Guidance Notes on Whipping and Springing ...

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1 Marine Product Development, Lloyd's Register, London, UK .... modules for linear frequency domain springing analysis and a time domain nonlinear hydroelastic code .... above waterline portion and a free surface lid were also modelled.
Guidance Notes on Whipping and Springing Assessment Nigel White1, Zhenhong Wang1, Yongwon Lee1 ABSTRACT The demand for larger container ships has increased dramatically in the last few years as world trade continues to grow and the marine industry requires more energy efficient ships. Currently the largest of these ships have capacities of 15,500 TEU and designs of 18,000 TEU or more are currently being prepared. Due to the large deck openings of these ships, whipping and springing phenomena can be critical for their design and operation. Springing of a ship is defined as continual hull girder vibration as a consequence of waves exciting resonant hull girder frequencies. The flexing of the hull girder due to springing may continue for a significant period once initiated. This can make springing important with regard to the fatigue life of a structure. Whipping of a ship is defined as the rapid flexing of the hull girder as a consequence of a wave impact on the hull. This usually results in high frequency cyclic oscillations of the hull girder which may result in increased vertical wave induced bending moments and shear forces compared to linear theory. The oscillations of the whipping responses usually decay rapidly after several wave periods due to damping effects. Whipping is primarily a strength issue. This report presents some methods to determine values of dynamic bending moments considering the effects due to whipping and springing which are suitable for design application. Examples of the use of these methods are also presented.

KEY WORDS Nonlinear Ship Motions, Hydroelasticity, Fluid Structural Interaction, Whipping, Springing, Container Ships, Classification Rules INTRODUCTION The whipping and springing phenomenon is not new and has occasionally been a critical design issue which has been dealt with on a case by case basis. However in recent years, this issue has become more important due to the rapid increase in size of container ships to match growth in world trade and marine industry requirements for cheaper and more energy efficient shipping. Currently the largest container ships have capacities of 15,500 TEU and designs of 18,000 TEU or more are on order. Due to their large ship length, large deck openings and high transportation speeds, the springing and whipping phenomena can be critical for the design and operation. Whipping and springing are also very important for other ship types; in particular Great Lakers are specifically designed for operation in the Great Lakes and St Lawrence Seaway and hence are very long and narrow with low hull inertia values. Whipping and springing are limiting design issues for these ships if they need to operate outside this region. Other ship types affected can include ultra large ore carriers and ultra large bulk carriers. The assessment of vertical wave bending moment and other global loads taking into account nonlinear wave effects including structural resonance issues, is very complex. The techniques used to solve this problem are classed as Fluid Structure Interaction (FSI) analyses, although the term used for the whipping and springing issue is hydroelasticity using specialist hydroelastic analysis codes. The state of the art with respect to ship motion analysis is still developing and will do so for many years to come, hence the assessment of the whipping and springing wave loads on ships using direct analysis is still very much a specialist issue. Currently almost all yards, designers and classification societies have access to linear ship motion analysis programs and these all generally give similar results, however this is not the case for hydroelastic codes where only the most technically advanced organisations have access to and are capable of using hydroelastic codes to get consistent results. In all cases these hydroelastic codes are in the development phase and specialist combined hydrodynamic and dynamic structural engineers are striving to improve and calibrate these codes. This paper looks at a suitable method to derive the extreme hull girder vertical wave bending moment for a very large container ship, around 13,000 TEUs, taking account of nonlinear hull form issues, wave impact issues and hydroelastic effects. The structural assessment procedure for assessing the capability of the ship to withstand such loads is also presented. The procedure is illustrated with an example calculation.

1

Marine Product Development, Lloyd’s Register, London, UK

The purpose of this paper is to provide methodologies for the practical evaluation of the hydroelastic response of the ship due to whipping effects and how to assess these for design verification purposes. The detailed theory of hydroelasticity will not be discussed in this paper, the reader can find the methodology used by Lloyd's Register in Lee 2011a and Lee 2011b. Wang et al 2012 (in draft) looks at the application of the guidance notes to derive springing bending moment loads for the fatigue assessment. WHIPPING AND SPRINGING OF SHIPS IN WAVES Description of springing Springing of a ship is the continual hull girder vibration as a consequence of waves exciting resonant hull girder frequencies. This vibration or flexing of the hull girder due to springing may continue for a significant period once initiated. Springing is an issue for ships which have low hull girder natural vibration frequencies. Particularly important are the vertical bending and hull girder torsional (twisting) modes, with the latter only really an issue for container ships. Springing is typically an issue when the lowest hull girder natural vibration frequency is greater than 2 seconds and the ship operational speed is above 20 knots. This is the case for large container ships due to their long length, high speed and open cross sections. Springing is an issue for other ships such as Great Lakers due to their high length/depth ratios. Ships that have hull girder natural frequencies close to the encounter frequencies of the wave energy region are potentially prone to springing. It should be noted that springing is not normally a strength issue because the magnitude of the hull girder stresses due to springing is usually low. However, the number of cycles of the springing stress is very large (about 4 to 8 times the number of wave cycles) and this can make springing important with regard to the fatigue life of a structure. Description of whipping Whipping of a ship is the rapid flexing of the hull girder as a consequence of wave impacts on the hull. This usually results in high frequency cyclic oscillations of the hull girder which may result in increased vertical wave induced bending moments and shear forces compared to linear theory. High whipping responses are usually driven by bow flare impacts due to large bow flare angle and high speed or by bottom slamming. Occasionally stern counter slamming can lead to high whipping responses. The oscillations of the whipping responses usually decay rapidly after several wave periods due to damping effects. Whipping is primarily a strength issue. It is not a fatigue issue as the whipping induced vertical bending moment oscillations usually damp out quickly and hence the total number of whipping cycles in the ship’s life is small. In addition springing may be excited after a wave impact as there is little damping resistance of the hull girder natural vibrations. Full scale measurements of the amidships vertical wave induced bending moment of an 8,100 TEU container ship are shown in Figures 1 and 2. A typical hull girder response due to bow slamming impact measured by a long base strain gauge is given in Figure 1. The hull girder natural frequency response has been extracted from the total response in Figure 1 and is shown in Figure 2. A whipping event is shown by the sudden amplitude increase at 418 seconds caused by the slamming impact, the initial high response decreases quite quickly due to hydrodynamic and structural damping effects. This time trace also shows a continuous springing hull girder vibration (Bakkers, 2009).

Figure 1 A typical hull girder response due to bow slamming impact measured by a long base strain gauge

Figure 2 Hull girder natural frequency vibration (springing and whipping) response obtained by filtering GUIDANCE NOTES FOR WHIPPING AND SPRINGING ANALYSIS Lloyd's Register is currently undertaking an extensive research program into whipping and springing issues and recently published a draft document "Guidance notes on the assessment of global design loads of large container ships and other ships prone to whipping and springing", draft version 1.1, dated June 2011, LR 2011. This document has been circulated in draft form to a few yards and designers as part of a consultation process prior to releasing a final version. The guidance notes cover: • assessment of the vertical wave bending moment for extreme strength purposes including nonlinear effects of hull form shape and hull girder whipping due to slamming. The guidance notes include details on how to assess the hull girder strength against these whipping induced hull girder loads. • assessment of the vertical wave bending moment for fatigue strength purposes to cover nonlinear effects of hull form shape including springing response and worldwide operation in any sea condition. The guidance notes provide details on how to assess the hull girder fatigue strength including the effects of springing. These guidance notes provide explicit details of the hydroelastic analysis procedures required to derive the hull girder design values including whipping and springing effects. Hence procedures are provided on ways of applying the hydroelastic codes in a consistent way that will allow designers to obtain consistent extreme and springing design vertical wave bending moments for the structural assessment. However the guidance notes recognise that both the hydroelastic analysis software and the use of this software for design application are currently in the development stage. As a consequence, there are currently several different approaches possible and hence the notes suggest recommended procedures for each of the principal approaches. This paper will concentrate on the Equivalent Design Seastate (EDS) methods as this is Lloyd's Register's preferred approach. The other major item of research is the development of in-house hydroelastic ship motion codes. This will include modules for linear frequency domain springing analysis and a time domain nonlinear hydroelastic code that will allow the wave impact forces acting on the ship in the bow and stern regions to be calculated as well as the resulting whipping response. This development is an extension of Lloyd's Register's WAVELOAD ship motion program, (Lin 2011, Lin 2012). Related research issues Lloyd’s Register along with KR, ABS, BV, GL, NK, DSME, HHI, SHI, SNU have participated in the WILS II Joint Industry Project (Wave induced loads on ships JIP) led by MOERI. The aim of this project was to enhance understanding of the combined effects of fully nonlinear wave induced loads on the global dynamic response of container ships. The main objectives of this JIP were to provide reliable model test data of a large container ship and to compare these results with predicted springing and whipping responses from current hydroelastic analysis tools. Lee 2011a, Lee 2011b and Hong 2010 present the predictions of springing and whipping responses for a 10,000 TEU container ship (WILS II container ship) in the frequency and time domain using hydroelastic analyses against the model test experiments, see Figure 3. An example of the time trace of the wave vertical bending moment for a regular wave is shown in Figure 4. For idealising the ship and handling the flexible modes of the structure, a boundary element method and a finite element method are employed for coupling fluid and structure domain problems. The hydrodynamic module takes into account nonlinear effects of Froude-Krylov and restoring force. This is also coupled with a slamming load module based on momentum theory to predict impulsive wave loads due to bow flare. The vibration modes and natural frequencies of the ship hull girder are calculated by idealising the ship structure as a 2D Timoshenko beam. The tools used were the PRECAL, PRETTI and TDWHIP suite from the CRS (Co-operative Research Ships) consortium. The same techniques have been applied to a real very large container ship design for the results presented in this paper.

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Figure 4: Typical nonlinear VBM response due to hull shape - model test results. Figure 3 WILS II JIP model tests

ASSESSMENT OF THE EXTREME WAVE BENDING MOMENT A full scale measurement time history of vertical wave bending moment of an 8500 TEU container ship with a typical whipping response in waves is shown in Figure 5. Note this is a different ship from that used for the model test.

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Figure 5: Typical whipping effects of VBM in the full scale measurement. Assessment procedure The procedure for deriving the extreme hull girder bending loads and for assessing these loads is summarised below and discussed in more detail in the following sections. The process is also illustrated in Figure 6. 1.

Assessment of the long term design linear wave loads • Determine the linear hull girder design loads along the ship length. The ship motions are calculated using a linear potential flow hydrodynamic program and statistical (short term and long term) results using North Atlantic wave scatter diagram, IACS Rec 34.

2.

Assessment of the design vertical wave bending moment due to nonlinear effect of hull form shape Determine the nonlinear hull girder design loads due to hull shape issues. This provides revised nonlinear sag and hog factors which can be applied in the standard rule assessment process. • Derive the Equivalent Design Sea State (EDS) that gives a linear vertical wave bending moment equivalent to the long term value.

• •

3.

Undertake nonlinear time domain simulations for ship motions and vertical wave bending moment for this EDS including nonlinear hull form issues only. The method also allows calculation of the effects of nonlinearities on vertical shear forces, horizontal bending and torsional moments. Replace the standard Rule hogging and sagging correction factors with these revised factors and update the standard structural assessment of the hull girder.

Assessment of the hull girder loads including whipping response Determine the non-linear hull girder design loads due to hull shape issues and whipping impact loads. From these responses, the non-linear whipping sag and hog factors are derived in order to be applied in the ultimate strength calculations. • Undertake nonlinear time domain simulations for ship motions and vertical wave bending moment for the same EDS as derived in 2 above including nonlinear hull form issue, impact loads on the bow regions of the ship and hull girder flexibility (whipping) issues. The method also allows calculation of the effects of nonlinearities on vertical shear forces, horizontal bending and torsional moments. • The whipping sagging and hogging wave bending moments are obtained by factoring the rule vertical wave bending moment by the whipping sag and hog factors. • Derive the ultimate strength capacity of the ship's hull girder and compare with the total still water plus whipping vertical wave bending moment.

For the final strength assessment, the strength along the whole ship is to be assessed, not just the midship section.

Figure 6 Flowchart of the main elements of the nonlinear design load assessment procedure ASSESSMENT OF THE DESIGN VERTICAL WAVE BENDING MOMENT DUE TO NONLINEAR EFFECT OF HULL SHAPE Reference ship details For this study, the following ship has been used: Container ship size: 13000 TEUs Lpp 350 m Beam 48 m Draught 15 m Cb 0.70 Hydrodynamic model

The hydro mesh has about 3,200 panels for the below waterline portion with an approximate panel length of 2.7 m. The above waterline portion and a free surface lid were also modelled. See Figure 7. The forward slamming region is defined by 16 cuts (intersection plane with the hydro mesh) over the forward 30% of the ship with a 30 degree cutting angle. The cuts are aligned approximately normal to the wave surface during slamming events in head seas making allowance for the ship forward speed.

Figure 7: Hydrodynamic mesh Determination of the Equivalent Design Sea State (EDS) The EDS is defined as the sea state which has the maximum contribution to the long term 10-8 probability of exceedance long term vertical wave bending moment amidships. The long term vertical wave bending moment is calculated in the standard way as specified in IACS Rec. 34. Hence this assumes equal probability of heading and linear ship motion analysis; the PRECAL linear ship motion code was used for a forward speed of 5 knots. The critical sea states that have the greatest contribution to the long term vertical wave bending moment amidships are listed in Table 1. From this table the Hs = 14.5 m and Tz = 11.5 s EDS is selected. Table 1: Individual contribution of each sea state to the long term 10-8 value 13.5 4.02% Significant 2.74% 3.69% wave height 14.5 4.93% Hs (m) 15.5 3.00% 4.44% 4.03% 16.5 3.36% 12.5 13.5 9.5 10.5 11.5 Zero crossing period, Tz (seconds) Calculations of Nonlinear Ship Motions in Time Domain The ship motion under the equivalent design wave condition in head seas was calculated using the CRS hydrodynamics program PRETTI V1.5. PRETTI is a nonlinear rigid body version of PRECAL and includes the nonlinear wave exciting and restoring forces due to variations in hull form above and below the waterline, the time domain aspects being solved by means of the convolution integral. The time interval for the time domain simulation was 0.025s and total simulation time was 3 hours. The ship motions and external loads are solved at each time step and this allows the total vertical bending moment to be derived. Unlike frequency domain codes, time domain codes include the still water load terms and hence the still water bending moment needs to be removed in order to derive the wave only components. The resultant time trace of the nonlinear vertical wave bending moment including hull form shape effects is shown in Figure 8.

VBM amidships - PM spectrum (Tz=11.5s, Hs=14.5m) 1.0E+07 Linear

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Figure 8 Time domain nonlinear vertical wave bending moment Having derived the vertical bending moment in the time domain, it is then necessary to extract the probable maximum values of hogging and sagging wave bending moment. The probability distributions of the sagging and hogging bending moment distributions of the time domain simulation are derived using a peak counting method. Both peaks and troughs (corresponding to the hogging and sagging wave bending moments, based on the usual sign convention of the vertical bending moment) of the time domain signal are counted separately as one peak or trough per mean zero crossing period, see Figure 9. Figure 9 shows the peak counting method applied to the nonlinear bending moment time trace, denoted as "nonlinear", and also to the comparable nonlinear bending moment including whipping time trace, denoted as "whipping". The probable maximum hogging and sagging bending moments in three hours were obtained by fitting a 3 parameter Weibull to the probability of exceedance of the peak values. The curve fitting routine was chosen such that it concentrates on a best fit over the tail of the distribution, hence the fitting distribution applied equal weighting across the distribution and did not take account of the number of values within each probability bin. In this case some of the smallest bending moment values may have been excluded in the curve fitting process in order to improve the fit over the tail. See Figure 11 and Figure 12 for the nonlinear hogging and sagging bending moment Weibull curve fits. The curve fitting routine adopted was as follows: The best fit was obtained by minimising Standard Deviation (SD) given by: 1 SD = Nb

2

Nb

∑ (M

a

−M f

)

n =1

where Nb Ma Mf

number of probability bins value of probability bin value derived using the curve fit parameters. The location parameter was adjusted incrementally and the shape and scale parameters derived from the curve fitting routine for each value of the location parameter. The SD value was derived for each location value and the location value with the minimum SD was taken as the best fit.

The probable maximum hogging and sagging bending moments in three hours for this ship are given in Table 3.

Example of counting for extremes

Linear Linear count

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Figure 9: Example for extremes of bending moment signal Derivation of the final nonlinear correction hogging and sagging factors The hogging and sagging correction factors to be applied to the linear wave bending moment term due to hull shape issues based on nonlinear time domain ship motion analysis of the ship in the EDS irregular wave are given by: M 3h nonlinear sagging correction factor: f fS = VS = -1.43 [1] 3h M VL nonlinear hogging correction factor: f fH =

3h M VH 3h M VL

= 0.94

[2]

where 3h M VS

is the “probable maximum sagging bending moment in 3 hours”.

3h M VH 3h M VL

is the “probable maximum hogging bending moment in 3 hours”. is the “probable maximum linear bending moments in 3 hours”. This can be derived from short term statistical analysis using the EDS or from a linear time domain simulation using the same time-train of the nonlinear time simulation but ignoring the nonlinear hydrostatic forces and wave incident forces due to the hull shape.

These values are effectively on the same basis of the standard rule approach which considers the effects of hull shape and wave height through the specification of hogging and sagging correction factors, see Lloyd's Registers Rules for the Classification of Ships, Part 4, Ch 2, Section 2.4. The standard rule values of these factors for this ship are: Rule sagging correction factor: ffS = -1.25 Rule hogging correction factor: ffH = 0.95 Hence the standard rule value for hogging is very close to the value derived using the nonlinear ship motion analysis method. The sagging correction factor is underestimated by the standard rule approach for this ship even though this standard rule approach takes account of bow flare and large stern flare. It should be noted that the standard rule value for tankers and bulk carriers is -1.1, hence the nonlinear sagging correction factor represents a 30% increase in the sagging wave bending moment. ASSESSMENT OF THE HULL GIRDER LOADS INCLUDING WHIPPING LOADS Structural model of the ship The hull structure is modelled as a non-uniform Timoshenko beam model using 50 beam elements. The longitudinal distribution of lightship and deadweight mass and of the hull girder inertia were applied to the free-free beam model. The natural frequencies of the hull girder beam FEM were obtained by undertaking a dynamic linear analysis to derive the eigenvectors and hence the modal shapes. At this stage only the mass of the ship is considered and hence the vibration frequencies and mode shapes are only for what is termed the dry mode. The wet mode frequencies are derived by the complete hydroelastic analysis which include the added mass due to the surrounding water.

For this assessment only vertical bending vibrational modes have been studied, hence each node of the beam element has only 3 degrees of freedom. The first 4 natural frequencies of vertical bending modes from the modal analysis are listed in Table 2.

Mode No. 1 2 3 4

Table 2: Natural frequencies of first 4 vertical bending modes, in Hz Mode shape Natural frequency of dry mode Natural frequency of wet mode 2 node VB 0.698 0.498 3 node VB 1.608 1.173 4 node VB 2.680 1.986 5 node VB 3.829 2.889

The damping coefficient of the first vertical bending (VB) mode (2 node vertical vibration) is assumed as 1.5%. Nonlinear hydroelastic analysis The ship motion under the equivalent design wave condition in head seas was calculated using the CRS hydrodynamics programs PRETTI V1.5 (nonlinear rigid body version of PRECAL) and TDWHIP (nonlinear flexible body code). In the simulation, bow slamming loads and the nonlinear wave exciting forces and restoring forces due to hull shape variation about the mean waterline were accounted for in the time domain as were the wave induced whipping (2 to 5 node vertical bending) responses. The bow slamming loads were derived as follows: at each timestep the relative vertical velocity at each of the bow cuts is assessed and if it exceeds a preset threshold value, then the impact force on that cut is evaluated using momentum theory (using the CRSLAM program) and then included in the ship motion analysis. The time interval in the time domain simulation is 0.025s and the total simulation time was 3 hours. The resultant time trace of the nonlinear vertical wave bending moment including whipping responses is shown in Figure 10. VBM amidships - PM spectrum (Tz=11.5s, Hs=14.5m) 1.0E+07 Whipping

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Figure 10 Nonlinear vertical wave bending moment including whipping responses Time domain simulation using the EDS approach The probability distributions of the sagging and hogging bending moment distributions of the time domain simulation are derived using a peak counting method as described above. For the whipping response time trace, only the maximum peak or trough per mean zero crossing period was used, see Figure 9. Determination of the maximum expected bending moment The maximum expected bending moment is obtained by extrapolating the realisation of extremes using a 3 parameter Weibull fit. The peaks and troughs in the bending moment signal for linear, nonlinear and whipping analysis are counted using the Rainflow Count Algorithm based on mean crossing period of the rigid-body, that is, counted by identifying one peak/trough per crossing of the mean value of the rigid ship. A typical example of peak/trough count for the bending moment of linear (rigid body), nonlinear (rigid body) and whipping (flexible body) signal is shown in Figure 9. The probability of exceedance of the hogging/sagging vertical bending moment including whipping and their Weibull fit curves are shown in Figure 11 and Figure 12. The probable maximum expected bending moment including the whipping response in 3 hours is given in Table 3.

The number of peak and trough events of the rain flow account in 3 hours is 965, hence the probability level for the 1 in 3 hours is 1.04x10-3. From this the probable maximum values of vertical wave bending moment in 3 hours at 95% confident interval extracted from the Weibull plots and are shown in Table 3. Hogging VBM

Sagging VBM

Nonlinear count Nonlinear fit

Whipping count Whipping fit

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P(x>My)

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Linear fit

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Whipping fit

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My(kNm)

My(kNm)

Figure 11: Weibull fit of hogging moment

Figure 12: Weibull fit of sagging moment

Equivalent Design Wave Hs = 14.5m, Tz = 11.5 s Hogging case Sagging case

Table 3: Maximum expected VBM in 3 hours Nonlinear VBM (due to hull Linear VBM form shape issues) VBM GNm 3h M VL

= 7.845

Nonlinear VBM including whipping response

VBM GNm

VBM GNm

3h M VH = 7.343

3h M WH = 11.12

3h M VS = -11.22

3h M WS = -15.51

Derivation of the final nonlinear whipping correction hogging and sagging factors When the effects of whipping and the momentum loads due to wave impact forces forward are included, the nonlinear hog and sag ratios induced by whipping in the irregular wave time domain simulation are: M 3h Whipping sagging correction factor: f fS −W = WS = -1.98 [3] 3h M VL Whipping hogging correction factor: f fH −W =

3h M WH 3h M VL

= 1.42

[4]

where 3h M WS

is the maximum value of the “probable maximum whipping sagging moment in 3 hours” from the time domain simulation including whipping of the EDS.

3h M SH

is the maximum value of the “probable maximum whipping hogging moment in 3 hours” from the time domain simulation including whipping of the EDS.

3h M VL

is the maximum value of the “probable maximum linear bending moments in 3 hours” from the nonlinear time domain simulation without whipping of the EDS. This can be derived from short term statistical analysis using the EDS.

The whipping sagging correction factor represents a massive 60% increase in the sagging wave bending moment compared to the standard rule value for this ship (ffS = -1.25). Fortunately large container ships usually have large hogging still water bending moments (SWBM) which mitigate this increase in sagging vertical wave bending moment. This is illustrated in the structural assessment section. Both the sagging and the hogging wave bending moments including whipping show a large increase over the standard rule values. One of the key issues is the accurate prediction of the bow flare impact loads and this is an area that is still under validation. (Storhaug 2010) present the results of model tests of the hydroelastic response of a similar sized container ship. They include the results for a range of seastates. For the severe seastate of Hs= 11.5, Tz = 11.5 and a forward ship speed of 10 knots, they obtain maximum measured bending moment values of 14.0GNm for hogging and -16.7GNm for sagging. They conclude that the effect of whipping can increase the standard IACS sagging wave bending

moment by 80% for this sea state. From this we can assume that the values derived in this assessment are comparable with model tests, although further work is required to compare these results in more detail. STRUCTURAL ASSESSMENT Application to the structural assessment including the effects of nonlinear hull shape issues The design values of vertical wave bending moments including nonlinear effects of hull shape are to be used for the normal structural assessment in accordance with the Ship Rules. Hence these values replace the Mw rule values in Pt 4, Ch 2 and are to be applied to the: • Rule inertial and section modulus requirements and local scantling requirements • Rule buckling requirements • SDA procedure For this design the Permissible Still Water Bending Moments used in the initial design assessment were as follows: Hogging SWBM = 7.4GNm Sagging SWBM = 0 GNm (hence the ship always hogs and consequently the sagging SWBM was set to zero) Using these values of SWBM and hogging and sagging nonlinear correction factors of 0.94 and -1.43 respectively does not cause any limiting criteria to be exceeded. Hence the direct calculation of the hogging and sagging nonlinear correction factors has no effect on the above rule requirements. Application to the structural assessment including the whipping loads The design values of vertical wave bending moments including nonlinear effects of hull shape and whipping are to be used for structural assessment as follows: • Rule buckling requirements for stiffeners. For this application the buckling factor β in Lloyd’s Register’s Ship Rules, Pt 3, Ch 4, 7.5 is be taken as 1.0 for longitudinal stiffeners. • Ultimate strength assessment in accordance with the IACS Common Structural Rules for Double Hull Oil Tankers (CSR-DHOT). The design values of vertical wave bending moments including whipping are to be taken as follows: VBM NL − H = f fH −W M wo for hogging VBM NL − S = f fS −W M wo for sagging For this ship Mwo = 8.63 GNm, f fH −W = 1.42

(this is the rule wave bending moment value excluding the hog and sag correction factor and the longitudinal distribution factor). f fS −W = −1.98

Hence the wave BM including whipping VBMNL-H = 12.26 GNm for hogging

VBMNL-S = -17.09 GNm for sagging

Ultimate strength assessment The ultimate strength of the hull girder can be evaluated using either the incremental-iterative approach in the CSR software or LR20202 and LR20203 or equivalent procedures. The incremental-iterative approach is based on the classic method (Smith 1977). For this study, the ultimate strength has been derived using the LR20202/LR20203 software, (Rutherford 1990). This approach is usually slightly more conservative than the CSR method as the load shortening curves derived using LR20202 are more conservative than the IACS method, especially in the post collapse region where the LR20202 post buckling capacity is significantly less that the CSR method for some stiffener/plate combinations. The criteria to apply is M SH + γ W VBM NL − H ≤

MU

γR

for hogging

M SS + γ W VBM NL − S ≤

MU

γR

for sagging

[5]

Where maximum sagging SWBM that is practical at the draught being considered. MSS MSH maximum hogging SWBM that is practical at the draught being considered. MU ultimate capacity based on half the standard deduction for corrosion, dt given in the Ship Rules, Pt 3, Ch 4, Table 4.7.1

γW

partial safety factor for wave bending moment, to be taken as 1.2

γR

partial safety factor for capacity, to be taken as 1.1

For this design the maximum and minimum values of the SWBM in the loading manual have been reviewed and these provide the following values: MSS =3.0 GNm for sagging MSH = 7.0 GNm for hogging hence this ship always has a considerable hogging bending moment in the still water condition. From these, the total ultimate design bending moments are: M H + γ W VBM NL − H = 21.71 for hogging

M SS + γ W VBM NL − S = -17.514GNm for sagging

The ultimate strength gross capacity calculated is as follows: MU = -20.40 GNm for sagging MU = 24.80 GNm for hogging Figure 13 shows screen shots of the ultimate strength calculation. Figure 13(c) shows the derived hogging and sagging ultimate hull girder bending moment capacity graphs. Figure 13(a) and (b) show the state of midship cross section structural members at the point of the maximum bending moment capacity of the hull girder, these points are shown as a blue or red dot on the curve. Each structural member is either in the post collapse state or the pre collapse state and the key at the top of these figures indicates what type of failure has occurred. The rule requirement specifies that net scantlings based on half the standard deduction for corrosion are to be used. For the deck plating, which is the limiting criteria for sagging ultimate strength, see Figure 13(b), the deck plating is in excess of 70mm and the standard corrosion deduction is 1mm. For the bottom shell, the standard corrosion deduction is 2.1mm and hence the gross thickness in the ultimate strength calculation is reduced by 1mm or approximately 5%. As the current ultimate strength software for non CRS ships only uses the gross scantling, then a 5% reduction was applied to the gross capacity values. This will be conservative for the sagging capacity and fairly neutral for the hogging capacity. For this study, the ultimate strength net capacity has been taken as 95% of the gross capacity, hence MU = 23.56 GNm for hogging MU = -19.380 GNm for sagging Rewriting the above equations in terms of achieved partial safety factors gives MU MU for hogging and γ AS = for sagging γ AH = M SH + γ W VBM NL − H M SS + γ W VBM NL − S where γ AH ≥ γ R for a satisfactory design For this ship

γ AH = 1.09 for hogging

and γ AS = 1.10 for sagging which are very close to the required γ R value of 1.10. Using the standard rule permissible still water BM would have meant that the sagging capacity was well short of the required standard. However by using a sagging SWBM that is actually based on the operational requirement of the ship leads to the conclusion that the design meets the draft guidance note requirements. The requirements for the other buckling strength criteria give almost identical results. This is not surprising as the shape of the ultimate strength curves, Figure 13 (c), show a rapid reduction in strength after the initial collapse of the deck (and coaming) in the sagging mode and of the bottom in the hogging mode.

(a) Status of structure at the point of maximum hogging capacity (red spot in c)

(b) Status of structure at the point of maximum sagging capacity (blue spot in c)

(c) hogging and sagging ultimate hull girder bending moment capacity graphs Figure 13 Ultimate strength assessment CONCLUSIONS This study presents results from a method to derive design loads for a large container ship taking into account bow flare impact loads and the whipping response of the hull girder based on hydroelastic ship motion analyses. Whilst methods to derive the long term linear design vertical bending moment and other long term ship motions parameters have been around for many years and are readily available, methods and tools to consider the effects of impact loads and the resulting whipping are not yet fully tested and verified. The method used has been taken from Lloyd's Register's recently issued draft guidance notes on whipping and springing assessment which also includes design requirements for the structural assessment. The study applies the derived whipping hull girder bending moments to the structural assessment in order to confirm that the design is adequate. The study uses an Equivalent Design Seastate (EDS) approach to select the most suitable seastate for the derivation of the extreme bending moment response. The resulting EDS is the seastate that provides the maximum contribution to the long term wave bending moment, so it is a severe seastate. Undertaking a time domain nonlinear ship motion analysis including bow impact loads and hull girder flexibility (whipping) results in a whipping enhancement factor for sagging of -1.98 for this ship; this factor is some 60% greater than the standard rule sagging correction factor. The predicted whipping enhancement factor for hogging is 1.43, so an increase of around 50%. These are obviously a lot greater than the standard IACS based rule wave bending moments and therefore it is necessary to ensure that the hull girder strength has sufficient capacity to withstand such bending moments.

The important issues to address are the buckling strength and the ultimate hull girder capacity. Ultimate strength approaches to hull girder strength have been applied in the past in post accident investigations. In recent years they have been included in the IACS Common Structural Rules for bulk carriers and double hull oil tankers. This approach has now been included in the Guidance notes keeping the same design margins and criteria. For this ship, assessment of the ultimate hull girder strength shows that the ship just complies with the IACS design criteria. Hence the predicted whipping wave bending moments would not cause collapse of the hull girder at midships. This ship had sufficient design margins from the initial strength assessment to comply with whipping design loads. The guidance notes produced by LR are in draft form as these need to be used in order to understand whether they will work adequately. As hydroelasticity is only now becoming a primary design issue, it is only now that we must have methods and procedures for being able to apply hydroelastic analysis tools and specify the resulting design criteria. The use of hydroelastic codes for real design purposes is still new; most of the hydroelastic codes are very specialist and require specialist knowledge to apply them consistently. This is very different to linear ship motion programs which are in very common use and all linear ship motion programs produce similar answers. Further validation work is required including the following: • Improved treatment of impact loads • Analysis of more ships • Comparison and validation with model tests and full scale measurements • Improved understanding of hull girder structural damping issues Most of this work is ongoing in the form of JIPs, such as the WILS JIP and the CRS consortium, and industry and university research.

ACKNOWLEDGEMENTS The authors would like to gratefully acknowledge the support of many other colleagues at Lloyd’s Register for their contributions to this study. The authors also wish to thank Lloyd's Register for permission to publish this paper. The views expressed in this work are those of the authors alone and do not necessarily represent the policy of Lloyd's Register or any of its affiliates or subsidiaries. Lloyd's Register, its affiliates and subsidiaries and their respective officers, employees or agents are, individually and collectively, referred to in this clause as the 'Lloyd's Register Group'. The Lloyd's Register Group assumes no responsibility and shall not be liable to any person for any loss, damage or expense caused by reliance on the information or advice in this document or howsoever provided, unless that person has signed a contract with the relevant Lloyd's Register Group entity for the provision of this information or advice and in that case any responsibility or liability is exclusively on the terms and conditions set out in that contract.

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