**4. Finite element analyses and model updating**

To validate the experimentally identified dynamic characteristics, finite element models of the bridges are constituted in the SAP2000 and ANSYS [25, 26] software. With modal analyses, the natural frequencies and related mode shapes are obtained (**Figure 25**). The analytically identified natural frequencies are summarized in **Table 7**.

It is seen that ambient vibration measurements are enough to identify the most significant modes of all bridge types. There is a good agreement between natural frequencies and corresponding mode shapes. The maximum differences are obtained as nearly as 10–20%. To eliminate these differences, the finite element models of the bridges should be updated by changing some uncertain parameters such as material properties, boundary conditions, section areas, etc. It can be evaluated that the maximum differences are reduced from 10–20 to 2–5% after model updating. More information can be found in the literature [11, 12, 15–18, 20–24, 27].

Also, to display the model updating effect, dynamic responses of the bridge are performed before and after model updating. It is seen that this procedure has vital importance to represent the real structural behavior. More information can be found in the literature [11, 12, 15–18, 20– 24, 27].

**Figure 25.** The finite element models of the bridges with first mode shapes.


**Table 7.** Natural frequencies identified by finite element analyses.
