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A tall building may be modeled as a shear beam since its bending is mainly induced by relative sliding of parallel floor slabs. Classical shear beams do not consider the presence of bending moment. Since the bending moment of a building can be originated from tension-compression force couple due to combined effects of strong wall-to-wall and wall-to-slab interactions, a modified shear beam theory cooperating with bending moment is needed. This paper gives a theoretical analysis of a refined shear beam model. Emphasis is placed on the determination of the natural frequencies of a shear beam on an elastic base such as soil and carrying a lumped mass. The characteristic equation for free vibration of a modified shear beam is obtained. The influences of translational and rotational spring stiffnesses, axially compressive loads and attached mass on the natural frequencies are illuminated.

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