1 STATIC AND DYNAMIC STABILITY OF UNIFORM SHEAR BUILDINGS UNDER GENERALIZED BOUNDARY CONDITIONS By J. Dario Aristizabal-Ochoa 1 1 125-Year International Professor, School of Mines, National University of Colombia, Medellín-Colombia ABSTRACT: The stability and dynamic analyses (i.e., the buckling loads, natural frequencies and the corresponding modes of buckling and vibration) of a 2-D shear beam-column with generalized boundary conditions (i.e., with semi-rigid flexural restraints and lateral bracings as well as lumped masses at both ends) and subjected to linearly distributed axial load along its span are presented in a classic manner. The two governing equations of dynamic equilibrium, that is, the classical shear-wave equation and the flexural moment equation are sufficient to determine the modes of vibration and buckling, and the corresponding natural frequencies and buckling loads, respectively. The proposed model includes the simultaneous effects (or couplings) of shear deformations, translational and rotational inertias of all masses considered, the linearly applied axial load along the span, and the end restraints (flexural and lateral bracings at both ends). The proposed model shows that the lateral stability and dynamic behavior of 2-D shear beam-columns are highly sensitive to the coupling effects just mentioned, particularly in members with limited end flexural restraints and lateral bracings. Analytical results indicate that except for members with perfectly clamped ends (i.e. zero rotation of the cross sections), the stability and dynamic behavior of shear beams, shear beam-columns, and shear-buildings are governed by the flexural moment equation, rather than the second-order differential equation of transverse equilibrium (or shear-wave equation). This equation is formulated in the technical literature by simple applying transverse equilibrium at both ends of the member “ignoring” the flexural moment equilibrium equation. This causes erroneous results in the stability and dynamic analyses of such members with supports that are not perfectly clamped. This is particularly critical in shear buildings. The proposed equations reproduce, as special cases: 1) the non-classical vibration modes of shear beam-columns including the inversion of modes of vibration (i.e. higher modes crossing lower modes) in shear beam- columns with soft end conditions, and the phenomena of double frequencies at certain values of beam slenderness (L/r); and 2) the phenomena of tension buckling in shear beam-columns. These phenomena have been discussed recently by the author (2004) and Kelly (2003) in columns made of elastomeric materials.