Resumen de Application of observability techniques to structural system identification including shear effects,
EmadiAccording to Timoshenko’s beam theory, nodal rotations in beam-like structures are produced by bending and shear effects. On the one hand, bending rotations can be easily calculated by the Euler-Bernoulli stiffness matrix method. On the other hand, shear rotations are traditionally neglected as their effects are practically negligible in most structures. In addition, calculating the shear rotation effects by the stiffness matrix method is not straight forward tasks and it presents practical limitations. Nevertheless, this assumption might lead to significant errors in the simulation of the structural response of some structures (such as deep beams and composite structures). The shear effects are also neglected in the inverse analysis of structures (Structural System Identification) used to calibrate the mechanical properties of the structural elements from the monitoring on-site. Recently, one of the first methods for the inverse analysis of structures including the shear effects (the Observability Method, OM) was presented. This method introduced Timoshenko’s beam theory into the Stiffness Matrix Method (SMM). In this way, the vertical deflections produced by shear effects were included into the simulation while the shear rotations were neglected. In this method, the mechanical properties of the structures could be obtained from the nodal deflections measured on static tests on site. One of the main controversial features of this procedure is the fact that the measurement set must include rotations. This characteristic might be especially problematic in those structures where rotations due to shear are not negligible. In fact, in this case, neglecting the shear rotations might lead to significant errors. This simplification might be especially problematic in those structures where only rotations can be measured. In addition to the OM, some other inverse analysis methods including shear deformation effects have been recently presented in the literature. Nevertheless, all these methods also fail to deal with the shear rotation effects, as they only take into account in the system of equations the vertical deflections produced by shear. Therefore, when actual rotations on site are used estimations with significant errors can be obtained. To fill these gaps, this Ph.D. Thesis deals with the analysis of the effects of the shear deformations in beam-like structures from a direct and inverse approach. First of all, the SMM is updated to enable the calculation of the shear rotations from a direct analysis. This method is used to evaluate the effects of the shear rotations in beam-like structures with different slenderness ratios. In addition, for the first time in the literature, the slenderness ratios where the shear rotation effects can be neglected from a direct analysis are identified. Secondly, the OM is updated to enable the inverse analysis of structures with shear effects from measurement sets with only vertical deflections. This modification is based on the introduction of a numerical optimization method. With this aim, the inverse analysis of several examples of growing complexity are presented to illustrate the validity and potential of the updated method. Finally, the OM is modified to enable the inverse analysis from shear rotations. This modification is based on the introduction of a new iterative process to estimate successively the values of the shear rotations. To illustrate the applicability and potential of the proposed method, the inverse analysis of several examples of growing complexity is presented. A set of calculation recommendations and future researches are also proposed.
