# Temperature Effects on the Natural Frequencies of Composite Girders
## 5 Summary and Conclusions  
In this study, the effects of temperature on the natural frequencies of composite girders were investigated. For this purpose, a specimen simulating a composite girder was fabricated, and modal tests were conducted by varying the temperature of the top deck. FE simulations were conducted to verify the test results and analyze temperature effects. Based on the test and simulation results, the following conclusions were drawn:  
1. The natural frequency of the composite girder tended to decrease, as the temperature of the top deck increased. The frequency decreased at a rate of 0.36% per degree according to the linear regression analysis of the test data in a range of 20-50 \({}^{\circ}\)C. The standard deviation of the linear model was 0.038 Hz.
2. The decreasing tendency of the frequency was primarily caused by the temperature dependency of the elastic modulus. Without this dependency, the frequency increases with temperature. It was presumed that the convex-shaped deformation induced by the temperature gradient increased the flexural stiffness of the composite girder such that the natural frequency increased. The frequency increased by up to 0.1%, as the temperature increased from 20 to 50 \({}^{\circ}\)C with a simply supported boundary condition. Considering the fact that the frequency decrease rate was 0.36% per degree, the effect of increased stiffness was negligible in the simply supported composite girder.
3. The specific heat and the thermal conductivity of steel are also dependent on temperature. They affect the natural frequency with temperature changes; however, the maximum difference in the case considering these temperature dependencies was only 0.03%. Therefore, they are not comparable to the elastic modulus effect.
4. The linear regression model exhibited a maximum frequency difference of 0.06% compared to the detailed FE simulation results at 20 \({}^{\circ}\)C, which decreased as the temperature increased. The difference fluctuated with temperature, which can be attributed to the nonlinear nature of the changes in specific heat with temperature.  
Figure 13: Differences in frequency compared to the FE model incorporating the temperature dependencies of the elastic modulus, the specific heat, and the thermal conductivity.  
The proposed linear regression model is an initial model designed to exclude the effects of temperature on composite girders. The model is based on simply supported boundary conditions and only covers a temperature range of 20-50 \({}^{\circ}\)C. Therefore, further research is required to develop a generally applicable model.  
J.K. and B.H.C. conceptualized the test set up and procedures; A.P. performed tests and simulations; A.P. wrote the draft for the article; S.K. and B.H.C. gave advices on the tests and simulations; J.K. supervised this research program and finalized the article. All authors have read and agreed to the published version of the manuscript.  
This research was supported by Basic Science Research Program of the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2021R1 IIA3049510).  
Not applicable.  
Data availability Statement: Data are available from the authors upon reasonable request.  
The authors declare no conflicts of interest.