Stability Functions for Members with Semirigid Joint Connections

The partial restraint of steel‐frame members, which depends on the solution adopted for joint connections, affects the structural stiffness of these structures, and thus affects the overall deflections, internal force distribution, and stability limit loads of these structures as well. To develop an inelastic second‐order analysis model for the analysis of space frames, in which the members are constrained elastically against axial and shearing forces as well as bending and twisting moments, connection springs for every possible degree of freedom at the ends of prismatic structural members have been introduced. A correction matrix—the equivalent stiffness matrix, ${\mathbf{K}}_e$, for incorporation in a displacement matrix analysis, in terms of various degrees of fixity involved—has been established. This matrix can be used for the second‐order nonlinear analysis as well as for the stability analysis of space frames with semirigid joint connections. The correction factors of the equivalent stiffness matrix ($C_{\mathrm{1y}}^A$, $C_{\mathrm{1y}}^B$, $C_{\mathrm{2y}}$, $C_{\mathrm{3y}}^A$, $C_{\mathrm{3y}}^B$, $C_{\mathrm{4y}}$, $C_{\mathrm{1z}}^A$, $C_{\mathrm{1z}}^B$, $C_{\mathrm{2z}}$, $C_{\mathrm{3z}}^A$, $C_{\mathrm{3z}}^B$, and $C_{\mathrm{4z}}$) are stability functions for members with semirigid joint connections—a generalization of Livesley's stability functions.