IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-ISSN: 2278-1684,p-ISSN: 2320-334X, Volume 12, Issue 3 Ver. II (May - Jun. 2015), PP 66-71 www.iosrjournals.org DOI: 10.9790/1684-12326671 www.iosrjournals.org 66 | Page Modified formulas for bucking length factor for rigid steel frame structures Abbas Moustafa 1 , Magdy I. Salama 2 1 (Associate Professor, Faculty of Engineering, Minia University, Egypt) 2 (Lecturer, Faculty of Engineering, Kafrelsheikh University, Egypt) Abstract: In most current codes for design of steel structures, specifications for the design of compression members utilize the effective length factor K. This parameter is employed to facilitate the design of frame members by transforming an end-restrained compression member to an equivalent pinned-ended member. The effective length factor is obtained either by solving the exact equations using a numerical iterative solution which may be computationally expensive or by using a pair of alignment charts for the two-cases of braced and sway frames. The accuracy of the solution using the second approach depends on the size of the charts and the reader’s sharpness of vision. To eliminate these approximations, simple equations for determining the effective length factor as a function of the rotational resistant at the column ends (GA, GB) are required. Similar equations are available in the French design rules for steel structures since 1966, and are also included in the 1978 European recommendations. In this paper, modifications to the French design rules equations for effective length factors are presented using multiple regressions for a tabulated exact values corresponding to different practical values of the rotational resistance at column ends (GA, GB). The investigated equations are more accurate than the current French rules equations recommended in steel codes of several countries. Comparisons between the numerical results of the equations developed in this study and those obtained by current equations with those obtained by exact solutions are given also in this paper. Keywords: Effective length; steel column; multiple regressions; new formula; braced frame; sway frame I. Introduction The design of compression members such as steel columns and frames starts with the evaluation of the elastic rotational resistance at both ends of the column (GA, GB), from which the effective length factor (K) is determined. The exact mathematical equations for braced and sway rigid frames were given by Barakat and Chen, 1990. These equations may be computationally expensive. An alternative approach to determine these parameter is could be by using a pair of alignment charts for braced and sway frames, which was originally developed by Julian and Lawrence, and presented in detail by Kavanagh (1962). These charts represent the graphical solutions of the mathematically exact equations which are commonly used in most design codes (e.g., Manual of American institute of steel construction (LRFD and ASD), 1989 and the Egyptian code of practice for steel constructions (LRFD and ASD), 2008. The accuracy of the alignment charts depends essentially on the size of the chart and on the reader’s sharpness of vision. Also, having to read K-factors from an alignment chart in the middle of a numerical computation, in spreadsheet for instance prevents full automation and can be a source of errors. Obviously, it would be convenient to have simple mathematical equations instead of the charts which are commonly used in most codes of steel constructions. The American Institute does publish equations but their lack of accuracy may be why they seem not to be used in steel design. Mathematical relations are available in the French design rule for steel structures since 1966, and are also included in the 1978 European recommendations (see e.g., Dumonteil, 1992). In this paper, a modification to the French rule equations is developed to achieve more accurate closed form expressions for the determination of the effective length factors as a function of the rotational resistance at column ends. The presented equations are more practical since they can be easily coded within the confines of a spreadsheet cell or within any mathematical software, such as Matlab, Maple or Mathematica. II. Background For Exact And Approximate Equations Consider a steel column AB elastically restrained at both ends. The rotational restraint at one end, A for instance, is presented by restraint factor GA, expressing the relative stiffness of all the columns connected at A to that of all the beams framing into A, given as:     / /    C C A b b I L G I L (1)