Dynamics of staircases : A case study to improve finite element modeling

University essay from KTH/Bro- och stålbyggnad

Abstract: Vibrations in staircases have during the last decades become an important issue in design. The main reasons are current architectural trends aiming for innovative, slender and high staircases, together with developments in material properties and building technique, making these aims possible. The improved material properties and slender design of the staircase makes the structure lightweight and have great impact on the flexibility and dynamic performance of the staircase. This have resulted in that vibration serviceability criteria increasingly often are becoming governing in design. The performance of staircases in serviceability under dynamic loads is however very hard to predict. In many cases hand calculations will not be sufficient, and a computerized model, e.g. a finite element model, need to be created. Creating a finite element model that performs well when subjected to dynamic loads is however not simple. Especially boundary conditions, connections and the effect of non-structural elements are hard to adequately represent. The formulation of the load is also a complex question. The main dynamic load that staircases are subjected to, that causes uncomfort for the user, is the load that the user themselves apply on the structure, when ascending or descending.  The main part of this master thesis project is a case study of two lightweight, steel staircases. To form a basis for the case study, current research have been summarized in a literature survey. An introduction of elementary dynamics is also made for less conversant reader. The literature survey reviews previous research about loads introduced by humans and how these can be formulated, both for single human excitation and group loading. How vibrations arise and how humans percept vibrations is also reviewed. The view and recommendations of standards and regulations about load formulation and vibration acceleration limits is presented. Recommendations in research for finite element modeling of staircases and dynamic loads is also reviewed. The case study consists of measurements and analyzing of finite element models of the staircases. Measurements of vibrations and the dynamic response of the staircases under human introduced loads have been conducted. The human introduced loads included are an impulse load created by a jump, ascent at a moderate pace of a single subject and descent at a moderate pace by a single subject. The measurements have been recreated in finite element models. Different modeling choices and formulations for ascending, descending, and impulse loads are studied.  The aim is to investigate how different modeling choices in connections, boundary conditions and adjacent structure, affects the natural frequencies and mode shapes of the staircase. Different load formulations for the loads are analyzed, both for the impulse load and for the loads created by a subject ascending and descending. With these results as a basis, some general recommendations about construction a finite element mode of a staircase and achieving appropriate load formulation for dynamic loads are made. 

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