Hosseini-Hashemi S, Nezamabadi A (2018) Buckling analysis of nonuniform nonlocal strain gradient beams using generalized differential quadrature method. Alexandria engineering journal 57 (3):1361-1368
[24] Kováč M, Baláž I (2019) Stability of centrically loaded members with monosymmetric cross-section at various boundary conditions. Journal of Constructional Steel Research 153:139-152
[25] Yang L, Shi G, Zhao M, Zhou W (2017) Research on interactive buckling behavior of welded steel box-section columns. Thin-Walled Structures 115:34-47
[26] Rezaiee-Pajand M, Shahabian F and Bambaeechee M (2016) Stability of non-prismatic frames with flexible connections and elastic supports. KSCE Journal of Civil Engineering 20(2):832-846.
[27] Rezaiee-Pajand M, Masoodi A, and Bambaeechee M (2018) Tapered beam–column analysis by analytical solution. Proceedings of the ICE-Structures and Buildings
[28] Toosi S, Esfandiari A, and Ranji AR (2019) Buckling Analysis of Tapered Continuous Columns by Using Modified Buckling Mode Shapes. Journal of Marine Science and Application 18(2):160-166
[29] Serna MA, Ibáñez JR, López A (2011) Elastic flexural buckling of non-uniform members: Closed-form expression and equivalent load approach. Journal of Constructional Steel Research 67(7):1078-85
[30] Timoshenko S (1955) Strength of materials, ed. 3, Princeton NJ: Van Nostrand
[31] ANSI B (2016) AISC 360-16, Specification for Structural Steel Buildings. Chicago, American Institute of Steel Construction
[32] ABAQUS Software.