## 2 Methodology  
### Description of Model  
The selected fixed jacket offshore platform for seismic investigation is four-storied with a total mass of 2500 tons applied at the upper joints of the jacket frame. Along with structural components, the platform includes non-structural components such as stiffeners, centralizers, pump caissons, flooding systems, etc. Only the major structural elements are included in the analysis model. This platform was designed and analyzed based on the recommendations of API RP2A-WSD [37]. The physical configuration of the offshore platform is illustrated in Figure 1. In this research, the total height of the jacket platform is 68.58 m, whereas the platform has been designed for a shallow water depth of approximately 65.53 m. The plan of the jacket is square shaped with a top dimension is 8 by 8 m, which extends and becomes 21.76 by 21.76 m at the mud line. The structural damping is adopted as 2% [38] of critical damping. The jacket's horizontal bracings are frame elements rigidly connected at the ends. The vertical bracings are provided as K-tracings to reduce buckling and to transmit more stiffness. The joints in the platform are assumed to be rigid joints. For the purpose of simulating the response of pile and jacket member elements, nonlinear beam-column elements with distributed plasticity whose analytical formulation is on the basis of flexibility method with or without iteration are used. The fiber discretization approach has been utilized for modeling the cross section of pile and jacket elements. The general geometric configuration of a fiber cross section is divided into several tiny components with various simple shapes such as square, rectangle, and triangle. The feasibility of creating a cross section of member with these subregion components provides appropriate flexibility in definition of sections composed of different materials. The geometric features considered for each of the fibers are the local \(x\) and \(y\) coordinates of fibers and their area. The continuity equation of the section is computed on the basis of the stress-strain relationships of the material used. The assumed material for the fibers is considered uniaxially and the strain in each fiber is calculated based on the strain at centroid strain and curvatures at the sections, considering [PERSON]'s assumption that plane sections remain plane and normal to element axis after bending. An example of a section comprising different types of materials is the leg element of the jacket with the pile element located inside it. In some cases, the space between the leg and pile is filled with grout. To capture the nonlinear response of the jacket platform, nonlinear beam-column elements with distributed plasticity are used. The fiber discretization approach is employed for modeling the cross section local elements. The general geometric configuration of a fiber cross section can be found in [PERSON] et al. [39]. The continuity equation of the section is derived based on the stress-strain relationships of the material used. The assumed material for the fibers is considered uniaxial and the strain in each fiber is computed based on the strain at centroid strain and curvatures at the sections. This formulation is based on [PERSON]'s assumption that plane sections remain plane and normal to element axis after bending. The force-based nonlinear beam-column elements along with fiber approach is used to develop the model. The jacket foundation is designed for fixed support conditions. The nonlinear dynamic analysis of the model frame structure is carried out using OpenSees. The structural members comprised of 11 section members as listed in Table 1, whereas the schematic diagram of a cross-section is illustrated in Figure 1e.