# Observing Material Properties in Composite Structures from Actual Rotations
In this theory, rotation between the cross-section and the bending line is allowed. The differences between methods in a simply supported beam with concentrated load, V, at the mid-span are presented in Figure 1, where [PERSON]'s beam theory (Figure 1b) and [PERSON]'s beam theory (Figure 1c) at the zoomed support of Figure 1a can be seen. The finite element method (FEM) is a numerical technique employed in engineering and computational science to solve partial differential equations and simulate physical phenomena. This approach entails the subdivision of a complex problem or domain into smaller, more manageable subdomains or elements, with the approximation of the solution within each element. This technique is a common method for computer-based analysis in engineering [16]. The stiffness matrix method (SMM) is one of the major methods of the FEM approach for analyzing the structural response of beam-like structures. The literature review showed that a number of SMM approaches included shear rotation into their SMM  
Figure 1: (**a**) A simply supported beam with a zoomed support. (**b**) [PERSON]’s beam theory on the beam support. (**c**) [PERSON]’s beam theory on beam support. formulations [17; 18; 19; 20; 21; 22]. However, most of these methods fail to simulate structural cases with discontinuities in the cross-sections, with non-collinear elements, or with non-uniform loads. The only SMMs that are able to analyze these models are the FEMs in which nodal variables are the bending rotation and transverse displacement (the effects of shear rotation are neglected in this SMM formulation). Many works, for instance in [PERSON] [23], contain a detailed formulation of the common Timoshenko beam theory SMM. The stiffness matrix presented in this approach overlooks the effect of the shear rotation. [PERSON] [24] highlighted the neglect of the shear rotation effects in some widely used commercial simulation software that rely on the stiffness matrix, such as SAP 2000, CSI 2016, and Midas Civil 2015. In fact, these programs only include the shear effects into the vertical deflections. However, it has been traditionally assumed that shear rotations have minimal practical significance in most structures. This assumption can introduce significant errors in the determination of the mechanical properties during the inverse analysis of structures that lack a unidimensional geometry, such as deep beams, laminated composite walls, or sandwich structures. In such cases, shear deformation can play a crucial role, and it is essential to incorporate its effects into the formulation. System identification (SI) represents a modeling process for unknown variables in a certain system of equations used in numerous engineering fields [25; 26; 27]. The SI goal is to be able to characterize adequately the parameters of a certain system. Since its introduction, SI has been extended to most engineering fields [18; 28]. Structural system identification (SSI) can be framed in the context of the SI that deals with the design of mathematical models for identifying structural parameters (such as the flexural or the axial stiffnesses) [29]. In the literature, many methods for SSI are proposed. Most of them are based on the SMM (see, e.g., [30; 31; 32; 33; 34]). The details of the main SSI methods are shown in the literature and addressed by [35]. Most SSI methods are not able to quantify correctly the structural parameters when shear effects are not negligible. This can be explained by the fact that most SSI methods based on SMM normally use [PERSON]'s beam theory (see, e.g., [36; 37; 38]), this assumption underestimates deflections and overestimates the natural frequencies since the shear effects are disregarded [39]. The effects of shear deformations in their SMM models are studied by some authors [8; 40]. Although the assumption of neglecting shear rotations may lead to wrong estimations for mechanical properties in SSI methods, normally these effects are overlooked.