Evaluation of Non-sway Flexural Buckling of One-bay Gabled Frames by Solving Characteristic Equation

Document Type : Research Article

Authors

1 Civil engineering department of Shahid Rajaee Teacher Training University. Tehran, Iran.

2 Engineering Department of Golestan University, Fazel-Abad, Ali-Abad Katool, Golestan Provonce, Iran.

Abstract

      Flexural buckling is one of the buckling limit states in columns, which have at least one symmetric axis. Due to the lack of analytical solution for the differential equation of deformation of a non-prismatic column, its flexural buckling load has been determined by numerical methods, resulting in approximate solutions. This research aims at the analytical evaluation of non-sway in-plane flexural buckling of gabled frames. The equilibrium and differential equations were simultaneously used in the elastic flexural energy, consequently the characteristic equation is achieved. The effective length coefficient can be determined only with having two geometrical parameters of a gabled frame, using the relevant graph. Accurate results and simple use of the drawn graphs are among the benefits of the introduced method.

Keywords

Main Subjects

References

[1] S.P. Timoshenko, Buckling of bars of variable cross section, Bull. Polytechnic Inst., Kiev, U.S. S. R., (1908(.
[2] A. Morley, Critical loads for long tapering struts, Engineering, 104 (1917) 295-298.
[3] A. Dinnik, Design of columns of varying cross-section, Trans. ASME, 51 (1929) 105-114.
[4] J.M. Gere, W.O. Carter, Critical buckling loads for tapered columns, Journal of the Structural Division, 88(1) (1962) 1-12.
[5] M. Iremonger, Finite difference buckling analysis of non-uniform columns, Computers & Structures, 12(5) (1980) 741-748.
[6] D. Karabalis, D. Beskos, Static, dynamic and stability analysis of structures composed of tapered beams, Computers & Structures, 16(6) (1983) 731-748.
[7] C.J. Brown, Approximate stiffness matrix for tapered beams, Journal of Structural Engineering, 110(12) (1984) 3050-3055.
[8] J.C. Ermopoulos, A.N. Kounadis, Stability of frames with tapered built-up members, Journal of Structural Engineering, 111(9) (1985) 1979-1992.
[9] J.C. Ermopoulos, Buckling of tapered bars under stepped axial loads, Journal of Structural Engineering, 112(6) (1986) 1346-1354.
[10] J. Banerjee, F. Williams, Exact Bernoulli‐Euler static stiffness matrix for a range of tapered beam‐columns, International Journal for Numerical Methods in Engineering, 23(9) (1986) 1615-1628.
[11] Y.B. Yang, J. D. Yau, Stability of beams with tapered I-sections, Journal of engineering mechanics, 113(9) (1987) 1337-1357.
[12] M.A. Bradford, P.E. Cuk, Elastic buckling of tapered monosymmetric I-beams, Journal of Structural Engineering, 114(5) (1988) 977-996.
[13] F.W. Williams, G. Aston, Exact or lower bound tapered column buckling loads, Journal of Structural Engineering, 115(5) (1989) 1088-1100.
[14] H.J. Al-Gahtani, Exact stiffnesses for tapered members, Journal of structural engineering, 122(10) (1996) 1234-1239.
[15] L. Zhang, G.S. Tong, Lateral buckling of web-tapered I-beams: A new theory, Journal of Constructional Steel Research, 64(1) (2008) 1379-1393.
[16] J.D. Yau, Stability of tapered I-beams under torsional moments, Finite Elements in Analysis and Design, 42(10) (2006) 914-927.
[17] B. Asgarian, M. Soltani, F. Mohri, Lateral-torsional buckling of tapered thin-walled beams with arbitrary cross-sections, Thin-walled structures, 62 (2013) 96-108.
[18] M. Soltani, B. Asgarian, F. Mohri, Elastic instability and free vibration analyses of tapered thin-walled beams by the power series method, Journal of constructional steel research, 96 (2014) 106-126.
[19] M. Soltani, B. Asgarian, F. Mohri, Finite element method for stability and free vibration analyses of non-prismatic thin-walled beams, Thin-Walled Structures, 82 (2014) 245-261.
[20] M. Kováč, Lateral-torsional buckling of web-tapered I-beams: 1D and 3D FEM approach, Procedia Engineering, 40 (2012) 217-222.
[21] A. Rahai, S. Kazemi, Buckling analysis of non-prismatic columns based on modified vibration modes, Communications in Nonlinear Science and Numerical Simulation, 13(8) (2008) 1721-1735.
[22] H.R. Valipour, M.A. Bradford, A new shape function for tapered three-dimensional beams with flexible connections, Journal of Constructional Steel Research, 70 (2012) 43-50.
[23] G. Konstantakopoulos, I. G. Raftoyiannis, G. T. Michaltsos, Stability of steel columns with non-uniform cross-sections, The Open Construction and Building Technology Journal, 6 (2012) 1-7.
[24] S. Darbandi, R. Firouz-Abadi, H. Haddadpour, Buckling of variable section columns under axial loading, Journal of Engineering Mechanics, 136(4) (2010) 472-476.
[25] A. Hadidi, B.F. Azar, H.Z. Marand, Second-Order Nonlinear Analysis of Steel Tapered Beams Subjected to Span Loading, Advances in Mechanical Engineering, (2014), Article ID 237983.
[26] D.J. Wei, S.X. Yan, Z.P. Zhang, X.F. Li, Critical load for buckling of non-prismatic columns under self-weight and tip force, Mechanics Research Communications, 37(6) (2010) 554-558.
[27] M. Taha, M. Essam, Stability behavior and free vibration of tapered columns with elastic end restraints using the DQM method, Ain Shams Engineering Journal, 4(3) (2013) 515-521.
[28] A. Shooshtari, R. Khajavi, An efficient procedure to find shape functions and stiffness matrices of nonprismatic Euler–Bernoulli and Timoshenko beam elements, European Journal of Mechanics-A/Solids, 29(5) (2010) 826-836.
[29] E. Ruocco, H. Zhang, C. Wang, Hencky bar-chain model for buckling analysis of non-uniform columns, Structures, 6 (2016) 73-84.
[30] A. Nikolić, S. Šalinić, Buckling analysis of non-prismatic columns: A rigid multibody approach, Engineering Structures, 143 (2017) 511-521.
[31] G.C. Lee, M. Morrell, R.L. Ketter, Design of Tapered Members, Welding Research Council Bulletin, No. 173, (1971)
[32] F. Irani, Stability of one bay symmetrical frames with nonuniform members, International Journal of Engineering, 1(4) (1988) 193-200.
[33] N. Bazeos, D.L. Karabalis, Efficient computation of buckling loads for plane steel frames with tapered members, Engineering Structures, 28(5) (2006) 771-775.
[34] H. Saffari, R. Rahgozar, R. Jahanshahi, An efficient method for computation of effective length factor of columns in a steel gabled frame with tapered members, Journal of Constructional Steel Research, 64(4) (2008)  400-406.
[35] R. Tajizadegan, A.M. Momeni, Development of Slope-Deflection Equations and use of them to obtain effective length coefficient and critical load, Fourth National Congress of Civil Engineering (NCCE04), Tehran University, Iran (in Persian), (2008).
[36] H. Tajmir Riahi, A. Shojaei Barjoui, S. Bazazzadeh, S. M. A. Etezady, Buckling analysis of non-prismatic columns using slope-deflection method, 15th World Conference on Earthquake Engineering, Lisbon, Portugal, (2012).
[37] M. Rezaiee-Pajand, F. Shahabian, M. Bambaeechee, Stability of non-prismatic frames with flexible connections and elastic supports, KSCE Journal of Civil Engineering, 20(2) (2016) 832-846.
[38] AISC, Specification for structural steel buildings, (1999).
[39] AISC, R. Kaehler, D. White, Y. Kim, Steel design guide 25; frame design using web-tapered members, Chicago, (2011).
Amirkabir Journal of Civil Engineering
Volume 54, Issue 8
November 2022
Pages 3179-3196

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