Inelastic Stability of Unbraced Building Frames

Strain reversal is taken into account in terms of generalized stress and generalized strain. The stiffness matrix is so derived that it is applicable to any piecewise elastic regime in the elastic-plastic deformation of a member, the effect of the axial force being taken into account by means of approximate stability functions. Numerical computation for the smallest critical load can be executed by following the standard matrix procedure for calculating eigenvalues. The proposed analysis facilitates the study of not only the stability limit, but also those states beyond and remote from this point. The proposed analysis can be applied to the practical design of such structures and is demonstrated in detail by means of simple numerical examples. A comparison of the result with that obtained by means of the exact stability functions is made and found to be in good agreement. The influence of unloaded plastic hinges on the ultimate load is illustrated.