Optimal Design of High-Rise Buildings with Respect to Fundamental Eigenfrequency

In modern tall and slender structures, dynamic responses are usually the dominant design requirements, instead of strength criteria. Resonance is often a threatening phenomenon for such structures. To avoid this problem, the fundamental eigenfrequency, an eigenfrequency of higher order, should be maximized. An optimization problem with this objective is constructed in this paper and is applied to a high-rise building. Using variational method, the objective function is maximized, contributing to a particular profile for the first mode shape. Based on this preselected profile, a parametric formulation for flexural stiffness is calculated. Due to some near-zero values for stiffness, the obtained formulation will be modified by adding a lower bound constraint. To handle this constraint some new parameters are introduced; thereby allowing for construction of a model relating the unknown parameters. Based on this mathematical model, a design algorithmic procedure is presented. For the sake of convenience, a single-input design graph is presented as well. The main merit of the proposed method, compared to previous researches, is its hand calculation aspect, suitable for parametric studies and sensitivity analysis. As the presented formulations are dimensionless, they are applicable in any dimensional system. Accuracy and practicality of the proposed method is illustrated at the end by applying it to a real-life structure.