Calculation (midship) of ship

Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I

MIDSHIP SECTION INTRODUCTION

Midship section design is in accordance with Part 4, Chapter 9 of “Lloyd’s Register”, Rules and Regulations for Classification of Ships, which has been revised to include requirements for Double Hull Oil Tankers. These requirements reflect regulation 13F of Annex I of MARPOL 73/78 with the other features. Fig.1 is a typical midship section of a double skin tanker.

Figure 1 - Typical midship section of a double skin tanker 1.1. Definitions (1)

L

:

Rule length, in m, is the distance, in meters, on the summer load water line from the forward side of the stem to the after side of the rudderpost or to the center of the rudder stock, if there is no rudder post. L is neither to be less than 96% nor to be greater than 97% of the extreme length on the summer load water line.

97% of extreme length of LWL = 229.89m (2)

B

:

Breadth at amidships or greatest breadth, in meters. B = 42.0 m

(3) D

:

Depth is measured, in meters, at the middle of the length L, from top of the keel to top of the deck beam at side on the uppermost continuous deck.

(4)

D

= 22.0 m

T

:

T

= 14 m

T is the summer load draught in m, measured from top of keel.


(5)

LPP

:

Distance

in

m

on

the

summer

LWL

from

foreside

of

the

stem

to

after

side

of rudder post, or to the center of the rudder stock, if there is no rudder post.

(6)

LPP

= 233 m

CB

:

Moulded

block

coefficient

at

draught

T

corresponding

to

summer

waterline, based on rule length L and moulded breadth B, as follows: moulded displacement (m3) at draught T CB

= L.B.T

(7)

B

:

The

width

of

plating

supported

by

the

primary

member

or

secondary

member in m or mm respectively. (8)

be

:

The effective width, in m, of end brackets.

(9)

bI

:

The

minimum

longitudinal

distance

bulkhead

from

measured

side

shell

to

inboard

at

right

the

inner

angles

hull

to

the

or

outer

centre

line

at summer load water line, in m (10)

le

:

Effective

length,

in

m,

of

the

primary

or

secondary

member,

cargo

tank

boundary

and

measured

between effective span points. (11)

ds

:

The

distance,

in

m,

between

the

the

moulded

line of the side shell plating. (12)

h

:

The load height applied to the item under consideration, in m.

(13)

db

:

The

distance,

moulded

line

in of

m, the

between bottom

the shell

bottom plating

of

the

measured

cargo at

tanks

right

angles

and

the

to

the

bottom shell plating. (14)

kL, k :

Higher tensile steel factors. For mild steel, kL, k may be taken as 1.

(15)

I

Moment

:

of

inertia,

in

cm3,

of

the

primary

or

secondary

member,

in

primary

or

secondary

member,

in

association with an effective width of attached plating. (16)

s

:

Spacing of secondary members, in mm.

(17)

S

:

Overall span of frame, in mm

(18)

t

:

Thickness of plating, in mm.

(19)

Z

:

Section

modulus,

in

cm3,

of

the

association with an effective width of attached plating. (20)

L1

:

Length of ship in meters, but need not be greater than 190m.

(21)

CW

:

Wave head, in m.

(22)

RB

:

Bilge radius, in mm.


(23)

FD,FB :

Local

scantling

respectively.

reduction

factor

above

neutral

axis

FD

= 0.67, for plating and 0.75, for longitudinals

FB

= 0.67, for plating and 0.75, for longitudinals

(24)

σO

:

Specified minimum yield stress, in N/mm2

(25)

σC

:

Maximum compressive hull vertical bending stress, in N/mm2

(26)

T1

:

T but to be taken not less than 0.05L m

and

below

neutral

axis

= 11.495 m (27)

hT1

:

T + CW m but need not be taken greater than 1.36 T

(28)

hT2

:

T + 0.5CW m but need not be taken greater than 1.2 T

(29)

c1

:

60 / (225 – 165 FD) at deck; 1.0 at D/2; 75 / (225 – 150FB) at base `

line

of ship (30)

c2

:

165 / (345 – 180FB) at deck; 1.0 at D/2;

165/(345 – 180FB) at base line of

ship (31)

R

:

sinθ, where θ is the roll angle in degrees sinθ R

(32)

D1

:

= (0.45+0.1 L/B)(0.54 – L/1270) =0 .358

D, in m, but is to be taken not < 10 and need not be taken >16 D1 = 16m sinθ = (0.45 + 0.1L/B)(0.54 – L / 1270 ) R = 0.358

(33) dDB

:

Rule depth of center girder, in mm

(34)

SS

:

Span of the vertical web, in m

(35)

tW

:

Thickness of web, in mm

(36)

tB :

Thickness of end bracket plating, in mm 1.1.2. Class Notation

Vessel is designed to be classed as ‘+100 A1 Double Hull Oil Tanker ESP.’ ESP means Enhanced Survey Program. This is for seagoing tanker having integral cargo tanks for carriage of oil having flash point > 60o C. 1.1.3. Cargo Tank Boundary Requirements Minimum double side width (ds) in m


ds

=

0.5 + (dwt/20,000) or ds = 2.0 m

whichever is lesser. But ds should not be less than 1 m. ds

=

0.5+(95,000/20,000) = 5.25 m

Double side width is taken as 2.0 m to get the required ballast volume. ∴ ds

=

2.0 m

Minimum double bottom depth (dB) dB

=

B/15 or dB = 2.0 m

whichever is lesser dB

= 42/15 = 2.8

m

A double bottom height of 2.0 m is provided to get the required ballast volume. ∴ dB

=

2.0 m

Structural configuration adopted has a single centerline longitudinal bulkhead. According to Maritime Law of India (Appendix V111:63, Regulation 24), Length of cargo hold shall not exceed 10m or (0.25bi /B +0.15) x LL (for longitudinal bulkhead provided at centerline), whichever is greater. [LRS Part 4, Chapter 9, Section 1.3.9] (0.25bi /B +0.15) × LL

=

35.85 m

For length of cargo tanks and tank boundaries refer General Arrangement Plan. Type Of Framing System

The bottom shell, inner bottom and deck are longitudinally framed (for L > 75m). The side shell, inner hull bulkheads and long bulkheads are also longitudinally framed (L > 150m). When the side shell in long framed, the inner hull bulkhead is also to be framed longitudinally. Primary members are defined as girders, floors, transverses and other supporting members. LONGITUDINAL STRENGTH Design vertical wave bending moment

(P3, C4, S5.2)

The appropriate hogging or sagging design hull vertical wave bending moment at amidships is given by the following: Mw Where,

=

f1 f2 Mwo


M wo

=

0.1C1 C2 L2 B (C b + 0,7) kN m

Cb is to be taken not less than 0,60 C1 is given in Table 4.5.1 = 10.163 C2

=

1, (also defined in 5.2.2 at other positions along the length L)

f1

=

ship service factor. For unrestricted sea-going service f 1 = 1,0

f2

=

–1,1 for sagging (negative) moment

f2

=

for hogging (positive) moment

=

1.025

=

0.1×10.163×1×(229.89) 2×42×(.825+0.7)

=

3440180.424 KNm

=

1×-1.1×3440180.424 =-3784198.47

=

1×1.025×3440180.424 =3526184.935

1.9C b

M wo

Mw

(C b + 0.7)

(sagging) (hogging)

Permissible Still water Bending Moment Ms

=

fsn×Cw×L2×B×(CB+0.7) KNm

fsn

=

0.072

Cw

=

10.75-{(300-L)/100}3/2

Ms

=

0.072×10.163×(229.89)2×42×(0.825+0.7)

=

247692.991 KNm

for sagging bending moment

Hull Moment of Inertia

(P3, C4, S5. 8) (| M s + M w |)

Imin

=

3L

=

139.373 m4

kL×σ

10 –5 m4

Minimum Hull Section Modulus [LRS Part 3, Chapter 4, Section 5]

The hull midship section modulus about the transverse neutral axis, at the deck or keel is to be not less than Z min

=

f1KL C1L2B (CB + 0.7) x 10-6 m3


f1

=

ship’s the

service service

factor.

restriction

T and

be in

any

specially event

For unrestricted sea going service f1 = 1.0 ∴f1 taken as 1 For M.S; KL

=

1 [Part 3 Chap.2 Sec 1.2]

C1

=

10.75 – [(300-L)/100] 1.5 for 90
=

10.163

CB

=

Block Coefficient = 0.825

∴ Zmin

=

34.4018 m3

Hull Envelope Plating

Itemization of parts is shown in figure 8.2.

Fig.2

For longitudinally framed system [LRS Part 4, Chapter 9, Section 4] α

=

σO/σC = 235/175 = 1.34

J

=

1720.5√{(1-1/α)/σO} for α < 2

=

56.53

t

=

s/J + 2.0

s

=

spacing of deck longitudinals = 850 mm

J

=

56.53

1) Deck plating

considered should

not

depending be

less

than

upon 0.5.


∴t

=

17 mm

2) Sheer strake The greatest of the following is to be taken: a)

t

=

0.0042 s √hT1k

s

=

spacing of longitudinals = 700 mm

hT1

=

1.36T = 19.04

k

=

1, for mild steel

t

=

15.17 mm

t

=

s/J + 2 = 17 mm

t

=

17 mm

Selected t

=

17 mm

or b)

3) Side shell above mid-depth The greatest of the following is to be taken: a)

t

=

0.001s(0.059L1 + 7) √ FD/ kL

s

=

spacing of side shell longitudinals = 700 mm

FD

=

0.67 (refer ‘DEFINITIONS’)

L1

=

190 m (refer ‘DEFINITIONS’)

kL

=

1 (refer ‘DEFINITIONS’)

∴t

=

12.67 mm

t

=

0.0042 s √hT1k, whichever is greater

hT1

=

19.04 m, as shown in pervious sections

k

=


t

=

15.18 m

Selected t

=

16 mm

or b)

4) Side shell below mid-depth

The greatest of the following is to be taken:


a)

=

0.001s (0.059L1 + 7) √ FB/kL

=

12.67 mm

t

=

0.0042 s√ hT1k

s

=

spacing of shell longitudinals = 850mm

∴t

=

15.18 mm

Selected t

=

16 mm

t

But not less than

5) Bottom shell and bilge

The greatest of the following is to be taken: a)

b)

t

=

s/J + 2.0

s

=

spacing of bottom and bilge longitudinals = 850 mm

J

=

56.53

∴t

=

17 mm

t

=

0.0052s

hT2

=

1.8-FB T + 0.5CW m but need not be taken greater than 1.2T

=

16.52

FB

=


k

=


∴t

=

16.61 mm

Selected t

=

17 mm

√

hT2k

6) Keel Plating

Keel plating should be equal to thickness of bottom shell + 2 mm ∴t but need not exceed t Selected t

=

19 mm,

=

25 √ k = 25 mm

=

19 mm

Width of keel plate is to be not less than 70B mm, but need not exceed 1800 mm and is to be not less than 750 mm. ( LRS part 4, chapter1,table 1.5.1) 70B

=

2940mm


w

=

1800 mm

t

=

t0 / √ 2-FB

t0

=

0.005s√ kh1

s

=

spacing of inner bottom longitudinals = 850mm

k

=

1

h

=

distance in m, from the plate in consideration to the highest

7) Inner bottom Plating

point of the tank, excluding hatchway. t0

=

0.72 (h+Rbi)

=

19.4

R

=

0.36 (refer previous sections)

b1

=

B/2 = 21 m

∴t

=

18 mm

8) Inner hull plating same as outer shell,t = 18mm Hull Framing [LRS Part 4, Chapter 9, Section 5] 1) Bottom Longitudinals

The section modulus of bottom longitudinals within the cargo tank region is not to be less than greater of the following: a)

Z = 0.056kh1sle2F1FS cm3 K

=


h1

=

(h0

+

(0.00L1

D1/8), +

but

0.7)

in

m,

no

case

whichever

be is

taken greater

less &

than need

L 1/56 not

m

be

or

taken

greater than (0.75 D + D1/8), for bottom longitudinals. h0

=

distance

in

m,

from

the

midpoint

highest point of tank, excluding hatchway. =

22 m

D1

=

16 m (refer ‘DEFINITIONS’)

∴h1

=

18.5 m

of

span

of

stiffener

to


s le

=

spacing of bottom longitudinals = 850 mm

=

s,

where

le

=

effective

span

of

longitudinals

assumed to be supported by web frames spaced at 5s, where s spacing in midship region = 850 mm

b)

le

=

4.25 m

F1

=

Dc1/(25D-20h)

c1

=

75/(225 – 150FB), at base line of ship.

FB

=


∴c1

=

0.667

h

=

distance of longitudinal below deck at side, in meters

=

22 m

D

=

22m (refer ‘DEFINITIONS’)

∴F1

=

0.1334

FS

=

1, at upper deck at side and at the base line

∴Z

=

2121.84 cm3

Z

=

0.0051kh3sle2F2 cm3

k

=


h3

=

ho+ Rbi

b1

=

21 m

R

=

(0.45+0.1 L/B)(0.54 – L/1270) = 0. 358

D

=

22 m

∴h3

=

29.52

but not greater than or equal to,0.75D+Rbi = 24.02 Therefore h3 = 24.02 ∴Z

=

1880.79 cm3

Greater of the two is to be taken, i.e. Z = 2121.84 cm3 Selected Half bulb section of scantling 430x21 . 2) Deck Longitudinals

=

which basic

are frame


The modulus of deck longitudinals within the cargo tank region is not to be less than greater of the following: a)

Z

=

0.056kh1sl2eF1FS cm3 ( LRS, part 4,chapter 9,5.3.1)

k

=


h1

=

(h0

h0

=

0 ( for deck longitudinals)

L1

=

190 m

D1

=

16

=

2

L1/56

=

3.39

∴h1

=

L1/56

s

=

850 mm

le

=

4.25m

F1

=

Dc1 / (4D + 20h)

h

=

0 (for deck longitudinals)

c1

=

60 / (225 – 165FD) at deck

FD

=


∴ c1

=

0.593

∴F1

=

0.1475

Fs

=

1, at upper deck at side and at baseline of ship

∴Z

=

429.9 cm3

R

=

0.36

bi

=

B/2

=

21m

h3

=

h0 + Rbi

=

7.56 m

s

=

850 mm

le

=

4.25m

F2

=

Dc2 / (D + 2.18h)

c2

=

165 / (345 – 180FD)

FD

=

0.75

∴c2

=

0.785

∴F2

=

0.785

(h0 + D1/8)

+

D1/8),

=

but

in

no

case

be

3.39

b) Z = 0.0051kh3sl2eF2 cm3

(refer ‘DEFINITIONS’)

taken

less

than

L 1/56

m

.


∴Z

=

464.7 cm3

Greatest of the two is to be taken, i.e. Z = 464.7 cm3 Taken half bulb section of scantling 260x12. 3) Side Shell Longitudinals

( LRS part 4, chapter 9,5.3.1)

From standardization point of view the side shell is divided into longitudinal fields as shown in fig 8.2. Design of the longitudinals for each field is done using the information for the lowest longitudinal in each field.

Fig. 1.3 Plate fields for the determination of side, inner hull and CL bulkhead longitudinals

The modulus of side shell longitudinals within the cargo tank region is not to be less than greater of the following: a)

Z

=

0.056kh1sle2F1Fs cm3

b)

Z

=

0.0051kh3sle2F2 cm3

h1

=

(h0

s

=

850 mm

le

=

4.25m

k

=

1

FD

=

0.75

D1

=

16

L1

=

190m

L1/56

=

3.39

where, +

D1/8),

but

in

no

case

be

taken

less

than

L 1/56

m

.


h

=

distance of longitudinal below deck at side, in meters

h3

=

h0 + 2xRb1

For side longitudinals above D/2, F1

=

Dc1 / (4D + 20h)

F2

=

Dc2 / (D + 2.18h)

For side longitudinals below D/2, F1

=

Dc1/(25D-20h)

F2

=

Dc2/(3.18D-2.18h)

Table 1.1 – Determination of scantlings of side longitudinals Item

REG 1

REG 2

REG 3

REG 4

ho

5

10

15

20

D1

16

16

16

16

h1= h0+D1/8

7

12

17

22

h3

20.12

25.12

30.12

35.12

F1

0.12

0.12

0.12

0.12

F2

0.73

0.73

0.73

0.73

Fs

1

1

1

1

a) Z

722.211

1238.076

1650.768

2063.46

b) Z

1141.82

1427.62

1656.25

1884.89

Taken Z

1141.82

1427.62

1656.25

2063.46

Section

Half bulb

Half bulb

Half bulb

Half bulb

Scantling

370x13

400x14

430x15

430x21

Z of taken section

1150

1450

1800

2150

1.2.4.

Inner Hull, Inner Bottom And Longitudinal Bulkheads

The inner hull, inner bottom and longitudinal bulkheads are longitudinally framed. The symbols used in this section are defined as follows: b1

=

the greatest distance in meters, from the centre of the plate panel or midpoint of the stiffener span, to the corners at top of the tank on either side.

c1

=

60 / (225 – 165FD) at deck

=

1.0 at D/2

=

75/(225 – 150FB), at base line of ship


c2

h (a)

=

165/(345 – 180FB) at deck

=

1.0 at D/2

=

165/(345 – 180FD) at baseline of ship

=

load height, in meters measured vertically asfollows:

for bulkhead plating the distance from a point one third of the height of the plate panel above its lower edge to the highest point of the tank, excluding hatchway

(b)

for bulkhead stiffeners or corrugations, the distance from the midpoint of span of the stiffener or corrugation to the highest point of the tank, excluding hatchway h1

=

(h + D1/8), but not less than 0.72(h + Rb1)

h2

=

(h + D1/8), in meters, but in no case be taken less than L1/56 m .

h3

=

distance of longitudinal below deck at side, in meters, but is not to be less than 0

h4

=

h + Rb1

h5

=

h2 but is not to be less than 0.55h4

t0

=

0.005s √kh1

t1

=

t0(0.84 + 0.16(tm/t0)2)

tm

=

minimum value of t0 within 0.4D each side of mid depth of bulkhead

1) Longitudinal Bulkhead Plating

For the determination of scantlings of longitudinal bulkhead plating [16, Part 4, Chapter 9], the fields in fig. 1.2 are assumed.

Region1 b1

=

21 m

h

=

3.33

h1

=

5.33

t

=

t0

=

0.005s √ kh1

=

11.85 mm

=

10.27 mm

t

but not less than t1

t0 √ 2-FB


=

t0 (0.84+0.16(tm / t0 )2

=

11.85 mm

b1

=

21 m

h

=

6.66

h1

=

10.18

t0

=

13.56

t1

=

t0 (0.84+0.16(tm / t0 )2

=

13.56 mm

t1

( Selected 12 mm)

Region2

( Selected 14mm)

Region3 b1

=

21 m

h

=

9.33

h1

=

11.33

t0

=

11.38t1 = t0 (0.84+0.16(tm / t0 )2

=

14.78 mm

t

=

12.81 mm

t1

=

14.78 mm (selected 15mm)

b1

=

21 m

h

=

12

h1

=

14

t0

=

15.91

t

=

13.79 mm

t1

=

t0 (084+0.16(tm / t0 )2

=

15.91 mm (Selected 16mm)

Region4

2) C.L Longitudinal Bulk Head Longitudinals and Inner Hull Longitudinals Inner hull and longitudinal bulkheads are to be horizontally stiffened. The modulus of longitudinals is not to be less than greater of the following:


(a)

Z = 0.056kh2sl2eF1 cm3

(b)

Z = 0.0051kh4sl2eF2 cm3

The inner hull and bulkhead plating is divided into various strakes for the determination of center line bulkhead longitudinals and inner hull longitudinals. L1/56

=

3.39

s

=

850 mm

le

=

4.25m

Table 1.2 Determination of scantlings of CL longitudinal bulkhead longitudinals . Region 1

Region 2

Region 3

Region 4

b1

21

21

21

21

h

5

10

14

18

h2

7

12

16

20

h4

12.488

17.488

21.488

25.488

F1

0.12

0.12

0.12

0.12

F2

0.73

0.73

0.73

0.73

Z1

722.211

1238.076

1650.768

2063.46

Z2

713.81

999.6

1228.24

1456.88

Taken Z

722.211

1238.076

1650.768

2063.46

Section

Half bulb

Half bulb

Half bulb

Half bulb

Scantling

300x14

370x16

430x15

430x21

Z of taken section

740

1300

1800

2150

Table 1.3 Determination of scantlings of inner hull longitudinals Region 1

Region 2

Region 3

Region 4

b1

21

21

21

21

h

5

10

14

18

h2

7

12

16

20

h4

18.536

23.536

27.536

31.536

F1

0.12

0.12

0.12

0.12

F2

0.73

0.73

0.73

0.73

Z1

722.211

1238.076

1650.768

2063.46

Z2

1059.51

1345.31

1573.94

1802.58

Taken Z

1059.51

1345.31

1650.768

2063.46

Section

Half bulb

Half bulb

Half bulb

Half bulb

Scantling

370x13

400x14

430x15

430x21


Z of taken section

1150

1450

1800

2150

3) Inner Bottom Plating and Longitudinals

The inner bottom is to be longitudinally framed and the inner bottom plating thickness is to be t

=

t0 / √ 2-FB

t0

=

0.005s√ kh1

h

=

20 m

D1

=

16

R

=

0.36

h1

=

h + D1/8 = 22m

∴t0

=

20mm

∴t

=

18.12 mm

Selected t

=

18 mm

The modulus of longitudinals is not to be less than greater of the following: (a)

(b)

Z

=

0.056kh2sl2eF1 cm3

h

=

20 m

D1

=

16 m

h2

=

h + D1 / 8 =

c1

=

0.667

F1

=

0.095

∴Z

=

2063.46 cm3

Z

=

0.0051kh4sl2eF2 cm3

h4

=

h + Rbi = 31.536m

c2

=

0.785

F2

=

0.64

but minimum value of F2 = 0.73 ∴Z

=

2063.46 cm3

22 m


. Hence, Half bulb section of scantling 430x21 is taken having section modulus of 2150 cm3. 1.2.5. Primary Members Supporting the Hull Longitudinal Framing 1) Centre girder

(LRS part 4 chapter 1,8.3.1)

(a) Minimum depth of centre girder dDB

=

28B + 205√ T mm

dDB

=

1943.04 mm

Given 2.0m. (b)

Minimum thickness of centre girder( LRS, part 4, chapter 9,14.2.5) t

Given thickness

=

(0.008 dDB + 1) √ k

=

17 mm

=

17 mm

2) Floors and Side Girders ( LRS part 4, chapter 9,14.2.5) =

(0.007dDB + 1) √ k

=

15 mm

but not to exceed 12√ k

=

12 mm

given thickness

=

12 mm

∴t

=

12 mm

t

3) Deck Transverses Section modulus of deck transverses is not to be less than Z

=

53.75 (0.0269sL + 0.8) (ST + 1.83)k cm3

s

=

4.25 m

L

=

233 m

ST

=

span of transverse

=

13.3 m

=

53.75 (0.269 × 4.25 × 233+ 0.8) (13.3 + 1.83) × 1

=

22313.4 cm3

∴Z

The section selected is a T-section with scantlings as follows


1500X25 web and 300X25 flange with the section modulus as 25400 cm3 4) Vertical web on centerline longitudinal bulkhead

Section modulus of vertical web is to be not less than Z

=

K3shsSs2k (sm3)

K3

=

1.88

s

=

4.25

hs

=

distance

between

the

lower

span

point

of

the

vertical

is

to

be

web

and the moulded deckline at centreline, in meters

Ss

=

18 m

=

span

of

vertical

web,

in

meters,

between end span points.

∴Z

=

13 m

=

24575.64 cm3

Taken 1500x 300x 25/25, with Z = 25400 cm3 1.2.6. Primary Members End Connections [LRS Part 3, Chapter 10, Section 3]

The following relations govern the scantlings of bracket: (a + b) ≥ 2l a

≥ 0.8 l

b

≥ 0.8 l

l

=

90

2

√ (14 +Z√ Z)- 1

mm

1) Bracket connecting deck transverse and inner hull l

2

√ (14 +Z√ Z) - 1

=

90

mm

=

90 { 2 (√ 25400 / [ 14 + √ 25400]) – 1}

=

2088.0 mm

a ≥ 0.8l

=

1670.4 mm

b ≥ 0.8l

=

1670.4 mm

and

measured


Given a

=

2300 mm and b = 2000 mm

t

=

thickness of web itself

= 21 mm

Flange breadth to be not less than bf

=

40 (1 + Z / 1000) mm, but not less than 50mm

=

40 (1 + 25400 / 1000 )

=

1056 mm

2) Bracket connecting deck transverse and center line bulkhead web l

2

√ (14 +Z√ Z) - 1

=

90

mm

=

90 { 2 (√ 25400 / [ 14 + √ 25400]) – 1}

=

2088.0 mm

a ≥ 0.8l

=

1670.4 mm

b ≥ 0.8l

=

1670.4 mm

Given a

=

2300 mm and b = 2000 mm

t

=

thickness of web itself = 21 mm

Flange breadth to be not less than bf

=


=

40 (1 + 25400 / 1000 )

=

1056 mm

3) Bracket connecting center line vertical web and inner bottom plating l

90

=

90 { 2 (√ 25400 / [ 14 + √ 25400]) – 1}

=

2088 mm

=

1670.4 mm

b ≥ 0.8l

=

1670.4 mm

Given a

=

2300 mm and b = 2000 mm.

tb

=

thickness of web itself = 15 mm

a

≥ 0.8l

2

√ (14 +Z√ Z)- 1

=

Flange breadth to be not less than

mm


bf

=


=

40 (1 + 25400 / 1000 )

=

1056 mm

1.2.7. Section Modulus Calculation Table 1.4 – Section Modulus Calculation AREA(m2)

20 20

N O: 2 2

AL

A L2

I own(m4)

0.924 0.374

LEVE R 22 15.25

19.404 5.2734

0 0.818

2

0.323

6.75

1.938

17

2

0.56695

0.008

2635

17

2

0.08959

1.15

2365 3600 18000 2800

20 19 18 18

2 1 2 2

0.10406 0.0684 0.648 0.1008

21 0 12 3.71

INN BOT PLATE CENTRE GIRDER SIDE GIRDER CL BKD reg 1 CL BKD reg 2 CL BKD reg 3 CL BKD reg 4 WING TANK HORI.GIRDER 1 WING TANK HORI.GIRDER 2 WING TANK HORI.GIRDER 3

17000 2000 2000 5000 5000 5000 5000 370*13 400*14 430*15

18 17 12 12 14 15 16

2 1 6 1 1 1 1 2 2 2

0.612 0.034 0.144 0.06 0.07 0.075 0.08 0.0139 0.0162 0.0188

2 1 1 19.5 14.5 9.5 4.5 9 14 20

0.118482 8 45.89046 0 93.312 1.387421 3 2.448 0.034 0.144 22.815 14.7175 6.76875 1.62 1.1259 3.1752 7.52

0

SHEERSTRAKE PLATE KEEL PLATE INN HULL PLATE MARGIN PLATE

0.00453 6 0.10302 9 2.18526 0 6.48 0.37396 8 1.224 0.034 0.144 1.17 1.015 0.7125 0.36 0.125 0.227 0.376

447.216 86.97837 5 14.71668 8 3.628E-05

8500

19

BOTTOM SHELL PLATE

16675

BOTTOM BILGE PLATE

DECK LONGITUDINALS

260*12

50

0.2065

21.87

4.13

98.76831

INNER HULL LONGITUDINALS

IH 1 IH 2 IH 3 IH 4 IH 5 IH 6 IH 7 IH 8 IH 9

2 2 2 2 2 2 2 2 2

0.01392 0.01392 0.01392 0.01392 0.01392 0.01628 0.01628 0.01628 0.01628

19.15 18.3 17.45 16.6 15.75 14.9 14.05 13.2 12.35

0.266568 0.254 0.242 0.231 0.219 0.242 0.228 0.214 0.201

5.104 4.661 4.238 3.835 3.453 3.614 3.213 2.836 2.483

ITEMS

L(mm)

B(mm)

DECK PLATE SIDE SHELLPLATE

21000 8500

SIDE SHELLPLATE

370*13 370*13 370*13 370*13 370*13 400*14 400*14 400*14 400*14

0.818 0

0.0082 0 5.46 0.029 0 0.011 0.008 0.125 0.146 0.15625 0.1666 0 0 0

Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I IH 10 IH 11 IH 12 IH 13 IH 14 IH 15 IH 16 IH 17 IH 18 IH 19

400*14 430*15 430*15 430*15 430*15 430*21 430*21 430*21 430*21 430*21

2 2 2 2 2 2 2 2 2 2

0.01628 0.01882 0.01882 0.01882 0.01882 0.024 0.024 0.024 0.024 0.024

11.5 10.65 9.8 8.95 8.1 7.25 6.4 5.55 4.7 3.85

0.187 0.2 0.184 0.168 0.152 0.174 0.153 0.133 0.112 0.092

2.153 2.134 1.807 1.507 1.234 1.261 0.983 0.739 0.53 0.355

BOTTOM LONGITUDINALS

430*21

40

0.444

0

0

0

INNER BOTTOM LONGITUDINALS

430*21

34

0.408

2

0.816

1.632

S1 S2 S3 S4 S5 S6 S7 S8 S9 S 10 S 11 S 12 S 13 S 14 S 15 S 16 S 17 S 18 S 19 S 20 S 21

370*13 370*13 370*13 370*13 370*13 400*14 400*14 400*14 400*14 400*14 430*15 430*15 430*15 430*15 430*21 430*21 430*21 430*21 430*21 430*21 430*21

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

0.01392 0.01392 0.01392 0.01392 0.01392 0.01628 0.01628 0.01628 0.01628 0.01628 0.01882 0.01882 0.01882 0.01882 0.024 0.024 0.024 0.024 0.024 0.024 0.024

19.15 18.3 17.45 16.6 15.75 14.9 14.05 13.2 12.35 11.5 10.65 9.8 8.95 8.1 7.25 6.4 5.55 4.7 3.85 3 2.15

0.266 0.254 0.242 0.231 0.219 0.242 0.228 0.214 0.201 0.187 0.2 0.184 0.168 0.152 0.174 0.153 0.133 0.112 0.092 0.072 0.051

5.104 4.661 4.238 3.835 3.453 3.614 3.213 2.836 2.483 2.153 2.134 1.807 1.507 1.234 1.261 0.983 0.739 0.53 0.355 0.216 0.11

BKD 1 BKD 2 BKD 3 BKD 4 BKD 5 BKD 6 BKD 7 BKD 8 BKD 9 BKD 10 BKD

300*14 300*14 300*14 300*14 300*14 370*16 370*16 370*16 370*16 370*16

1 1 1 1 1 1 1 1 1 1

0.0058 0.0058 0.0058 0.0058 0.0058 0.00807 0.00807 0.00807 0.00807 0.00807

19.15 18.3 17.45 16.6 15.75 14.9 14.05 13.2 12.35 11.5

0.111 0.106 0.101 0.096 0.091 0.12 0.113 0.106 0.099 0.092

2.126 1.942 1.766 1.598 1.438 1.791 1.593 1.406 1.23 1.067

370*16

1

0.00807

10.65

0.085

0.915

SIDE LONGITUDINALS

BULKHEAD LONGITUDINALS

Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I 11 BKD 12 BKD 13 BKD 14 BKD 15 BKD 16 BKD 17 BKD 18 BKD 19 BKD 20 BKD 21

430*15

1

0.00941

9.8

0.092

0.903

430*15

1

0.00941

8.95

0.084

0.753

430*15

1

0.00941

8.1

0.076

0.617

430*15

1

0.00941

7.25

0.068

0.494

430*15

1

0.00941

6.4

0.06

0.385

430*21

1

0.024

5.55

0.133

0.739

430*21

1

0.024

4.7

0.112

0.53

430*21

1

0.024

3.85

0.092

0.355

430*21

1

0.024

3

0.072

0.216

430*21

1

0.024

2.15

0.051

0.11

53.0416

912.233

6.239

Height of the neutral axis, hNA

Σ AL

=

ΣA 53.042

=

6.239

=

8.502 m from base line

=

ΣAh2 + ΣIXX

=

912.233 + 7.371

=

919.604 m4

=

I KEEL - ΣA x (hNA)2

=

919.604- 6.239x (8.502)2

=

468.65 m4

Moment about keel, I KEEL

Moment about neutral axis, I NA

Section modulus about deck, INA ZDECK

= = =

Section modulus about keel,

h DECK 468.65 21-8.71 37.788m3

7.3708


ZKEEL

= =

=

Required section modulus, ZMIN

INA hNA 468.65 8.507 55.124m3

=

34.402 m3

Here ZDECK and ZKEEL are getting more than the minimum section modulus required. So the design is satisfactory. The maximum hull vertical bending stresses at deck, σ DECK, and keel, σKEEL, are given by the following, using the appropriate combination of bending moments to give sagging and hogging stresses: σDECK =( |Ms+Mw|x 10–3) / ZDECK N/mm2 = 94.347 N/mm2 σKEEL = (|Ms+Mw|x 10–3 )/ ZKEEL N/mm2 = 67.271 N/mm2

Calculation (midship) of ship

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