## 1 Introduction  
As an important piece of load-bearing equipment in the oil platform system, the derrick is key to ensuring oil and gas drilling. In an offshore operation, complex loads such as the hook load, stand load and wind load play a crucial role in the structural strength and reliability of the offshore derrick. It is necessary to evaluate its safety and reliability under complex loads, providing a reliable guarantee for oil and gas drilling. To prevent failure and potential hazards, the strength safety of the derrick, as a typical piece of steel structure equipment, should be paid attention to firstly. Some relevant studies have been conducted. The stress and displacement variation of the double derrick at different sectional parameters under typical working conditions have been explored in [1]. Considering the hook load, wind load and stand load individually, [PERSON] et al. [2] analyzed the strength of the 350-type workover derrick according to 24 cases. Studies have also investigated the maximum deformation and stress variation of the derrick. However, the influence of each variable load on the strength of the derrick remains unknown in this study, and other typical derricks have not been further discussed. The wind load is a unique offshore load for an offshore derrick. The previous study of [3] calculated the shape coefficient of the wind pressure and wind pressure coefficients, and the displacement and stress response of the derrick structure in four wind load conditions were analyzed. The constant gravity load and maximum hook load were taken into account to perform the static analysis and modal analysis of a towering derrick, then comparing the outcomes of the experiment described in [4]. In the static research, [PERSON] et al. explored the static strength of a derrick after its members were partly removed. The results in [5] showed that the strength of the derrick after its partial member removal was larger than that of the original derrick structure. [PERSON] et al. established a truck-mounted workover rig derrick and analyzed the location of the maximum Mises stress of the derrick in 12 work conditions. The results in [6] showed that the structural strength of the derrick met the requirements of the design. [PERSON] et al. designed a new derrick structure. Through the strength analysis in [7], the maximal stress of the new structure decreased by 12 percent compared to the previous one. The derrick structure is not only necessary for ensuring the strength of each beam during the operation, but it also plays an important role in the structural reliability. For a reliability analysis, [PERSON] et al. [8] obtained the stress and displacement distribution of the double derrick structure through a static analysis. Through the stress-strength limit state function, the overall reliability index of the double derrick structure was calculated according to the results of static strength. [PERSON] et al. [9] established a residual-life-prediction model based on time-varying reliability and the fatigue effect, which is applied to predict the residual life of the derrick structure by using the \(S\)-\(N\) curve and the rain-flow-counting method. Considering the weakness of the operational terms in the derrick structure strength, a time-dependent reliability analysis method was proposed and applied to the strength analysis of a towering derrick in [10]. A similar structural reliability analysis was also performed by relevant scholars. For example, the safety level of long-span bridge structures was evaluated according to the reliability index of their components and systems, and the temperature-induced intensity response was also taken into account in [11]. The probabilistic safety analysis of truss roof systems under different snow loads was studied, and the failure probability of each component was calculated in [12].