Reinforced concrete seismically-excited frame design with a new mixed $$\varvec{H}_2/\varvec{H}_{\infty }$$H2/H∞ optimization approach

A new approach is proposed for the optimal design of seismically excited reinforced concrete frames. Unlike most existing methods that do not exploit the input/output relationship between the base acceleration and the structural response, the main feature of the presented approach is to directly shape the input/output transfer function so as to reduce the dynamic amplification factors that govern the structural response. The approach is general with respect to distinctive issues: on the one side the structural output may encompass different quantities of engineering interest such as the overall compliance, the lateral displacement of a representative point (typically the averaged top-storey displacement) and the interstorey drift vector, on the other two system norms may be considered (or a combination thereof) as to the transfer-function amplitude to be minimized, namely the $$H_{\infty }$$H∞-norm and the $$H_2$$H2-norm. The former allows to reduce the peak-gain response whereas the latter the squared power energy of the response. By cleverly combining the two, typically by means of a convex combination, one may end up with significant peak gain as well as power response reduction. A numerical investigation on a 2D frame is conducted to validate the theoretical framework that is modeled following Eurocode 8 (CEN in Eurocode 8: design of structures for earthquake resistance. Part 1: general rules, seismic actions and rules for buildings. European Standard EN 1998-1, Brussels (2004)) in medium ductility class (DCM) but the method applies to any regulations including modern displacement based codes such as the fib Model Code 2010 (Bulletins Nos. 65/66, Federation Internationale du Beton, Lausanne 2012).