Analysis of the multi storey buildings with finite element methods

Internal load distribution of the staircases of multi storey buildings depends on the supporting conditions of staircase to building, geometric and material properties of the staircase, number of the storeys, rigidity ratio between the components of the staircase and building and location of the staircase. Literature contains very few research about these subjects [1-3]. In general, internal load distribution along the staircases of the first storey and upper storey is different than those of the intermediate storeys. Approximate analysis methods which are prepared for hand calculations does not consider the effects caused by the location of the staircase and the number of the stories. Staircase is assumed to have a fixed support at the floor level and have a hinged support at the mid height in the formulation of the simple analysis methods. In some cases, both ends of the staircase between two floor levels are considered to be simply supported and the continuity is not satisfied. Because the span between the supports is taken into consideration only. The analysis results of a single storey staircases are applied to all storeys. Shearing force and momentdistributions along the staircase are used in design. Axial force distribution are not taken into consideration. Because the axial loads obtained by using approximate methods are compressive loads in general (depending on the considered boundary conditions). In reality, inplane loads are not equal to zero. Tensile or compressive stresses occur in the plane of the staircase components depending on the loading and the supporting conditions. Actual internal load distribution depends on many parameters. One of these parameters is the interaction of staircase with the building. Geometry of the system and rigidies of the components of the staircase interacting with building affects the internal load distribution along the staircase significantly. Therefore analysis of the staircase which is interacting with buildings in 3D form is the most appropriate analysis method. This analysis can be performed by using finite element method. But modeling the staircase together with the building requires large amount of input data preperation and is not practical. In this study a typical staircase system which is mostly used in conventional buildings is analysed for different number of storeys and under different loadings conditions. Three dimensional Finite Element Models are used to perform the analyses. Some tables for practical hand calculation are prepared. These tables include the correction factors for the analysis results of simple two dimensional, one storey staircase. Using these correction factors, three dimensional stress distribution and most critical stresses can be obtained from the analysis results of two dimensional one storey staircase which is modeled by frame type of finite elements.