, Volume 53, Issue 6, pp 1547–1564 | Cite as

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

  • Paolo Venini
  • Carlo Cinquini
Novel Computational Approaches to Old and New Problems in Mechanics


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 \(H_{\infty }\)-norm and the \(H_2\)-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).


Compliance with ethical standards

Conflicts of interest

The second author Carlo Cinquini is Treasurer and Past President of AIMETA. The authors declare that they have no conflict of interest.


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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Civil Engineering and ArchitectureUniversity of PaviaPaviaItaly

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