Design, construction, and maintenance of large-span bridges require an accurate assessment of the temperature field in flat steel box girders (FSBGs). While this field is controlled by various environmental (meteorological) factors, including temperature, solar radiation, humidity, wind speed, and wind direction, there is no comprehensive model for its prediction based on multiple environmental variables. Given this, two novel methods for calculating the cross-sectional effective temperature (ET) of the FSBG were proposed in this study. Based on the bridge’s environmental variables measured on-site, regression models for predicting ET and vertical temperature difference (VTD) in FSBG were introduced, including a random forest (RF) model and empirical formulas. The RF model’s hyperparameters were derived by the Bayesian optimization algorithm. The proposed approach was applied to the case study of the Sutong Bridge, China, using 2 years’ data samples collected via the bridge health monitoring system and Copernicus Climate Change Service. The model’s training and testing results proved that the predictive performance of the multifactor random forest model significantly exceeded that of the single-factor linear model by about 60%. The RF model’s accuracy in the ET/VTD prediction also outperformed the support vector regression model and back-propagation neural network model. Besides, the correlation analysis of environmental variables revealed a significant time-lag between ET/VTD and the surface solar radiation intensity (about 3 h). The predictive performance of the RF model considering the time-lag effect was further improved (by about 20%–30%).

Construction of suspension bridges and their structural analysis are challenged by the presence of elements (chains or main cables) capable of large deflections leading to a geometric nonlinearity. For an accurate prediction of the main cable geometry of a suspension bridge, an innovative iterative method is proposed in this article. In the iteration process, hanger tensions and the cable shape are, in turns, used as inputs. The cable shape is analytically predicted with an account of the pylon saddle arc effect, while finite element method is employed to calculate hanger tensions with an account of the combined effects of the cable-hanger-stiffening girder. The cable static equilibrium state is expressed by three coupled nonlinear governing equations, which are solved by their transformation into a form corresponding to the unconstrained optimization problem. The numerical test results for the hanger tensions in an existing suspension bridge were obtained by the proposed iterative method and two conventional ones, namely, the weight distribution and continuous multiple-rigid-support beam methods. The latter two reference methods produced the respective deviations of 10% and 5% for the side hangers, respectively, which resulted in significant errors in the elevations of the suspension points. To obtain more accurate hanger tensile forces, especially for the side hangers, as well as the cable shape, the iterative method proposed in this article is recommended.

Comprehensive bridge design should consider simultaneous actions of wind and temperature. The current load combination method of directly superposing extreme wind and temperature actions ignores the correlation between wind and temperature, resulting in too conservative bridge load estimates, and limiting the further development of the bridge span. Therefore, this paper proposes a method to determine the joint distribution of wind speed, wind direction, and air temperature actions on long-span bridges based on trivariate metaelliptical and Plackett copulas. First, the technique of establishing the trivariate joint distribution via trivariate metaelliptical and Plackett copulas is introduced. Next, the conditional joint distributions of wind speed and air temperature under the specific wind directions are derived from these. Using the concept of conditional bivariate Kendall return period (KRP) proposed in this paper, the conditional KRP isolines of wind speed and air temperature for specific wind directions are constructed. Then, conditional joint estimates of wind speed and air temperature actions for several specific wind directions are obtained using the following principle: the conditional bivariate design return period should be equal to the conditional univariate one. The method feasibility is verified by the case study of the Changtai Yangtze River Bridge in China, which is currently under construction and will be the largest cable-stayed bridge in the world. The results show that the joint actions of wind and temperature on the bridge greatly reduce as compared with the simple superposition of extreme wind and temperature actions specified in the design code. Moreover, a significant contribution of wind direction in the above joint distribution on the large-span bridge load is proved.

Triple-tower suspension bridges with two asymmetrical main spans can adapt to complicated terrain conditions. If the top and bottom main cables with different sags are used on the two main spans, the longitudinal constraint on the central tower can be significantly improved, which is more conducive to the promotion and application of three-tower suspension bridges. Based on the widely used multisegment catenary theory, this paper proposes an analytical calculation method to determine the main cable shape in three structural states: completed bridge state, under live load action, and free cable state. In the completed bridge state, each span is solved independently, with the longer main span being calculated first. The two main spans and two side spans require an altitude difference closure condition, while the two anchor spans require an altitude difference closure condition and a splay-saddle moment balance condition. Under live load, due to the media effect of tower displacement and splay-saddle rotation, all spans need to be solved simultaneously. In addition to the conditions of altitude difference closure and splay-saddle moment balance, conditions such as span length closure and main cable unstressed length conservation are required. In the free cable state, due to the media effect of the cable saddle preoffset, all spans need to be solved simultaneously. The solution is similar to that under live load, and thus, it only requires minor modifications of the equations corresponding to live load. During the calculation of these main cable shapes, the deformations and internal forces induced by the live load, together with key construction parameters including the unstressed length of the main cable, the saddle preoffset, the elevations of free cable, and the installation positions of cable clamps can also be calculated. The method proposed in this paper is applied to a double-cable suspension bridge spanned as 248 m + 860 m + 1,070 m + 310 m. The cable shape of the completed bridge is determined first. Subsequently, the deformations and internal forces under live load are calculated for two cases: live load covered in the longer main span and live load covered in the shorter main span. Finally, the cable shapes and construction parameters of the two free cable states, that is, the bottom-cable-only state and the double-cable state, are calculated. This example is employed to verify the effectiveness of the approach presented in this paper. Some useful conclusions are also obtained, which lays the foundation for the promotion of this bridge type.

Finding the main cable shape is an essential step in the design and construction of suspension bridges. In this paper, shape-finding and force-assessment of suspension bridges based on loop adjustment are proposed and realized via the finite-element method. Here, loop adjustment refers to the process where the appropriate adjustment coefficient is chosen based on the results of the last modeling and deviations from the design goals to approach the target main cable shape gradually and to satisfy the design requirements. This method adopts a full-bridge model, which provides the comprehensive account of interactions between different components of the suspension bridge, including towers and stiffening girders, as well as the effect of tower compression and splay saddle rotation. Based on the full-bridge model in the completed bridge state, the inverted removal method is used for the calculation of key construction parameters in the free cable state, such as prebias of tower saddles, predeflected angle of splay saddles, and installation position of cable clamps. The proposed method’s feasibility and effectiveness are verified by its application to two particular suspension bridges, namely, the Great Belt Bridge (Denmark) with a main span of 1,624 m and the Jindong Bridge over the Jinsha River (China), with a main span of 730 m. Results of shape-finding and force-assessment both have good accuracy, which are generally consistent with those obtained by other methods.

The cable configuration of a suspension bridge is very sensitive to temperature changes. On the basis of multisegment catenary theory in combination with the conditions of geometric compatibility, mechanical equilibrium, and conservation of the unstrained cable length, an analytical method is proposed to model the temperature sensitivity of the cable configuration of suspension bridges. The main considerations were the elevation of the main cable and installation positions of cable clamps. The proposed method can adapt to different construction states (the completion state of the bridge, the free cable state, and the datum cable strand), boundary conditions (considering or not considering the saddle arc), and the stiffness of the towers (considering or not considering tower bending deformation). It is possible to switch between different cases by changing only a few parameters. An engineering example analysis was then performed for a suspension bridge with a main span of 730 m, which demonstrated the feasibility and effectiveness of the proposed method. The results showed that the deformation of the suspension bridge had a linear relationship with temperature. The construction state and bending deformation of the towers had a large impact on the temperature sensitivity coefficient of the main cable elevation. The bending deformation of the towers aggravated and lessened the temperature sensitivity coefficient of the main cable elevation for the main span and side span, respectively. The temperature sensitivity coefficient of midspan point elevation of the main cable correlated negatively to the span length. The maximum temperature sensitivity coefficient of the installation position of the cable clamp occurred near the interquartile point of the main span.