## 1 Introduction  
For multi-point continuous incremental launching construction, the structural system undergoes continuous changes from a continuous beam to a cantilever beam, resulting in complex structural forces. Therefore, analyzing the forces on the beam during the incremental launching process is particularly important. [PERSON] [1] simulated and analyzed the entire process of a large-span steel truss incremental launching construction. The results showed that the finite element method can effectively predict the pushing force on the foundation and temporary piers during the incremental launching process. [PERSON] [2] analyzed the maximum stress distribution and deflection deformation during the incremental launching process of a tied arch and a guiding beam. The research results indicated that within the range of the guiding beam, the end of the guiding beam exhibited the most unfavorable deflection. It is necessary to control the overall rigidity of the guiding beam and the vertical adjustment of the devices on the auxiliary piers to avoid a collision between the guiding beam and the piers. [PERSON] [3], in order to address the complex local stress changes in the incremental launching construction of wide steel-box girders, conducted a dynamic simulation analysis during the construction process. The experimental results showed that the stress and local stability coefficients of the steel-box girder met the relevant specifications and had sufficient safety reserves. [PERSON] et al. [4] established a finite element model for the incremental launching construction of an open steel-box girder and analyzed the stress and strain during the process. The research found that the incremental launching method for open steel-box girders can effectively ensure structural stability. [PERSON] et al. [5] collected stress response data of steel plate girders under local loads during an incremental launching construction, using parameters such as web thickness, web length, flange width, and thickness as feature vectors and applied the XGBoost algorithm to predict the local stress of the girders. In the incremental launching construction, it is easy to have the problem that the incremental launching equipment at each point does not work synchronously. When the vertical jack lifting stroke is different, the base plate will have an angle with the horizontal plane; when the pushing strokes of the horizontal jacks are different, the beam axis will experience a lateral offset [6]. The above phenomena will lead to a change in the contact position, which has a great influence on the local stress of the beam. [PERSON] [7] simulated the phenomenon of lateral deviation and an inconsistent jacking height of the beam during various incremental launching construction processes and analyzed the stress variation patterns. The results showed that the stress of each component increased as the lateral offset value and jacking height difference increased. [PERSON] [8] simulated the stress change in the beam when the jacking point had a lateral offset, longitudinal offset, and vertical height inconsistency. It was found that the stress of the component in direct contact with the incremental launching equipment was greatly affected by the asynchronous jacking. The hazards of unsynchronized jacking were demonstrated by simulating extreme conditions of a lateral offset (where the base plate stiffeners disengaged from the contact area, and the support reaction was borne solely by the base plate). [PERSON] [9], through an analysis of the impact of unsynchronized jacking on the stress of various components of the beam structure, found that the stress variations in different components exhibited varying levels of sensitivity to unsynchronized jacking. [PERSON] [10] suggests that the lateral offset value, which causes a sharp increase in the maximum local stress of the beam structure, should be used as the control threshold for a lateral offset during an incremental launching construction.