3.2.3. Optimization of Load Application Points' Weighting Values

In comparison to the original bridge, the model bridge design exhibits an increase of 12.30~30.27% in the cross-sectional areas of steel tubes, an increase of 7.42~23.77% in the chord members in the cross-sectional areas, a thickening in specific regions of the external concrete web, and additional thickening of the concrete near the steel tubes. Applying a nine-fold weighting value as per the model bridge would be unreasonable; thus, optimization of the weighting values for each load application point at various construction stages is required.

Given that the design of the model bridge, in comparison to the original bridge, only features scaling up without scaling down, the load value at each application point is determined based on the model bridge. These load values exceed the theoretical weighting values for the original bridge after scaling down, which prompts the introduction of the concept of a weighting reduction factor. This factor is defined as the ratio of the required weighting values for the actual model test design and the original bridge at a 1:10 scale without any modifications to component dimensions. During calculations, the following principles should be followed for the weighting reduction factor:


Thus, in the *i*th construction stage, the weighting reduction factor *Ps*(*i*, *j*) for the *j*th load application point can be calculated using the following formula:

$$P\_s(i,j) = \frac{\sum \rho\_1 A\_1 + \sum \rho\_2 A\_2}{\sum \rho\_0 A\_0} \tag{5}$$

In this formula, ∑ *ρ*0*A*<sup>0</sup> represents the sum of the product of the component area and the corresponding material density near the *j*th load application point of the model bridge in the *i*th construction stage; ∑ *ρ*1*A*<sup>1</sup> represents the sum of the product of the overall force-bearing component area and the corresponding material density near the *j*th load application point of the model bridge in the *i*th construction stage; and ∑ *ρ*2*A*<sup>2</sup> represents the sum of the product of the cross-sectional area and the corresponding material density of the original bridge's localized force-bearing components, which have been scaled down to 1:10, near the *j*th load application point in the *i*th construction stage.
