Analytical Investigation of the Vibration Performance of Tie Rods with Sensitivity Analysis of Effective Factors on Beam Frequency

The historical application of tie rods in historical buildings was used in the past to ensure the stability of arches and vaults against gravity and horizontal loads. Therefore, the necessity of tie rod health monitoring is a prevalent subject in the vulnerability assessment of historical buildings. The main purpose of this research is to evaluate the dynamic characteristics of tie rods. Also, the eect of several parameters, such as known and unknown boundary conditions, length and cross section, exural stiness and axial load, on fundamental frequency, has been evaluated. As a result, after a series of analytical modeling, practical graphs for three types of beam end connection have been developed. It is possible to calculate axial force with the fundamental frequency of in-situ testing with the proposed graphs. Results showed that the frequency is sensitive to all the aforementioned factors. For instance, under known boundary condition, the eect of the support type is more tangible for long span beams. Also, under constant tensile stress, changes in the boundary condition of tie rods with small cross sections did not aect the frequency considerably. Furthermore, length factors for a pinned-pinned beam with small tensile force are not sensitive in comparison with other support conditions. Comparison of analytical results of axial load and exural stiness with experimental data of reference 1, showed an acceptable conformity between them. The maximum error for tensile stress was calculated as 12%. This error was 5% for compressive stress. Furthermore, analytical exural stiness approached a full rigid support condition, while tensile force increased. This is due to the geometric eect of tensile force on the stiness matrix of the beam. Also, for unknown boundary conditions, estimated buckling force, regarding Newmark's analytical formulation, had 3.1% error, with the corresponding force from in-situ dynamic testing obtained from reference 1.