A PRACTICAL ASSESSMENT OF EXISTING BULK CARRIER LOCAL STRUCTURAL STRENGTH IN RELATION TO THE ALLOWABLE HOLD MASS CURVES K Chatzitolios, Bureau Veritas, Greece G de Jong, Bureau Veritas, France Dr JE Kokarakis, Bureau Veritas, Greece SUMMARY The allowable hold mass curves for vessels built after 1998 are mandatory in the loading manual & the loading instrument as per IACS Unified Requirements S1A. The majority of the bulk carriers in service have been constructed before 1998 and generally do not have allowable hold mass curves. Pre-1998 bulk carriers engaged in multi-port operations need to have allowable hold mass curves to control the local strength of the cargo hold structure for the envisaged loading conditions. The curves are produced according to the loading conditions of the approved loading manual as a function of the draught. For the case of an individual hold they are determined by examining bending and shear stresses in floors and girders, as well as buckling stresses in the associated plating. For the case of two adjacent holds the strength of the transverse bulkhead and cross deck is considered as well. The curves can be checked with finite element analysis or other methods to obtain the applicable safety margin. The paper presents a theoretical derivation of the hold mass curves as function of the draught and provides some comparisons with formulations by other class societies and IACS requirements. A practical methodology to determine the hold mass curves when not available is proposed. An interesting application, presented in a case study in the paper, is the determination of the maximum draught as a function of the static still water bending moment at the empty holds. The combination of a hogging hull girder bending moment and hydrostatic pressure at 60 to 70% of the scantling draught may cause severe buckling of the bottom plating and exceed its ultimate strength. A methodology on how to assess this loading condition for holds which are not usually empty is proposed. 1. INTRODUCTION In 1998 IACS adopted Unified Requirement (UR) S1A, effectively introducing additional requirements for loading conditions, loading manuals and loading instruments of both new and existing bulk carriers1. UR S1A requires existing bulk carriers (that is, bulk carriers contracted for construction before 1 July 1998) with a length of 150 m and above to be provided with a class approved loading instrument in order to enable the ship’s master to check the envisaged loading conditions (whether at sea or in port) against permissible longitudinal strength criteria (hull girder bending moments and shear forces). In this context a loading instrument is considered as an effective means to preventing overstressing of the hull girder, which could potentially result in global structural collapse. In addition, UR S1A requires single side skin bulk carriers of 150 m length and above to be provided with a class approved loading manual with typical loading sequences where the vessel is loaded from commencement of cargo loading to reaching the full deadweight capacity, and vice versa. The reasoning behind this requirement is to ensure that

1 UR S1A was introduced as an addition to UR S1, which provides more general requirements for loading conditions, loading manuals and loading instruments. UR S1 is considered to be an implementation of the requirements of Regulation 10(1) of the International Convention on Load Lines, 1966.

the vessel is not overstressed during loading and discharging in port, which can happen due to faulty loading sequences or (de)ballasting operations. The sequence of loading the cargo holds, as well as the amount of cargo which is loaded in each hold in one time greatly influences the induced hull girder loads. This issue is still very actual, in particular due to high speed cargo loading at iron ore terminals (up to 16,000 tonnes per hour) [1]. For new bulk carriers (contracted for construction on or after 1 July 1998) of 150 m length and above, UR S1A requires the class approved loading manual to additionally include the following data: • Maximum allowable and minimum required mass of

cargo and double bottom contents of each hold as a function of the draught at mid-hold position;

• Maximum allowable and minimum required mass of cargo and double bottom contents of any two adjacent holds each hold as a function of mean draught in way of these holds.

The values of maximum allowable and minimum required mass of cargo can be plotted as a function of the draught and are generally referred to as hold mass curves. The loading instrument is required to display whether the cargo hold mass is within permissible limits and therefore needs to incorporate the hold mass curves. This requirement for “new ships” effectively regulates that, for any given loading condition, the local strength capacity of the hull structure (strength of double bottom,

transverse bulkheads, etc.) is not exceeded and therefore is to be considered as a complementary safety criterion to the longitudinal strength criteria applicable to both new and existing bulk carriers. As pre 1998 bulk carriers are not required to have hold mass curves, from an operational viewpoint they are inherently less flexible than there newer counterparts, as in practice they can only sail in the loading conditions which have been approved in the loading manual. This becomes a handicap if they are engaged in multi-port operations, where the vessel will experience a wide variety of loading conditions which may not be included in the loading manual. Therefore, pre 1998 bulk carriers effectively need hold mass curves in order to operate safely on multi-port trades. As about 60% of the approximately 7,000 bulk carriers in service today have been built before 2000 (assuming a time delay of 18 months between contract signing and ship delivery), this is by no means an academic issue [2]. For an individual hold the hold mass curves are determined by examining shear stresses in floors and double bottom girders, while for adjacent holds the strength of cross deck and transverse bulkheads are of main concern. The adjacent holds model is further studied by evaluation of cross deck stresses stemming from bending of the transverse bulkhead and hull girder torsion. The curves can be checked with Finite Element Analysis (FEA) or other methods to obtain the safety margin. This paper presents a comparison between various formulations of hold mass curves amongst classification societies and proposes ways to determine the curves for existing ships when not available (pre 1998 bulk carriers), as such creating a safe and easy way to expand the trading flexibility of older bulk carriers. In section 2 the technical background of the hold mass curves is presented, considering formulations by different class societies as well as IACS. Section 3 explains the importance of hold mass curves for bulk carriers engaged in multi-port operations; the focus is on the maximum permissible draught in way of the empty holds as a function of the hogging SWBM (Still Water Bending Moment). Section 4 proposes a methodology for deriving the hold mass curves on the basis of the theoretical considerations presented in the previous sections and presents an interesting application of hold mass curves: the determination of the maximum draught as a function of the static bending moment at the empty holds. The combination of a hogging hull girder bending moment and hydrostatic pressure at 60 to 70% of the scantling draft is considered, which may cause severe buckling of the bottom plating and exceed its ultimate strength capacity. A methodology on how to assess this loading condition for holds which are not usually empty is proposed. Finally, in section 5 the main conclusions are drawn and further recommendations are made.

2. TECHNICAL BACKGROUND 2.1 HOLD MASS CURVES FOR SEAGOING

CONDITIONS As explained above, the hold mass curves are a means for the master to decide obtain the maximum allowable or minimum required cargo mass for an envisaged loading condition which is not included in the loading manual. The goal is to prevent overloading of the local structure, such as the double bottom structure (plating, floors and girders), the transverse bulkheads and the cross deck structures. For example, if for an individual cargo hold a cargo mass P has been approved for a loading condition with a draught T1 at mid-length of the considered hold, the double bottom structure might experience excessive flexural deformation if the same cargo mass is loaded for a loading condition with a corresponding draught less than T1 (e.g. 0.5T1), as depicted in Figure 1. Figure 1: Excessive flexural deformation of double bottom structure [3] The basic idea behind the derivation of the hold mass curves is to use the approved loading conditions from the loading manual as a starting point for an inverse analysis in order to obtain acceptable new conditions. As the net resultant load on the double bottom is the governing parameter for the variation in the local structural response, the objective of the exercise is to control this load, which is defined as the difference between the downward force exerted by the mass of the cargo in the hold & ballast water in the double bottom tanks and the upward force resulting from the sea pressure. Both forces are composed of a static and a dynamic component. The downward force consists of the own weight of the mass of the cargo and ballast water (static part) plus the inertia loads caused by the ship motion induced accelerations acting on this mass (dynamic part)2. The upward force consists of the hydrostatic load (static part) plus the hydrodynamic loads caused by ship motions in waves (dynamic part). In linear rigid body dynamics the hydrodynamic load is considered to be the sum of the hydromechanical (reaction) loads caused by the ship moving (oscillating) in the undisturbed fluid surface and

2 The own mass of the ship structure is neglected as it is small compared to the mass of the cargo.

the forces exerted by the waves on the restrained body (wave exciting loads). An example of the net resultant load on the double bottom is presented in Figure 1, in which only the static parts are considered. For the purpose of structural analysis it is sufficiently accurate to approximate the hydrodynamic load by a Froude-Krylov type of wave load using the ship relative motion as wave amplitude (as opposed to the wave elevation relative to the undisturbed free surface) [4]. As the variation of the net resultant load on the double bottom is the highest for the upright ship condition (usually the head sea condition is considered) the analysis focuses on this condition, see Figure 2. Figure 2: Wave load distribution on the basis of the relative ship motion hU in upright ship condition [4] In a generic form, the net resultant load on the double bottom of a single cargo hold, in terms of the average pressure DBp , can be expressed as follows:

⎟⎟⎠

⎞⎜⎜⎝

⎛+ρ−

++=

π−L

T2

U1H

ZUDBCDB

1

ehTgB

)ag)(MM(pλ

(1)

where MC is the mass of the cargo, MDB the mass of the ballast water in the double bottom tanks, g the gravity acceleration, aZU the vertical acceleration at mid-length of the cargo hold, λH the length of the considered hold, B the moulded breadth, ρ the density of seawater, T1 the draught at mid-length of the considered hold, hU the relative motion at mid-length of the considered hold corresponding to the vertical acceleration aZU and L the

ship length (as defined in the Rules)3. The factor LT2 1

eπ−

is a correction on the relative wave motion (or elevation), taking into account the rapid decrease in orbital motion and velocity of the fluid particles with increasing distance from the free surface, effectively reducing the hydrodynamic pressure on the bottom with increasing draught and vice versa. The corrected wave elevation is usually called the “effective” wave elevation [5]. In hydrodynamic literature this effect is sometimes referred to as the ‘Smith Effect’. It is to be noted that for reasons of simplicity the presence of the hopper tanks and lower stool of the (corrugated) transverse bulkheads is ignored;

3 It is assumed that the ship is moving in deep water with wavelength equal to the ship length.

an issue which needs to be accounted for later on in the analysis4. The vertical acceleration aZU and relative motion hU need to be evaluated simultaneously (at the same time instant) to satisfy Newton’s Second Law. This can be done on the basis of ship motion calculations (2D or 3D radiation-diffraction analysis) and or by applying reference values of the load cases defined in the Rules (which have been obtained from a statistical analysis of a large amount of ship motion calculations) [6]. The goal is to obtain the maximum values of the net resulting upward and downward loads, which can then be compared to the net loads of the corresponding approved loading conditions. By plotting the known approved combinations of cargo mass and draught in a graph, the hold mass curves are obtained, as schematically shown in Figure 3. Curve (a) connects the approved loading conditions 1 (maximum cargo mass P at scantling draught T) and 2 (part load condition), denoting the maximum permissible cargo mass. Curve (b) connects the approved loading conditions 3 (loading condition at the maximum permissible draught Tmax at which the considered hold may be empty) and 4 (minimum required cargo mass at scantling draught). The enclosed (shaded) area is considered to be the safe loading area in which the net resulting load on the double bottom is within acceptable limits. Figure 3: Example of hold mass curves It is to be noted that the approach is rather conservative, as curve (a) suggests that the maximum permissible cargo mass which can be taken in the hold can only be loaded when sailing at the scantling draught. Most designs, however, have sufficient margin to sail with the maximum cargo mass at a draught less than the scantling draught. In that case curve (a) is replaced by the two segmented curve (c), thus enlarging the loading flexibility of the ship 5. It is also to be noted that the hold mass curves are not necessarily straight lines.

4 It is also assumed that the cargo upper surface is horizontal, but this assumption is also made in the base case (loading condition in the approved loading manual). 5 This is explicitly taken into account by UR S25 and the CSR.

The hold mass curves can be computed by demanding that the net resultant double bottom pressure in the envisaged loading condition is to be equal to the net resultant pressure in the approved reference loading condition. Considering that the variation in vertical acceleration and relative motion is small over the range of operational draughts [7], the maximum permissible cargo mass Pmax at draught TT1 < , where there is no ballast water in the double bottom tanks, can be written as follows (curve (a) in Figure 3):

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+−

+ρ

−=π−π−L

T2L

T2

U1ZU

Hmax

1

eeh)TT(agBgPP λ (2)

where P is the maximum cargo mass at scantling draught T (see above). The worst load case for the downward net resulting double bottom pressure, which is relevant for the maximum permissible cargo mass, is the case where the vertical downward acceleration aZU reaches the maximum value. In BV Rules this is represented in load case ‘b’, for which the relative wave motion is half of the maximum value. The maximum value is attained in load case ‘a’, which is essentially a Froude-Krylov case as the vertical acceleration for this load case is zero (ship fixed in the undisturbed wave) [6]. Expression (2) can be simplified by considering that, for practical loading conditions, the absolute value of the

term ⎟⎟⎠

⎞⎜⎜⎝

⎛−

π−π−L

T2L

T2

U

1

eeh is much smaller than )TT( 1−

and also has a negative value which increases Pmax. Therefore, if this term is neglected for reasons of simplicity this is on the safe side. Applying this simplification, expression (2) reduces to:

)TT(ag

gBPP 1ZU

Hmax −+

ρ−= λ (3)

which is still dependent on the vertical acceleration aZU. Computation of the value of aZU utilising the formulae from the Rules is straightforward and can today easily be incorporated in the on-board loading computer. For older ships with less modern on-board tools, however, this may be more difficult. In order to achieve fast and practical results, suitable for on-board calculation, the term

ZUagg+

may be set to unity (essentially neglecting aZU).

This is again a simplification on the safe side, as in reality the term is always less than unity6. Applying this second simplification, expression (2) further reduces to:

)TT(BPP 1Hmax −ρ−= λ (4)

6 For a capesize bulk carrier the term typically varies between 0.7 (midship region) and 0.85 (hold no 1), where the accelerations are calculated for a probability level of 10-5.

which is very easy to apply. On the basis of equation (4), the slope of curve (a) in Figure 3, dPmax/dT, is constant and equal to BHλρ , which is in essence the hold water-plane area multiplied by the water density. Following the same reasoning as above, the minimum required cargo mass Pmin at draught max1 TT > , where the amount of ballast water in the double bottom tanks is the same for both loading conditions (may be empty or full), can be written as follows (curve (b) in Figure 3):

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+−

+ρ

=π−π−LT2

LT2

Umax1ZU

Hmin

max1

eeh)TT(agBgP λ (5)

The worst load case for the upward net resulting double bottom pressure, which is relevant for the minimum required cargo mass, is the case where the positive relative motion hU reaches the maximum value. In BV Rules this is represented in load case ‘a’, for which the vertical acceleration is zero (see above). Application reduces (5) to:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+−ρ=

π−π−LT2

LT2

Umax1Hmin

max1

eeh)TT(BP λ (6)

Expression (6) can be simplified by considering that, for practical loading conditions, the absolute value of the term

⎟⎟⎠

⎞⎜⎜⎝

⎛−

π−π−LT2

LT2

U

max1

eeh is much smaller than )TT( max1 −

and also has a negative value which decreases Pmin. Therefore, if this term is neglected for reasons of simplicity, this is on the safe side. Applying this simplification, expression (6) reduces to:

)TT(BP max1Hmin −ρ= λ (7) which is independent of the relative motion hU and the vertical acceleration aZU and therefore very easy to apply. Similarly to the development above, the slope of curve (b) is equal to the one of curve (a). Consequently curves (a) and (b) are parallel. Further analysis of expressions (4) and (7) learns that, due to the simplifications, the imposed conservation of load (net resulting double bottom pressure) has in fact been reduced to imposed conservation of mass, which is easier to compute. For the case of the maximum cargo mass the reduced hold displacement due to the reduction in draught equals the reduction in permissible cargo mass, while for the case of the minimum cargo mass the increased hold displacement due to the increase in draught equals the increase in required cargo mass. As mentioned above the presence of the hopper tanks and transverse bulkhead lower stool have been ignored. The consequences of these simplifications are depending on the height of the rated upper surface of the bulk cargo above the tank top hm, see Figure 4.

Figure 4: Effect of cargo filling level on double bottom cargo pressure For the maximum permissible cargo mass we consider case a, denoted by hm,a, where the rated upper surface is above the hopper tank and can be considered as the maximum filling level corresponding to the maximum cargo mass P at the scantling draught T. If a new loading condition with less draught is envisaged, application of (4) yields a reduction in cargo mass of )TT(B 1H −ρλ .

This is achieved by reducing hm by )TT( 1B

−ρρ , where

ρB is the bulk cargo density. This expression is valid only if the new rated upper surface cargo level is above the top of the hopper tank; in other words: DBHTm hhh −≥ . If the rated upper surface would be less (case b), the amount of cargo mass reduction to keep constant the net resultant pressure on the double bottom (flat part) would be less due to the presence of the hopper tank and transverse bulkhead lower stool volumes. This means that the results are slightly conservative but on the safe side. For the minimum required cargo mass the draught is increased above the maximum Tmax draught for which the cargo hold has may be empty in accordance with the approved loading manual. So the hold is filled from zero to a certain value to compensate for the increase in sea pressure exerted on the double bottom. Application of (7) yields an increase in cargo mass (from zero) of

)TT(B max1H −ρλ . However, due to the presence of the hopper tanks and transverse bulkhead lower stool less cargo mass is required to achieve the necessary cargo pressure increase on the double bottom (flat part) than is computed by expression (7), where the full displacement addition (acting on the total width of the ship’s bottom) is compensated as cargo mass increase (gradually increasing it’s influence from the width of the flat part of the double bottom to the total ship breadth). Therefore, the minimum required cargo mass is overestimated by expression (7) and can be corrected for the presence of the non cargo carrying volumes. For a rated upper surface cargo level above the top of the hopper tank ( DBHTm hhh −≥ ), the correction includes the complete volume of the hopper tanks, which gives:

[ ]LSDBHTHTHBmax1Hmin V)hh(b)TT(BP −−ρ−−ρ= λλ (8) where, bHT is the width of the hopper tank, hHT the height of the hopper tank and hDB the height of the double bottom. For a rated upper surface cargo level below the top of the hopper tank ( DBHTm hhh −< ), the correction is dependent on the value of hm, which is not known a priori

but can be estimated by )TT(h max1B

m −ρρ

= . As the

hopper tanks are neglected, this is a conservative approach (hm is overestimated). The minimum cargo mass can than easily be calculated by considering the cargo volume up to filling level hm and the associated bulk cargo density. As the transverse bulkhead lower stool is low compared to the height of the cargo hold, hm will usually be higher than the height of the lower stool. This justifies a correction on Pmin by subtracting the term

LSBVρ . Defining bm as follows, see Figure 5:

)TT(hh

bb max1DBHT

HT

Bm −

−ρρ

= (9)

we can write for the minimum required cargo mass:

⎥⎦

⎤⎢⎣

⎡−−

−+ρ= LSDBHT

HT

mHTmHBmin V)hh(

bb)b2Bb(P λ (10)

Figure 5: Definition of bm The verification of the maximum permissible and minimum required cargo mass is to be performed for the case of individual cargo holds, as described above, and for the case of two adjacent cargo holds. In fact, the case of individual cargo holds addresses the maximum bending moment and shear force in the floors, the maximum bending moment in the double bottom girders at mid-length of the cargo hold and the maximum shear force in the double bottom girders at the ends of the cargo hold when considering alternate loading conditions (angular deformation at hold ends due to asymmetrical loading produces the maximum bending moment in the double bottom girders at mid-length of hold). The case of two adjacent cargo holds considers the maximum bending moment and shear force in the double bottom girders acting simultaneously at the transverse bulkhead (the condition of zero angular deformation at the hold ends due to symmetric loading produces the maximum bending moment in the double bottom girders at the hold ends) and the shear strength of the (corrugated) transverse bulkhead.

Based on the derivations and considerations above, it is easy to see that a straightforward application of the conservation of mass principle provides quick and conservative estimates of the maximum permissible and minimum required cargo mass. The maximum permissible cargo mass for two adjacent holds

max21 )PP( + at a draught TT1 < can be written as follows:

)TT(B)(PP)PP( 12H1H21max21 −+ρ−+=+ λλ (11) where 21 PP + is the maximum mass of cargo in two adjacent holds at the scantling draught, while λH1 and λH2 denote the length of the two adjacent cargo holds, respectively. Following the same reasoning, the minimum required cargo mass for two adjacent holds min21 )PP( + at a draught max1 TT > can be written as follows:

)TT(B)()PP( max12H1Hmin21 −+ρ=+ λλ (12) 2.2 HOLD MASS CURVES FOR HARBOUR CONDITIONS During loading and unloading in port the maximum allowable cargo mass is higher than at sea due to the absence of waves generating large vertical accelerations and relative motions. In a similar fashion the minimum required cargo mass is less than at sea. Due to this reduction of dynamic loads, the ship has more flexibility in loading conditions during port operations, which is regulated by providing specific hold mass curves for the harbour conditions in addition to the seagoing conditions. In the ideal port situation of no accelerations and no relative motions expression (1) reduces to:

1H

DBCDB gT

Bg)MM(p ρ−

+=

λ (13)

The maximum permissible cargo mass for a single hold in harbour condition Pmax is derived on the basis of the known maximum permissible cargo mass from seagoing condition at the scantling draught. Equating expression (1) for seagoing condition with PM C = , 0M DB = and

TT1 = to expression (14), after some algebra, gives:

DB1L

T2

UHZU

max MTehTBgagPP −⎟

⎟⎠

⎞⎜⎜⎝

⎛−−ρ−

+=

π−

λ (14)

This expression requires computation of aZU and hU. Simply ignoring them would yield extremely conservative results, as expression (15) would be effectively reduced to expression (4) for seagoing conditions, with the exception of the double bottom ballast water mass which is very small compared to the maximum cargo mass. In other words, the loading flexibility of the ship would be too much restricted. Therefore, any attempt for simplification of (15) must

still include one of the two dynamic parameters. Rewriting (14) into a static and a dynamic part gives:

( ) DB1Hstaticmax, MTTBPP −−ρ−= λ (15)

LT2

UHZU

dynamicmax, eBhg

aPPπ−

ρ−= λ (16)

The key point for simplification is to evaluate the two terms of (17) against each other. Making use of practical data on typical bulk carriers and considering the worst load case for the downward net resulting double bottom load (maximum downward vertical acceleration), it can

be shown that approximately LT2

UHZU eBh3g

aPπ−

ρ×≥ λ .

Therefore, (17) can be approximated by:

LT2

UHdynamicmax, eBh2Pπ−

ρ≈ λ (17) It can further be shown that the L/T ratio for typical bulk carriers from 10k DWT is between 12.5 and 19.

Therefore, the term LT2

eπ−

will be between 0.60 and 0.70.

By setting LT2

eπ−

to a conservative value of 0.5 (the corresponding L/T ratio is 9), expression (18) can be conservatively further reduced to:

UHdynamicmax, BhP λρ≈ (18) This is conservative, as the value of the dynamic part, giving a positive contribution to the maximum permissible cargo mass, is underestimated. As such, expression (14) can be safely simplified as follows: ( ) DB1UHmax MThTBPP −−−ρ−= λ (19) where hU corresponds to the relative motion for the load case where the vertical acceleration is maximum, which is easy to calculate (BV Rules load case ‘b’). The minimum required cargo mass for a single hold in harbour condition Pmin is derived on the basis of the known minimum required permissible cargo mass from seagoing condition at the scantling draught. Equating expression (1) for seagoing condition with

0M C = , 0M DB = and max1 TT = to expression (14) results in the following expression

DBmaxLT2

U1Hmin MTehTBPmax

−⎟⎟⎠

⎞⎜⎜⎝

⎛−−ρ=

π−

λ (20)

which is independent of the vertical acceleration aZU.

Following the reasoning above, LT2

eπ−

can be taken as 0.5. This underestimation is on the safe, side as it increases the minimum required cargo mass. In doing so, expression (21) can be reduced to:

DBmaxU1Hmin M)Th5.0T(BP −−−ρ= λ (21) where hU corresponds to the relative motion for the load case where the relative motion is maximum, which is easy to calculate (BV Rules load case ‘a’).

In a similar fashion as above, applying the conservation of mass principle, expressions for the maximum permissible and minimum required cargo mass for two adjacent holds can be derived. The maximum permissible cargo mass for two adjacent holds max21 )PP( + at a draught TT1 < can be written as follows:

2DB1DB1U2H1H

21max21

MM)ThT(B)(PP)PP(

−−−−+ρ−+=+

λλ (22)

where 21 PP + is the maximum mass of cargo in two adjacent holds at the scantling draught, λH1 and λH2 denote the length of the two adjacent cargo holds, respectively, hU corresponds to the relative motion for the load case where the vertical acceleration is maximum (BV Rules load case ‘b’), while MDB1 and MDB1 represent the mass of the double bottom ballast water of the two adjacent cargo holds, respectively. Applying the same reasoning, the minimum required cargo mass for two adjacent holds min21 )PP( + at a draught max1 TT > can be written as follows:

2DB1DB

maxU12H1Hmin21

MM)ThT(B)()PP(

−−−−+ρ=+ λλ

(23)

where hU corresponds to the relative motion for the load case where the relative motion is maximum (BV Rules load case ‘a’). 2.3 CONSIDERATIONS FOR IMPROVEMENT In order to make the process of evaluating hold mass curves as practical and efficient as possible, the formulae derived in this section have been simplified as far as possible. This enables easy calculation on-board which does not require complicated mathematics. In order to stay on the safe side, the simplifications give a rather conservative result, which inherently means that there is room for optimisation of loading flexibility when the more complex formulae are used instead of the simplified ones. The obvious conservative assumption in all formulations for the generation of the mass hold curves is that it is assumed that the shear strength at full draft is marginal and it is necessary to preserve shear force at different drafts. With the availability of good on-board computation tools, in particular the loading instrument, this has become relatively easy to implement. In fact, improvements in the Rules after the introduction of UR S1A are mandating the implementation of the hold mass curves in the loading instrument, as will be described in the following section. 2.4 DEVELOPMENTS OF IACS UNIFIED

REQUIREMENTS FOR HOLDS MASS CURVES FOR NEW RULES AFTER UR S1A

As described in the introduction, UR S1A makes the inclusion of the hold mass curves in the approved loading

instrument mandatory for new ships 7 . UR S20 has introduced the development of the hold mass curves have taking into account cargo hold flooding, UR S20 is applicable to new single and double side skin bulk carriers of 150 m length and over with cargo density equal to or higher than 1.0 m3 (applicable for single side skin bulk carriers contracted for construction on or after 1 July 1998 and double side skin bulk carrier contracted for construction on or after 1 July 1999 or 1 January 2000, depending on the width of the double side skin) and considers the allowable hold loading in the case of flooding of any (individual) cargo hold on the basis of the cargo carried (volume, density and permeability), effectively increasing bulk carrier safety. Due to the change in the maximum permissible cargo mass at the maximum draft, the hold mass curves for the maximum permissible cargo mass for a reduced draught are changed as well. In a similar fashion UR S22 has changed the allowable hold loading of the foremost cargo hold of bulk carriers bulk carriers contracted for construction before 1 July 1998, with length of 150 m or more and cargo density of equal to or higher than 1.78 t/m3. With the introduction of UR S25 the hold mass curves have been further developed. UR S25 is applicable to bulk carriers of 150 m in length and over, which are contracted for construction on or after 1 July 2003. With UR S25, harmonised notations and associated design loading conditions have been introduced. This has created a uniform way to assess bulk carrier designs with regard to their cargo carrying capacity and loading flexibility. This in turn has generated a high degree of transparency for ship owners and operators, as well as a technical level playing field for designers and class societies, and as such further enhanced bulk carrier safety. The three basic notations are as follows [8]: BC-A: for bulk carriers designed to carry dry bulk

cargoes of cargo density 1.0 t/m3 and above with specific holds empty at maximum draught in addition to BC-B conditions

BC-B: for bulk carriers designed to carry dry bulk cargoes of cargo density 1.0 t/m3 and above with all cargo holds loaded in addition to BC-C conditions

BC-C: for bulk carriers designed to carry dry bulk cargoes of cargo density less than 1.0 t/m3

For each of the three notations UR S25 provides a list of design loading conditions to be checked. These loading conditions are chosen in such a way that the design incorporates multi-port operations which affect the local strength and therefore directly define the hold mass curves.

7 In the context of UR S1A new ships are ships contracted for construction on or after 1 July 1998.

Key seagoing loading conditions in this respect are the following [8]: • Any cargo hold is to be able to of carrying full cargo

mass with fuel oil tanks in double bottom in way of the cargo hold, if any, being 100% full and ballast water tanks in the double bottom in way of the cargo hold being empty, at 67% of the maximum draught8;

• Any cargo hold is to be capable of being empty with all double bottom tanks in the way of the cargo hold being empty, at 83% of the maximum draught;

Similar conditions apply for the case of two adjacent cargo holds, with the empty cargo holds condition at 75% of the maximum draught. In addition, loading conditions while in harbour are addressed. In applying these seagoing conditions, the loading conditions 5 and 3 presented in Figure 3 are fixed. In fact, curve (a) is replaced by curve (c), as shown in Figure 6. Only if the ship is assigned the additional notation {no MP} these conditions can be waived. Figure 6: Hold mass curves based on UR S25, including multi-port operations For BC-A bulk carriers, which are capable of sailing in alternate conditions, specific additional loading conditions are specified, including a margin in cargo loading for the carriage of high density cargo (equal to 10% of full cargo mass). UR S25 specifically addresses the issue of the hold mass curves as based on the design loading conditions. For other draughts than those specified in the design loading conditions, the maximum allowable and minimum required mass is to be adjusted for the change in buoyancy acting on the bottom (to be calculated using the water plan area at each draught). This is, in fact, an implementation of the principle of the conservation of mass as derived and justified in section 2.1.

8 The full cargo mass is defined as the cargo mass in a hold corresponding to cargo with a virtual density (homogeneous mass/hold cubic capacity, minimum 1.0 t/m3) filled to the top of the hatch coaming and is not to be less than the actual cargo mass in a cargo hold corresponding to a homogeneously loaded condition at maximum draught [8].

2.5 OTHER CLASS SOCIETIES Similarly to the developments described above, other class societies apply the same basic concept in order to estimate the mass hold curves. Examples of other pre-CSR methods utilised by other classes are depicted on Figure 7 for the seagoing case only. The upper curve in essence preserves the “net load”, i.e. the difference between the cargo weight and the buoyancy of the cargo hold on the basis of purely static considerations. The maximum cargo is deduced adding the “net load” to the buoyancy force. Of course the maximum cargo has been determined beforehand for each hold by structural analysis. The minimum cargo at design draft is determined by subtracting the “net load” from the buoyancy. The abscissa for the minimum cargo curve is determined from similar triangles, being parallel to the maximum cargo curve. Figure 7: Hold mass hold curves, pre-CSR, seagoing The lower curve is based on the same philosophy, but it accounts for dynamic effects as shown in the derivation above. Parameter k ranges from 0.67 to 1 depending on the load cases studied at the design stage. It is known that IACS UR S25 dictates that the case of 67% of full draft with the maximum cargo hold load be studied in the design stage, with respect to local and global strength. The minimum cargo curve, although not shown in the lower part of Figure 6, is determined by the following relationship:

⎟⎟⎠

⎞⎜⎜⎝

⎛−= 4

TT5P11.0Pmax

maxmin (24)

Equation (24) provides the interesting relation between the minimum and the maximum cargo in the hold. This relation is based on statistical evaluation of many bulk carriers instead of computations. According to (24), the minimum cargo load is 11% of the maximum one. 2.6 DEVELOPMENT OF HOLDS MASS

CURVES FOR THE COMMON STRUCTURAL RULES

Hold mass curves generation is necessary for all bulk carriers above 90 meters according to the CSR. The approach follows the logic introduced in UR S25, see section 2.4. According to the formulation, the maximum cargo mass for a draught less than 67% of the maximum is given by:

( )h

TT67.0V025.1M1.0M)T(P maxHHHDmax

−−+= (25)

where h is the vertical distance from the top of the inner bottom to the main deck at centre-line, VH is the volume of the hold excluding the volume enclosed by the hatch coaming, MH is the actual cargo mass corresponding to a homogeneously loaded condition at maximum draught, MHD is the maximum cargo mass allowed to be carried in a cargo hold according to the design loading conditions with specified holds empty at maximum draught, Tmax is the maximum draught and T is the actual draught under consideration. Similarly for the minimum load:

( )h

T83.0TV025.1)T(P maxHmin

−= (26)

Equation (26) is valid for a draught above 83% of the maximum as dictated by UR S25. The two relations above which are depicted pictorially on Figure 8, are valid for holds designed to be always full, like the ore holds. For holds which can be empty at maximum draft, there is no meaning for minimum cargo, whereas the maximum cargo for draught less than 67% of the maximum is given by:

( )h

TT67.0V025.1M)T(P maxHFullmax

−−= (27)

where MFull is the cargo mass corresponding to cargo with virtual density filled up to the top of hatch coaming. The density is the maximum between one and MH/VH. Figure 8: Mass hold curves according to CSR (ore hold)

The curves are simplified greatly at the expense of operational flexibility when the limitation {No MP} is added to the vessel notation (see also section 2.4), as this notation removes the need to evaluate additional loading conditions dictated by UR S25, such as the carriage of the maximum cargo at 67% of the maximum draught and empty ore hold at a draught as high as 83% of the maximum. 3. INFLUENCE OF STILL WATER

BENDING MOMENT Bulk carriers are sometimes engaged in multi-port loading operations, although the great majority are not designed for such. It is possible in such a multi-port operation that the designated ore holds may be unloaded at one port with the vessel proceeding to another port for further unloading. In such a case, the combination of hogging hull girder bending moment and external pressure corresponding to a reduced draught of the order of 60 to 70% of the maximum one may result in buckling of the bottom plating. Importantly, this is a case which is not routinely checked. A simple procedure is derived below which aims to calculate the maximum permissible draught in way of the empty ore hold (designed to carry heavy cargo but operating empty) as a function of the hogging SWBM (Still Water Bending Moment). This procedure does not require performing a finite element analysis. Typically the calculations are performed for the midship ore hold and are applicable to all ore holds when operating empty. In case the draught is severely limiting, local reinforcement of the bottom may be necessary to resolve the buckling problem. It is thus proposed to develop a graph of the maximum permissible graph as a function of the SWBM on the basis of satisfying the buckling strength criterion:

0.1BF9.1

y,crit

yRm9.1

x,crit

xRm ≤=⎥⎥⎦

⎤

⎢⎢⎣

⎡

σ

σγγ+

⎥⎥⎦

⎤

⎢⎢⎣

⎡

σσγγ (28)

Where Rm ,γγ are the material and the load factors, both equal to 1.02, BF is the buckling factor defined by equation (28), σcrit,x and σcrit,y are the critical buckling stresses for the panel under consideration, while σx and σy are the stresses exerted on the bottom panels in the longitudinal and transverse directions, respectively. Transverse stress σy results from the hydrostatic and hydrodynamic pressures on the bottom, computed from analysis of the elementary bottom panel. This stress is determined from a grillage analysis through the BV program STEEL described in the next section. It can also be estimated by simple panel response relations with the handicap that the fixity of the plate boundaries needs to be assumed as either fixed or clamped. Longitudinal stress σy stems from the contribution of hull girder static and dynamic bending moments and the bottom pressure. The former can be determined by :

wavestaticgirderhull,x 05.1 σ+σ=σ (29)

where the factor 1.05 is a safety margin type factor due to the higher uncertainty of the wave induced stress. The wave induced and the static stress are computed on the basis of simple beam theory. The wave induced stress is multiplied by a factor equal to 0.625 which represents the maximum in 105 wave encounters. Satisfaction of equation (28) above needs to be ensured at all combinations of draught and SWBM (which can be controlled). An application of the procedure described will be presented in the examples section. A limitation for the SWBM for a given draught should be obtained as well from the buckling requirements of the upper sloping bulkhead and side shell in the upper wing tank (due to sagging bending moment). This limitation could be critical for the bulk carriers with transversely framed side shell in upper tank and thin sloping bulkheads. The shear strength of the side shell between the loaded and empty holds (in block loading) should also be checked for the allowable cargo mass. The sagging SWBM at any seagoing condition is not to exceed:

WIBMyISWBM critsagmax −σ= (30)

where I is the hull girder net moment of inertia at the mid-hold section, y is the distance between the hull girder neutral axis and the structural member under consideration (plate panel or longitudinal stiffeners), σcrit is the critical buckling stress of the structural member under consideration and WIBM is the Wave Induced Bending Moment as prescribed in the Rules. 4. CASE STUDIES 4.1 DERIVATION OF HOLD MASS CURVES As has been described previously, the hold mass curves may provide the pre-1998 bulk carriers with the ability to safely operate a variety of loading conditions apart from the ones checked in the design stage. It is very common, from an operational point of view, for a vessel to be needed to load cargoes at reduced draughts and in loading patterns different from the ones shown in the loading manual. These loading conditions, apart from the stability and longitudinal strength aspect which are examined on-board with the aid of the loading instrument, have also to be checked from local strength point of view in the plan approval office. The aim of this examination is to verify the structural integrity of the plating, the ordinary stiffeners and the primary supporting members for each hold under the given loading condition. The plating and the stiffeners are checked at various sections of the ship’s length with the ‘MARS’ program (a typical section in MARS is shown in Figure 9). MARS is a panel-to-panel 2D analysis tool based on the requirements of the BV Rules. The primary supporting members (girders and floors) are assessed using the ‘STEEL’ program. STEEL is a 3D beam analysis program which calculates all deformations, local moments, forces and stresses in structures modelled by

beams subjected to static loads (in Figure 10 a STEEL model is shown extending from the middle of one hold to the middle of the next hold is depicted). Depending on the loading condition at hand, the review may also include the examination of the transverse bulkheads and the cross deck areas. All this process is time consuming and is also specific for each loading condition, which means that it has to be repeated every time the proposed condition deviates from the loading manual. In order to bypass the process described above, the hold mass curves can be formulated based on the vessel’s existing loading manual. By the time these curves have been created and implemented on board (as a supplement to the loading manual), the vessel gains the flexibility to be loaded in ways, otherwise restrictive, without further examination. Figure 9: Typical MARS section for the assessment of the plating and ordinary stiffeners Figure 10: Two-hold model in STEEL for the assessment of the primary supporting members of the bottom Application of the mathematical equations presented in section 2 on a capesize bulk carrier yields the hold mass curves for each hold and for the pairs of adjacent holds. These are depicted in Figures 11 and 12 for No 5 and No 6 cargo holds, respectively, and in Figure 13 for the adjacent No 5 and No 6 cargo holds. The main particulars of the vessel are given in Table 1.

Table 1: Main particulars of the case study vessel Length over all (Loa) 253.92 m Length between perpendiculars 241.00 m Moulded breadth 40.00 m Moulded depth 21.00 m Scantling draught 14.60 m Block coefficient (CB) 0.822 Deadweight (approx.) 100,000 t

Figure 11: Hold mass curves for No 5 cargo hold Figure 12: Hold mass curves for No 6 cargo hold The loading manual can provide directly points 3 and 5 (see Figure 11), that produce the Pmax curve (a) and the Pmin curve (b) for seagoing conditions. More specifically, point 5 corresponds to a loading condition at which the hold is fully loaded at the minimum possible draught Tactual calculated at mid length of the hold. The critical condition for the even holds that fulfils this requirement is usually the full load homogeneous condition (in particular the arrival condition, which has a smaller draught than the departure condition) or the full load alternate (arrival) condition for the ore holds. Since Tactual (as depicted by the actual full load condition) is usually smaller than the scantling draught T, the Pmax curve obtains the flat section between points 5 and 1 by applying TTactual = in expression (4). It is important to note at this point that when calculating the minimum and maximum mass for each hold from the actual loading conditions, the mass of double bottom contents MDB (if any) should be added to the mass of cargo in the hold, as

this weight also counteracts to the upward acting sea pressure. This MDB should not be confused as being only ballast water, since it represents any liquid weight in the double bottom situated underneath the flat inner bottom of the cargo hold. It is common to have fuel and diesel oil tanks underneath the aft holds of bulk carriers and this weight is bound to be present in the full load condition, while ballast water is not.

By following the same approach as above, point 3 corresponds to a loading condition at which the hold may be empty, at the maximum possible draught Tmax (calculated at mid-length of the hold). For an (uneven) ore hold this is typically the heavy ballast condition (and especially the departure condition, which has a greater draught than the arrival condition), whereas for an even hold this is, in most cases, the alternate condition at full draught (departure condition). Due to these different draughts, the Pmin curve of the even holds (curve (b) of Figure 12) is usually a flat line which coincides with the axis of the draughts (horizontal axis). The relevant curve for the ore hold (curve (b) of Figure 11) starts at Tmax and ends at T, being at the same time parallel to the Pmax curve. Following the procedure described above for No 5 cargo hold, with a length of 26.6 m, points 5 and 3 would be the following for the vessel under consideration (draught in m, cargo mass in t):

)26949,15.14()P,T(P maxactual5 == (associated bulk cargo density: 1.67 t/m3)

)0,07.10()0,T(P max3 == The Pmin and Pmax curves for seagoing conditions can now be derived from expressions (4) and (7), respectively. In order to produce the relevant curves for harbour conditions, we need to calculate the relative motion hU.. According to BV Rules, the reference value of the relative motion, at any hull transverse section, can be obtained from the formulas in Table 2 [9]. Table 2: Maximum relative motion h1 in the upright ship condition [9]

T1 shown in Table 2 (for a location between 0,3L and 0,7L) may be taken equal to Tactual (for the Pmax curve) and Tmax (for the Pmin curve). The wave parameter is calculated on the basis of the wave parameter C (see Table 3) and the navigation coefficient n (see Table 4). Based on the above, for No 5 cargo hold (mid-length situated at x = 0.43L), the relative motion hU is equal to

m291.32hh 1

U == for the Pmax curve (load case ‘b’), and

m582.6hh 1U == for the Pmin curve (load case ’a’). The relevant curves for harbour conditions (curves (c) and (d)) can now be produced by substituting the data of points 3 and 5 and hU to expressions (19) and (21). In case that Pmax (seagoing) is calculated from a loading condition with a liquid weight MDB underneath the hold, then this weight has to be deducted in (19) and (21). Table 3: Wave parameter C [9] Table 4: Navigation coefficient n [9] Figure 13: Hold mass curves for No 5 and No 6 adjacent cargo holds The same procedure should be followed for producing the hold mass curves for two adjacent holds. The loading conditions in the loading manual will provide points 3 and 5 of Figure 13. Point 5 represents the loading condition at which the sum of the cargo mass in the two adjacent holds and the related double bottom contents )MM( 2DB1DB + (if any) is maximum, at the

minimum possible draught Tactual (calculated at mid-length of the holds). This could be a full load homogeneous condition at the maximum draught (arrival condition). Again by applying TTactual = in (11), the

max21 )PP( + curve (a) shows the flat section between points 5 and 1. In a similar manner, point 3 now corresponds to a loading condition at which the sum of cargo in two adjacent holds and their relative double bottom contents

)MM( 2DB1DB + (if any) is minimum, at the maximum possible draught Tmax (calculated at mid-length of the holds). An expected loading condition for this point would be the heavy ballast condition in which the adjacent holds are empty. This condition will not apply to the heavy ballast hold and its adjacent holds because of the weight of ballast water in the cargo hold. For this pair of holds, the light ballast condition could be a possible determinant for point 3. For the vessel under consideration, points 5 and 3 are the following (draught in m, cargo mass in t):

)29407,46.14())PP(,T(P max21actual5 =+= )0,09.10()0,T(P max3 ==

The min21 )PP( + and max21 )PP( + curves for seagoing conditions can now be derived by substituting the data of points 3 and 5 to the expressions (11) and (12), respectively (with length of No 6 cargo hold 26.6 m). Similarly expressions (22) and (23) will yield the relevant max21 )PP( + and max21 )PP( + curves for the harbour conditions. In case that max21 )PP( + (seagoing) is calculated from a loading condition with a liquid weight )MM( 2DB1DB + underneath the hold(s), then this weight has to be deducted in expressions (22) and (23). In the description given above for the creation of the hold mass curves from the actual conditions of the loading manual, points 5 and 3 have been correlated to typical conditions found in all loading manuals. While this is true most of the times, it is not always the case. Sometimes these points correspond to different loading conditions which involve combination of slack holds and ballasted double bottom tanks. This is due to the fact that bulk carriers built prior to the UR S25 requirements would include in their loading manuals each condition pattern (i.e. slack holds) that the vessel was designed for to sail. The UR S25 solved this issue by applying generic loading conditions during the design stage depending on the type of the vessel. 4.2 MAXIMUM DRAFT AS A FUNCTION OF

STATIC BENDING MOMENT (ORE HOLDS) The capesize bulk carrier utilised in the previous section to demonstrate the derivation of the hold mass curves will also be used to apply the method described in Section 3 to study the influence of draught and static bending moment on the bottom strength of the ore holds

(loaded in the alternate condition). The vessel does not have BC-A, BC-B or BC-C notation in compliance with URS 25. If it did, then it is known that (excluding the case where {No MP} is assigned) the maximum draft which can be tolerated for the ore holds with 100% hogging SWBM is 83% of the scantling draught. The question for the vessel under study, which is a pre-URS25 ship, is to determine the maximum draught for which the ore holds can be left empty. We choose to study No 5 cargo hold, which is located in the middle of the vessel and therefore subjected to the highest hull girder stresses. Conclusions drawn for this hold can be conservatively extended to the other ore holds as well. The hogging SWBM is 2,538,000 KN.m and the wave induced (vertical) bending moment WIBM equal to 3,650,000 KN.m. The moment of inertia of the cross section in No 5 cargo hold and the position of neutral axis are 330 m4 and 9.5 m, respectively. On the basis of these data, the buckling factors (defined by equation (28)) are computed as a function of the draught (percentage of scantling draught Ts) and the hogging SWBM. The results are depicted in Figure 14. Figure 14: Buckling factor versus draft and static bending moment It is evident that No 5 cargo hold cannot be empty close and below the scantling draught. Calculations for the maximum draught, assuming 100% of the SWBM is acting, are depicted in Figure 15 as a function of the buckling factor. It is found that the buckling factor BF is lower than one below (approximately) 78% of the scantling draught. Figure 15: Buckling factor versus draught (at 100% SWBM)

The sensitivity of the bottom plating buckling strength to the static bending moment is depicted in Figure 16, which is a multi-modal version of the previous one. Figure 16 depicts the maximum permissible draught as a function of the hogging SWBM. The sensitivity of the buckling strength to the bottom thickness is shown in Figure 17. As expected, there is a parabolic relation between the buckling strength (BF) and the bottom thickness. Figure 16: Sensitivity to the hogging SWBM Figure 17: Sensitivity to the bottom thickness 5. CONCLUSIONS In order for bulk carriers to safely sail a certain loading condition, three key points need to be checked. First, the longitudinal strength characteristics, in terms of still water bending moment and shear force, need to be verified against the permissible values. Second, the ship’s intact and damage stability particulars need to be checked in accordance with the applicable criteria. Third, the local strength of the cargo hold structure, loaded by the cargo mass forces and external sea pressures, is to be checked against applicable yielding, buckling and fatigue criteria. The first two points can be readily dealt with on-board by entering the loading condition into the loading instrument (or loading computer), which is mandatory for all bulk carriers of 150 m in length and over. The loading instrument of modern bulk carriers, contracted for construction on of after 1 July 1998, IACS UR S1A requires the hold mass curves, making verification of the third point straightforward for the master. For pre-UR S1A bulk carriers the hold mass curves are not mandatory. Therefore, if loading conditions other than

the conditions of the approved loading manual are envisaged, the hold mass curves need to be specifically derived to check the local strength of the cargo hold structure. This is particularly important when the vessel will be engaged in multi-port operations with strong variation of cargo mass against draught for the different cargo holds. As the majority of the in-service of bulk carriers consists of pre-UR S1A ships, a practical method for establishing the hold mass curves is needed. On the theoretical level (section 2), the basic requirement for the derivation of the hold mass curves is the conservation of the net vertical load on the double bottom structure. These curves have been derived in this paper and it was shown that, by conservatively simplifying the derived expressions, the conservation of load requirement reduces to the conservation of mass requirement generally adopted in UR S25. With this method simple expressions are obtained for calculating the hold mass curves for individual cargo holds and two adjacent cargo holds, in seagoing as well as harbour conditions. With the introduction of UR S25, later followed by the CSR, the minimum envelope of the hold mass curves has been clearly defined and the hold mass curves follow directly from the application of the rule strength requirements to the prescribed loading conditions. For pre-UR S25 bulk carriers the situation is more complicated. Generally speaking, the set of approved loading conditions from the loading manual serves to define the hold mass curves on the basis of the expressions derived in this paper, which provides the ship owner with more loading flexibility. In case the envisaged loading condition is outside the hold mass curves obtained in this manner, additional strength checks are to be performed in order to accept the new loading condition. It is obvious that the loading flexibility obtained from the hold mass curves is somewhat limited due to the conservative simplifications which have been made in order to ensure an easy and quick process. When the more general expressions (before application of the simplifications) are applied, more loading flexibility can be obtained in result. In section 3 the importance of the combination of draught and hogging still water bending moment for the case of empty holds in multi-port conditions was emphasised, as there is a significant risk of buckling of the bottom plating due to the combination of local and global compression stresses. This issue needs to be specifically addressed when deriving the hold mass curves for multi-port operations. A practical application of the derived hold mass curves is presented in the case studies on a 100k DWT capesize bulk carrier. Hold mass curves have been derived for No 5 cargo hold, No 6 cargo hold and the adjacent No 5 and No 6 cargo holds. In addition, the maximum draught at which No 5 cargo hold can be empty, while the

maximum hogging still water bending moment is acting, has been derived from a buckling analysis of the bottom plating. Finally, a sensitivity study into the effect of the value of the still water bending moment and bottom plating thickness was carried out. In conclusion, a practical methodology for the derivation of the hold mass curves has been presented, which is easy to apply to existing bulk carrier and can be used to extend the operating profile of bulk carriers in a safe way, taking into account the relevant strength limits of the cargo hold local structure. This is particularly relevant for existing ships which need to engage in multi-port operations. 6. REFERENCES 1. Intercargo, ‘Intercargo Briefing: Loading Rates’,

Rev.0.1, 21 November 2008 2. Lloyd’s MIU, ‘SeaWay’, May 2009 3. IACS, ‘Bulk Carriers - Guidance and Information on

Bulk Cargo Loading and Discharging to Reduce the Likelihood of Over-stressing the Hull Structure’, Rec. 46, 1997

4. Bureau Veritas, ‘Rules for the Classification of Steel Ships’, Pt B, Ch 5, Sec 5, [2], April 2009

5. Journée JMJ, Massie WW, ‘Offshore Hydrodynamics’, First Edition, Delft University of Technology, January 2001

6. Bureau Veritas, ‘Rules for the Classification of Steel Ships’, Pt B, Ch 5, Sec 4, April 2009

7. Bureau Veritas, ‘Rules for the Classification of Steel Ships’, Pt B, Ch 5, Sec 3, [2], April 2009

8. IACS, ‘Harmonised Notations and Corresponding Design Loading Conditions for Bulk Carriers’, UR S25, Rev. 2, July 2004

9. Bureau Veritas, ‘Rules for the Classification of Steel Ships’, Pt B, Ch 5, April 2009

7. AUTHORS’ BIOGRAPHIES Kostantinos Chatzitolios currently works in Bureau Veritas as a hull surveyor in the plan approval office (HPO) of Piraeus, Greece. He joined Bureau Veritas in 2005 after obtaining a Diploma in Naval Architecture and Marine Engineering from the National Technical University of Athens. In the four years that he has worked in HPO he has dealt with stability and hull matters of bulk carriers, oil tankers and passenger ships. In the last two years he is specialized in the hull structure of bulk carriers (existing and CSR) and oil tankers. Konstantinos is currently undertaking a Masters degree in Business Administration (International MBA) in the Athens University of Economics and Business. Gijsbert de Jong holds the current position of product manager at Bureau Veritas and is based in the Head Office in Paris. He is responsible for the international business development in the field of container ships and

dry bulk carriers, as well as a number of specialised ship types. Gijsbert joined Bureau Veritas in 2001 after obtaining an MSc in Naval Architecture & Marine Engineering from Delft University of Technology. Before moving to Sales & Marketing Management in 2007, he has worked as hull surveyor and department manager for the Bureau Veritas plan approval office in Rotterdam. During this period Gijsbert has built up extensive experience with dry cargo & container ships, dredgers, asphalt carriers, product tankers, reefers & tugs. In his present position he is working closely together with BV’s technical specialists and extensive international network to develop new products and services meeting with the maritime industry’s specific needs. Gijsbert has published technical papers on container ships, bulk carriers, arctic shipping and fuel cell power systems and regularly writes articles for marine industry magazines. Dr John Emmanuel Kokarakis, a 1979 graduate of National Technical University of Athens, he holds PhD (1986) and Masters degrees in Naval Architecture (1983) and Masters in Mechanical Engineering (1984) from the University of Michigan. He worked for over ten years as a consultant undertaking technical problems worldwide. His specialization was in the area of technical investigation of marine accidents. In his capacity as a forensic engineer he participated in the technical investigation of the Exxon Valdez grounding, Sea-crest Capsize, Piper Alpha fire and explosion, Aleutian Enterprise foundering in Alaska as well as many other accidents of less notoriety. The last eleven years he works in Greece, in the area of classification. Having served in the plan approval office of American Bureau of Shipping in Piraeus, he then joined Germanischer Lloyd heading their tanker and bulk carrier team in Greece. He is currently the Technical Director of Bureau Veritas in the Hellenic and Black Sea Region. In his duties Dr. Kokarakis is responsible for the smooth technical operation in the region as well as in the harmonic cooperation with the BV offices worldwide to the benefit of the BV clients in Greece. He was a member of the team which developed the Common Structural Rules.