# Observing Material Properties in Composite Structures from Actual Rotations
## 2 Materials and Methods
Since the COM method was based on [PERSON]'s SMM, it was not able to consider the effects of shear deflections. This problem was solved by [PERSON] et al. [43], who introduced the effects of shear deformation into the COM process. Due to a lack of considering the shear rotation in SMM, COM is not able to observe the value of the material properties correctly when rotations are included into the measurement sets. This method is not suitable for measuring rotations as wrong results are obtained even in noise-free measurements when these types of deformations are considered. [PERSON] studied the effects of this impotence in considering the shear rotations in SSI methods based on SMM [44]. It showed the effects of neglecting the shear rotation in the inverse analysis were not negligible, even in the cases where beams cannot be considered deep beams (based on Eurocode EN [13] and by the ACI Committee 318 [14]). In this section, a new procedure is developed to take into account the effects of shear rotations in the SSI of two-dimensional structures modeled with beam elements. Providing that a static load test is performed in a structure and measurements are taken from some nodal displacements (total deflections and rotations including bending  
Figure 2: Flow chart of structural system identification by COM. and shear displacements and rotations), the first step will be trying to separate the bending and shear rotations. Then, the direct analysis is performed assuming those beam elements have their theoretical mechanical properties. Then, the shear rotation of each element is calculated based on the assumed mechanical properties. Equation (4) can be used to calculate shear rotation vs. in each element based on [PERSON]'s beam theory. \[\mathrm{W_{s}}=\frac{Q}{A_{v}*G} \tag{4}\]  
where \(\mathrm{A_{v}}\) is the shear area, \(\mathrm{Q}\) is the shear force, and the shear modulus \(\mathrm{G}\) might be written as:  
\[\mathrm{G}=\frac{\mathrm{E}}{2(1+\mathrm{v})} \tag{5}\]  
where the coefficient \(\mathrm{v}\) refers to the Poisson's ratio. According to Equation (4), the shear rotation for each element only depends on shear forces, shear area, and shear modulus. On the other hand, shear area and shear modulus are directly obtained from the assumed mechanical properties of the structure, while the shear forces can be obtained from the results of the direct SMM analysis. By subtracting the value of shear rotation from the measured rotation of each node the bending rotation can be obtained (it is important to highlight that the measured rotation can be expressed as the sum of shear and bending rotations). Therefore, the COM process can be used as it is based on neglecting the shear rotation effects. Once COM provides an estimate of the mechanical properties of the structure, these can be used to calculate new shear rotations. In this way, an iterative process should be performed until the adequate structural response of all the elements is satisfied. In order to limit the computational cost of the optimization process, the stopping criteria are defined: (1) when the iterative process is performed more than 200 times without leading to an improvement of the solution, and (2) when the difference between the values of the observed structural properties in 2 subsequent iterative steps are less than \(1\times 10^{-3}\). The main steps of this procedure are described as follows:  
Step 1: Assume the initial values of the structural properties as the theoretical ones  
Step 2: Calculate the shear rotation of each element from the assumed structural properties and static loads. It is important to highlight that the stiffness properties can be obtained through either theoretical values (for the first time) or observed structural properties provided by the COM optimization (in the iterative process). Step 3: Obtain the bending rotation from the calculated shear rotation in Step 2 and perform COM analysis.