CHAPTER 3 ANALYSIS METHOD 3.1 ELASTIC STATIC ANALYSIS Elastic static analysis is done to calculate stress ratio between before and after subsidence. The structure will behave elastic when the first yield doesn t exceed. In SACS program, the elastic condition can be shown when the stress ratio is smaller than 1. If the stress ratio is greater than 1, it means that the condition of the members or joints are in in-elastic condition and an in-elastic analysis is need to be done to know the structure s behavior. 3.1.1 SACS Computer Program SACS system has full static and dynamic structural analysis, as well as offshore transportation and installation capabilities consist of numerous compatible program modules that full interfaced to one another. The following is a list of SACS program along with its capabilities. 3.1.1.1 Precede In precede we can model beam and/or finite element including plate and shell elements. After modeling, we can see interactive full screen color graphics of the platform s model and generate geometry, material, section properties and loading of the platform. Code checks parameter generation including K-factors and compression flange un-braced lengths also can be done in precede. 3.1.1.2 Data Generator Data generator is used as an editor which labels and highlights data fields, and provides help for data input. A form filling data input is also available to add coefficients, change/input loads or to change sea-state data such as water depth, wave crest etc. Chapter 3-1
3.1.1.3 Sea-state Sea-state is an environmental loads generator which implement the API 20 th edition and supports five wave theories. In sea-state, we can include or exclude current data, generate loads to wind, gravity, buoyancy and mud flow and also add marine growth, flooded and non flooded members. Other capability of sea-state is the automatic wave positioning for max/min base shear or overturning moment. 3.1.1.4 Joint CAN Joint CAN is used for checking tubular joints code and redesign. In joint CAN the connection strength between tubular joints are checked and overlapping joints are analyzed. Joint CAN used present and past code including API 20 th, LRFD 1 st edition, NPD and DNV. 3.1.1.5 Post Post is used for beam and plate element code check and redesign. Post can modify code check parameters and creates updated model with redesigned elements. Post can also do hydrostatic collapse analysis and gives detailed summary report. Post supports code from 1977 to present. 3.1.1.6 Postvue Postvue is an interactive graphics post-processor which can checked member code and redesign by individual group of elements. Postvue is also the user control of all code checks parameters which can display shear, bending moment diagrams, deflected shapes for static and dynamic analyses. Postvue labels UC ratio, stresses, and internal forces on elements. Postvue supports the same code as post. 3.1.1.7 PSI PSI stands for Pile and Structure Interaction. PSI can be used for a nonlinear soil, non uniform piles and includes the beam column effects. Full plotting and graphical representation of soil data and results including stresses, P-Y, T-Z curve are done in PSI. Chapter 3-2
The main screen of SACS computer program : Figure 3.1 SACS Console 3.2 IN-ELASTIC STATIC ANALYSIS 3.2.1 USFOS In analyzing pushover conditions we use another program besides SACS, we use USFOS. Both SACS and USFOS can be used to analyze elastic and in-elastic condition but in USFOS the graphical drawings about the inelastic condition is better viewed than SACS so it will be easier to determine which member or joints that failed. USFOS is a finite element program for nonlinear static and dynamic analysis of frame structure. The structure may be exposed to external loads, acceleration fields or temperature fields. The structural model can be obtained from the linear analysis in SACS with changing the file name into.uss. Chapter 3-3
The basic philosophy behind USFOS is to use a very coarse finite element mesh and still obtain reliable and accurate results. USFOS requires only one finite element in each physical element of the structure and it operates on element stress resultant such as forces and moments. Material nonlinearities in USFOS are modeled by plastic hinges at element midspan and element ends. The basic element formulation of USFOS is based on the exact solution of the differential equation for a beam subjected to end forces. Benefits of using USFOS : - Gives a very accurate representation of element behavior including membrane effects and column buckling because of the effects of large displacement and coupling between lateral deflection and axial strain are included using strain relations (green strain) instead of conventional linear strain (engineering strain). - The tangent stiffness matrices are derived in a consistent manner from energy principles which will preserve symmetry in the equations and allows the use of an efficient skyline equation solver. - The elastic tangent matrices are calculated from closed form expressions with no numerical integration over the element cross section or over the element length which will give a very efficient formulation and reduces the time on calculating the matrices. 3.2.1.1 Analytical model The analytical model used in USFOS is similar in some respects to those adopted for other types of steel structure. There are a few minor adjustments being made to suit the specific conditions, e.g. at supports in particular, relating to each analysis. The models consist from few parts. Stick models (beam elements assembled in frames) are used extensively for tubular structures (jackets, bridges, flare, booms) and lattice trusses (modules, decks). Chapter 3-4
3.2.1.2 Joints In this analysis, joint capacity check module is used. The capacity of the connection brace/chord is less than the brace capacity which means that the brace cannot be utilized 100%. In conventional joint models the limitations in load transfer through the chord surface are neglected. First the user specifies the nodes where tubular joint capacity should be considered then USFOS will calculates the geometry of the tubular joints and introduces extra elements, nodal points, geometries and materials in the finite element model. The material properties are set equal to the properties of actual chord, but hardening is not permitted. Element model developed from shell theory connected to beam element using a Navier transformation. The transition element takes care of the shell properties of the joints, and makes an integrated shell/frame analysis possible. This technique determine the point where strain and strain distribution occurs with good accuration (from the comparison with analysis element model until shell). The capacity is calculated based on API. Figure 3.2 (a) shows the input of element model in the tubular joint by user, and figure 3.2 (b) shows the input model that has been modificated. The numbering of node and additional element follow the rules that illustrated in figure 3.3 Figure 3.2 (a) Conventional Joint Model (b) Joint with Capacity Check Chapter 3-5
Figure 3.3 Additional Element Numbering (From Program) If more accuracy is needed, further natural vibration analysis and local flexibility may be covered by joint stiffness matrix. Main model must be calculated for eccentricity and local in the joint. The typical model is the jacket in the North Sea which has 800 nodes and 4000 members. 3.2.1.3 Members In addition to its geometrical and material properties, each member is characterized by hydrodynamic coefficients, e.g. relating to drag, inertia, and marine growth, to allow wave forces to be automatically generated. 3.2.1.4 Foundation models Since the used of USFOS is for non-linear behavior, foundations are usually analyzed separately from the structural model. Foundations are represented by an equivalent load dependent secant stiffness matrix; coefficients are determined by an iterative process where the forces and displacements at the common boundaries of structural and foundation models are equated. This matrix may need to be adjusted to the mean reaction corresponding to each loading condition. Chapter 3-6
3.2.1.5 Loads The main type of loads is: Gravitational loads : Consist of self weight and equipment, live loads (fluids, human). Depends on the structure area, live loads must be positioned in the point where produce heaviest configuration. Environmental loads : Consist of current, wave, and wind which put on assumption react in the same direction. Usually we choose only one direction which produces the biggest load. 3.2.2 Step of Analysis The inelastic static analysis is performed in two stages, at first stage, gravity load (dead and live load) is applied to the structure and response due to gravity load is computed. Conductor framing do not contribute to the system stiffness yet and the structure remains elastic. At second stage, environmental load is applied. Conductor framing is activated (contribute to the system stiffness). A load pattern representing the environmental load is applied incrementally. For each step the structure stiffness is assembled and the global displacement increment is calculated. The element force increment is calculated by using tangential stiffness matrix and the elements are checked to see whether buckling or plastic capacity has been reached. A plastic hinge is introduced in the element at the position where the capacity was reached. A modified stiffness matrix accounting for the plastic hinge is calculated and the process proceeds to the next load step. A cross section that has reached the plastic capacity remains on the plastic interaction surface move tangentially to this surface. The environmental load is increased progressively until extreme environmental load is reached. Chapter 3-7
Chapter 3-8