## 1 Introduction
In fact, the various types of FEMs for [PERSON]'s beam elements proposed in the literature [23, 24, 25] only present small differences with [PERSON]'s formulation. The most common variant of the FEM is the stiffness matrix method (SMM) [26,27]. This simulation procedure relates the nodal forces and the nodal displacements with the stiffness matrix of the element and it is widely used for the computer analysis of beam-like structures from both a direct [28] and inverse [29] approach. Different authors developed their own stiffness matrices to include the shear effects in the SMM formulations [30, 31, 32, 33, 34]. Unfortunately, these formulations only enable the analysis of the vertical deflections pro  
Figure 1: Support rotation of a beam support according to [PERSON]’s (**a**) and [PERSON]’s beam theories (**b**). duced by shear and neglected the shear rotations. In order to include the effects of shear rotations in the SMM, different authors developed their own models [35; 36; 37; 38]. In these works, specific boundary conditions were considered to remove unnecessary equations from the beam equilibrium system and specific formulations were needed. The applicability of these methods is limited to relatively simple isostatic structures under a limited number of loading cases. Most commercial software (such as Midas/Civil [39] and many others) include [PERSON]'s stiffness matrix to model the shear effects on beam-like structures. Nevertheless, as shown in [PERSON] [34], this matrix only takes into account the effects of shear on vertical deflections. In fact, despite what could be expected, in isostatic structures, the same rotation diagrams are obtained independent of whether the shear effects are considered or not. In the case of statically redundant structures, differences in the rotation diagrams between [PERSON] and Timoshenko models are only due to the changes in the bending diagram produced by the change in reactions at the boundary conditions. These problems in the calculation of the actual rotations might also lead to significant errors in the application of inverse analysis methods to estimate the mechanical properties of the beam elements from measurements on site. This is the case with parametric methods, such as the observability technique, where [PERSON]'s beam theory is traditionally considered for slender beam-like structures [40; 41; 42]. This method was improved to deal with the inverse analysis of deep beams (defined by the Eurocode EN 1992-1-1:2004 [43] as beams with less than three times the overall section depth and by the ACI committee 318 [44] as beams whose spans are equal to or less than four times the depth of the beam). To include the shear effects on the vertical deflections of these structures, the system of equations was upgraded to [PERSON]'s stiffness matrix by [PERSON] et al. [45]. Nevertheless, this procedure presented the same limitations as the rest of the methods based on [PERSON]'s stiffness matrix, as it was not able to evaluate the shear rotations. This characteristic leads to a simulation error [46] in the system of equations that jeopardizes the identification of the right structural properties. To avoid this problem, [PERSON] et al. [47] presented a methodology to calculate the mechanical properties of deep beams with observability techniques, avoiding the use of nodal rotations by using only the values of the vertical deflections measured on site. Despite its important role in both the direct and inverse applications of the SMM, no other works studying the shear rotations on beams were found in the literature. To fill this gap, this paper presents the results of a detailed study of the effects of the shear rotations in both isostatic and statically redundant beams with different slenderness for direct and inverse analysis. To do so, first, a simply supported structure was analyzed to illustrate the errors of traditional structural software in the calculation of the shear rotations.