WP3

Development of Simplified and/or Analytical Methods

Elastoplastic Winkler Models

A boundary element method has been developed for the nonlinear static and dynamic analysis of shear deformable beam-columns of arbitrary doubly symmetric simply or multiply connected constant cross section, partially supported on tensionless Winkler foundation, undergoing moderate large deflections under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. The beam-column is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to the two stress functions, and solved using the Analog Equation Method, a BEM based method (static problem), or by employing the average acceleration method in combination with the modified Newton-Raphson method (dynamic problem). The model takes into account the coupling effects of bending and shear deformations along the member as well as the shear forces along the span induced by the applied axial loading. Numerical examples have been worked out to illustrate the efficiency, and wherever possible the accuracy and the range of applications of the developed method.

Relevant Publications: A17 and A18 [Sapountzakis and Kampitsis, 2010a; b] ; B16 and B17 [Sapountzakis and Kampitsis, 2009a; b]

The aforementioned boundary element model is extended to the more complex but potentially more realistic three parameter viscoelastic foundation. The beam-column is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading. As for the previous cases, to account for shear deformations, the concept of shear deformation coefficients is used. Then, in Conference publication B20, the proposed model is applied for the analysis of two major Valley Bridges (Viaducts) in Greece : Metsovo Bridge, and Metsovitikos River Bridge.

Relevant Publications: A19 and A20 [Sapountzakis and Kampitsis, 2010c; d] ; B18 and B19 [Sapountzakis and Kampitsis, 2009c; d]




Macro-element Modelling


The dynamic response of a typical highway bridge pier under seismic excitation has been studied through macro-element modelling. The analysed bridge systems is the same with the one studied in Journal publication A1 [Anastasopoulos et al., 2009], to allow for comparisons. The bridge pier has been modelled with non-linear beam elements. However, the foundation and the soil are replaced by one unique 2-node link element, which is the non-linear dynamic macroelement for shallow foundations. The macroelement is formulated with a non-linear constitutive law that is reproducing the non-linear phenomena arising at the soil-footing interface; these include: (a) the elastoplastic soil behavior leading to irreversible foundation displacements ; and (b) the possibility of the footing to get detached from the soil (foundation uplift). Additionally, the macroelement is coupled with a viscous damping element, which is used to reproduce the effects of radiation damping.

Relevant Publications: C1 [Chatzigogos & Pecker, 2010].