Marine_Structural_Design Episode 9 doc

298 Part 11 Ultimate Strength The plastic yield condition used in this example is the same as in EXAMPLE 14.2. The ABAQUS FEM analysis employs the true stresdtrue strain curve, shown in Figure 14.5 (b). This analysis assumes the material has linear kinematic strain hardening and each side of the beam is modeled as one element. Figures 14.5 (c-e) show that the structural response is sensitive to the yield stress. However, the agreement between the results predicted by both programs is good. The examples presented in this section demonstrated that the nodal displacements and forces predicted by the actual beam-column element agree with those obtained by experiments and by general finite element program analyses. Reasonable results can be obtained by the beam- column element even when the structural member is discretized by the absolute minimum number of elements (normally one element per member). 14.4.3 Application to Practical Collision Problems The procedure implemented in the SANDY program can be used to simulate many different ship collision problems, such as side central collisions, bow collisions, and stem collisions against structures like offshore platforms and ridges. The simulation results include: motion (displacements), velocities/accelerations of the striking and the struck structures, indentation in the striking ship and the hit member, impact forces, member forces, base shear and overturning moments for the affected structures, kinetic energy, and elastidplastic deformation energy of the striking and the affected structures. In this section three typical ship collision problems are selected. These are ship-unmanned, platform, and ship-jacket platform collisions. EXAMPLE 14.5: Unmanned Platform Struck by a Supply Ship The small unmanned platform, shown in Figure 14.6 (a), which is struck by a 5000 ton supply vessel, is considered first. The dominant design criterion for this platform type is often ship collisions, while it is normally wave loading for traditional platforms. The supply ship is supported to drift sideways with a speed 2.0 ms-1 under calm sea conditions. The added mass for the sideways ship sway motion is taken to be 0.5 times the ship mass. The force- indentation relationship for the ship is taken as is shown in Figure 14.6 (b). The added mass is included following Morison's equation and the added mass and drag coefficients are taken to be 1.0. The tubes under the water surface are assumed to be filled with water. Therefore, the mass due to the entrapped water is also included. The force-indentation relationship is established by following Eqs. (14.2) and (14.7) by following further approximations such as multi-linear lines, as illustrated in Figure 14.6 (c). The soil-structure interaction is taken into account using linear springs. First, a linear analysis was carried out by using a load vector given by the gravity loading on the structures. Then, a dynamic analysis considering large displacements, plasticity, and hardening effects followed. The plastic yield condition was taken to be: (14.24) It is noted that the indentation in the hit tube will reduce the load carrying capacity of the tube greatly. This effect has not been taken into account in the present analysis. However, a Chapter 14 qffshore Structures Under Impact Loads 299 possible procedure to account for the indentation effect is to reduce the plastic yield capacity of the element nodes at the impact point using the procedure suggested by Yao et a1 (1986). The numerical results are shown in Figures 14.6 (d-e). The effect of strain hardening in these figures is indicated; when the strain hardening is included, the structure becomes stiffer and more energy will be absorbed by the ship. Therefore, the deck displacement is smaller, and the collision force and overturning moment increase. woracnonq rate 4285 7 MN m-' 20m bl c- I V.1. . 1 0 OS0 100 150 OW 250 100 Indentation (rn) Figure 14.6 Response Caused by Collision between Supply Ship and Unmanned Platform a. Ship-platform collision b. Local load-indentation relationship for the ship side (Continued overleaf) 300 t Cl 20 c Part II UItimate Strength I I I I 1 0 2 s Tmt (SI Time (11 Figure 14.6 (continued). c. Local force-indentation relati nship for the hit tube d. Deck displacement time history of the platform e. Impact force time history f. Overturning moment time history of the platform EXAMPLE 14.6: Jacket Platform Struck by a Supply Ship The four-legged steel jacket platform shown in Figure 14.7 (a) is struck by a 4590-ton supply ship. Both the platform and the ship are existent structures. The ship is supposed to surge into the platform with the velocities 0.5, 2, and 6 ms-1 corresponding to operation impact, accidental impact, and passing vessel collision, respectively. The force-indentation relationship for the ship bow is obtained using axial crushing elements in which a mean crushing force applied by a rigid-plastic theory has been adopted. The local indentation curve for the hit tubular member in the jacket platform is established following Eqs. (14.2) and Chapter I4 qffshore Structures Under Impact Loads 301 (14.7). Both indentation curves are hrther approximated as multi-linear curves. First, a linear static analysis is carried out for the gravity loading and after, a nonlinear dynamic analysis is performed which includes fluid-structure interaction, soil-structure interaction, large displacements, and plasticity and kinematic strain-hardening effects for the affected platform. The time history of the impact deflections is shown in Figure 14.7 (b). Figures 14.7 (c-e) show how the energy is shifted between the ship and the platform and between kinetic energy, elastic deformation energy, and plastic deformation energy. Using the present procedure, impact forces, dent in ship, and local dent depth of the hit member, can be obtained, provided the impact velocity and indentation curve of the ship are known. The main results of the example are listed in Table 14.2. Finally, the distribution of the plastic nodes for an impact velocity of 5ms-1 at time 1.45s is shown in Figure 14.7(a). Table 14.2 Main Results of Ship-Jacket Platform Collisions 302 Part II Ultimate Strength Figure 14.7 Response caused by Collision between Supply Ship and Jacket Platform a. Jacket platform struck by supply ship showing distribution of plastic nodes (Ship velocity, vo =Sins-' time 1.45s) b. Impact displacement time histories of the platform c. Time history of energies during ship impact on jacket platform (Impact velocity, V, = 0.5ms-') d. Time history of energies during ship impact on jacket platform Ompact velocity, V, = 2ms-' ) e. Time history of energies during ship impact on jacket platform (Impact velocity, V, = 5ms-' ) Chapter I4 Offshore Structures Under Impact Loads 303 14.5 Conclusions A consistent procedure has been presented for collision analysis. A nonlinear force- displacement relationship has been derived for the determination of the local indentation of the hit member and a three-dimensional beam-column element has been developed for the modeling of the damaged structure. The elastic large displacement analysis theory and the plastic node method have been combined in order to describe the effects of large deformation, plasticity, and strain hardening of the beam-column members. The accuracy and efficiency of the beam-column elements have been examined through simple numerical examples by comparing the present results with those obtained by experiments and finite element program analyses using the MARC and ABAQUS programs. It is shown that the present beam-column elements enable accurate modeling of the dynamic plastic behavior of frame structures by using the absolute minimum number of elements per structural member. In addition, examples, where the dynamic elastic-plastic behavior of offshore platforms and bridges in typical collision situations is calculated, have been presented. All examples show that strain-hardening plays an important role in the impact response of the struck or affected structure. The strain-hardening results in smaller deformations and more energy will be absorbed by the striking structure. Therefore, the impact force is bigger. Thus, a rational collision analysis should take the strain hardening effect into account. 14.6 References 1. 2. 3. 4. 5. 6. 7. 8. Bai, Y., (1991), “SANDY-A Structural Analysis Program for Static and Dynamic Response of Nonlinear Systems”, User’s Manual, Version 2, Department of Ocean Engineering, The Technical University of Denmark. Bai, Y. and Pedersen, P. Temdrup, (1991), “Earthquake Response of Offshore Structure”, Proc. 10th int. Conf. on Offshore Mechanics arctic Engineering, OMAEP1, June. Bai Y. and Pedersen, P. Temdrup, (1993), “Elastic-Plastic Behavior of Offshore Steel Structures Under Impact Loads”, Intemat. J. Impact Engng, 13 (1) pp.99-117. Ellinas, C.P. and Walker, A.C. (1983), “Damage of Offshore Tubular Bracing Members”, Proc. IABSE Colloquium on Ship Collision with Bridges and Offshore Structures, Copenhagen, pp. 253-261. Fujikubo, M., Bai, Y., and Ueda, Y., (1991), “Dynamic Elastic-Plastic Analysis of Offshore Framed Structures by Plastic Node Method Considering Strain-Hardening Effects”, Int. J. Offshore Polar Engng Conf. 1 (3), 220-227. Fujikubo, M., Bai, Y., and Ueda, Y., (1991), “Application of the Plastic Node Method to Elastic-Plastic Analysis of Framed Structures Under Cyclic Loads”, Int. Conf. on Computing in Engineering science, ICES’91, August. Petersen, M.J., and Pedersen, P. Temdrup, (1981), “Collisions Between Ships and Offshore Platforms”, Proc. 13th Annual offshore Technology Conference, OTC 41 34. Pedersen P. Temdrup and Jensen, J. Juncher, (1991), “Ship Impact Analysis for Bottom Supported Offshore Structures”, Second Int. Conf. on advances in Marine 304 Part 11 Ultimate Strength structures, Dunfermline, Scotland, May 1991 (edited by Smith and Dow), pp. 276-297. Elsevier, Amsterdam. 9. Smith, C.S. (1983), “Assessment of Damage in Offshore Steel Platform”, Proc. Int. Conf. on Marine Safety, Paper 15. 10. Snrreide, T.H., (1985), “Ultimate Load Analysis of Marine Structures”, Tapir, Trondheim, Norway. 11. Ueda, Y. Murakawa, H., and Xiang, D. (1989), “Classification of Dynamic Response of a Tubular Beam Under Collision”, Proc. 8th Int. Conf. on Offshore Mechanics and Arctic Engineering, Vol. 2, pp. 645-652. Ueda, Y. and Fujikubo, M., (1986), “Plastic Node Method Considering Strain- Hardening Effects”, J. SOC. Naval Arch. Japan 160,306-317 (in Japanese). Yao, T., Taby, J. and Moan, T. (1988), “Ultimate Strength and Post-Ultimate Strength Behaviour of Damaged Tubular Members in Offshore Structures”, J. Offshore Mech. Arctic Engng, ASMA 110,254-262. Yu, J. and Jones, N. (1989), ‘1vumerical Simulation of a Clamped Beam Under Impact Loading”, Comp. Struct. 32(2), 281-293. 12. 13. 14. Part I1 Ultimate Strength Chapter 15 Offshore Structures Under Earthquake Loads 15.1 General Bottom supported offshore structures in seismic areas may be subjected to intensive ground shaking causing the structures to undergo large deformations well into the plastic range. Previous research in this area has mainly resulted in procedures where the solutions have been sought in the frequency plane (Penzien, 1976). The present chapter is devoted to time domain solutions such that the development of plastic deformations can be examined in detail. The basic dynamics of earthquake action on structures has been discussed in Clough and Penzien (1975) and Chopra (1995). There have been extensive investigations on earthquake response of building structures in the time domain (Powell, 1973). Unfortunately, most of works have been limited to plane frames. Furthermore, for offshore structures hydrodynamic loads have to be taken into account and the geometrical nonliearities become more important than in building structures. Therefore, there is a need for a procedure to predict earthquake response of offshore structures including both geometrical and material nonlinearities. Methods for analysis of frame structures including geometrical nonlinearities have been based on either the finite element approach (Nedergaard and Pedersen, 1986) or on the beam-column approach (Yao et al, 1986). Nedergaard and Pedersen, (1986) derived a deformation stiffness matrix for beam-column elements. this matrix is a function of element deformations and incorporates coupling between axial and lateral deformations. It is used together with the linear and geometrical stiffhess matrices. Material nonlinearity can be taken into account in an efficient and accurate way by use of the plastic node method (Ueda and Yao, 1982). Using ordinary finite elements, the plastic deformation of the elements is concentrated to the nodes in a mechanism similar to plastic hinges. Applying the plastic flow theory, the elastic-plastic stiffness matrices are derived without numerical integration. In this Chapter, a procedure based on the finite element and the plastic node method is proposed for earthquake response analysis of three-dimensional frames with geometrical and material nonlinearities. Using the proposed procedure, earthquake response of a jacket platform is investigated. Part of this Chapter appeared in Bai and Pedersen (1991). The new extension is to outline earthquake design of fixed platforms based on API RF'2A. 15.2 Earthquake Design as per API FW2A API RP2A (1991) applies in general to all fixed platform types. Most of the recommendations are, however, typical for pile steel jacket platforms. The principles and procedures given in 306 Part II Ultimate Strength API (1991) are summarized below. The design philosophy for earthquake leads in API (1991) is illustrated in Table 15.1. Table 15.1 Earthquake Design Philosophy, API RP2A I Strength Level Earthquake (SLE) ~~ Prevent interruption of normal platform operations. Ground shaking which has a reasonable likelihood of not being exceeded during the platform life. No significant structural damage, essentially elastic response. Ductility Level Earthquake @LE) I Prevent loss of life and maintain well control. Rare intense ground shaking that unlikely to occur during the platform life. No collapse, although structural damage is allowed; inelastic response. The AFT’S seismic design recommendation are based upon a two level design approach, these are Strength Requirements The platform is designed for a severe earthquake which has reasonable likelihood of not being exceeded during the platform life (typical return period hundreds of years, Strength Level Earthquake SLE). Ductility Requirements. The platform is then checked for a rare earthquake with a very low probability of occurrence (typical return period thousands of years, Ductility Level Earthquake DLE). The objective of the strength requirements is to prevent significant interruption of normal platform operations after exposure to a relatively severe earthquake. Response spectrum method of time history approach is normally applied. The objective of the ductility requirements is to ensure that the platform has adequate capacity to prevent total collapse under a rare intense earthquake. Member damage such as in-elastic member yielding and member buckling are allowed to occur, but the structure foundation system should be ductile under severe earthquakes, such that it absorbs the imposed energy. The energy absorbed by the foundation is expected to be mostly dissipated through non-linear behaviour of the soil. For some typical jacket structures, both strength and ductility requirements are by API considered satisfied if the below listed previsions are implemented in the strength design of these platforms: Strength requirements for strength level earthquake loads (SLE) are in general documented. Strength requirements are documented for jacket legs, including enclosed piles, using 2 times the strength level earthquake loads (Le. 2*SLE). Rare, intense earthquake ground motion is less than 2 times the earthquake ground motions applied for documentation of strength level requirements (Le. DLE < 2*SLE). Chapter15 offshore Structures Under Earthquake Loads 307 Geometrical and ultimate strength requirements for primary members and their connections as given in API are satisfied. These requirements concern number of legs, jacket foundation system, diagonal bracing configuration in vertical frames, horizontal members, slenderness and diameter/thickness ratio of diagonal bracing, and tubular joint capacities. 15.3 Equations and Motion 15.3.1 Equation of Motion The equations of motion for a nonlinear offshore structure subjected to a earthquake loading can be expressed as [M]{diij+ [C]{dii}+ [K']{dU} = -[M]{diig}+ (&Ye} (15.1) where {dU}, {dU} and {dd} are the increments of nodal displacement, velocity and acceleration relative to the ground respectively. [MI is the structural mass matrix, while [C] is the structural damping matrix. [KT] denotes the structural tangent stiffness matrix. (a} are the increments of the hydrodynamic load. The ground acceleration vector {oz} is formed as an assembly of three-dimensional ground motions. We shall here assume that at the time of the earthquake there is no wind, wave or current loading on the structure. According to the Morison equation (Sarpkaya and Isaacson, 1981), the hydrodynamic load per unit length along a tubular beam member can be evaluated as where p is the mass density of the surrounding water, D is the beam diameter, CA is an added mass coefficient, CD the drag coefficient, A=xD2/4, and {ti"} denotes the normal components of the absolute velocity vector. The absolute velocity vector is {%J={4+bg) (15.3) Using a standard lumping technique, Eq. (15.1) can be rewritten as ([MI+ [M, ){do}+ [c]{&}+ [K']{~u} = -([MI+ [M, D{diig}+ @F,} (15.4) where [Ma] is an added mass matrix containing the added mass terms of Eq. (15.2). The increments of drag force terms from time (t) to (t+dt) are evaluated as (@D 1 = c [T+dt I' VD - c [T 1' {fD >o (15.5) where denotes summation along all members in the water, while {fD} are results of integration of the drag force terms of Eq. (15.2) along the member. [TJ is the transformation matrix. the equations of motion Eq. (1 5.4) are solved by the Newmark-P method (Newmark, 1959). [...]... by Almar-Naess ( 198 5), Gurney ( 197 9), Maddox ( 199 1), Suresh ( 199 1), Dover and Madhav Rao ( 199 6) An extensive list of recently published papers may be found from the proceedings of ISSC ( 198 8, 199 1, 199 4, 199 7, 2000) AWS ( 198 5) can be considered as a representative code for fatigue strength design Recent developments in ship fatigue research may be found in Xu ( 199 7) and Xu and Bea ( 199 7) As part of the... ISSC ( 198 8, 199 1, 199 4, 199 7, 2000), “Fatigue and Fracture, Report of technical Committee III.2”, Proceedings of the International Ship ad Offshore Structures Congress 12 Maddox, S.J.( 199 2), ‘&Fatigue Strength of WeldedStructures”,Abington Publishing 13 Manson, S.S and Hirschberg, M.H ( 196 4), ”Fatigue:An Interdisciplinary Approach”, Sycracuse University Press, N.Y., pp 133 14 Marshall P W ( 199 2), “Design... Dretvik, S ( 199 9), “The Asgard Flowlines Project - Limit State Design Experience”, IBC Conference on Risk-Based & Limit-State Design & Operation of Pipelines, Oslo, Oct 199 9 4 Boller, C and Seeger, T ( 198 7), “Materials Data for Cyclic Loading, Part A-E”, Elsevier, Amsterdam 5 Broek, D ( 198 9), “The Practical Use of Fracture Mechanics”, Kluwer Academic Publisher 6 Coffin, L.F and Tavernelli, J.F ( 195 9), ”The... fatigue criteria in this chapter will be mainly based on NORSOK (NTS, 199 8) However, readers are recommended to refer the codes relevant to their projects such as IIW (Hobbacher, A ( 199 6), Eurocode 3 ( 199 2), IACS ( 199 9), ABS ( 199 2) and DNV (2000), among of others 17.1.2 Effect of Plate Thickness The thickness effect is due to the local geometry of the weld toe in relation to the thickness of the adjoining... BS 791 0, Eurocode 3, NS 3472 Offshore industry: NORSOK, UK HSE (UK Den), MI, etc Ship industry: classification Rules, IACS requirements IIW (International Institute of Welding), AWS (American Welding Society) Automobile industry, aerospace & aircraft industries, etc Bridges industry: BS5400 @SI, 197 9), AASHTO ( 198 9) ASME Pressure Vessels Codes Welded Aluminum Codes: BS8118 (BSI, 199 1), ECCS ( 199 2)... Amsterdam 15 Miner, M.A ( 194 5), “Cumulative Damage in Fatigue”, Journal of Applied Mechanics, ASME, Vol 12(3), pp.1 59- 164 16 Paris, P and Erdogan., F ( 196 3), “A Critical Analysis of Crack Propagation Laws”, Journal of Basic Engineering 17 Rolf, S.T and Barsom, J.T ( 199 9), “Fracture and Fatigue Control in Structures”, 3rd Edition, Prentice-Hall, Englewood Cliffs, N.J 18 Suresh, S ( 199 1), “Fatigue of Materials”,... N.J 18 Suresh, S ( 199 1), “Fatigue of Materials”, Cambridge Press 19 Xu, T ( 199 7), “Fatigue of Ship Structural Details - Technical Development and Problems”, Journal of Ship Research 20 Xu, T and Bea, R.G ( 199 7), “Fatigue of Ship Critical Structural Details”, Journal of Offshore Mechanics and Arctic Engineering, ASME, Vol 199 (2), May, pp 96 -107 Part I11 Fatigue and Fracture Chapter 17 Fatigue Capacity... Y and Terndrup Pedersen, P ( 199 1), “Earthquake Response of Offshore Structures”, Proc 10” int Conf on Offshore Mechanics Arctic Engineering, OMAE 91 , June 5 Chopra, A.K ( 199 5), “Dynamics of Structures, Theory and Applications to Earthquake Engineering”,Prentice-Hall, Inc 6 Clough, R.W and Penzien, J ( 197 9, “Dynamics o Structures”,MsGrwa-Hill f 7 Haythomthwaite, R.M., ( 195 7), “Beams with Full End Fixity”,... Strength 3 14 15.6 References 1 API ( 199 1), “Recommendations for Planning, Designing and Constructing Fixed Offshore Platforms”, API Recommended Practice 2A (RP 2A), 19th Edition, August 1, American Petroleum Institute 2 Archer, J.S., ( 196 5), “Consistent Matrix Formulations for Structural Analysis using Finite Element Techniques”, AIAAjoumal, Vol 3, pp 191 0- 191 8 3 Bai, Y., ( 199 0), “SANDY-A Structural Analysis... Fatigue of Metals”, Trans Of the Metallurgical Society of AIME, Vol 215, p. 794 7 Dover, W.D and Madhav Rao, A.G ( 199 6), ”Fatigue in Offshore Structures”, A.A Balkema 8 Fricke, W., Petershagen, H and Paetzold, H., “Fatigue Strength of Ship Structures, Part I: Basic Pronciples, Part 2: Examples”, GL Technology 9 f Gurney, T.R ( 197 9), “Fatigue o Welded Structures”, 2nd Edition, Cambridge University Press . ( 198 5), Gurney ( 197 9), Maddox ( 199 1), Suresh ( 199 1), Dover and Madhav Rao ( 199 6). An extensive list of recently published papers may be found from the proceedings of ISSC ( 198 8, 199 1, 199 4,. Archer, J.S., ( 196 5), “Consistent Matrix Formulations for Structural Analysis using Finite Element Techniques”, AIAAjoumal, Vol. 3, pp. 191 0- 191 8. Bai, Y., ( 199 0), “SANDY-A Structural Analysis. 199 7, 2000). AWS ( 198 5) can be considered as a representative code for fatigue strength design. Recent developments in ship fatigue research may be found in Xu ( 199 7) and Xu and Bea ( 199 7).