Seismic behavior of capacity designed masonry walls in low seismicity regions

Eurocode 8 representing a new generation of structural design codes in Europe defines ‎requirements for the design of buildings against earthquake action. In Central and ‎Western Europe, the newly defined earthquake zones and corresponding design ground ‎acceleration values, will lead in many cases to earthquake actions which are remarkably ‎higher than those defined so far by the design codes used until now in Central Europe. ‎ In many cases, the weak points of masonry structures during an earthquake are the corner ‎regions of the walls. Loading of masonry walls by earthquake action leads in most cases ‎to high shear forces. The corresponding bending moment in such a wall typically causes a ‎significant increase of the eccentricity of the normal force in the critical wall cross ‎section. This in turn leads ultimately to a reduction of the size of the compression zone in ‎unreinforced walls and a high concentration of normal stresses and shear stresses in the ‎corner regions. ‎ Corner-Gap-Elements, consisting of a bearing beam located underneath the wall and ‎made of a sufficiently strong material (such as reinforced concrete), reduce the effect of ‎the eccentricity of the normal force and thus restricts the pinching effect of the ‎compression zone. In fact, the deformation can be concentrated in the joint below the ‎bearing beam. According to the principles of the Capacity Design philosophy, the ‎masonry itself is protected from high stresses as a potential cause of brittle failure. ‎ Shaking table tests at the NTU Athens Earthquake Engineering Laboratory have proven ‎the effectiveness of the Corner-Gap-Element. The following presentation will cover the ‎evaluation of various experimental results as well as a numerical modeling of the ‎observed phenomena.‎

Time Discretization of the SST-generalized Navier-Stokes Equations: Positive and Negative Results

In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.