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Abstract:In the present paper, a General Algorithm is applied to the analysis of high-rise structures. This algorithm is to be used as a calculation tool in preliminary design; it allows to define the interaction between closed and open, straight or curved shear-walls, and the forces exchanged in structures subject to mainly horizontal loads. The analysis can be performed in both static and dynamic regimes, the mode shapes and the natural frequencies being assessed. This general formulation allows analyses of high-rise structures by taking into account the torsional rigidity and the warping deformations of the elements composing the building without gross simplifications. In this way it is possible to model the structure as a single equivalent cantilever, thus minimising the degrees of freedom of the system, and consequently the calculation time. Finally, potentials of the method proposed are demonstrated by a numerical example which emphasizes the link between global displacements and stresses in the elements composing the structure.

Background: When a high-rise building is designed, the main aim is to limit transversal displacements. In addition, when vertical bracings, made up of thin open sections, are subjected to external torsion, warping and secondary torsional moment stresses arise which need to be evaluated using Vlasov’s Theory. Objective: This work analyzes the Piedmont Region Headquarters Tower, using an analytical formulation which enables the calculation of structural displacements and stresses. Methods: The analytical formulation used in the static and dynamic analysis of the structure was implemented using Matlab computation code. A computational model was also created using a commercial Finite Element Code to validate the results. Results: The results obtained with the analytical model were compared with those obtained with the FEM model. The transversal displacements, bending, torsional, and axial stresses in the vertical bracings were calculated, along with the principal natural frequencies of the structure. Conclusion: It has been proved that analytical calculation codes are a good tool for the preliminary design of a high-rise building. In particular, the proposed formulation, which has only three degrees of freedom per floor, provided results similar to those obtained using a FEM model. The great advantage of this analytical code is to speed up the computation time, which is proportional to the square of the degrees of freedom. In a FEM model, these have orders of magnitude greater than in the analytical model. Moreover, the proposed formulation allows the load distribution between the structural elements to be determined.

In this paper, an original analytical formulation to evaluate the natural frequencies and mode shapes of high-rise buildings is proposed. The methodology is intended to be used by engineers in the preliminary design phases as it allows the evaluation of the dynamic response of high-rise buildings consisting of thin-walled closed- or open-section shear walls, frames, framed tubes, and dia-grid systems. If thin-walled open-section shear walls are present, the stiffness matrix of the element is evaluated considering Vlasov’s theory. Using the procedure called General Algorithm, which allows to assemble the stiffness matrices of the individual vertical bracing elements, it is possible to model the structure as a single equivalent cantilever beam. Furthermore, the degrees of freedom of the structural system are reduced to only three per floor: two translations in the x and y directions and a rigid rotation of the floor around the vertical axis of the building. This results in a drastic reduction in calculation times compared to those necessary to carry out the same analysis using commercial software that implements Finite Element models. The potential of the proposed method is confirmed by a numerical example, which demonstrates the benefits of this procedure.

Diagrids are tubular structural systems made up of mega-diagonals arranged in a triangular or tetrahedral pattern, which are placed all over the external surface of the building and usually span across several floors. In the last two decades, diagrids have experienced a remarkable development as efficient structural systems in tall building design and construction. This was mainly due to their high lateral stiffness, capability to realize complex-shaped structures and obtain impressive aesthetic results, flexibility of the external diagonals' layout, etc. The structural analysis of these systems is usually carried out by the Finite Element Method (FEM) or by numerical calculations based on simplified assumptions. Recently, we developed a matrix-based method (MBM) to perform the structural analysis of diagrid systems under static forces. The MBM was then coupled with an analytical formulation developed in the past years by some of the authors, the so-called General Algorithm (GA), in order to study the structural response of an external diagrid tube coupled with an internal shear wall under lateral and torque static actions. The study allowed to investigate the influence of the diagonal inclination on the lateral and torsional flexibility of the diagrid-core system. In the past years, the analytical formulation of the GA was also made suitable to analyze the response of threedimensional tall building in the dynamic regime. In this contribution, we show new results regarding the dynamical behavior of an external diagrid structural system coupled with an internal shear wall, as obtained from the GA calculations. Modal analysis was carried out in order to obtain the natural frequencies and mode shapes of the tall building, and the influence of the diagonal inclination on the results was also investigated. Moreover, by applying different harmonic oscillations at different frequencies at the base of the building, the damped dynamical response of the different diagrid-core systems was investigated.