The vibration problem of multistory buildings, considering both shear and bending deformations in floors and in stiffening walls, is formulated and methods for calculating the normal modes and associated natural frequencies are described and illustrated.

A generalized slope deflection equation is used which takes into account shear deformation in addition to the flexural deformation conventionally included. This generalization permits the inclusion of shear deformation effects with no increase in the number of equations. Using this equation to represent the action of walls, a method for calcuating the modes and frequencies of stiffened multistory buildings is described. Going further and using the generalized equation to represent the action of floor slabs, a method for determining the two-dimensional modes and frequencies of stiffened and unstiffened multistory buildings with relatively long and narrow floors is presented. These modes and frequencies, which are not obtainable through the use of the usual analytical model, may be quite important in seismic design of this type of building.

As illustrative examples, the theory and method are applied to the calculation of several modes and frequencies of a 10-story building and a 20-story stiffened building.

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