Effect of Local Pressure Loads on Ultimate Hull Girder Strength

(1)

Effect of Local Pressure. Loads on Ultimate Hull Girder

Strength ** *

_{DeIft University of Technology.}

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Key Words Uliimate Hull Girder Strength; Buckling/PlasL

ErnaiI:

deheerUde1ft.I

Kinya Ishibashi, Toshiyu/çi Shigerni, Minoru Harada**

1. INTRODUCTION

A large number Of studies have been carried out on

longitudinal bending strength, the most important component of hull structure strength, by estimating the ultimate lOading, moment (ultimate strength) with regards to yield and buckling responses. As a result of these studies, it was confirmed it was

possIble to calculate ultimate strength by estimating only the

longitudinal bending moment's effect on the hull structure, and

a, number of new assessment methods 1)

based on Smiths

method2), which considers the structural response

of

longitudinal members between transverse frames of the hold

structure, have been developed, allowing ultimate strength to

be calculated relatively simply using only ultiìnated loading moment rather than complicated and time-consuming FEM

analysis.

Classificatioñ societies have begun to include ultiinate hull

girder strength requirements based on these strength

assessment methods in their rules in receüt years, and these requirements have also been included in the lACS Common

Structural Rules for Bulk Carriers3) and Oil Tankcrs4) Thus, ültimate hull irder strength requirements are now commonly applicable to a large number of ships.

In practiáe, howes.,er, local pressure loads, such as the loads

from the cargo and the sea water, act simultaneously on the

hull structure in addition to the vertical bending moment, and there are sufficient grounds to concludè that these loads affect the maximum moment capacity.

This study investigated the effects of local pressure loads on the maximUm moment capacity of the hold structure of a bulk carrier using a series of calculations developed from

elastoplastic large deflection analysis carried out by valying the method of applying the local pressure loads. An FEM

model of 3 holds capable of correctly reproducing the response of hold structUres subjected to local pressure loads Was used, and., all elements of the central

hold were

assigned elastoplastic materiál characteristics so that the collapse could be correctly reproduced in the hold.

2. Analysis conditions

2.1 FEM model

An FEM model of a Panamax singlé hull bulk carrier was

created, as shown iñ Fig. 1.

From holds No. 5-7, only the central No. 6 hold was

considered for assessment, and fine meshes were assigned for

this hold. The theshing afrañgemeñt shoWn in Table I was

used so that the buckling of panels between ordinary stiffeners, stiffener buckling, çtc., could be reproduced. The model was

created with all shell elements including ordinary stiffeners

and web stiffeners.

Altérnatively, fOr hOlds No. 5 añd NO. 7, comparatively coarse meshes were used. A model was created using shell

elemeúts for plates and girders, and beam elements for

ordinary siffeners

and web

stiffeners. Elastic material

characteristics were assigned and steps taken io ensure that

collapse of these parts did not occur. The total number of

nodes in the model was 266,695.

2.2 Loading conditions

The analysis accounts for applying longitudinal bending moment and local pessure loads simultaneously to the FEM

model described in Sec. 2.1. The three cases shown in Fig. 2,

that is, loading conditiòns (1) to (3) below are considered for

the combination of local pressure loads, including conditions without local pressure loads acting on the three holds.

LCI (no local pressure lOads)

No local pressure loads; only longitudinal bending moment is applied at both ends of the model LC2 (alternate loading condition 1)

The No. 6 hold is considered to be loaded, with the No. 5 and No. 7 hQlds empty; draft is the full load draught

(14m).

LC3 (alternate loading condition 2)

The No. 5 hold and the No. 7 hold are considered to be loaded, with the No. 6 hold empty; draft is the full load draught.

* _{Development Department, Nippon Kaiji Kyokdi (ClassNK)}

-** _{Research Institute, Nippon Kaiji Kyokai (ClassNK).}

This is an English translation of the paper onginally submitted at the Technical Meeting of Japan Society of Naval

ClassNK TECHNICAL BULLETIN 2009

Architects and Ocean Eñgineers (29-30 May 2008, Nagasaki, Japan).

(2)

The deadweight of each hold (òniy on one side) is taken as follows:

No. 5 hold: 8,400 tons No. 6 hold: 5,100 tons No. 7 hold: 6,700 tons

The sequence of application ofioads in he FEM model isas

shown in Fig. 3. After applying a local pressure load tO a specific level, the load level is maintained constant, and a

longitudinal bending moment on the hoggiñg side i's applied by

fòrced displacement on both ends of the model. This load is

increased until total collapse of the structure occurs.

Table 1 Principle of meshing

Table 2 Boundary coiiditions

coarse mesh elastic material

fine mesh eltatoplastic ostenti

(a) Whole view1

coarse mesh elastic material

2.3 Boundary conditions

Symmetric conditions about the hull center line are assigned

since this model is a one-sided model. Moreover,, conditions

for retaining the cross' section are assigned to the lçft and right

ends of the model of Fig. i(a) using rigid body elements, and the boundary conditions of Table 2 are assigned to the rigid

body elements at the two ends.. Longitudinal bending moment is assigned at

the two eflds of the model by forced

displacement.

2.4 Other analysis conditions

The comrnerciál analysis code, MSC.Marc was used in the

analysis. The Newton-Raphson method was used as

the convergence algorithm. The material characteristics used were:

Young's modulus E=206.0 GPa; yield stress oy=235, 315,

355 N/mm2 depending on the type of steel

used; strain hardening rate H'=O assuming a perfectly elastoplastic body. No initial deflection or residual stress was assigned.

No.7 No.6 No.5

LC 1

C

)

LC2 (

LC3 (

tif ft f t

titi ti f

Figure 2 Loading conditions

Local load Longitudinal mdmerìt

)

i Number of elements

Between lonjtudiñal stiffeners... 8

Between transverse web frames 20 Across the hei htof IOn :itudinal stiffener 3

Across the height 6f longitudinal and

transverse irder 14 Across the death of the web of hold frame 3

Fixed ' displacement Forced displacement leftend

ü,v,w,rx,tz

ri ht end y, w, rx .,rz

(b) Zooming view Progress level of Analysis Figure 1 Three holds model tobç analyzed Figure 3 Load history

(3)

3. Results of analysis

3.1 Collapse behavior

Fig. 4 shows the deformation diagram at ultimate strength obtained from the analysis of Sec. 2 above. The position at which collapse occurred for each analysis case was: section near the aft bulkhead of central hold for LC1; sections near

both bulkheads of the central hold for LC2; and near the center of the hold in the central hold for LC3.

3.2 Longitudinal bending moment in the

collapsed section

In addition to the longitudinal bending moment applied

through forced displacement at the two ends of the model in the analytical cases for LC2 and LC3, longitudinal bending

moment due to local pressure loads occurs, and it is distributed

in the longitudinal direction of the ship. Accordingly, the

longitudinal bending moment acting on the collapsed section

must be determined in order to know the ultimate hull girder

strength for each analysis case. The longitudinal bending

moment was determined by integrating the normal stress in the longitudinal direction of the ship as shown in Eq. (1) for the three cross sections shown in Fig. 7.

The maximum moment capacity

is derived from the

longitudinal bending moment that occurred at the collapse

position in each analysis case from Fig. 6, as shown in Table 3.

Compared to LC1 in which local pressure loads were not

considered, the maximum moment capacity for LC2 and LC3 in which local pressure loads acted, decreased by 6% and 21% respectively.

i.

A A

(a) LCI

ClassNK TECHNICAL BULLETIN 2009

13

M =

ZN.A.) _(I)

Here, M is the longitudinal bending moment acting on the

relevant section; is the normal stress in the longitudinal

direction of the ship in element i included in the relevant

section; A is the sectional area of the element i;

z, is the

position in the vertical direction of element i;

ZN.A. is the

position in the vertical direction of the neutral axis.

Fig. 5 shows the comparison of longitudinal bending moment

acting on the section determined by equation (1) and the

longitudinal bending moment derived from the beam theoty in the condition where only local pressure loads act. This figure confirms that both the moments coincide very well.

Fig. 6 shows the relationship between moment and rotation

angle for each cross section. However, the rotation angle of the

transverse axis is the value at the two ends of the model. The

moment does not become zero at the rotation angle of zero in

Fig. 6(b) and (c). This

is because of the effect of the

longitudinal bending moment acting on the relevant section

due to local pressure loads. From Fig. 6,

it can also be

confirmed that for all analysis cases, the analysis was

continued until the value of the moment decreased.

(b) LC2

L

(c)LC3

* Deformation is magnified by 5 times

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E E z C E o E 6e+1 I 4e+1 2e+1 1 4e+1 7

No.7 Caigo hold No.6 Cargo hold No.5 Cargo hold position in o direction

Figure5 Distribution of longitudinal moment due to local

loads 3e+12 2.5e+12 2e-i-12 E

z

1.5e-i-12 a, E o le+12 5e-i-11 0 3e-i-12 2.5e-i-12 2e12 E

z

1.5e-i-12 a, E o lei-12 5e-iii o aft sction mid section fore section aft sction mid section tore section aft section mid section foresection

Figure 7 Positions of three measured sections

Table 3 Maximum moment capacity in each load case

*_{Values in parenthesis show the ratios to moment capacity of LC 1.}

4. Considerations related to difference in

the reduction rate of the maximum

moment capacity

In analysis cases LC2 and LC3, in which both longitudinal bending moment and local pressure loads act simultaneously

on the model, maximum moment capacities decrease considerably compared to analysis case LC I, in which only the longitudinal

bending moment acts. The value for LC3

especially is smaller. The cause leading to this difference in reduction rate is attributed to the difference in internal and external pressures of the double bottom structure in the two

cases. For LC2, sea water pressure acts on the bottom plating, and pressure from cargoes acts on the inner bottom plating, so

that the pressures on the double bottom structure are more or less balanced in the vertical direction. In contrast, for LC3,

only the pressure load acts on the bottom shell plating so as to

push up the double bottom structure. Fig. 8 shows the

deformation of the double bottom structure for the two

analysis cases in the condition where only local pressure loads act. The deformation of the double bottom structure is large in case of LC3. A severe biaxial compression condition occurs in

the bottom shell plating at the center of the hold for LC3.

Moreover, high shear stress acts in the inner bottom plating

and in the bottom shell plating near the girders and in the

girders near the bulkhead. The superposition of these stresses

and the longitudinal bending stress cause collapse of the

structural members at lower longitudinal bending stress values,

and is considered to be the cause of the reduction in the

Load Case Maximum moment capacity in Hogging (MINm)

LC1 2.58 x l0

LC2 2.42 x l0 (0.94)

LC3 2.04 x l0 (0.79)

0 0.002 0.004 0.006 0.008

Rotation angle (rad)

LC1

3e-i-1 2

aft sction

mid section

2.5e+12 tore section

2e-i-12 E E

z

i .5e+12 a, E o lei-12 5e-i-11 o O 0.002 0.004 0.006 0.008

LC2

0 0.002 0.004 0.006 0.008

(e) LC3

o

-2e-i-11

-6e+7 1

(5)

!1I1m!ItII!t .IJ!!

JjIHII1IHHII mmcm

'ittl!Wflituminhit nil

H fl!H!H 11.9

LC2

LC3

* Deformation is magnified by 40 times Figure 8 Cbmparisoñ on defotrnatioñ of double bottom

structure

5..

CONCLUSIONS

Senes caiculatiöns using elastoplastic large deflectioñ analysis were performed oti the hóld structure of a bulk rrier

with the objective of examining the effects Of local pressure

loads on the hull girder maximum moment capacity.

This study confirmed that local pressure loads caused the maximum moment capacity to vary in the collapsed cross

sections. Results of the examihatiön also showed that the

larger thé difference iii the internal and extemál pressures of the double bottom, the higher is the rate of reduction in the

maximum moment capacity.

This is attribute4 to he superposition of various stresses in the double bottom structure afisiuig frOm the differetice in internal and éxternal pressures,

and the longitudinal bending stress, which probably caused structural collapse at lower longitudinal bending stress than

when the structure was subjected to longitudinal bending stress alone.

From the results of the present stiidy it can be shown that the maxithuth mothent capacity cah be evälùated at a rather high level using the itimate hull girder strength aSsesSment method without considering the effects of local pressure loads. In ships, however, the máximum moment capacities on the hogging side

have high safety factors compared to the value, required by

classificatioù rules generally; thus, even if the maximum

moment capacity decreased due to local pressure loads, the required strength would be adequately maintainedi This is

because superposition

of local

structural respPnse and

longitudinal bending have been coñsidered for structural

requirements other than ultimate hull girder streñgth, such as

yield and buckling strength requirements by direct strength calculation or prescriptive requiremçnts for stiffeners and

panels.

REFERENCES

(I) Yao, T. and Nikolov, P. 1., "Progressive Collapse Analysis of a Ship's Hull under Longitudinal Bending (2nd Rep.)", J Soc. Naval Arch. of Japan, Vol.172, 1972, pp.4Y7-446 Smith, C., "Influence of Local Compressive Collapse on Ultimate Longitudinal Strength of a Ship's Hull", Proc. Int. Symp. PRADS, Tokyo, Japan, 1977, pp.73-79

Nippon Kaiji Kyokai (ClassNK), "Rules for the Survey and Construction of Steel Ships, Part CSRB (Common Strùctural Rules for Bulk Cárriers)", 2001, pp.148-156 Nippon Kaiji Kyokai (ClassNK), "Rules for the Survey and Construction of Steel Ships, Part CSR-T (Common Structural Rules for Double Hull Oil Tankers)", 2007, pp. 377-390

Effect of Local Pressure Loads on Ultimate Hull Girder Strength