Marine_Structural_Design Episode 13 pps

45 8 Pari IV Siructural Reliabiliq - cov=o.o6 I cow.10 0 5 10 15 20 25 30 35 t, years (1) No Corrosion 5.0 1 I 4.0 3.0 2.0 1 .o 5.0 e 4.0 3.0 v e 2.0 1 .o 5.0 Q 4.0 v @$ 3.0 2.0 1 .o * COV=0.08 4- cov=o. 10 0 5 10 15 20 25 30 35 t, years (2) Slight Corrosion *cov=0.08 *coV=o.lO 0 5 10 I5 20 25 30 35 t, years (3) Nominal Corrosion 0 5 IO I5 20 25 30 35 1, years (4) Severe Corrosion Figure 25.10 Uncertainty Analysis for Ultimate Strength Chapter 25 Reliability of Ship Structures 459 25.5.3 Conclusions Time-variant structural reliability assessment of an FPSO hull girder relative to the ultimate strength requires the consideration of the following three aspects: (1) load effects and their combination, (2) the hull ultimate strength, and (3) methods of reliability analysis. The environmental severity factors are introduced to fit the the wave-induced bending moments accounting for the specific-site conditions. The Ferry-Borges method is applied to combine stochastic processes of still-water and wave-induced bending moments and to evaluate time-variation of the maximum combined bending moment. The mean value first order second moment method was applied to calculate failure probability of ship structures. A procedure for time-variant reliability analysis has been developed. An effective response surface approach is used to evaluate the failure hnction at sampling points. A modified Monte Carlo simulation technique is applied to evaluate the failure probability. The time-variant reliability and parametric analysis for an FPSO hull girder are quantified. It is found that the steady corrosion rate, combination of SWBM and VWBM, environmental severity factors and transition time in the present corrosion model are very important in estimating the reliability of the hull girder. It is concluded that the load combination factors obtained from this method are dependent on mean arrival rate of SWBM, service lifetime and the environmental seventy factors. 25.6 References 1. 2. 3. 4. 5. 6. 7. ABS (2000), “Guide for Building and Classing Floating Production Installations”, American Bureau of Shipping. Bucher, C.G., Bourgound, U.A., (1990), “A Fast and Efficient Response Surface Approach for Structural Reliability Problems”, Structural Safety, Vol. 7, pp. 57-66. Casella, G., Rizzuto, E., (1998), “Second-level Reliability Analysis of a Double-hull Oil Tanker”, Marine Structures, Vol. 11, pp.373-399. Frieze, P.A. and Lin, Y.T. (1991), “Ship Longitudinal Strength Modeling for Reliability Analysis”, Proc. of Marine Structural Inspection, Maintenance and Monitoring Symposium, SNAME, Arlington, VA. Ghose D.J., Nappi N.S., Wiemicki C.J., (1995), “Residual Strength of Marine Structures”, Ship Structure Committee, SSC-381. Gordo J.M., Guedes Soares C., Faulkner D. (1996), “Approximate Assessment of the Ultimate Longitudinal Strength of Hull Girder”, Journal of Ship Research, Vol. 40( l), Guedes Soares, C., (1 984), “Probabilistic Models for Load Effects in Ship Structures”, Department of Marine Technology, Norwegian Institute of Technology, Trondheim, Norway, Report No. UR-84-38. pp.60-90. 460 Part IVShvcturaI Reliability 8. 9. Guedes Soares C., (1990), “Stochastic Models of Loads Effects for the Preliminary Ship Hulls”, Structural Safety 1990; 8: 353-368. Guedes Soares, C. and Moan, T., 1985, “Uncertainty Analysis and Code Calibration of the Primary Load Effects in Ship Structures”, Proc., 4th International Conference on Structural Safety and Reliability (ICOSSAR ‘85), Kobe, Japan, Vol. 3, pp. 501-5 12. 10. Guedes Soares, C. and Moan, T., 1988, “Statistical Analysis of Still-water Load Effects in Ship Structures”, Trans. SNAME, Vol. 96, pp. 129-156. 11. Guedes Soares, C., Dogliani, M., Ostergaard, C., Parmentier, G. and Terndrup Pedersen, P., (1996), “Reliability Based Ship Structural Design”, SNAME Transactions, Vol. 104, pp.357-389. 12. Guedes Soares, C., Garbatov, Y., (1999), “Reliability of Corrosion Protected and Maintained Ship Hulls subjected to Corrosion and Fatigue”, Journal of Ship Research 13. Guedes Soares, C., Garbatov, Y., (1999), “Reliability of Maintained, Corrosion Protected Plates subjected to Nonlinear Corrosion and Compressive Loads”, Journal of Marine Structures, Vol. 12, pp.425-445. 14. IACS (1995), “Requirement Sll, Longitudinal Strength Standards”, Int. Association of Classification Societies. 15. Liu, Y.W., Moses, F. (1994), “A Sequential Response Surface Method and Its Application in the Reliability Analysis of Aircraft Structural System”, Journal of Structural Safety, Vol. 16, pp. 36-46. 16. Mansour, A.E. (1972), “Probiblastic Design Concept in Ship Structural Safety and Reliability”, Trans. SNAME, Vol. 80, pp. 64-97. 17. Mansour, A. and Faulkner, D. (1973), “On Applying the Statistical Approach to Extreme Sea Loads and Ship Hull Strength”, RINA Trans., Vol. 115, pp. 277-313. 18. Mansour, A.E., (1 974), “Approximate Probabilistic Methods of Calculating Ship Longitudinal Strength”, Journal of Ship Research, Vol. 18. 19. Mansour, A.E., (1987), “Extreme Value Distributions of Wave Loads and Their Application to Marine Structures”, Marine Structural Reliability Symposium, Arlington, VA. 20. Mansour, A.E. (1990), “An Introduction to Structural Reliability Theory”, SSC Report ssc-351. 21. Mansour,, A.E., Lin, M., Hovem, L., and Thayamballi, A. (1993), “Probability-Based Ship Design Procedure - A Demonstration”, SSC Report, SSC-368. 22. Mansour A E. (1994), “Probability Based Ship Design Procedures: Loads and Load Combination”, Ship Structure Committee, SSC-373. 23. Mansour, A.E. (1995), “Extreme Loads and Load Combination”, J. of Ship Research, Vol. 39, No. 1. 24. Mansour7 A. E. and Wirsching, P.H. (1995), “Sensitivity Factors and Their Application to Marine Structures”, Journal of Marine Structures, Vol. 8. Vol. 43(2), pp.65-78. Chapter 25 Reliability of Ship Structures 46 1 25. Mansour, A. E. (1997): “Assessment of Reliability of Ship Structures”, SSC Report, 26. Nikolaidis, E. and Kaplan, P. (1991), “Uncertainties in Stress Analysis on Marine Structures”, Ship Structure Committee Report SSC-363. 27. Nikolaidis, E. and Hughes, O.F., Ayyub, B.M., and White, G.J. (1993), “A Methodology for Reliability Assessment of Ship structures”, Ship Structures Symposium 93, SSCISNAME, Arlington, VA, pp H1-H10. 28. Ochi, M.K. (1978), “Wave Statistics for the Design of Ships”, Transactions of SNAME, 29. Sikora, J.P., Disenbacher, A., and Beach, J.E. (1983), “A Method for Estimating Lifetime Loads and Fatigue Lives for SWATH and Conventional Monohulls”, Naval Engineering Journal, ASNE, Vol. 95, No. 4, pp. 63-85. 30. Smith, C.S. (1977), “Influence of Local Compressive Failure on the Ultimate Longitudinal Strength of a Ship Hull”, In: Proc. of Int. Symposium on Practical Design of Ships (PR4DS’77), Tokyo, Japan, pp. 73-79. 3 1. Stiansen, S.G. and Mansour, A.E. (1980), “Reliability Methods in Ship Structures”, J. of MNA. 32. Sun, H.H., Chen, T.Y., (1997), “Buckling Strength Analysis of Ring-Stiffened Circular Cylindrical Shells under Hydrostatic Pressure”, ISOPE-97, pp.361-366, Honololu. 33. Sun, H.H., Xiao, T.Y. and Zhang, S.K., (1999), “Reliability Analysis based on Ultimate Strength of Midsections for Corroding Ship Primary Hulls”, Proc. 18th 34. Sun, H.H. and Bai, Y. (2000), “Reliability of Corroded and Cracked Ships”, ISOPE’2000. 35. Sun, H.H. and Bai, Y. (2001), “Time-Variant Reliability of FPSO Hulls”, SNAME Transactions, Vol. 109. 36. Wang X., Jiao G., Moan T. (1996), ”Analysis of Oil Production Ships Considering Load Combination, Ultimate Strength and Structural Reliability”, SNAME Transaction, 37. White, G.J. and Ayyub, B, N., (1985), “Reliability Methods for Ship Structures”, J. of 38. Wirsching P.H. et al. (1997), “Reliability with Respect to Ultimate Strength of a 39. Yamamoto, N.(1998), “Reliability Based Criteria for Measures to Corrosion”, SSC-398. 86: 47-76. OMAE/S&R-6007, St. Jo~s. V01.104, pp. 3-30. Naval Engineers, Vol. 97, No. 4. Corroding Ship Hull”, Journal of Marine Structures, Vol.10. pp. 501-518. Proc. 17th OMAE’98. Part IV Structural Reliability Chapter 26 Reliability-Based Design and Code Calibration 26.1 General The most important applications of structural reliability methods is perhaps reliability-based design and calibration of the safety factors in the design codes. These two topics will be addressed in detailed in this chapter. In structural design, there are always uncertainties involved in determining loads and capacities. Historically, the engineering design process has compensated for these uncertainties by the use of safety factors. However, with reliability technology, these uncertainties can be considered more quantitatively. Specifically, the use of probability-based design criteria has the promise of producing better-engineered designs. For a marine structure, implementation of a probability-based design code can produce a structure having, relative to structure designed by current procedures, (1) a higher level of reliability, or (2) lower overall weight (which means cost savings), or (3) both. 26.2 General Design Principles General design principles used in practice are outlined in this subsection. Reliability-based design is one of the design methodologies, but it is highlighted as a separate section in this Chapter. 26.2.1 Concept of Safety Factors Structural safety measures of different kinds are generally used and referred to without always giving a clear picture about their physical meaning. The safety factor concept is frequently applied without giving any corresponding quantitative measure related to the actual structural safety level. Traditional design practice is based on application of some kind of deterministic safety measures. The greater the ignorance about an event, the larger the safety factor should be applied. In principal, the safety factors of design check of components should depend upon the consequence of failure and the type of structural mode. 26.2.2 Allowable Stress Design ASD criterion has been used since a long time ago by use of explicit design formulae, which can be expressed as CL Y 050, where 0, =-=qoL (26.1) 464 Part IV Structural Reliabiliv where D is the stress in the structures obtained by linear-elastic theory for the maximum loads, oA is the allowable stress, DL, typically the yield stress, y is the safety factor, q(=l/y) is the usage factor. In the ASD methods the design check is made at a capacitylload effect level below first yield of a component. Linear elastic analyses are used to describe the structure response characteristics for the given nominal design loading. The complexity of the design format depends on the failure mode considered, i.e. failure in compression, in tension, in buckling, etc. Design codes formulate these equations and provide the safety factors to be used. However, there are some objections to the application of ASD due to differences in the uncertainties with the various loads and resistances, and also due to the over-design. The ASD design used by AISC is called WSD by API RP2A. 26.2.3 Load and Resistance Factored Design Due to statistical variability in the applied loads and components resistance and due to certain assumptions and approximations made in design procedure, use of a single safety factor for all load combinations cannot maintain a constant level of structural safety. Partial safety factors may generally reflect the inherent uncertainties in load effects and strength as well as the consequence of failure and safety philosophy The Load and Resistance Factored Design (LRFD) procedure was issued by the American Institute for Steel Construction (AISC) in 1986. The AISC LRFD criteria were developed under the leadership of T.V. Galambos, see a series of 8 papers published in ASCE journal of the Structural Division, e.g. Ravindra and Galambos (1 978). Further, the American Petroleum Institute (MI) has extrapolated this technology for offshore structures with the development of API RP2A-LFWD, in 1989. Loads acting on the structures can be divided into several types such as functional loads, environmental loads, etc. If the concept of multiple load factors is introduced, the LRFD design criterion can be reformulated as (26.2) where yfi are load factors to account for uncertainties in each individual load Qi, y~i are load combination factors. The safety factor in Eq.(26.2), y,,,, reflects the uncertainty of a given component due to variations in the size, shape, local stress concentrations, metallurgical effects, residual stress, fabrication process, etc. The safety factors applied to loads, 'yf, reflect the uncertainty in estimating the magnitude of the applied loads, the conversion of these loads into stresses, etc. If R and S are linear functions of fk and Qi, respectively, the above format can be written as vi are load combination factors. In the API - LRFD code, resistance factors $(=l/-ym) is defined instead of material factors. It is emphasized that the safety factors ym and yfi should be seen in conjunction with the definition of the characteristic values of resistance and loads, and the method used to calculate these values. Even if the characteristic values are the same in design codes for different Chapter 26 Reliabiliiy-Based Design and Code Calibration 465 regions, the safety factors may be different due to the difference in uncertainties involved in resistance and load, difference in target safety levels and difference in environmental and soil conditions. Comparing LRFD with WSD methods, it is seen that in the LRFD method the loads and capacities are modified by factors representing their statistical uncertainties. This results in a more uniform safety for a wide range of loads and load combinations and component types. Even though the LRFD format is similar in form with ASD format, there exists a substantially different physical interpretation. The design format should account for the different load conditions and relevant magnitude of uncertainties encountered by structures. As briefly reviewed by Efthymiou et a1 (1997) that the load and resistance factors in API RPZA LRFD were derived on the basis of calibration to the API-RP2A WSD. The objective was to derive load and resistance factors that would achieve, on average, the same calculated component reliabilities as obtained using API-RP2A WSD. To achieve this objective, reliability analyses were used to derive safety indices for components designed to API-RP2A WSD for a range of gravity and environmental load situations and averaged to obtain the target safety index for the LRFD code. 26.2.4 Plastic Design Traditionally, Part 2 of the AISC Specification was called Plastic Design. Plastic Design is a special case of limit states design, wherein the limit state for strength is the achievement of plastic moment strength Mp. Plastic moment strength is the moment strength when all fibers of the cross-section are at the yield stress. The design philosophy as per AISC applied to flexural members such as beam-columns. In recent years, Plastic Design became a component of LRFD. 26.2.5 Limit State Design (LSD) Marine structures are composed of components, e.g. tubular joints, brackets, panels, etc. which are subject to different load conditions including finctional loads, environmental loads, accidental loads, etc., and may fail in different failure modes. Usually, the ultimate limit state (ULS) for a specified failure mode is expressed by a mathematical formula in which uncertainties associating with loads, strength and models cannot be avoided. LSD examines the structural condition at failure, comparing a reduced capacity with an amplified load effect for the safety check. Besides, LSD covers various kinds of failure modes, such as 0 Ultimate limit state (ULS) 0 Fatigue Limit state (FLS) Accidental limit state (ALS) The LSD criteria may be formulated in ASD format or LRFD format. The relation between ASD and LSD has been discussed by e.g. Song, Tjelta and Bai (1998), Bai and Song (1997, 1998). 26.2.6 Life Cycle Cost Design With the application of structural reliability methodology, an optimum life cycle cost (LCC) structural design, meeting complex combinations of economic, operational and safety 466 Part IV Structural Reliability requirements may be targeted. These targets may vary both in time and geopolitical location and further, may be continuously affected by technological changes and market forces. To deal with such design targets in structure design, formal procedures of optimization are required to make decisions about materials, configuration, scantling, etc. In the optimal design process, therefore, the key stage is the specification of optimum design targets. General types of design targets may be cost (initiaYoperational), functional efficiency and reliability. By using LCC design, it is possible to express the total costs of a design alternative in terms of mathematical expression, which can be generically described as follows: TOTAL (NPV)=CAPEX(NPV) + OPEX(NPV)+RISKEX(NPV) (26.4) Where, CAPEX OPEX = the operational costs RISKEX = unplanned risk costs NPV = net present value = the capital expenditure of initial investment One main difficulty that often arises is identification of the costs to include accidental situations such as grounding or collision of ships. In this case, safety is the primary design objective while economy takes on the role of important side constraints. One of the ways to deal with this particular situation is introduction of high cost penalty for certain failure modes, e.g. high value of CF in the following equation (26.5) C, =C, +P,C, =C, +R or R = P,C, = C(P,C, )= zRi (26.6) where PA is the failure rate of a particular mode i, and CF~ is the cost penalty associated to that failure mode. 26.3 Reliability-Based Design 26.3.1 General The role of safety factor in traditional deterministic design is to compensate for uncertainties affecting Performance. Such safety factors evolved through long term experience. Experience, however, is not always transferable from one class of structure to another, nor can it be readily extrapolated to novel structures. Further, any single class of a traditionally designed structure has been typically found to have a large variability in actual safety levels, implying that resources could perhaps have been more optimally used. Particularly in the context of the present trend toward reliability-based design, reliability methods are suitable to bridge such gaps in traditional design. This is because performance uncertainty can be considered both directly and quantitatively with reliability methodology. Relative to a conventional factor of safety code, a probability-based design code has the promise of producing a better-engineered structure. Specific benefits are well documented in the literature. Chapter 26 Reliability-Based Design and Code Calibration A more efficiently balanced design results in weight savings andor an improvement of reliability. Uncertainties in the design are treated more rigorously. Because of an improved perspective of the overall design process, development of probability-based design procedures can stimulate important advances in structural engineering. The codes become a living document. They can be easily revised periodically to include new sources of information and to reflect additional statistical data on design factors. The partial safety factor format used herein also provides a framework for extrapolating existing design practice to new ships where experience is limited. Experience has shown that adoption of a probability-based design code has resulted in significant savings in weight. Designers have commented that, relative to the conventional working stress code, the new AISC-LRFD requirements are saving anywhere from 5% to 30% steel weight, with about 10% being typical. This may or may not be the case for ships and other marine structures. In reliability-based marine structural design, the effect of uncertainties in loads, strength and condition assessment is accounted for directly. Safety measures are calculated, for assessing designs or deciding on design targets. 26.3.2 Application of Reliability Methods to ASD Format A design equation may be formulated using ASD format as R, 2q-S, (26.7) Alternatively, the safety factor could be referenced to the capacity of the entire structure system Based on characterization of the demands and capacities as being log-normally distributed, the usage factor, q, in ASD can be expressed as @ea, et al, 1997) q = a-exp[(po Bs - 2.330,)] BR (26.8) where, q = usage (safety) factor a Bs BR /3 = annual safety index 0- os = factor that incorporates the interactive dynamic effects - transient loading and dynamic behavior of the system = median bias in the maximum demand (loading) = median bias in the capacity of the element = total uncertainty in the demands and capacities = uncertainty in the annual expected maximum loadings The number 2.33 in Eq. (26.8) refers to 2.33 standard deviations from the mean value, or the 99'h percentile. This is equivalent to the reference of the design loading to an average annual return period of 100 years. In case of installation conditions are defined on the basis of a 10- year return period condition, a value of 1.28 could be used (goth percentile). [...]... “Load and Resistance Factor Design for Steel”, J of the Structural Division, Vol 104, pp .133 7 -135 3 12 Song, R, Tjelta, E and Bai, Y (1998), “Reliability-based Calibration of Safety Factors for Tubular Joint Design”, Proc 8th International Offshore and Polar Engineering Conference (ISOPE’98), Montreal, Canada, May, 1998 13 Sun, H.H and Bai, Y (2001), “Time-Variant Reliability of FPSO Hulls”, SNAME Transactions,... Newman's approximation (Newman and Raju, 1981) given by AK = Ss,Y(a,X)J;;I; (27 .13) where S is the stress range and Y(a,X) is a geometry function accounting for the shape of the specimen and the crack geometry, EY is a randomized model uncertainty of geometry function By separating variables in Eq(27.12) and introducing Eq (27 .13) (27.14) Then, the differential equation can be expressed as: da N = C c... experience with use of safety factors for the specified tubular joints should be considered in the judgment 26.6 Numerical Example for Hull Girder Collapse of F’PSOs With a reference to Part 1 Chapter 13 and Part IV Chapter 25, this Section presents a 1 reliability-based calibration of hull girder collapse for FPSO(Sun and Bai, 2001) As an illustration, the bending moment criteria may be expressed as... parameters for simple tubular joint connections Figure 26.2 According to API RP2A-LRFD, the strength check of simple joints can be performed based on joint capacity satisfying the following Po < 4 jP"j (26 .13) Mo < +jM"j (26.14) where, PDis the factored axial load in the brace member, P,j is the ultimate joint axial capacity, MD is the factored bending moment in the brace member, M,j is the ultimate joint... reliability analysis is based on the probabilistic data given in Table 26 I Table 26.1 Basic Probabilisti 'arameter Descriptions Distribution Mean Random Variable Model uncertainty, X, Lognormal 1.16 COV 0 .138 Yield strength uncertainty, X, Lognormal 1.14 0.04 Diameter uncertainty, XD Normal 1.02 0.02 Thickness uncertainty, XT Normal 1.04 0.02 Load uncertainty, & Lognormal 0.90 0.08 Strength uncertainty, . Reliability Analysis of Aircraft Structural System”, Journal of Structural Safety, Vol. 16, pp. 36-46. 16. Mansour, A.E. (1972), “Probiblastic Design Concept in Ship Structural Safety and Reliability”,. Wave Loads and Their Application to Marine Structures”, Marine Structural Reliability Symposium, Arlington, VA. 20. Mansour, A.E. (1990), “An Introduction to Structural Reliability Theory”, SSC. the use of probability-based design criteria has the promise of producing better-engineered designs. For a marine structure, implementation of a probability-based design code can produce a structure