Elastic buckling load of multi-story frames consisting of Timoshenko members

Abstract The objective of this paper is to propose a method for the evaluation of the elastic critical buckling load of columns in frames consisting of members susceptible to non-negligible shear deformations, such as built-up members in steel frames, based on Engesser's approach. To that effect, a stability matrix is proposed and three general stability equations are derived for the cases of unbraced, partially braced and braced frames. Indicative graphic interpretation of the solutions for the stability equations of the braced and unbraced cases is shown. Slope-deflection equations for shear-weak members with semi-rigid connections are also derived and used for the presentation of a complete set of rotational stiffness coefficients, which are then used for the replacement of members converging at the bottom and top ends of the column in question by equivalent springs. All possible rotational and translational boundary conditions at the far end of these members, as well as the eventual presence of axial force, are considered. Five examples are presented, dealing with braced, unbraced and partially braced frames, with rigid and semi-rigid beam to column connections, loaded with concentrated or uniformly distributed loads, in a symmetrical or non-symmetrical pattern. In all cases the proposed approach is in excellent agreement with finite element results.

[1]  D. Choi,et al.  New method of inelastic buckling analysis for steel frames , 2008 .

[2]  J. Dario Aristizabal-Ochoa,et al.  Slope-deflection equations for stability and second-order analysis of Timoshenho beam-column structures with semi-rigid connections , 2008 .

[3]  The Effect Of Shear Deformation On The Critical Buckling Of Columns , 1994 .

[4]  Murray C. Temple,et al.  Local effective length factor in the equivalent slenderness ratio , 1995 .

[5]  Mohammad Ali Jafari,et al.  Experimental evaluation of elastic critical load in batten columns , 2009 .

[6]  Luís Simões da Silva,et al.  Design of Steel Structures: Eurocode 3: Design of Steel Structures, Part 1-1: General Rules and Rules for Buildings , 2010 .

[7]  Atle Gjelsvik,et al.  Buckling of Built‐Up Columns with or without stay plates , 1990 .

[8]  Alexander G. Razdolsky.  Euler Critical Force Calculation for Laced Columns , 2005 .

[9]  Hans H. Bleich,et al.  Buckling strength of metal structures , 1952 .

[10]  Hoon Yoo,et al.  Improved system buckling analysis of effective lengths of girder and tower members in steel cable-stayed bridges , 2009 .

[11]  Zdenek P. Bazant,et al.  Shear buckling of sandwich, fiber composite and lattice columns, bearings, and helical springs: Paradox resolved , 2003 .

[12]  H. Ziegler,et al.  Arguments for and against Engesser's buckling formulas , 1982 .

[13]  Subhash C. Goel,et al.  An Analytical Criterion for Buckling Strength of Built-up Compression Members , 2003 .

[14]  Jürg Von Nänni,et al.  Das Eulersche Knickproblem unter Berücksichtigung der Querkräfte , 1971 .

[15]  Engesser Fr.,et al.  Die Knickfestigkeit gerader Stäbe , 1891 .

[17]  John E. Johnson,et al.  Steel Structures : Design and Behavior , 1980 .

[18]  S. Timoshenko.  Theory of Elastic Stability , 1936 .

[19]  Sritawat Kitipornchai,et al.  Stability criteria for Timoshenko columns with intermediate and end concentrated axial loads , 2002 .

[20]  Theoretical and Experimental Study on Buckling of Built-up Columns , 1995 .

[21]  J. Dario Aristizabal-Ochoa,et al.  Column Stability and Minimum Lateral Bracing: Effects of Shear Deformations , 2004 .

[22]  Murray C. Temple,et al.  Buckling of built-up compression members in the plane of the connectors , 1993 .

[23]  M. Paul.  Buckling Loads for Built-up Columns with Stay Plates , 1995 .

[24]  Charis J. Gantes,et al.  Buckling strength of multi-story sway, non-sway and partially-sway frames with semi-rigid connections , 2006 .

[25]  Z. Bažant,et al.  Sandwich buckling formulas and applicability of standard computational algorithm for finite strain , 2004 .

[26]  Murray C. Temple,et al.  Equivalent slenderness ratio for built-up members , 1993 .

[27]  Theodore V. Galambos,et al.  Guide to stability design criteria for metal structures , 1998 .

[28]  M. A. Bradford,et al.  Buckling and Second-Order Effects in Dual Shear-Flexural Systems , 2008 .

[29]  Charis J. Gantes,et al.  Improved stiffness distribution factors for evaluation of effective buckling lengths in multi-story sway frames , 2005 .

[30]  A. Gjelsvik.  Stability of Built-up Columns , 1991 .

[31]  Z. Bažant,et al.  Stability Of Structures , 1991 .

[32]  Robert H. Bryant,et al.  Slope Deflection Analysis Including Transverse Shear , 1977 .

[33]  Hoon Yoo,et al.  Iterative system buckling analysis, considering a fictitious axial force to determine effective length factors for multi-story frames , 2009 .

[34]  J. A. Haringx.  On highly compressible helical springs and rubber rods, and their application for vibration-free mountings , 1950 .

[35]  Johan Blaauwendraad.  Timoshenko beam–column buckling. Does Dario stand the test? , 2008 .