###### Abstract  
The use of equivalent beam models to estimate the dynamical characteristics of complex tall buildings has been investigated by several authors. The main reason is the structural response estimation to stochastic loads, such as wind and earthquake, using a reduced number of degrees of freedom, which reduces the computational costs and therefore gives the designer an effective tool to explore a number of possible structural solutions. In this paper, a novel approach to calibrate the mechanical and dynamical features of a complete 3D Timoshenko beam, i.e., describing bending, shear and torsional behavior, is proposed. This approach is based on explicitly considering the sub-structures of the tall building. In particular, the frames, shear walls and lattice sub-systems are modeled as equivalent beams, constrained by means of rigid diaphragms at different floors. The overall dynamic features of the tall building are obtained by equating the deformation energy of an equivalent sandwich beam with that of the selected sub-structures. Finally, the 3D Timoshenko equivalent beam parameters are calibrated by minimizing a suitable function of modal natural frequencies and static displacements. The closed form modal solution of the equivalent beam model is used to obtain the response to stochastic loads. t 2021 11 4655. [[https://doi.org/10.3390/app11104658](https://doi.org/10.3390/app11104658)]([https://doi.org/10.3390/app11104658](https://doi.org/10.3390/app11104658))  
Academic Editors: [PERSON] and [PERSON]  
Received: 16 April 2021  
Accepted: 15 May 2021  
Published: 19 May 2021  
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**1. Introduction**  
In the last five decades, the reduction of complex structural systems to equivalent beam models has been investigated by several authors. The availability of simple models that can accurately describe the global response is appealing because it can reduce the time and computational costs required by detailed numerical finite element (FE) models with a large number of degree of freedom [1] and simplify the structural analysis increasing both the efficiency and understanding of the system behavior. This aspect becomes crucial when designing complex tall buildings with irregular shapes that have been built around the world in the last decades. Indeed, the development of structural optimization algorithms capable of reducing the cost of such buildings while maintaining appropriate safety levels might be time-consuming and even not feasible with a large-dimension problem that could require special techniques. For this reason, reliability-based design optimization (RBDO) has been proposed as a framework to obtain minimum building costs constrained to prescribed safety levels. In particular, [PERSON] and [PERSON] proposed an RBDO algorithm for member size optimization based on the definition of explicit sub-problems driven by safety constraints on both global and local structural response to stochastic wind load and with uncertain mechanical parameters [2, 3, 4]. The development of reduced-order models is also crucial for improving the effectiveness of preliminary sensitivity analysis in which the influence of random loads and uncertain mechanical parameters on the linear and nonlinear structural response is of interest [5; 6]. For all these reasons, a number of reduced-order equivalent beam models have been proposed in the literature, where a combination of in-series and/or in-parallel bending, shear and torsional stiffnesses are considered to model the typical tall building bracing resisting systems (e.g., walls, frames, lattice structures, frames, coupled shear walls). Appendix A reports a detailed summary of the main contributions to the literature about this topic. Recent papers on equivalent beam models [7; 8; 9; 10] testify that there is still interest in finding effective solutions to find reduced-order systems to describe complex structures.