Hybrid-member stiffness matrix accounting for geometrical nonlinearity and member inelasticity in semi-rigid frameworks

This article presents the derivation of a generic stiffness matrix for steel members accounting for the combined influence of P-delta effects, member shear deformation, inelasticity, semi-rigid connection, and joint damage. Member stiffness coefficients accounting for rotational stiffness degradation are derived using the modified moment distribution method. The displacement method is applied to derive the member stiffness coefficients due to translational stiffness degradation, and the force method is utilized to obtain the axial stiffness coefficients caused by normal axial stiffness degradation. Incorporating the derived member stiffness matrix into the conventional matrix displacement method, a computational procedure with increment loading steps is achieved for the nonlinear analysis of steel frameworks subjected to normal and/or abnormal loadings. Example case studies are carried out to illustrate the progressive collapse behaviour of two steel frameworks under abnormal loadings. Results show that the effect of damage to joints may considerably affect the local response of damaged structures, but its effect on the global loading capacity is insignificant. A building framework designed in a non-seismic zone is less robust against progressive collapse than that designed in a seismic zone.