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The chapter initially provides a summary of the contents of Eurocode 8, its aim being to offer both to the students and to practising engineers an easy introduction into the calculation and dimensioning procedures of this earthquake code. Specifically, the general rules for earthquake-resistant structures, the definition of design response spectra taking behaviour and importance factors into account, the application of linear and non-linear calculation methods and the structural safety verifications at the serviceability and ultimate limit state are presented. The application of linear and non-linear calculation methods and corresponding seismic design rules is demonstrated on practical examples for reinforced concrete, steel and masonry buildings. Furthermore, the seismic assessment of existing buildings is discussed and illustrated on the example of a typical historical masonry building in Italy. The examples are worked out in detail and each step of the design process, from the preliminary analysis to the final design, is explained in detail.
Rapid Tooling
(2019)
Suppose we have k samples X₁,₁,…,X₁,ₙ₁,…,Xₖ,₁,…,Xₖ,ₙₖ with different sample sizes ₙ₁,…,ₙₖ and unknown underlying distribution functions F₁,…,Fₖ as observations plus k families of distribution functions {G₁(⋅,ϑ);ϑ∈Θ},…,{Gₖ(⋅,ϑ);ϑ∈Θ}, each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not (F₁,…,Fₖ) belongs to the parametric family {(G₁(⋅,ϑ),…,Gₖ(⋅,ϑ));ϑ∈Θ}. New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions.