Approximate formulae for natural periods of plane steel frames

Approximate formulae for determining by hand with a high enough accuracy the first three natural periods of vibration of plane steel unbraced and braced frames are provided. These formulae are based on the modeling of a plane steel frame as an equivalent cantilever beam for which analytical expressions for the natural periods are available. Extensive parametric studies involving the finite element computation of the first three natural periods of 110 plane steel unbraced and braced frames are employed to establish correction factors for the equivalent beam modeling formulae which are functions of the number of stories and bays of the frame. The resulting corrected formulae permit a highly accurate determination of the first three natural periods of plane steel frames.