## 5 Model Updating for the Segmental Beam  
### Parametric Sensitivity Analysis  
Parametric sensitivity analysis for selecting the parameters to be updated is conducted to determine which model parameters significantly affect the neutral axis locations and static displacement responses, before updating the original segmental beam model. The geometric parameters of the prestress tendons are measured, and therefore not considered in the model updating analysis. For the segmental beam model, the model parameters, including three material parameters and two joint parameters, are selected as the parameters to be updated. The geometric parameters of the prestress tendons are measured and therefore not considered in the model updating analysis. The selected material parameters comprise the elastic modulus of concrete Ec, density of concrete pc, elastic modulus of the prestress tendon Ec, normal contact stiffness factor NSct, and tangent contact stiffness factor TSct. NSct and TSct are the scale parameters of contact stiffness. In ANSYS, for the normal contact stiffness, there are two possible approaches to determine their values, which include defining a stiffness factor NSct that acts as a scale factor of the contact stiffness Kn, or specifying the magnitude of the contact \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Static Loads (kN)** & **EL\({}_{1}\) (mm)** & **ML\({}_{1}\) (mm)** & **RE (\%)** & **EL\({}_{23}\) (mm)** & **ML\({}_{23}\) (mm)** & **RE (\%)** & **EL\({}_{4}\) (mm)** & **ML\({}_{4}\) (mm)** & **RE (\%)** \\ \hline \(15\) & \(-0.80\) & \(-0.83\) & \(3.75\) & \(-1.03\) & \(-1.01\) & \(-1.94\) & \(-0.94\) & \(-0.84\) & \(-10.64\) \\ \(20\) & \(-1.04\) & \(-1.11\) & \(6.73\) & \(-1.35\) & \(-1.4\) & \(3.70\) & \(-1.27\) & \(-1.12\) & \(-11.81\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the deflections between experimental tests and numerical analysis. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Prestress** & **ENAL2** & **MNAL2** & **RE (\%)** & **ENAL3** & **MNAL3** & **RE (\%)** \\
**Force (kN)** & **(mm)** & **(mm)** & **(mm)** & **RE (\%)** & **(mm)** & **(mm)** & **RE (\%)** \\ \hline \(62\) & \(305.05\) & \(301.55\) & \(-1.15\%\) & \(314.72\) & \(308.85\) & \(-1.87\%\) \\ \(107\) & \(297.54\) & \(290.36\) & \(-2.41\%\) & \(303\) & \(298.08\) & \(-1.62\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of the neutral axis locations between the experimental and numerical results. stiffness Kn directly. It is not evident if the determined stiffness value from these approaches is correct or reasonable for each contact problem since the value of the contact stiffness Kn is determined by certain parameters, such as Young's modulus, contact area, and scale factor NSct. Thus, scale factors are used to define the stiffness of the contact elements. For the normal contact stiffness, the normal stiffness factor NSct has a range of 0.01-1.0. The default value in ANSYS is 1.0, and a higher stiffness value leads to a lower amount of penetration or slip [29]. The method for selecting more influential parameters from these candidate parameters is based on the sensitivity analysis, where the corresponding change in the structural displacement responses and neutral axis locations is calculated when there is a 10% change in these parameters. The sensitivity analysis results are given in Table 7. When the sensitivity of displacement responses is greater than 2%, and the sensitivity of neutral axis position calculated from S2 and S3 is larger than 0.03%, the corresponding structural parameters are considered as candidate parameters for model updating. Based on the aforementioned criteria, it can be observed from Table 7 that the elastic modulus of the concrete and prestress tendons have significant influences on the displacement response and the neutral axis location. The density of concrete affects the displacement responses more significantly than that of the neutral axis location.