Iterative system buckling analysis, considering a fictitious axial force to determine effective length factors for multi-story frames

Traditional elastic buckling analysis, based on the system buckling approach, is a convenient tool for the evaluation of effective length factors of columns, in the stability design of multi-story frames. This method is superior to other analytical approaches, such as the isolated subassembly and story-based approaches, in that the inter-story and inter-column interactions are inherently taken into account. Nevertheless, use of the conventional critical load expression, in combination with results of elastic buckling analysis, may yield an excessively large effective length in members having relatively small axial forces. The present paper proposes an iterative elastic buckling analysis to determine reasonable effective length factors of columns in multi-story frames. In this paper, numerical procedures for an iterative buckling analysis using a modified geometric stiffness matrix, are described to obtain the effective length factors of the columns in multi-story frames. The axial force term in the geometric stiffness matrix is modified by adding a fictitious axial force to make the columns buckle along with the overall buckling of the frame. Iterative eigenvalue analysis is performed using the modified geometric stiffness matrix, to obtain the effective length factors of each column using the critical load expression. Example frames presented in this paper demonstrate that the proposed method not only provides excellent outcomes by amending the weakness associated with traditional elastic buckling analysis for determining the effective length factor, but is also a competitive alternative in the design of multi-story frames.

[1]  Seung-Eock Kim,et al.  Direct design of three-dimensional frames using practical advanced analysis , 2001 .

[2]  Jostein Hellesland,et al.  Improved Frame Stability Analysis with Effective Lengths , 1996 .

[3]  Dimitris L. Karabalis,et al.  Efficient computation of buckling loads for plane steel frames with tapered members , 2006 .

[4]  Lei Xu,et al.  Storey-based column effective length factors with accounting for initial geometric imperfections , 2008 .

[5]  Nicholas S. Trahair,et al.  Out-of-plane advanced analysis of steel structures , 2003 .

[6]  Francois Cheong-Siat-Moy.  Multiple K-factors of a leaning column , 1997 .

[7]  J. Dario Aristizabal-Ochoa.  K‐Factor for Columns in any Type of Construction: Nonparadoxical Approach , 1994 .

[8]  Russell Q. Bridge,et al.  Improved G‐Factor Method For Evaluating Effective Lengths of Columns , 1987 .

[9]  Eric M. Lui,et al.  Structural Stability: Theory and Implementation , 1987 .

[10]  Jun Wang,et al.  Column effective lengths considering inter-story and inter-column interactions in sway-permitted frames , 2006 .

[11]  Günay Özmen,et al.  Buckling lengths of unbraced multi-storey frame columns , 2005 .

[12]  Francois Cheong-Siat-Moy.  K‐Factor Paradox , 1986 .

[13]  J. Lemessurier.  A Practical Method of Second Order Analysis Part 2—Rigid Frames , 2003 .

[14]  Jerome F. Hajjar,et al.  Effective Length and Notional Load Approaches for Assessing Frame Stability: Implications for American Steel Design , 1997 .

[15]  Donald W. White,et al.  Buckling models and stability design of steel frames: a unified approach , 1997 .

[16]  J D Aristizabal-Ochoa.  Stability Problems of Columns and Frames , 1997 .

[17]  J. Hajjar,et al.  Accuracy and simplicity of alternative procedures for stability design of steel frames , 1997 .

[18]  J. Dario Aristizabal-Ochoa.  Tension and Compression Stability and Second-Order Analyses of Three-Dimensional Multicolumn Systems: Effects of Shear Deformations , 2007 .

[19]  J. Dario Aristizabal-Ochoa.  Slenderness K factor for Leaning Columns , 1994 .

[20]  Donald W. White,et al.  Stability of steel frames: the cases for simple elastic and rigorous inelastic analysis/design procedures , 2000 .

[21]  Lei Xu,et al.  Story stability of semi-braced steel frames , 2002 .

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

[23]  Jean-Pierre Jaspart,et al.  Design of Composite Sway Building Frames for Global Instability , 2005 .

[24]  Francisco J. Pallarés,et al.  Proposal to evaluate the ultimate limit state of slender structures. Part 1: Technical aspects , 2007 .

[25]  W. M. Kim Roddis,et al.  K Factors for Unbraced Frames: Alignment Chart Accuracy for Practical Frame Variations , 1998 .

[26]  Wai-Fah Chen,et al.  Structural stability: from theory to practice , 2000 .

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