Abstract The vibration characteristics of steel mill buildings designed according to standard specifications are investigated. The dynamic stiffness influence coefficient method is used in deriving a simple, yet rigorous, method of extraction of the first few planar horizontal and vertical natural frequencies and modal shapes. The advantage of this method is that the final system matrix is only of rank two. The finite element method is also used for the complete three-dimensional representation of a typical steel mill building with an overhead crane at two different positions. In all cases, the representation of real structures by idealized mathematical models is meticulously performed in order to ensure that all salient structural features are correctly included. It is concluded that the two-dimensional representations yield natural frequencies and modal shapes that are in good agreement with the corresponding ones obtained from complete three-dimensional representations.
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