*3.2. Array-Based Loading System's Load Calculation Method* 3.2.1. Load Point Counterweight Calculation Intervals

The main arch ring has a cross-section with constant width and varying height, and the thickness of the external concrete at different longitudinal positions is not the same. It would be unreasonable to simply distribute the weight of the main arch ring evenly among the various loading points. Instead, the counterweight should be calculated and allocated based on the actual size and weight of the structure near each loading point. The specific calculation method is as follows:

Let the longitudinal coordinates of the centroid of the arch springing plane on the left and right arch feet be 0 and 60, respectively. Denote the longitudinal coordinates of the 29 loading points from left to right as *X* = {*X*1, *X*2, ··· , *X*29}, and the longitudinal coordinates of the midlines between adjacent loading points as *x* = {*x*1, *x*2, ··· , *x*28}. We have

$$\mathbf{x}\_{i} = (\mathbf{X}\_{i} + \mathbf{X}\_{i+1}) \times 0.5, \quad (i = 1, 2, \dots, 28) \tag{3}$$

The counterweight value *F* for the *i*th loading point is

$$F\_i = \begin{cases} 9 \times G\_j(0, \mathbf{x}\_1) & \text{, } i = 1 \\ 9 \times G\_j(\mathbf{x}\_i, \mathbf{x}\_{i+1}) & \text{, } i = 2, 3, \dots, 28 \\ 9 \times G\_j(\mathbf{x}\_{28}, 60) & \text{, } i = 29 \end{cases} \tag{4}$$

In the formula, *Gj*(*xi*, *xi*+1), (*xi*, *xi*+<sup>1</sup> ∈ [0, 60]) represents the total self-weight of all constructed components within the range of the centroid longitudinal coordinates (*xi*, *xi*+1) during the *j*th construction stage.
