Effective length factor of columns in semirigid and unbraced frames

In current engineering practice, to evaluate the stability of columns in frames with rigid and semirigid connections, one must estimate the effective length factor (K-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 K-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 K-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 K-factor are numerically studied and the K-factors obtained by two simplified methods are also compared with the present method.