## 1 Introduction  
In half-through and through arch bridges (HTABs and TABs), bridge decks are connected to arch ribs by hangers. Hangers transfer loads from the bridge decks to the arch ribs and they are arranged evenly along the longitudinal directions of bridges to transmit the load on the bridge decks to the arch ribs uniformly. HTABs and TABs have long been considered to be safe and reliable structural patterns. However, in the past few decades, many HTABs and TABs with floating deck structures have failed due to the sudden failure of their hangers [1; 2; 3], such as Nanmen Bridge (2001) (as shown in Figure 1a), Peacock River Bridge (2011), Gongguan Bridge (2011), and Nanfang'ao Bridge (2019). It is clear that corrosion and fatigue are the main factors that lead to the fracture of tension-resisting elements in hangers and further cause the sudden failures of bridge hangers [4; 5; 6; 7]. In recent years, some scholars have suggested that, besides corrosion and fatigue, the bending deformation of both end-fixed hangers might be an important factor in the sudden failure of hangers [8; 9; 10]. The bending stress that is caused by the bending deformation (as shown in Figure 1b) of hangers could accelerate the corrosion rates of the tension-resisting elements in hangers and, therefore, shorten the lives of hangers significantly [11; 12; 13]. However, bending stress is difficult to correctly measure in hangers using sensors and few numerical studies have been conducted on bending stress. Therefore, it remains difficult to further study the effect of bending on the corrosion and fatigue of hangers. Besides bending stress, the strength and fatigue properties of tension-resisting elements under bending are poorly understood; these elements may be greatly weakened by bending deformation, but only a few scholars have studied this topic. The neglect of the decrease on properties of tension-resisting elements in hangers might lead the safety of hangers is overrated under bending. According the above literature review, it is of great necessity to conduct a detailed study on the bending stress of hangers and the strength and fatigue properties of tension-resisting elements in hangers under bending deformation. In this paper, the types of hangers, the boundary conditions, and arch bridge structures are first discussed. We propose that end-fixed hangers consisting of parallel seven-wire strands (or hangers could be simplified as both end-fixed hangers) have sufficient bending stiffness to bear the bending moment. Moreover, it is found that HTABs and TABs with floating deck structures can cause a significant lateral bending to hangers. Therefore, the bending stress of HTAB and TAB hangers with floating deck structures and the strength and fatigue properties of seven-wire strands are studied. Firstly, the two possible factors of the bending of hangers, the longitudinal deformation of the deck, and the rotation of deck are discussed. The floating deck structure is only connected to the arch ribs by hangers and bearings at both ends allow for the deck to produce longitudinal deformation and rotation. In this case, the bridge deck can produce significant deformation along the longitudinal direction of the bridge under the effect of temperature and rotate under the effect of the temperature gradient [14]. The deformation of arch ribs would be restricted at skewbacks and there would be difference in longitudinal displacements between the arch and deck. The different displacements at both ends of hangers and the rotation of the bridge deck will cause bending deformation of hangers  
Subsequently, the theoretical formulations for the bending angles and maximum bending stress of hangers caused by the effects of temperature and the temperature gradient are developed. The finite element method (FEM) then verifies the accuracy of the formulas for bending angles and the maximum bending stress of the hangers.