In current engineering practice, to evaluate the stability of columns in frames with rigid and semirigid connections, one must estimate the effective length factor (\iK-factor) of columns considering the effects of the nonlinear moment-rotation characteristics of beam-to-column connections. Herein, using the alignment chart approach and based on a recent study on the stability of semirigid frames and the concept of Shanley’s inelastic column buckling theory, the governing equations on the \iK-factor of columns for various boundary conditions with rigid and semirigid beam-to-column connections are derived for unbraced frames. With a proper evaluation of the tangent connection stiffness for semirigid beam-to-column connections at buckling state and with the introduction of the modified relative stiffness factors, the alignment chart in the present American Institute of Steel Construction-load and resistance factor design specification can be applied to find the corresponding column \iK-factor in semirigid frames. This is described in the present paper. Furthermore, using a semirigid and unbraced portal frame example, the effects of the nonlinear moment-rotation characteristics of connections on the \iK-factor are numerically studied and the \iK-factors obtained by two simplified methods are also compared with the present method.
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