Simplified Equations for Estimating the Period of Vibration of Existing Buildings

Currently, seismic design of new European buildings follows a force-based approach, whilst the assessment of existing buildings is moving towards a displacement-based philosophy. In forcebased design, conservative estimates of the period of vibration should be produced such that the base shear force will be conservatively predicted from an acceleration spectrum, and thus the use of gross section (uncracked) stiffness in analytical calculations is perhaps acceptable. For the assessment of buildings, the use of the uncracked stiffness in the determination of the period is certainly inappropriate considering cracking of critical elements such as beams generally occurs under gravity loading alone. Even if cracking is not found to have occurred before the design seismic level of excitation (considered unlikely as this level of excitation would with all probability have been preceded by a number of lower intensity events), it will occur early on in the response to excitation and thereafter the stiffness will reduce rapidly leading to the loss of the tension stiffening effect of the concrete. Thus, the reliable stiffness of the members of an existing RC frame can only be confidently taken as the yield/cracked stiffness. The uncracked and yield period of existing European reinforced concrete buildings of varying height is analytically calculated herein using eigenvalue analysis. A simplified equation is proposed to relate the yield period of vibration of existing buildings to their height for use in large-scale vulnerability assessment applications.