A simple formula is proposed that provides interstorey velocities of steel framed structures at specific interstorey drift levels. The proposed equation is statistically derived from the variation of floor relative velocity results along the height of the structure. These results are obtained by non-linear inelastic time history analyses of a number of plane steel moment resisting frames. The proposed equation can then be used for seismic retrofit purposes, i.e., in dimensioning the linear or non-linear viscous dampers to be inserted in a steel frame. A detailed numerical example is provided and conclusions regarding the accuracy and the potential use of interstorey velocity are drawn.

Introduction

The variation (distribution) of maximum interstorey velocities have been recognized as key parameter for the evaluation of the along-theheight effectiveness of and demand for viscous dampers [1]. This variation (distribution) seems to depend mainly on the modes (number of stories) of the structure under consideration. In building codes, e.g., ASCE 7–۱۰ [۲], peak (design) interstorey velocity (IV) is approximately calculated in the fundamental and higher modes using the design (maximum) interstorey drift (IDR). This approximation permits the calculation of the maximum damping force in terms of the design IDR. Moreover, building codes, e.g., ASCE 7–۱۰ [۲], seem to accept that the most effective way of allocation of viscous dampers is to place them where large IDRs are exhibited. Therefore, the maximum IDR is used to estimate the maximum IV, without, however, providing an insight about the real relationship of maximum IDR and IV values. In literature so far, the relationship between IDR and IV is formulated either by using simplified building models and the first mode shape [3,4] or by employing single-degree-of-freedom systems and their maximum displacement [5,6]. The importance of having reliable estimates of the true IV is initially stressed by Pekcan et al. [7] in view of the operating velocities of non-linear viscous dampers and very recently by Favvata [8] in the context of seismic pounding of adjacent structures. It is the purpose of this paper to establish a relationship between IDR and IV values for steel moment resisting frames (MRFs). More specifically, the seismic responses in terms of floor relative displacements and relative velocities are obtained by non-linear inelastic seismic analyses of 20 plane steel MRFs under 22 real and as recorded seismic motions (accelerograms). Then, for each frame-accelerogram pair, height-wise variations of IDR and IV are constructed. Considering a specific value for IDR along-height, i.e., 1.5%, the corresponding IV values are maintained. Statistical processing of these IV values permits the derivation of an equation that provides IV along-the-height of a structure for this specific IDR. The proposed equation is then used in a seismic retrofit scheme, where dimensioning of viscous dampers is based on IV and targets a specific IDR range. An example that involves the retrofit of a 12-storey with 4-bays, steel MRF is presented. This steel MRF is retrofitted either with linear viscous dampers or with non-linear ones. For each kind of dampers, two cases of target IDR are considered. The retrofitted MRFs are then subjected to non-linear inelastic time history analyses and IDR, IV and damper forces are computed. On the basis of the numerical results of the present work, it can be concluded that the proposed IV equation is quite effective in satisfying target IDR. It is also demonstrated that for a specific level of seismic demand (in terms of mean acceleration spectra) the proposed IV equation offers controlled IV and IDR values as well as damper forces under the condition that plastic hinge formations to columns due to additional axial forces induced by the damper forces are within acceptable limits.