A mathematical formulation to estimate the fundamental period of high-rise buildings including flexural-shear behavior and structural interaction

The objective of the current study is to develop a simple formula to estimate the fundamental vibration period of tall buildings for using in equivalent lateral force analysis specified in building codes. The method based on Sturm-Liouville differential equation is presented here for estimating the fundamental period of natural vibration. The resulting equation, based on the continuum representation of tall buildings with various lateral resisting systems for natural vibration of the buildings, is proved to be the forth-order Sturm-Liouville differential equation, and a quick method for determining the fundamental period of natural vibration of the building is presented. Making use of the coupled wall theory for natural vibration, the method is extended to deal with vibration problem of other buildings braced by frame, walls or/and tube. The proposed formulation will allow a more consistent and accurate use of code formulae for calculating the earthquake-induced maximum base shear in a building. Use of the method is economical with respect to both computer time and equipment and can be used to verify the results of the finite element analyses where the time-consuming procedure of handling all the data can always be a source of errors.