# Stressing State Analysis on a Single Tube CFST Arch Under Spatial Loads
## 1 Introduction  
Concrete-filled steel tubular (CFST) arches, which consist of thin-walled steel tubes and concrete cores, are gaining more and more popularity in bridge construction because of their high bearing capacity, light self-weight, and convenient construction [1; 2]. The thin-walled steel tube could provide effective confinement for the concrete core and significantly improve its compressive performance and ductility; meanwhile, the concrete core can also provide restraint to improve the local buckling of the steel tube [3]. Therefore, CFST arches are considered good alternatives for reinforced concrete bridges or steel arch bridges. The well-bonded steel tube and concrete core composite cross section can provide enough structural stiffness and strength in practical application. Furthermore, the steel consumption can be minimized to reduce project cost [4]. The composite members have hitherto been constructed throughout the world with rapid development because of the mutual promotion between concrete and steel tubes [5; 6]. Especially in China, more than 400 CFST arch bridges have been built or are currently under construction [7]. As the development of CFST arches is fast-growing, the working behavior of CFST arches is of more and more concern. Over the last 20 years, many researchers have paid attention to the in-plane stabilities of CFST arches and obtain important achievements. Theories and methods were proposedto investigate the stability of arches. Furthermore, experimental analysis were conducted [8; 9; 10; 11; 12]. Some simplified formulas were also proposed to evaluate the load-bearing capacity of arch bridges [13]. As for out-plane stability of the CFST arches, research findings are quite limited. [PERSON] [14] carried out the experimental study on a CFST (single tube) arch with one rib under spatial loads and laid the foundation for future research on the spatial load-carrying capacity of CFST arches. [PERSON] et al. [15] used the finite element (FE) method to carry out the dual non-linearity analyses for CFST arches with a single rib under spatial loads and found that the influence of geometric nonlinearity increased, compared to arches under in-plane loads. [PERSON] [16] analyzed the out-plane stability of CFST arches and proposed corresponding design formula. [PERSON] et al. [17] established a co-rotational formulation in the setting of finite elements for three-dimensional nonlinear analysis of ultimate bearing capacity of a circular CFST arch subjected to in-plane and out-plane loads, considering both geometric and material nonlinearities. [PERSON] et al. [18] analyzed the out-plane elastic stability of typical tube CFST arch bridge by FE method, and the results indicate that the FE model, based on the statistical data, could reflect the working performance of the structure. [PERSON] et al. [19] presented a self-adaptive method of elastic modulus reduction to evaluate the ultimate load bearing capacity of CFST arch bridges. [PERSON] et al. [20] proposed designing equations on the basis of the FE analysis to predict the ultimate loads of CFST arches. As noted, the limited research in the open literature indicates that there are a shortage of sufficient large-scale experiments on CFST arches to analyze the complex out-plane working behaviors and instability mechanisms [21]. The high experimental cost confines the development of research to some degree. Furthermore, the experimental data are always not fully utilized, leading to the negligence of extensive unseen information of structural working behavior characteristics. It is significant to use appropriate methods to analyze the working behavior of CFST arches on the basis of existing experimental data. Besides, in the simulation analysis, the FE models are simplified on the basis of assumptions. Consequently, the calculation results are deficient in universality and conservative in application, leading to the overuse and/or irrational use of materials.