Study on Torque Characteristics and Structural Strength of Large Container Shipsunder Oblique Waves

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(1.Jiangsu University of Scienceand Technology,Zhenjiang 212003,China;2.Shanghai Rulesand Research Institute,China Classification Society,Shanghai200135,China)

Abstract:With the rapid development of large container ships,study on the characteristics of torque load and structural strength under oblique waves is becoming increasingly important.In this paper,a wet surface model and a mass model were built up based on a large container ship to determine the design wave parameters according to the torque response function and dominant load parameters.The relationship between the exceeding probability level and calculated torque was analyzed.Considering the typical oblique wave parameters and exceeding probability level,the calculated torques were studied respectively to indicate the differences based on the methods of dynamic load approach(DLA),American Bureau of Shipping(ABS)and Common Structural Rules for Bulk Carriers and Oil Tankers(HCSR).The main reasons of the difference were highlighted.Some proposals on how to calculate and apply the torque load to container ships were also presented.Based on those proposals,three wave conditions(45°,60°and 75°)were chosen for further case study,where the key structural positions were identified under oblique waves by calculating the stress distribution.This study can serve as a good reference for structural design of large container ships,such as the torsional strength calculation of hull girder,the design of hatch corner and the strength evaluation of torsional box.

Key words:container ship;dynamic load approach(DLA);torque;structural analysis;ship rule

0 Introduction

Large container ships have been developing rapidly in recent years,and the loading capacity has increased up to 20000 TEU.However,it is a profound lesson that the container ship MOL COMFORT(8110 TEU)broke and sunk in 2013,which reminds us of paying great attention to the structural safety[1-2]of large container ships.A typical container ship has a large opening deck and a low torsional rigidity.When a container ship encounters severe sea conditions(such as oblique sea or asymmetric waves)during navigation,the large torque load[3]may occur and affect ship structural response and structural bearing capacity[4].The study on structural analysis[5-9]of a container ship usually focuses on how to combine the multifarious loads[10]and how to calculate the structural stress under the complex load conditions.Generally,wave load numerical prediction[11-12]and structural finite element analysis[13-14]are adopted for that process,where torsion load during structural design is often neglected.Study of torque load under oblique waves[15]is of great importance,which can improve anti-torsional capability,design of hatch corner and torsion box for the ship.

The torque characteristics and structural strength of a large container ship under oblique waves were studied in this paper.Firstly,a wet surface model and a mass model were built up based on hull lines and loading manual.The torque’s frequency response functions by dynamic load approach(DLA)were calculated,considering different locations along the ship length and various design wave parameters.The characteristics of torque’s frequency response functions were analysed.Secondly,long-term torque load on the ship was predicted by using the North Atlantic wave spectrum considering the main factors which may affect the parameters of design oblique wave.Then a series of wave parameters were used based on different dominant load parameters and exceeding probability level.Thirdly,we studied the torque’s characteristics,including torque distribution along the ship length and the torque envelope curve under different oblique wave conditions.Based on torque results,gap analysis was performed between DLA and ship rule formula considering the typical oblique wave parameters and exceeding probability levels.We chose American Bureau of Shipping(ABS)container ship’s rule and Common Structural Rules for Bulk Carriers and Oil Tankers(HCSR)for rule study,and made some useful proposals on how to calculate and apply the torsional load for large container ships.Finally,three wave conditions(45°,60°and 75°)were chosen for further case study.The key structural positions under oblique waves were identified by calculating the stress distribution.In conclusion,thispaper could be useful to structural design of large container ships,such as the torsional strength calculation of hull girder,the design of hatch corners and the strength evaluation of torsional boxes.

1 Whole ship hydrodynamic analysis

1.1 Hydrodynamic model

A hydrodynamic model including both a wet surface model and a mass model(See Fig.1)is built up to simulate the hydrodynamic characteristics of a container ship[16].The wet surface model consists of panel elements based on the hull lines,while the equivalent mass model consists of rod elementsbased on ship’sloading manual.

The length of the massrod istaken according to ship rule[17]asfollows.

whererroll-gyristhe roll gyration radius,whose unit is m.

1.2 Transfer function of torque load

Twenty transverse-sections(see Fig.2)are set to study the distribution characteristics of torque load along the ship length.The frequency response functions of torque in 5L/20(Lis the ship length),10L/20 and 15L/20 transverse-section are shown in Fig.3.

Fig.1 Hydrodynamic model of a container ship

Fig.2 Transverse-section setting along ship

Fig.3 Torque’s frequency response functions

The frequency response functions of torque show two peak values,where the corresponding design wave length is aboutL/3 or 2L.The maximum torque value of frequency response function at 5L/20 transverse-section corresponds to the design wave length ofL/3,which is about 126 m for the container ship.The maximum torque value at 15L/20 transverse-section corresponds to the design wave length of 2L,about 685 m.Fig.3 also shows that the torque load caused by oblique waves has its specific characteristics.So it is important to do further study on the torque characteristics under oblique wave conditions[18-19].The distribution of large torque load and concrete transverse section of weak structures should be considered when determining the dominant factors for structural strength analysisin oblique waves.

1.3 Parametersof design waves

The random distribution of ocean waves is described by North Atlantic wave scatter diagram.The design waves’parameters are established by long-term prediction based on ship rule’s formulae[17]

whereλis wave length,with the unit of m;gis gravity acceleration,its unit is m/s2;ωais wave frequency due to dominant load parameter,whose unit israd/s.

whereawis amplitude of design waves,the unit is m;Lis long-term prediction of dominant load parameters;Ais peak value of frequency response functions.

Torque loads at different transverse-sections along the ship length is set to be dominant load.A series of design waves are shown in Tab.1.

Tab.1 Design wave parameters

Unlike other loads,torque load has its own characteristics,which are closely related to the exceedance probability,dominant load parameter,wave direction and wave amplitude.The severe torque may occur in oblique waves with directions of 45°,60°and 120°,and wave lengths of 76.1 m and 125.8 m.The design wave amplitude can be approximated to two times corresponding to the exceeding probability levels of 10-2,10-4and 10-8.The design wave amplitude reaches the peak value when the dominant load parameters are set to be 4L/20,10L/20 and 14L/20.

2 Design analysis of oblique wave condition

2.1 Distribution of torque along the ship length

We used five design waves(see Tab.2)to study the characteristics of torque distribution,where the exceedance probability is taken to be 10-8.

The torque loads along the ship length under five design oblique waves were calculated.Then the distribution curves expressed by location-torque relationship are shown in Fig.4.

As seen from Fig.4,the maximum torque occurs at 7L/20 transverse-section under the design oblique waves of 60°or 120°direction andL/4～L/3 wave length,whose distribution curves are similar to sine curve.The torque curves under the design oblique waves of 45°and 105°direction are different from others.Several peaks would appear along the ship length and the maximum value may occur at the location between 12L/20 and 16L/20.The design wave with a direction of 60°or 120°and a wave length ofL/4～L/3 is the most severe condition.Moreover,we should consider the combination of large torque load and weak structural carrying capacity for building the structural calculation condition.

Tab.2 Parametersof five design waves

Fig.4 Distribution curves of torque along ship

2.2 Envelope torque along the ship length

The envelope torque curves along the ship length are shown in Fig.5 as a factor of exceedance probability level(such as10-2,10-4and 10-8).

The envelope torque at different exceedance probability levels has the following characteristics.The torque extremum of the latter half hull is usually larger than that of the front half hull related to the hull line.The extreme values at different probability levels show constrained proportion,which can be approximated by 1.93 times conversion.The maximum value of the envelope torque curve usually occursat the 7L/20,though there are also several peaksalong the ship length.

The torque at 7L/20 transverse-section should be taken as the dominant load parameter for calculating the maximum torque load under oblique waves.The torque curve is concavo-convex at high exceedance probability(such as 10-8),which is used for total structural strength under extreme torque load.The torque curve is relatively mild at low exceedance probability(such as 10-2),which is used for fatigue strength under frequent torque load.

Fig.5 Envelope torque curves along ship

2.3 Comparison of torque between rule and DLA

Two rule torque formulae are included in the present study.One is from American Bureau of Shipping(ABS)container ship’s rule,and the other isfrom Common Structural Rules for Bulk Carriers and Oil Tankers(HCSR).

The torque formula of ABScontainer ship’s rule[20]is written as

whereksis the coefficient,taken as( )1.61-0.47Cb0.5;kis the coefficient,taken as 2.7;c0is the coefficient,taken as 0.14;dis the draught,whose unit is m;eis the distance from calculated transverse-section to perpendicular,with the unit of m;CWis water plane coefficient;Lis the ship length,the unit is m;Bis the ship breath,its unit ism;andDis depth,the unit ism.

The torque formula of HCSR[21]is given as

wherefβis the heading correction factor,ft1andft2are the torque distribution coefficients;Cbis the block coefficient.

The results on the basis of ABSand HCSR rules are compared with those of DLA in Fig.6.The exceedance probability levels of DLA calculation are set to be 10-4and 10-8,and the wave direction is set to be 60°.

Fig.6 Comparison of torques between rule formula and DLA calculated at different exceedance probability levels

ABS rule specifies that the torque formula is used to calculate the local structural strength.The torque curve can be approximated as a piecewise line.The maximum torque is calculated at 3L/20～11L/20,which is approximately equal to the DLA torque at 10-4exceedance probability.However,the range of maximum torque is larger than that of DLA along the ship length.

HSCR rule specifies that the torque formula is used for total strength calculation of the hull girder.The torque curve is composed of multiple curves,whose shape is similar to that of DLA result.The maximum torque appears at the position of 7L/20～8L/20,which is about 30%lower than that of DLA torque at 10-8exceeding probability level.The maximum value of HCSR torque formula is approximately equivalent to the DLA torque at 10-6.5exceeding probability level.

The rule results of ABSand HCSR are also compared with that of DLA at wave directions of 45°,60°and 75°,as shown in Fig.7.

Fig.7 Comparison of torques between rule and DLA calculated at different wave directions

The ABStorque result is approximately equal to the DLA torque calculated at 45°wave direction,but the shape of the curve is opposite.The HCSR torque result is approximately equal to the DLA torque calculated at 75°wave direction,and the shape of the curve is similar.

From the above analysis，the difference between rule results and DLA calculation may be caused by several reasons.The first one is due to different ship types.In this paper,the container ship is taken as the research object,while HSCR is the rule for bulk carriers and oil tankers.The torque formula can only be used for reference.The second reason is different design wave and loading conditions.DLA calculation takes into account the combination of the worst oblique waves and load conditions in this study while ABSis a statistical regression value which combines many factors.Last but not least,different exceedance probability levels may result in the discrepancy.The exceedance probability levels calculated by DLA in this paper are 10-2,10-4and 10-8while the total strength in the ship rule mainly considers the probability level once in 20 or 25 years.

In conclusion,the maximum value and range of torque curve calculated by ship rule are different from those of DLA.Therefore,it is necessary to make additional DLA torque analysis on the basis of ship rule formulae for large container ships.

3 Whole ship structural calculation

3.1 Determination of calculation conditions in oblique waves

The exceedance probability level is set to be 10-8for the whole ship structural analysis.Torque loads at 7L/20,10L/20 and 13L/20 are dominant,considering the structural characteristics of a container ship.Three design oblique waves are chosen as shown in Tab.3.

Tab.3 Three design oblique waves for structural calculation of a container ship

3.2 Results of whole ship structural analysis

The stress results of the whole ship structure are shown in Fig.8.

Fig.8 Stress distribution of a container ship under different calculation conditions

As seen from Fig.8，the maximum stresses appeared at the location of topside,hatch corners,and other regions with weak torsion resistances.They would differ from each other under different design conditions.For Case A,the calculated stress level is relatively high at the topside tank.The maximum stress calculated is about 224 MPa,which is located at the topside tank near the engine room.For Case B,the calculated stress level is high near the engine room.The maximum stress is about 212 MPa near the after bulkhead of the engine room.For Case C,the calculated stress level is high on starboard.The maximum stress is about 214 MPa,which is located at the hatch corners near the engine room.According to stress distribution patterns,it is found that stress concentration occursat the structural connections of the container ship under oblique waves.

The structural analysis of a container ship should consider different analytical objectives,such as torsional strength assessment of typical transverse sections,warping stress analysis of hatch corners,structural strength calculation of torsion boxes.The oblique waves should be obtained by DLA analysis matched with respective analytical objectives.

4 Conclusions

Study on the torque characteristics based on DLA was carried out in this paper,concluding influence factors and distribution characteristics,and the results were compared with those by the torque rule formulae from ABSand HCSR.Then three wave conditions(45°,60°and 75°)were chosen for further structural strength study.The main findings of thisstudy are summarized asbelow:

(1)The design parameters of oblique waves are the key factors for torque load calculation.This study indicates that the most severe wave directions are 60°and 120°while the wave length is 125.8 m(aboutL/3～L/4).The maximum DLA torque result usually occursat the 7L/20 location.

(2)The exceeding probability level reflects the structural strength safety levels.The torque curves are in similar shape along the ship length with the exceeding probability levels of 10-2,10-4and 10-8.Generally,we suggest 10-8for total strength calculation,10-4for local strength calculation,and 10-2for fatigue strength calculation.

(3)The torque value of ABSrule is roughly equivalent to DLA result at 10-4exceeding probability level,but the distribution trend is discrepant.The HCSR rule and DLA have a similar torsion distribution trend,but the torque value of HCSR is approximately equal to DLA result only at 10-6.5exceeding probability level.Therefore,it is necessary to make additional DLA torque analysis for large container ships.

(4)The calculation results show that the design parameters of oblique waves have a large influence on the stress distribution.The key structural positions include top cabin,hatch corner,end of the engine room.Special attention should be paid to detailed structural analysis,such as torsional strength assessment of typical transverse sections,warping stress analysis of hatch corners,structural strength calculation of torsion boxes.