Smart Super Elements in Slender Structures Subjected to Wind

Structural analysis of tall buildings of asymmetric plan and irregular geometry subjected to wind load eventuates in complicated calculus. This is among others the case if parts of the building or stability elements stop at a lower height than the rest. FEM programs are at disposal; however the modeling takes a lot of time and a quick and deeper understanding of the force flow is not provided. In this paper this want is supplied by developing a closed-form super element method for two frequently occurring building types. For two types of a tall building of irregular geometry, an insight-providing closed-form analysis method of combining super elements is presented. The main-structure is subdivided in only two super elements. The super elements are based on closed-form solutions describing the force flow in the stability elements. Within an element no change of floor plan, wall and shaft geometry occurs. A node between elements is only chosen where the properties of the building change. The in-plane stiffnesses of the floors are included and act as distributed coupling springs between the stability elements. For each super element a set of simultaneous differential equations is derived and closed-form solutions are obtained; see [

1

]. For each super element the stiffness matrix is composed from the homogeneous solution and the load vector is composed from both the particular and the homogeneous solution. Foundation stiffness is accounted for. At each change of geometry (node) a marked disturbance in the moment and shear force diagram is found, attenuating along a number of storeys depending on the ratio of the characteristic length and the length of the building. Closed-form expressions for the influence lengths of these disturbances are obtained. Including the rotational stiffness of the foundation may result in substantial disturbances in the stress state at the base of the building. No disturbance occurs if the ratio of the rotational stiffnesses of wall and shaft equals the ratio of the base moments of wall and shaft for an ideal rigid foundation. Results have been presented in [

1

]. Because of the use of a very small number of super elements with closed-form solutions, the method contributes to the understanding of the behaviour of the considered tall buildings with a discrete change along the height. In a preliminary design stage a fast analysis can be made without spending much time in modelling. It is shown that the modelling and calculating time of the present method is reduced significantly in comparison with complete finite element analysis and accurate results are obtained.