RELIABILITY ASSESSMENT OF WATERTIGHT SHIP DECKS AND BULKHEADS

Transcription

1 8 th ASCE Specilty Conference on Probbilistic Mechnics nd Structurl Relibility PMC RELIABILITY ASSESSMENT OF WATERTIGHT SHIP DECKS AND BULKHEADS J. A. Pires, M. ASCE, R. H. Sues, M. ASCE, nd Mrk Cesre, M. ASCE Applied Reserch Assocites, Inc., Albuquerque, NM, B. Bttchry nd R. I. Bsu Prdeep Senshrm ABS Americs, Houston, TX Designers nd Plnners, Arlington, VA Abstrct This reserch is developing frmework for relibility ssessment of eisting wtertight boundries of vitl spces of U.S. Nvy ships. These structurl components re essentil for ship survivl during flooding conditions tht occur fter dmge cused by collisions tht my tke plce s prt of norml pecetime opertions. The gol is to use this relibility ssessment frmework to estblish relibility levels inherent in present design prctices nd then develop relibility-bsed lod nd resistnce fctor design (LRFD) pproch for the wtertight boundries of new ships. Work to dte is presented nd includes probbilistic loding model, probbilistic structurl response nd dmge model, nd relibility nlysis techniques nd corresponding softwre. The methodology is illustrted for n emple bulkhed with the clcultion of relibility indices implicit in the current design prctice. While this work is being done for the U.S. Nvy, it is pplicble to commercil ships, which must meet similr dmge stbility criteri. Introduction Relibility-bsed design codes nd relibility ssessment frmeworks permit systemtic nd rtionl tretment of uncertinties, direct nd meningful comprisons of sfety levels, possible svings in structurl steel weight, nd risk ssessment studies. These benefits led the government nd privte sectors to emphsize implementtion of relibility-bsed structurl ship design (Mnsour et l., 1997, Melton nd Ayyub, 1999, Hughes et l., 1994, Hess, Bruchmn nd Ayyub, 1997). These efforts hve delt with the structurl design of the min ship structure while the work reported here ddresses the relibility nd design of wtertight boundries (WTBs) of vitl spces of U.S. Nvy ships. The primry objective of this work ws the development nd demonstrtion of frmework for the relibility ssessment of these wtertight boundries. Its gol is the ssessment of current design codes with the clcultion of underlying relibility levels nd then the development of relibility-bsed lod nd resistnce fctor design (LRFD) pproch for the WTBs of new ship structures. The mjor elements of the proposed methodology re probbilistic lod model, structurl response nd dmge model, which includes geometric nd mteril uncertinties, nd the relibility nlysis techniques nd corresponding softwre. These elements re briefly described in the following. Then, the methodology is illustrted with the clcultion of underlying limit stte probbilities for n emple bulkhed designed following the current design codes. Given the spce limittions only summry of the developments nd results produced is presented here. For complete descriptions the reders re referred to Pires et l. (2000). Pires, Sues, Cesre, Bttchry, Bsu nd Senshrm 1

2 Probbilistic Lod Modeling A probbilistic model ws developed to chrcterize internl sewter pressures on WTBs under the flooding conditions tht my follow collision dmge. The mjor ttributes of this model re s follows: (1) it is mechnics-bsed which mkes it pplicble to ships of different sizes nd clsses nd different dmge-cusing events; (2) reltes hydrosttic pressures to redily vilble ship design prmeters, which fcilittes its integrtion into design prctices; nd (3) the lods hve eplicit functionl dependence on the dmge-relted vribles. For more detils see lso Bttchry nd Bsu (2000). A combintion of mechnics- nd simultion-bsed pproches is used in the derivtion of the model, which consisted of the following steps: 1. Identify significnt vribles nd select those for inclusion in the model. 2. Identify distinct lod components on WTBs. 3. Develop simplified description of the ship dmge. 4. Estblish predictive equtions (mechnics-bsed) nd functionl forms (modified predictive equtions tht eplicitly relte lods to design vribles) for ech lod component. The functionl forms will hve undetermined coefficients to be determined s indicted in step 6 below. 5. Adopt n dequte but simple ship response model tht includes the vribles identified in step 1, nd eercise it over the rnge of vlues of the bsic vribles. 6. Identify the undetermined coefficients in the functionl models (step 4) using the results of step 5 nd regression nlysis. 7. Estblish the probbility distribution functions (PDFs) for the bsic vribles. 8. Use sttisticl simultion together with the functionl forms determined in steps 4 nd 6 nd the PDFs of step 7 to obtin the necessry lod sttistics. The force vector on WTB (F) is function of time nd spce nd is, generlly, the sum of two loding sources: F liquid nd F hull. F liquid represents the effects of liquids, either ingressed or liquid crgo, in direct contct with the bulkhed, nd F hull represents lods tht derive from the hull girder response. Lods from F liquid ct mostly norml to the WTB nd hve sttic s well s dynmic components. The dynmic components include wve ction, roll ction nd sloshing while the sttic components include drft, prllel sinkge nd trim. F hull represents lods from the hull girder response, which re mostly in plne forces, e.g., sher forces cused by bending nd torsion of the hull girder, s well s dynmic effects cused by environmentl lods, e.g., springing nd whipping. In this project, the focus is on the survivbility of WTBs under flooding conditions nd it is ssumed tht F liquid is the result of sewter ingress (F flood ). It is lso ssumed tht F hul is wekly dependent on the dmge vribles nd tht under flooding conditions the flooding forces govern the WTBs performnce. For these resons, F hull is not considered in this study. For convenience, the loding terms were seprted in those tht vry longitudinlly, i.e., with the distnce b from midships, nd those tht vry trnsversely (roll), i.e., with the distnce y from the centerline s follows: h( b, y) = h ( b ) + hy ( y). Functionl forms for the vrious loding terms were derived (steps 4 nd 7 bove) for militry Selift ship nd the following eqution ws obtined for the wter pressures: Pires, Sues, Cesre, Bttchry, Bsu nd Senshrm 2

3 h ( b ) = T + α b 11 sin α µ LBT l A L 21 w α 12 ep[ ε µρgbt ( LCF) + α ( MTm) fit 1 22 ] B1 µρglbt ( MTm) D + ε L fit 2 B 2 + ς (1) h y ep( kt / 2) * ( y) = y sinφ = y sin kς B (1 Λ ) + ν φ Λ (2) where µ = volume permebility for dmged comprtments, A W = wterplne re, = sewter density, g = ccelertion of grvity, L= ship length, B = bredth t midsection, T = drft t midsection, l = flooded length (depends on dmge loction nd ship subdivision),, 11, 12 = regression coefficients, D = distnce of center of dmge from midships, (LCF) = longitudinl center of flottion, MTm = moment to trim, Λ = frequency rtio ω/ω 0, ω = wve frequency, ω 0 = nturl roll frequency of the ship, k = wve number, ν φ = dmping fctor (between 0.1 nd 0.2) nd ζ = wve mplitude. Equtions 1 nd 2 contin terms tht ccount for curve fitting errors ( fit1 nd fit1 ) nd modeling errors (B 1, B 2 nd B 3 ). In the derivtion of these equtions, symmetric flooding is ssumed which removes the heel term. It is lso ssumed tht dmged ship will stop nd tke bem configurtion (regulr se stte), which elimintes the pitch term. Finlly, the vrition of roll nd wve with time re not considered nd only their mplitudes re included in the model. These ssumptions cn be reled with future developments. Sttisticl simultion ws used together with Equtions 1 nd 2 to clculte the sttistics of h nd h y. Rndom vribles included in the simultion were those for the curve fitting nd modeling errors, the geometric nd ship vribles T, A W,, 0, nd MTm, the independent dmge vribles l D (dmge length) nd D, nd the dependent dmge vrible l. The clculted sttistics re shown in Tble 1 below. Goodness-offitting tests suggest lognorml PDF for h. However, no PDF ws found for h y tht would pss goodness-of-fitting tests t cceptble significnce levels. On the bsis of its very lrge coefficient of vrition, Weibull distribution ws dopted for h. Tble 1. Sttistics of y h nd φ clculted with the Monte Crlo simultion Smple h φ Correltion coefficient Size men (ft) sd (ft) Men (deg) sd (deg) ( h nd φ ) 1,000, Response nd Dmge Model This model includes the definition of the filure modes or limit sttes for the WTBs, the lgorithms for the clcultion of lod effects nd the uncertinty model for the geometric Pires, Sues, Cesre, Bttchry, Bsu nd Senshrm 3

4 nd mteril properties of wtertight boundries. In its current form, the model considers strength nd stbility filure modes of stiffened bulkheds nd uses closed-form methods for the clcultion of lod effects. The filure modes or limit sttes considered in this study re s follows: 1. Ail loding nd bending of the stiffener-plte bem-column. 1.1 Limit Stte 1 Compressive stresses in the stiffener flnge Limit Stte 1 Defined by the design code equtions for limit stte Limit Stte 1b Defined in Chpter 14 of Hughes (1988). 1.2 Limit Stte 2 Plte buckling 2. Stiffener tripping (Limit Stte 3) Defined in Chpter 13 of Hughes (1988). Uncertinty models for the geometric nd mteril properties of stiffened bulkheds lredy published were used for this study. Specificlly, the uncertinty model proposed by Hess, Bruchmn nd Ayyub (1997) nd simplified form of it were used. The vribles considered in these models re: the ultimte nd yield strength of steel, the Young s modulus of steel, the thickness of the deck plting, stiffener flnge nd stiffener web, the width of the stiffener flnge, nd the height of the stiffener. In the emple pplictions, it ws ssumed tht the sme steel ws used for the deck plting nd stiffener. It is noted tht the coefficients of vrition for these properties re significntly smller thn the coefficient of vrition for the lod. Relibility Anlysis Algorithms nd Softwre Relibility ssessments were performed using first-order relibility methods (FORM) nd Monte Crlo simultions to verify the ccurcy of the FORM lgorithms. FORMs were chosen becuse of their computtionl efficiency nd becuse they yield sensitivity coefficients useful to interpret the results nd identify significnt rndom vribles. A commercil softwre tool clled ProFES (Probbilistic Finite Element Softwre) (Cesre nd Sues, 1999) ws used for ll relibility ssessments. ProFES is user-friendly softwre tht links probbilistic mechnics engine with either finite element codes or with user defined softwre tht eecutes the lgorithms tht clculte the response vribles needed to evlute the limits stte functions. Currently, the proposed relibility ssessment frmework for the WTBs uses closed-form epressions to clculte these response vribles nd ssumes liner-elstic structurl response. Future developments of this frmework will use finite element nlysis (including nonliner inelstic nlyses) to clculte the lod effects. This will tke full dvntge of ProFES cpbilities. Illustrtive Appliction The proposed methodology is illustrted with the preliminry clcultion of underlying limit stte probbilities for n emple bulkhed designed using current design codes. Schemtic representtions of the ship nd bulkhed cross-sections re shown in Figure 1. The ship dimensions nd comprtments re comptible with those used for the derivtion of the probbilistic lod model. A limited sensitivity nlysis ws conducted to ssess the effect of the rtio of the ded lod to the hydrosttic flooding pressures. Accordingly Pires, Sues, Cesre, Bttchry, Bsu nd Senshrm 4

5 low, medium nd high lod rtios (ded lod to hydrosttic lod) were considered. A summry of the relibility indices clculted for bulkhed DE is shown in Tble Fore tnk ft ft ft ft ft ft ft Section A B C D E F G H Bulkhed Pnel Wter Pressure, H Figure 1. Schemtic models of longitudinl nd trnsverse ship cross-section Emintion of the results in Tble 2 indictes tht for limit stte 1, the relibility indices re smller when the design equtions re used to represent the limit stte thn when the more ccurte equtions of limit stte 1b re used. It is interesting to notice tht the criticl filure mode ppers to be limit stte 2 (buckling of the deck plting). This is somewht unepected becuse the design mrgins for this limit stte were somewht greter thn those for limit stte 1. Sensitivity of the limit stte relibilities to vrious rndom vribles ws investigted by compring the sensitivity coefficients (director cosines squred) clculted with FORM. These coefficients re shown in Figure 2 for bulkhed DE, limit sttes 1b, 2 nd 3 s defined bove nd for the medium ded lod intensity. 1 Tble 2. Relibility indices for bulkhed DE Ded Limit Stte Lod 1 1b 2 3 Low Medium High Sensitivity Coefficient Lod Flnge Thickness Plte Thickness Yield Strength Limit Stte 3 Limit Stte 2 Limit Stte 1b Figure 2. Sensitivity coefficients (bulkhed DE) Emintion of these results indictes the higher significnce of the loding for ll limit sttes. However, for limit stte 2, the relibility is lso quite sensitive to the bulkhed Pires, Sues, Cesre, Bttchry, Bsu nd Senshrm 5

6 plte thickness. This seems to be consequence of the fct tht the llowble stress for this limit stte is proportionl to the squre of the bulkhed plte thickness. Conclusions A frmework for the relibility ssessment of the wtertight boundries of vitl spces of U.S. Nvy ships ws described. This frmework ws illustrted with the preliminry clcultion of underlying relibility indices for n emple bulkhed designed using the current llowble stress design codes. The gol of the proposed frmework is the ssessment of current design codes, in terms of underlying relibilities, nd the development of relibility-bsed lod nd resistnce fctor design pproch for the wtertight boundries of new ship structures. Acknowledgements The work reported here ws performed s prt of the U.S. nvy Phse I SBIR contrct number N C The technicl monitor for this contrct ws Mr. Nt Nppi. His mny contributions to this study re lso grtefully cknowledged. References Mnsour, A., et l., (1997), ssessment of Relibility of Eisting Ship Structures, Ship Structures Committee, Report SSC-398. Melton, W. M. nd B. Ayyub, (1999), LRFD Rules for Nvl Surfce Ship Structures: Relibility-Bsed Lod d Resistnce Fctor Design Rules, Report No. NSWCCD-65-TR-1998/4. Huges, O., E. Nikolidis, B. Ayyub nd P. Hess, (1994), Uncertinty in Strength Models for Mrine Structures, Ship Structures Committee, Report SSC-375. Hess, III, P. E., D. Bruchmn nd B. Ayyub, (1997), Uncertinties in Mteril nd Geomteric Strength vribles in Mrine Structures, Chpter 14 in Probbility, Sttistics & Relibility for Engineers, Bill M. Ayyub nd Richrd H. McCuen, editors, CRC Press, Boc Rton, Florid. Bttchry, B., nd R. I. Bsu, (2000), Relibility of Wtertight Boundries, ABS Project ID: P39934R4. Pires, J. A., M. Cesre, R. H. Sues, B. Bttchry, R. I. Bsu nd P. Senshrm, (2000), Relibility Assessment of Wtertight Boundries, Finl Report, Nvy SBIR Topic N99-088, Contrct No. N C-4143, Prepred by Applied Reserch Assocites, Inc., for Nvl Se Systems Commnd. Hughes, O.F., (1988), Ship Structurl Design A Rtionlly-Bsed, Computer-Aided Optimiztion Approch, Society of Nvl Architects nd Mrine Engineers (SNAME), Jersey City, New Jersey. Cesre, M. A. nd R. H. Sues, (1999), ProFES, Probbilistic Finite Element Softwre Bringing Probbilistic Mechnics to the Desktop, Americn Institute of Aeronutics nd Astronutics, pper AIAA Pires, Sues, Cesre, Bttchry, Bsu nd Senshrm 6