New simple equations for effective length factors

In most current codes of design steel members and frames, specifications for the design of compression columns or of beam-column use the effective length factor; K. The effective length factor is employed to facilitate the design of framed members by transforming an end-restrained compressive member to an equivalent pinned-ended member. The effective length factor is obtained by solving the exact equations numerically which require many routine calculations or by using a pair of alignment charts for the two cases of braced frames and sway frames. The accuracy of these charts depends on the size of the chart and the reader’s sharpness of vision. Instead of using complicated equations or charts, simple equations are required to determine the effective length factor directly as a function of the rotational resistant at column ends (GA, GB). In this paper, new simple and accurate equations for effective length factors are presented using multiple regressions for tabulated exact values corresponding to different practical values of the rotational resistance at column ends (GA, GB). The investigated equations are more accurate than equations that are recommended in some steel constructions codes. Comparisons between the results of the present equations and those obtained by equations presented in previous researches with those obtained by exact solutions are also given in this paper.