# Seismic Responses of a Cable-Stayed Bridge with Consideration of Uniform Temperature Load
## 1 Introduction  
In recent decades, cable-stayed bridges have been favored by bridge engineers due to their aesthetic configuration, fast and economical construction, and efficient utilization of materials. However, bridges of this type are susceptible to seismic excitation due to their low damping ratios and flexible components. Meanwhile, the effects of uniform temperature changes on the responses of cable-stayed bridges are significant due to their long spans. However, the concurrent of uniform temperature and earthquake loads are not considered in current design specifications. Therefore, it is necessary to investigate the seismic responses of cable-stayed bridges subjected to earthquake and uniform temperature. The seismic behavior of cable-stayed bridges has been extensively investigated by many researchers in the past two decades. The impacts of near-fault ground motions [1; 2] on the seismic responses of cable-stayed bridges were concerned by scholars, and different isolation devices [3; 4; 5] were designed to alleviate these influences. The nonlinear dynamic responses of cable-stayed bridges [6; 7; 8], including cable sag, geometry change of the whole bridge, soil-structure interaction, etc., were widely investigated due to the geometric and dynamic properties of these bridges. Passive control, as an effective seismic mitigation strategy, has been frequently used for seismic isolation of cable-stayed bridges in recent years [4; 9; 10; 11; 12; 13]. The isolation systems can be approximately divided into four types:isolation bearings, cable restrainers, dampers, and innovative devices. The seismic isolation of these devices can be attributed to lengthening the fundamental period of structure or absorbing input seismic energy. For example, [PERSON] and [PERSON] [14] adopted a passive control system consisting of hysteretic devices between the deck and piers of a cable-stayed bridge, and these devices not only dissipate the seismic energy introduced into the structure, but also shift the natural frequencies of the bridge far from the most dangerous input frequencies. The effects of temperature on the vibration properties of long-span bridges have attracted the attention of researchers in recent years. These studies [15; 16; 17] mainly focus on the correlations between temperature and dynamic properties of these bridges, including frequency, mode shapes, and damping ratio. It is found that temperature is a critical source causing the variability of vibration properties of long-span bridges, and there is an overall decrease in modal frequency with the increase of temperature for these bridges. Some researchers [18; 19] investigated the response of elastic cables with flexural-torsional stiffness and thermal effects, the result shows that the stresses within the boundary layers of cables will be significantly underestimated without consideration of flexural-torsional stiffness and thermal effects and their influence on the frequencies of cables. These effects will not only influence the dynamic behaviors of cables, but also the global dynamical response of whole bridge. This paper will mainly consider the impacts of thermal load on the seismic responses of a cable-stayed bridge. However, the concurrent of temperature and earthquake loads are usually not accounted in bridge design specifications. Some researchers have started to investigate the combination of these two loads. [PERSON] and [PERSON] [20] adopted Turkstra combination method to calculate the combination coefficient of temperature and earthquake loads, and the actions of these two loads are considered as stochastic variables with their own probabilistic distributions respectively. [PERSON] and [PERSON] [21] proposed a load combination that added uniform temperature load to the existing extreme event load combination. It is found that pylon reactions and deck axial forces are more vulnerable to concurrent loadings for cable-stayed bridges of longer spans.