Abstract
A geometrical stiffness matrix for a flexibly-connected member is developed for the analysis and design of semirigid framed structures when geometrical non-linearity (P — Δ effects and other second-order effects) must be considered. A “fixity factor” defining the rigidity of a connection relative to the attached member is introduced to model different types of member connectivity. The sensitivities of the geometrical stiffness matrix with respect to the fixity factor are developed with a view to conducting structural optimization. As an example of optimum design, a semi-rigid steel framework is presented along with discussion of the necessity of considering second-order effects.
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