In cable-stayed bridges, especially asymmetric bridges, counterweights are always made to work together with cable pretension forces to get a reasonable finished state. To solve the optimization problem of the cable-stayed bridge considering the counterweights, the integrated optimization method (IOM) for estimating cable forces and counterweights is proposed. In this method, the counterweights are proposed to act on the anchor points. After that, the summary of the minimum weighted total bending energy and the summary of the counterweights are considered as two objective functions of a multiobjective problem. Finally, the dynamic weighted coefficient method is used to solve this problem and realize the Pareto solution set. IOM presents detailed procedures in a simple numerical model and is then applied to the Yong-ding special-shaped cable-stayed bridge. The results show that not only IOM can realize the priority selection of the loading position of the counterweights but also get a better reasonable finish state because of the introduction of the counterweight dimension; the dynamic weighted coefficient method can quickly find the Pareto optimal solution set and be further screened by decision-makers; counterweight is very helpful to reduce torsion and other spatial effects in cable-stayed bridges. IOM can be used as a universal optimization method for cable-stayed bridges.

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Rapid construction of ripple web (RW) is a new construction technology that can be applied to the prestressed concrete (PC) box girder bridge with corrugated steel webs (CSWs). In order to analyse the mechanical behaviour in the construction process when the RW method is applied, the main bridge of Zhao-Jun Yellow River Super Large Bridge was adapted as the engineering background, and a three-dimensional simulation finite element model was established. Thereafter, detailed mechanical analyses were carried out for CSWs, top concrete and bottom concrete, lining concrete, temporary support and other structures in the construction process when the RW method was used. The results reveal the excellent quality of the mechanical properties of the structure, thus indicating the structure's safety and reliability. This study can provide a reference for similar research and have a positive impact on the further promotion of the RW method for application in the continuous girder bridge with CSWs.

To study the probabilistic distribution of maximum wheel unloading rate of high-speed trains and its temporal correlation when a train passes over a bridge, a method for the estimation of the extremal index is proposed. Using the time series threshold theory, the maximum value cumulative distribution function (CDF) when the wheel unloading rate is regarded as a time series is derived and validated. This approach can also address dependent series, which the traditional probability distribution function formulas could not. Then, the difference between treating the wheel unloading rate as a time series and independent series is investigated using Monte Carlo simulations. Finally, the influence of the number of calculation steps on the threshold is studied, and the differences between thresholds calculated by different extremal indices when considering the number of trains running during the service period of the bridge are explored. The maximum value CDFs of the wheel unloading rate for different track irregularities, bridge lengths, and vehicle speeds are investigated for a three-span simply-supported bridge. The results show that the differences in the maximum value probability density functions (PDFs) obtained by considering the wheel unloading rate as time series and independent random series cannot be ignored. However, when studying a high-confidence level problem, such as the threshold of the wheel unloading rate, the difference between the two approaches is small enough. As the number of calculation steps increases, the extremal index will gradually decrease. When considering a long-distance high-speed rail line, its shorter segment can be used to study the threshold of the wheel unloading rate.