Transverse vibrations of beams are an interesting topic for numerous engineering fields. The equations of motion develop under various assumptions and associate a frequency equation. This paper expresses the frequency equation for two specific models, using the Timoshenko beam theory. The first model is a typical cantilever beam with an additional mass attached to the free end. The second model considers a beam partially clamped at the base and with an elastic connection of the additional mass to the free end. The relevance of the used theory is discussed and the importance of each term of the equation is studied. These models find applications in unreinforced masonry. They are indeed fitted to identify, from white noise tests, equivalent mechanical properties of unreinforced load-bearing clay masonry walls including soundproofing devices in the perspective of modelling these elements with a macro-scale approach. Discrepancies with respect to current standards are underscored.
The paper presents the studies carried out on a big storage gas tank for the seismic vulnerability assessment and the retrofit through isolation system. This Gasometer, constructed in the early eighties, consists in a steel cylinder of 70 m height and 44 m diameter. The tank bearing structure is composed by a classical steel frame closed with curved steel plates. Inside the tank, a piston-fender and rubber sealing system allow the variation of the container volume and control the gas pressure. The latter represents half of the seismic mass and its position can vary along the tank height. The seismic vulnerability of the steel structure of the Gasometer on its as-it-is state is assessed through the execution of Incremental Dynamic Analyses, placing particular attention on the definition of possible limit states. Subsequently, the seismic retrofit through base isolation system, adopting Double Curved Surface Sliders, is proposed and numerically assessed. The results and comparison between the as-it-is state and the retrofitted state supplies important information about the effectiveness of base isolation for the risk mitigation of gas tanks.
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